Abstract

Long-range surface plasmon polaritons (LRSPPs) are optical surface waves that propagate along a thin symmetric metal slab or stripe over an appreciable length (centimeters). Vigorous interest in LRSPPs has stimulated a large number of studies over three decades spanning a broad topical landscape. Naturally, a good segment of the literature covers fundamentals such as modal characteristics, excitation, and field enhancement. But a large portion also involves the LRSPP in diverse phenomena, including nonlinear interactions, molecular scattering, fluorescence, surface-enhanced Raman spectroscopy, transmission through opaque metal films and emission extraction, amplification and lasing, surface characterization, metal roughness and islandization, optical interconnects and integrated structures, gratings, thermo-, electro- and magneto-optics, and (bio)chemical sensing. Despite the breadth and depth of the research conducted to date, much remains to be uncovered, and the scope for future investigations is broad. We review the properties of the LRSPP, survey the literature involving this wave, and discuss the prospects for applications. Avenues for further work are suggested.

© 2009 Optical Society of America

1. Introduction

Surface plasmon polaritons (SPPs) are transverse magnetic (TM) polarized optical surface waves that propagate, typically, along a metal–dielectric interface [1, 2, 3], henceforth termed the single interface. One purely bound (nonradiative) SPP wave (mode) is supported by this structure, with fields that peak at the interface and decay exponentially away into both media. Its fields are associated with a charge density wave in the metal; so the SPP is a coupled excitation (plasmon polariton).

The single-interface SPP exhibits interesting and useful properties such as an energy asymptote in its dispersion curve, very high surface and bulk sensitivities, and subwavelength confinement near its energy asymptote. But it is also characterized by a high attenuation, especially near the energy asymptote, limiting the scope for applications. For a metal bounded by an ideal dielectric, the attenuation is caused primarily by free-electron scattering in the metal and, at short enough operating wavelengths, by interband transitions. Roughness along the interface causes additional attenuation.

A practical way of reducing the SPP attenuation is to use a thin metal film or stripe bounded on all sides by the same dielectric and operating the structure in the so-called long-range SPP (LRSPP) mode. “Long-range” is taken to mean that the LRSPP attenuation is at least a factor of 2 to 3 lower than that of the single-interface SPP, resulting in propagation over a longer distance. Indeed, attenuation reduction factors, or equivalently, range extension factors, greater than 100 have been demonstrated experimentally with the LRSPP. The range extension mitigates an important limitation of the single-interface SPP, but this comes at the expense of reduced confinement. Nevertheless, the extended range may outweigh the reduced confinement potentially enabling better and more competitive applications.

Our purposes in this paper are to highlight the attributes of the LRSPP, review its origins and the body of work that has been conducted on this wave, and to discuss potential applications based on its use. The LRSPP has appeared in a large number of studies, either as the focal point or peripherally within another context. Literary contributions that include consideration of the LRSPP are cited, and, generally, only the salient points involving the LRSPP are described. In many cases, there is more to a cited contribution than this narrow perspective, so the reference list should not be regarded as listing exclusively LRSPP studies. The discussion is at times broadened to include the single-interface SPP, or the short-range (high-attenuation) modes supported by the structures considered, in order to provide context and comparison or to underline important points of differentiation. The references are organized by subsection, then chronologically.

The literature on SPPs in general is of course much broader. The texts edited by Boardman [1] and by Agranovich and Mills [2], and the monograph by Raether [3], review early work and remain important literary landmarks in the field. Papers by Sambles et al. [4], Welford [5], and Barnes [6], serve as good introductions to SPPs, as does a recent textbook by Maier [7]. Good recent reviews of the field include those of Barnes et al. [8], Zayats et al. [9], Maier and Atwater[10], Ozbay [11], and Atwater [12]. Ebbesen et al. [13] and Degiron et al. [14] have recently discussed integrated optical circuitry based on SPPs.

Work conducted on or with the LRSPP can be organized in many ways. The main division adopted here follows the dimensionality of the guiding structures: Section 2 reviews the LRSPP in the metal slab, which provides confinement in one dimension, and Section 3 reviews the LRSPP in the metal stripe, which provides confinement in two dimensions. Subsections 2.1, 3.1 briefly and didactically summarize the properties of the bound modes in these structures in order to provide context and introduce relevant symbols and terminology. Section 4 discusses the prospects for applications, and Section 5 gives concluding remarks.

1.1. Notation

Throughout this paper, an e+jωt time dependence is assumed with modes propagating in the +z direction according to eγz. The complex propagation constant γ in inverse meters expands as γ=α+jβ, where α and β are the attenuation and phase constants, respectively. The normalized propagation constant is γeff=γβ0=αβ0+jββ0=keff+jneff, where β0=2πλ0=ωc0 is the phase constant of plane waves in free space, λ0 the wavelength in free space, and c0 the speed of light in free space. The complex effective index of a mode Neff is then given by Neff=jγeff=neffjkeff, where neff is the effective index and keff the normalized attenuation. The mode power attenuation (MPA) in decibels per meter is given by MPA=α20log10e.

The propagation length Le is the distance from the launch point where the mode power decays by a factor of 1e and is given by Le=1(2α). (A less used definition of the propagation length, the 1e2 power decay length, is also found in the literature and yields a larger length for the same attenuation.)

The group velocity of a mode vg is given by ωβ, and its lifetime is given by τ=Levg.

The relative permittivity εr is related to the permittivity ε in the usual way, εr=εε0, where ε0 is the permittivity of free space. The relative permittivity is related to the optical parameters n, k via εr=(njk)2. A numerical subscript i identifies these quantities in a specific region. The relative permittivity of a metal at optical wavelengths is decomposed into real and imaginary parts as εr=εRjεI. For good metals εRεI in the infrared and over at least part of the visible (e.g., Au, Ag, Cu, and Al).

2. Metal Slab (w=)

2.1. Modes of the Metal Slab

The single interface is sketched in Fig. 1(a), and the structures sketched in Figs. 1(b), 1(c) are important variations. The variation shown as Fig. 1(b) consists of a thin metal film of thickness t and relative permittivity εr,2 bounded by optically semi-infinite dielectrics (claddings) of relative permittivity εr,1 and εr,3, henceforth referred to as the metal slab. Another variation consists of a thin dielectric film of thickness t and relative permittivity εr,1 bounded by optically semi-infinite metals of relative permittivity εr,2, as sketched in Fig. 1(c), and henceforth referred to as the metal clads. The metal slab is said to be symmetric when εr,1=εr,3 and asymmetric otherwise (εr,1>εr,3 or εr,1<εr,3). The distribution of the main transverse electric field component of the modes (Ey) is sketched as the red curves over the cross section of each structure. Mode propagation occurs along the +z axis (upward perpendicular to the page).

In the symmetric metal slab, the bound single-interface SPPs supported by the individual metal–dielectric interfaces at large t, couple as t is reduced, forming two TM-polarized (Ex=Hy=Hz=0) bound supermodes, sometimes termed coupled modes, that exhibit distinct dispersion characteristics and a distinct evolution with structure parameters (ε and t). These supermodes are denoted herein as ab and sb for asymmetric bound and symmetric bound, respectively, since their main transverse electric field component (Ey) varies either asymmetrically or symmetrically across the structure (along the y axis), as sketched in Fig. 1(b). The Hx field component of the modes has the same symmetry as the corresponding Ey field, but the longitudinal electric field Ez has the opposite symmetry. The charge density in the metal linked to the ab mode has a symmetric distribution over t, as indicated by the pluses in Fig. 1(b), whereas the charge density associated with the sb mode is asymmetric over t, as indicated by the plus and minus signs.

The LRSPP is the sb mode of the thin metal slab.

In a symmetric structure with lossless claddings, the attenuation and effective index of the sb mode decrease smoothly as t is reduced, with its mode fields increasingly expelled from the metal film and penetrating more deeply into the claddings. Indeed, as t0, the confinement and attenuation of this mode vanish as it evolves smoothly into the vertically polarized TEM (transverse electromagnetic) wave of the background. The LRSPP is the sb mode of the thin metal slab. The ab mode exhibits increasing confinement and penetration into the metal with decreasing t and, consequently, increasing attenuation. For large t the ab and sb modes are degenerate with the single-interface SPPs supported by the uncoupled top and bottom metal–dielectric interfaces.

The trends are similar in an asymmetric slab except that (i) the sb mode cuts off below a certain thickness t that depends on the permittivities and operating wavelength, and (ii) with increasing t the ab mode evolves into the SPP supported by the metal interface with the high-index cladding, while the sb mode evolves into the SPP at the interface with the low-index cladding. These trends with t are apparent from Fig. 2, which plots the effective index and normalized attenuation of the ab and sb modes in an asymmetric slab at λ0=632.8nm assuming Ag for the metal εr,2=(0.0657j4)2 and claddings of relative permittivity εr,1=1.52 and εr,3=1.552. The symmetric structure may be more convenient for working with the LRSPP because the mode remains nonradiative (purely bound) for t0, whereas in an asymmetric structure the LRSPP (sb mode) remains nonradiative only for t greater than a cutoff thickness.

The ab and sb modes exhibit distinct dispersion characteristics if t is small enough. For example, Fig. 3 shows normalized dispersion curves for the ab and sb modes propagating along a lossless metal film modeled as a Drude metal and bounded symmetrically by semi-infinite vacuum for three normalized thicknesses. For very thin metal films (U=0.1) the dispersion of the ab and sb modes are distinct, but for thick films (U=2) they merge and coincide with the corresponding single-interface SPP. The dispersion curves are asymptotic with the light line as β0, and they are asymptotic with Ω=12ω=ωp2 as β, where ωp is the plasma frequency of the Drude model. The β limit is termed the SPP energy asymptote. The dispersion curve of the sb mode is above that of the ab mode, so a given β occurs at a higher ω for this mode. The confinement increases, vg tends to zero, and the optical density of states diverges near the energy asymptote. A region of negative vg occurs for the sb mode before the energy asymptote. The trends are the same for structures having symmetric dielectric claddings, with the asymptotic limits taking on appropriate values in the dielectric [light line, ω=βc0n1; energy, ω=ωp(1+εr,1)12]. The trends are similar for real metals, except that the attenuation of the modes increases dramatically toward the energy asymptote, and the depth of the asymptote is limited by bendback. The sb mode is generally long range away from the energy asymptote (and for small t).

The nomenclature used for identifying the ab and sb modes varies greatly throughout the literature, and occasionally erroneous assignments are made. The nomenclature that we have adopted follows the integrated optics convention of identifying a mode by features in the spatial distribution of its main transverse electric field (Ey in the structures of Fig. 1). Other mode nomenclatures are based on identifying features in the longitudinal electric field, in the charge distribution across the metal, or on the mode’s location on a dispersion diagram. Thus, in the literature, one finds the sb mode sometimes termed the asymmetric mode based on Ez or on charge distribution (Fig. 1(b)), or the ω+ mode because it corresponds to the highest curve on a dispersion diagram (Fig. 3). Likewise, the ab mode has also been termed the symmetric mode or the ω mode.

The LRSPP can be excited by p-polarized light by using a high-index prism as sketched in longitudinal cross-sectional view in Fig. 4 (case 1, εr,3=εr,1). In typical experiments, the angle of incidence θ is varied beyond the critical angle of the εr,4|εr,3 interface, and the reflected power is monitored by using a detector. The excitation of a mode occurs when the in-plane wavenumber of the incident light β0n4sinθ equals the mode’s wavenumber β, resulting in a drop of the reflected power. If the reflectance is plotted versus θ, then dips appear for each excited mode as shown in Fig. 5. The sb mode is excited at a smaller θ than the ab mode, since the former has a smaller β at the operating ω (Figs. 2, 3). Lower attenuation results in a narrower dip, a signature of the LRSPP. As t increases, the ab and sb dips merge into one, because the modes become degenerate and identical to the single-interface SPP. The plot of Fig. 5 is termed an attenuated total reflection (ATR) angular spectrum, since the excitation of modes results in attenuation of the reflected light as measured by the detector.

The LRSPP can also be excited by a TM-polarized optical beam via end-fire coupling as sketched in longitudinal cross-sectional view in Fig. 6. In this arrangement the beam is focused onto the end facet of the structure such that it overlaps well with the fields of the LRSPP. End-fire coupling can be efficient, since the transverse mode fields of the LRSPP are symmetrically distributed over the structure cross section, as are the exciting fields in such arrangements. The technique can be easier to implement than prism coupling, and it eliminates problems associated with prism loading (mode perturbation and unwanted outcoupling); however, it requires access to high-quality end facets, which can be difficult or inconvenient to create in some structures, and it is not β selective; thus all modes that overlap the input beam will be excited to some extent (including radiative modes); so outputs must be interpreted carefully.

The metal clads depicted in Fig. 1(c) also support coupled modes, such as the symmetric mode for which the main transverse electric field distribution is also sketched. Table 1 summarizes modal information for the three structures of Fig. 1, assuming λ0=1550nm, Ag for the metals, SiO2 for the dielectrics, t=20nm for the metal slab, and t=50nm for the metal clads; δw is the 1e mode field width. The trade-off between confinement and attenuation across these structures is evident from these data. The LRSPP in the metal slab is at one end of the trade-off, having a low attenuation but also low confinement (smaller neffn1 and larger mode size δw), whereas the symmetric mode of the metal clads is at the other end of the trade-off (higher attenuation and confinement). The single-interface SPP is between them. Neither the metal clads nor the single interface support LRSPPs.

2.2. Origins of the LRSPP [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36]

The LRSPP builds on a number of previous studies involving the single interface and the metal slab, including, for example, the work of Ritchie [15], Kliewer and Fuchs [17], Otto [18, 19], Economou [20], Kretschmann [23], and Abelès and Lopez-Rios [25].

The coupled modes in the symmetric metal slab were studied long ago through dispersion computations, for example, such as those produced by Kliewer and Fuchs [17] for an ideal thin metal film bounded by vacuum (Fig. 3) and by Economou [20] for a similar structure and a number of variants thereof. These early studies did not include the effects of damping; so the range of mode propagation could not be assessed.

Otto described and demonstrated prism coupling as a means of exciting the single-interface SPP [18] (the Otto configuration), by introducing a low-index gap between the prism and the metal film (Fig. 4, case 2). Otto also considered, theoretically, prism coupling to the ab and sb modes of the metal slab, including damping in the metal, bounded symmetrically by low-index claddings and high-index prisms [19], and computed the reflection and transmission responses of the system. Interestingly, in Fig. 3 of [19], he showed a narrow linewidth in the reflection and transmission resonances of the system mediated by the sb mode (ω+ in the notation of [19]) at λ0=546.1nm for a Ag slab 30nm thick and for a prism-metal spacing of 400nm (the largest considered). He also showed this resonance narrowing as the prism-metal spacing increases, a behavior later understood to be characteristic of the LRSPP (e.g., [48]). He showed theoretically that the transmittance of the system could be very high, 70% in the case of a 70nm thick Ag film, and that the transmission was mediated primarily by the sb mode. (Transmission through a Ag film of this thickness bounded by air is essentially zero.) He suggested using the system in transmission as a polarizer. The arrangement was studied experimentally shortly thereafter [22], confirming the main findings of Otto [19], and exploring its possible application as a polarizing spectral filter. (Dragila et al. studied a similar system [43]).

During the same time, Tien et al. [21] proposed and demonstrated the prism coupling approach to excite dielectric waveguide modes, and Kretschmann [23] demonstrated a variant of the Otto configuration [18] (the Kretschmann–Raether configuration) for exciting the single-interface SPP where the metal film is deposited directly onto the base of the prism (Fig. 4, case 3). (This configuration was also considered by Turbadar years earlier [16], as pointed out by Welford [5].) The Otto [18] and Kretschmann–Raether [23] configurations are not suitable for exciting LRSPPs, but Otto’s other configuration [19] is suitable.

Abelès and Lopez-Rios [25] combined the Otto and Kretschmann–Raether configurations (Fig. 4, case 4) to excite the (essentially) uncoupled single-interface SPPs supported at the opposite interfaces of a highly asymmetric thin metal slab.

Although much had been learned regarding the coupled modes of the metal slab, their attenuation (and range) had remained unexplored until the work of Kovacs [26, 28]. Kovacs computed the propagation constant of the ab and sb modes at λ0=450nm in In slabs (εr,2=20.358j6.019) of thickness t=50,30,10  nm, bounded symmetrically by semi-infinite MgF2 (n1=n3=1.382) (pp. 97–99 of [26] or Table 1 of [28]). His computations show that neff and α of the ab mode are larger than those of the sb mode and that they move further apart with decreasing t. Specifically, his results show neff and α of the ab mode both increasing with decreasing t, and neff and α of the sb mode both decreasing with decreasing t. From his computations, it is also noted that α of the sb mode for t=10nm is 29× lower than for t=50nm. Prism coupling to the coupled modes was also investigated theoretically and experimentally for different In thicknesses (t=19,27,42nm).

Kovacs also explored theoretically and experimentally prism coupling to the ab and sb modes of thin Ag slabs bounded by identical dielectrics (Fig. 4, case 1; Fig. 5) [26, 27]. The experimental structures comprised an Ag slab 4055nm thick bounded by cryolite and were excited at λ0=632.8nm by angle scanned (θ) prism coupling. These structures allowed the experimenters to unambiguously differentiate and identify the sb and ab modes, observing that their angular separation (in θ) decreased with increasing t as expected. Informative plots of the Poynting vector through the structure, and of the current density in the metal, were also given, from which one notes, for instance, that the power flow in the metal has a large component in the direction antiparallel (z) to the direction of modal propagation (+z). Effects caused by the finite thickness of the claddings were also investigated, revealing the importance of the gap s (Fig. 4, case 1) on the coupling efficiency of the modes. The sb mode was not really long range in these structures because of the large thickness of the metal film, the roughness of the interfaces, and inhomogeneities in the bounding cryolite films.

Thus, many essential features of the LRSPP were uncovered by Kovacs [26, 28]. And by making slight modifications to then-known prism coupling techniques [18, 19, 21, 23, 25], particularly by removing the second prism in Otto’s other geometry [19], he demonstrated experimentally via optical means the existence of the coupled modes in symmetric metal slabs [26, 27]. (Many of his results [26] were subsequently summarized in Chap. 4 of [1].)

At about the same time, Fukui et al. [29] (in collaboration with G. I. Stegeman) included damping in the metal and computed the lifetime τ of the ab and sb modes in thin unsupported Ag films bounded symmetrically by vacuum (ε1=ε3=1) as a function of the Ag film thickness t. They predicted a propagation length of Le=3cm for the sb mode on a 16nm thick Ag film in vacuum at λ0=1.06μm. The propagation length of the corresponding single-interface SPP is 0.06cm; so the predicted range extension was a factor of 50. They also showed the sb mode guided as t0, with no cutoff thickness being apparent in their results.

Sarid [30, 31] then studied theoretically the ab and sb modes in the metal slab bounded by asymmetric dielectrics (εr,1=1.52, εr,3=1.552). From his results, reproduced here as Fig. 2, it is apparent that the LRSPP does not exist below a cutoff thickness, t20nm in this case. He modeled the prism coupling arrangement (Fig. 4, case 1), noting that the half-width angle corresponding to the excitation of the LRSPP was very narrow, about 0.004°. He also commented on the criticality of the gap s, pointing out that if it is too large the coupling efficiency suffers, but if it is too small then the prism loads and wipes out the LRSPP. The terminology “long-range” for identifying the low-loss version of the sb mode originated here.

Experiments on improved structures [32, 33, 34, 35] were reported shortly after [27], leading to long (measured) sb propagation lengths, and thus to the first experimental observations of the LRSPP.

The structure explored experimentally by Kuwamura et al. [32] consisted of a 14.6nm thick Ag film deposited on CaF2 with index-matching oil used as the other cladding. The structure was excited at λ0=632.8nm in a prism-coupled configuration. The measured propagation length of the sb mode in this structure (Le100μm) is approximately 10× longer than that of the SPP on the corresponding single interface.

Craig et al. [33] reported a propagation length of Le=250μm for the sb mode supported by a 10nm thick Ag film, bounded by glass on one side and index-matching oil on the other, and excited at λ0=632.8nm by using a retroreflecting prism [36]. This measured propagation length is 63× longer than that of the corresponding single-interface SPP.

Quail et al. [34] characterized a 17nm thick Ag film and a 14.5nm thick Al film, both on glass and covered by index-matching oil, at λ0=632.8nm in a prism-coupling configuration. They measured propagation lengths for the sb mode that are about 10× longer than the corresponding single-interface SPPs.

Dohi et al. [35] measured a propagation length of Le265μm for the sb mode supported by an Ag film about 15nm thick on Pyrex and covered with oil having a slightly different index than that of the Pyrex (i.e., in a slightly asymmetric structure εr,1εr,3). Their structures were excited at λ0=632.8nm in a prism coupling arrangement. Their range extension is comparable with that achieved by Craig et al. [33].

2.3. Prism Coupling and Field Enhancement [37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53]

Difficulties with prism coupling to the LRSPP (Fig. 4) were identified early on [27, 30, 31, 32, 33, 34, 35, 36]. Experimental difficulties include controlling the gap spacing s and parallelism between the base of the prism and the metal slab, as well as the angle of incidence of the input light θ, while ensuring that the permittivities of both claddings remain closely matched (ε1=ε3). These requirements suggest the need for high-performance optomechanical components and working with index-matching oils or custom-fabricated structures.

Another difficulty is that the mode fields of the LRSPP extend deeply into the claddings; so the loading effect of the higher-index prism on the mode is quickly apparent, perturbing its fields and propagation characteristics and rendering it radiative into the prism, as is readily apparent from the plane wave computations of Wendler and Haupt [48]. If the prism is too far from the metal slab, the coupling efficiency is poor, but if it is too close, loading destroys the LRSPP (cf. Figs. 1 and 7 of [48]). Under conditions of perfect coupling to the LRSPP, radiative damping equals intrinsic damping (damping without the prism), so its range is halved (i.e., its attenuation is doubled) [40, 48], as is the case for the single-interface SPP in the Otto [18, 37] and Kretschmann–Raether [3, 23] configurations.

Thus, the reflected field in a prism coupling experiment includes a specularly reflected contribution as well as an outcoupled (reradiated) contribution due to the propagating LRSPP. Since the LRSPP has a long propagation length, the outcoupled contribution extends over a large spatial cross section and can interfere with the specular reflection. The contributions can, however, be distinguished if a finite-size input beam is used [41, 42, 45] (as for the single-interface SPP [38] in the Otto [18] and Kretschmann–Raether [23] configurations). For example, Fig. 7(a) shows a finite-width input beam prism coupled to the LRSPP on a Ag film supported by a Pyrex substrate and covered by index-matching oil, and Fig. 7(b) shows the measured intensity profile at the observation plane (λ0=632.8nm, w=1.27mm, s=1.35μm, t=16nm, Le=274μm, Lew=0.2157) [42]. From Fig. 7(b) two bumps separated by a null are noted, the leftmost one due to specular reflection of the input beam and the rightmost one due to the outcoupled LRSPP. In such a situation, the measured profile of the outcoupled contribution follows the decay of the LRSPP [42, 45]. The importance of considering the finite size of the input beam and of its angular spread when interpreting prism coupling experiments with LRSPPs has also been highlighted in other papers [46, 49, 50, 51, 53].

Barnes and Sambles [47] excited the LRSPP via prism coupling in a 40nm thick Ag slab bounded symmetrically by Langmuir–Blodgett layers (22-tricosenoic acid) about 600nm thick at λ0=632.8nm. They achieved a modest increase in propagation length over the corresponding single-interface SPP, due in part to the large thickness of the Ag film, to loss in the Langmuir–Blodgett layers, and to suspected damage caused to one of the Langmuir–Blodgett layers during Ag evaporation. However, it is interesting to note that a multilayer structure incorporating organic claddings could be fabricated with some success.

The LRSPP was also seemingly observed in a thin Ag film bounded on both sides by thin layers of Teflon and excited by using prism coupling, presumably at λ0=632.8nm [52].

Sarid et al. [40] computed the field enhancement in a prism coupling arrangement at λ0=632.8nm assuming Ag films 70 and 10nm thick bounded by dielectrics of index 1.5. The field enhancement was defined as the ratio of the squared magnitude of the magnetic field in the vicinity of the metal surface to the squared magnitude of the magnetic field in the prism. They reported field enhancements of 40 and 600 at the excitation angle of the sb mode in the 70 and 10nm thick films, respectively, for near perfect coupling into the modes. The sb mode in the 70nm thick case is not long-range and corresponds almost to the single-interface SPP in the Otto geometry [18] (distinct sb and ab modes still occur at this thickness); the sb mode in the 10nm thick case corresponds to the LRSPP. They mentioned computing the field enhancement in the Kretschmann–Raether geometry and observing that they are similar to the Otto case. Thus, they concluded that the field enhancement associated with the excitation of the LRSPP via prism coupling (600) can be 1 order of magnitude larger than that in the Otto and Kretschmann–Raether geometries (40). Indeed, assuming that Eq. (10) of [39] holds, then the field enhancement of the LRSPP relative to the single-interface SPP should follow the ratio of their propagation lengths (Le’s) or the inverse ratio of their attenuations (α’s). LRSPP field enhancements were later shown to exist on corrugated gratings as well (e.g., [56]).

Lévy et al. [44] compared theoretically the prism-coupled LRSPP field enhancement to that of the prism-coupled TE0 and TM0 modes supported by a dielectric slab waveguide (equivalently, a 1D cavity). Results for the structures investigated show that the field enhancement of the TE0 and TM0 modes along the core center was about 6× greater than the enhancement of the LRSPP fields.

This enhancement [39, 40, 44] might loosely be termed an intensity enhancement, since another definition for the field enhancement found in the literature forms the ratio of the field magnitudes, yielding the square root of the former.

2.4. Corrugated Gratings [54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70]

Symmetric periodically corrugated metal slabs supporting LRSPPs have also been explored as an alternative to prism coupling and as structures having rich and interesting properties in their own right. Generally (TM) p-polarized light is used to illuminate a corrugated grating, with the plane of incidence oriented perpendicular to the grooves, and the response in reflection and/or transmission recorded as a function of the angle of incidence (angle scan) or the wavelength of operation (wavelength scan).

Different theoretical approaches have been used to model grating responses (cf. Barnes et al. [63] for a good discussion), many rooted in Chandezon’s coordinate transformation formalism [54], whereby corrugated boundaries are mapped to flat surfaces allowing the straightforward application of boundary conditions and transfer matrices for handling many layers. Cotter et al. [62] improved on the method by using scattering matrices instead of transfer matrices to eliminate numerical instability when modeling thick structures.

Inagaki et al. [55] reported the excitation of the sb and ab modes at λ0=632.8nm in a thin free-standing 44nm thick corrugated Ag slab in air, with the measured resonance width of the sb mode being considerably narrower than that of the ab mode. Further experiments were conducted by the same group [57] on free-standing corrugated Ag slabs having thicknesses in the range of 26212nm, showing splitting of the sb and ab modes for a slab thickness of about 91nm. The measured phase and attenuation constants of these modes compared qualitatively well with theoretical expectations for a flat slab over the thickness range investigated, but larger phase and attenuation constants were measured throughout. The coupling efficiency was also found to be strongly dependant on the thickness of the slab.

This symmetric free-standing corrugated slab was subsequently studied theoretically by Dutta Gupta et al. [58], supporting the main conclusions of Inagaki et al. [55, 57]. They also study the effects of damping by outcoupling to free radiation for various corrugation amplitudes.

Cavalcante et al. [59] studied theoretically the metal slab bounded symmetrically by dielectrics where one of the metal–dielectric interfaces is smooth and the other interface has a sinusoidal profile. They computed the reflectivity and the intensity of the field near the metal slab, both as a function of the angle of incidence for various grating amplitudes. They observed, among other points, an increase in the linewidth of the reflectivity dip for both the ab and sb modes, indicating increased attenuation, as the corrugation amplitude increases.

The study of Chen and Simon [60] also pointed out that an additional loss contribution to the LRSPP in corrugated gratings may be expected that is due to scattering from the grating grooves.

Bryan-Brown et al. [61] measured the reflection response of symmetrically cladded thin corrugated Ag slabs through the LRSPP excitation angle and deduced the grating groove depth as well as the thickness and optical parameters of the embedded Ag films via comparisons with a theoretical model of the experiment.

Salakhutdinov et al. [64] investigated sinusoidally corrugated metal slabs where the upper and lower surfaces of a slab are corrugated in phase or phase shifted by π. They computed the perturbed propagation constant of the LRSPP for corrugations of both types in a Cu film, as a function of groove depth and t. They found that the corrugations increase the attenuation of the mode, but much more so for π-shifted corrugations than for in-phase corrugations. They found that neff increases for the π-shifted corrugations but that it either increases or decreases for in-phase corrugations depending on t. They modeled and demonstrated experimentally anomalous reflection (interference between reflected and outcoupled guided fields) from in-phase corrugations.

Hooper and Sambles [65] reported a theoretical study pertaining to the excitation and nature of the modes in unsupported (air on both sides) corrugated thin Ag slabs where both surfaces of the slab were corrugated either conformally (identical profiles, in phase) or nonconformally (identical profiles, phase shifted). Sinusoidal profiles with and without the first harmonic in grating wavenumber were explored. The reflection, transmission, and absorption of incident radiation were determined for a variety of structure parameters. Four coupled modes (two ab-like and two sb-like) were found in the nonconformal case that incorporates the first harmonic in grating wavenumber, which are due to new symmetries for the charge distribution that are allowed by the grating features. The second harmonic also leads to anticrossings and bandgaps in the dispersion diagram. This grating architecture for small t (30nm) is capable of an unusually large transmittance over a wide frequency band, almost independently of the angle of incidence, with the transmittance mediated by one of the ab modes.

Chen et al. [67] further explored this grating concept experimentally and theoretically by way of a 27nm thick Ag slab deposited conformally onto a corrugated SiO2 substrate, covered with index-matching fluid, and clamped with a pair of SiO2 prisms (one on each side of the slab). A sinusoidal grating profile with the first harmonic in grating wavenumber was implemented. The origin of anticrossings and bandgaps was discussed in terms of structure parameters and the role of the ab-like and two sb-like modes.

Lévêque and Martin [66] investigated theoretically the excitation of the LRSPP by a Gaussian beam normally incident onto gratings consisting of either periodic rectangular grooves etched into the top surface of an Au slab, or periodic rectangular Au protrusions deposited onto the top surface of an Au slab. The Au slab was assumed to be free standing (bounded by vacuum), 70nm thick, and the groove depth or protrusion height in the range of about 4060nm. The length of the gratings was set to 5 periods, the width of the incident Gaussian beam matched the grating length, and the other grating parameters were varied (period, duty cycle, and groove depth or protrusion height). Lévêque and Martin predicted an optimal coupling efficiency of 33% from the Gaussian beam into LRSPPs propagating in both directions along the slab (i.e., along ±z) at λ0=633nm, using a grooved grating. (They also investigated coupling into the single-interface SPP, using similar grating structures.)

Sellai and Elzain [70] computed the total p-polarized reflectivity from gratings formed by modulating the thickness of the metal slab, predicting sharp reflection dips at specific operating wavelengths where the incident light is efficiently coupled into the ab and sb modes of the structure.

Agarwal [56] studied a different kind of structure, consisting of a smooth metal slab bounded by dielectrics of the same index but with the top dielectric being of finite thickness and having a sinusoidal corrugation applied to its top surface. He showed that the excitation of the LRSPP under plane wave illumination leads to a field enhancement near the grating surface.

A less studied geometry for exciting corrugated gratings is where the plane of incidence is rotated 90° in the plane of the grating (azimuthally) such that it is parallel to the grating grooves. This case was investigated experimentally and theoretically by Chen et al. [69] for a 23nm thick Ag slab deposited conformally onto a sinusoidally corrugated SiO2 substrate, covered with index-matching fluid, and clamped with SiO2 prisms (a structure similar to those investigated in [67] but without the harmonic in the grating vector). They measured a coupling efficiency of about 24% into the ab mode and predicted strong coupling into the LRSPP but under different design and excitation conditions.

Korovin [68] developed a formulation for modeling multilayer corrugated gratings based on a curvilinear coordinate transformation, but, in contrast to Chandezon [54], he used an established solution to Maxwell’s equations in Cartesian coordinates having eigenvalues that are determined analytically, thus improving on the efficiency and accuracy of the method. He then applied this formulation to model the reflectance from a 50nm thick Au film bounded by glass (400nm thick on one side, semi-infinite on the other) with all interfaces conformally corrugated. Reflectance dips due to coupling to the sb and ab modes are apparent from his computations.

2.5. Modal Studies [71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104]

A good number of studies have been reported concerning the modes supported by metal slabs [Fig. 1(b)] and variations thereof. The modes are typically obtained by solving a suitably defined 1D boundary value problem based on the wave equations written in the frequency domain for lossy isotropic media. Necessary boundary conditions are applied between layers, and modes are found as solutions to a characteristic (transcendental) equation much in the same way as for 1D dielectric waveguides. The permittivity of the metal layer is usually obtained from the Drude model of the metal or from measurements. Additional 1D layers (metallic or dielectric) can be included in the analysis, and transfer matrices can be developed for the stack (e.g., [91]). The solution approach typically does not involve the discretization of spatial variables, and although the transcendental equation is solved numerically, the approach is essentially analytical.

Tomaš and Lenac [71] derived expressions to estimate the damping properties (lifetime and propagation length) of the LRSPP in thin unsupported metal slabs at long wavelengths.

The study by Stegeman et al. on asymmetric metal slabs (ε1ε3) [72] included consideration of leaky modes in addition to the bound modes supported by the structure. The mode nomenclature, sb or ab, originated here. A cutoff thickness exists in their asymmetric structures below which the LRSPP no longer propagates as a purely bound mode, corroborating the results of Sarid [30].

The follow-up study by Burke et al. [80] reports a comprehensive treatment of the structure and its modes. The bound modes in symmetric structures, and the bound and leaky modes in asymmetric structures, are discussed in detail, and their evolution over good ranges of structure parameters (t,ε1,ε3) and operating wavelength are given. A physical interpretation is given to the leaky modes.

Burton and Cassidy [84] presented modal results for the metal slab at λ0=1.3μm for various metals and cladding indices near silica, as a function of slab thickness and asymmetry.

Smith et al. [102] also investigated the metal slab, emphasizing the power dissipation spectra of a dipole into the modes supported, and modal dispersion.

The excitation of the modes was also considered by Burke et al. [80], and a suggestion was made to use end-fire coupling, as sketched in Fig. 6, as the means to excite the modes (following [73], where Stegeman et al. computed high excitation efficiencies for the single-interface SPP). This coupling technique was used by Vaicikauskas [93] to obtain Fourier-transform infrared spectra of the LRSPP in a GaAsAuAirGeGaAs multilayer 1D structure.

Stegeman and Burke [74] explored the bound modes of two coupled thin metal slabs as a function of their separation for a few refractive index values of the intervening dielectric. They found supermodes of the system consisting of symmetrical and asymmetrical couplings of the ab mode, and of symmetrical and asymmetrical couplings of the sb mode. The supermodes formed from coupled sb modes can be long-range. Yoon et al. [100] computed the dispersion of the symmetrically coupled sb modes supported by the same structure as a function of the separation between the thin metal slabs for an intervening dielectric that has a higher or lower index compared with the claddings. They found for a high-index intervening dielectric that the dispersion curves insect a common point for all separations between the metal slabs. At the intersection frequency, the effective index of the mode is independent of separation and equal to the index of the intervening dielectric, the propagation length varies linearly with separation, the transverse mode fields have a constant magnitude between the metal slabs (i.e., they are uniform), and the mode fields normalized to the separation are invariant.

Economou [20] also studied the modes of two and three coupled thin metal slabs, but without loss in the metals. Avrutsky et al. [98] investigated the supermodes supported by a multilayer stack constructed from (five) alternating thin metal and (six) dielectric slabs and found (among other modes) one long-range supermode consisting of symmetrical couplings of sb modes. Davis [103] investigated a similar structure and found two long-range supermodes for their stack (three metal and four dielectric layers), symmetrically and asymmetrically distributed.

Stegeman and Burke [75] investigated the effects of one air gap on the propagation of the LRSPP. In this study, the gap was positioned along the top surface of the metal film and various parameters of the system were altered. In general, the effects of the air gap were found to be deleterious, causing the LRSPP to become cut off for very thin gaps (5nm). Methods for mitigating air gaps include using index-matched fluids to fill them [75] or carefully controlling the thickness of the gap while compensating for its effects by using a high-index layer deposited on the opposite surface to form an index-matched effective medium [93].

Lenac and Tomaš [77, 78, 79] studied theoretically the metal–dielectric slab system and found that the modes of the system were hybridized or coupled modes of the individual constitutive structures. They found that the LRSPP was very sensitive to the presence of a thin dielectric layer, leading to increased damping. They also studied the frequency dispersion of the system applying Drude [77, 78, 79] and dielectric [79] dispersion models to the metal and dielectric layers, respectively. Yang et al. [82] studied a similar system.

Kou and Tamir [83] proposed placing a high-index dielectric layer within one of the claddings near the metal film, essentially forming a dielectric waveguide therein that couples with the metal slab. When the structural parameters are properly selected, one of the coupled modes of the system retains the character of the LRSPP but has a longer propagation length. Prism coupling to this structure (among others) was discussed in [49, 51].

Guo and Adato [95, 97] proposed to extend the range of the LRSPP in the metal slab by introducing thin low-index layers on both sides of the metal film with high-index outer claddings bounding the system and operating the LRSPP near cutoff, where it has lower loss. In [95], they also investigated the effects of placing thin high-index layers alongside the film, finding that they increase both the confinement and attenuation of the LRSPP. Durfee et al. [101] investigated similar structures and, additionally, the case where only one low-index layer is placed alongside the metal film. Adding low-index layers in this manner [95, 97, 101] allows a thicker metal slab to be used with lower attenuation compared with a corresponding conventional symmetric slab, but care must be taken to operate sufficiently far from cutoff to avoid radiation loss (neff>index of outer claddings). As with the LRSPP in the conventional symmetric structure, consideration to mode size and coupling efficiency must also be given.

Yun et al. [104] investigated theoretically the modes supported by a buried rectangular dielectric waveguide with a thin metal slab bisecting the structure along its horizontal plane of symmetry. The modes investigated are similar in character to the sb and ab modes of the metal slab but perturbed by the high-index dielectric core which provides strong horizontal and vertical confinement. Propagation lengths and mode areas are reported revealing that the sb-like mode is capable of long-range propagation when the metal slab is thin enough.

Stegeman [76] studied the metal slab bounded symmetrically by birefringent media (neno=0.05), finding that the effective index of the LRSPP was determined primarily by the perpendicular (to the metal slab) refractive index and that birefringence was essentially negligible. Mihalache et al. [89] investigated the modes of thin metal films on a uniaxial substrate having its optic axis in the plane of the film, covered with an isotropic cladding. They computed mode cutoff thicknesses assuming quartz as one cladding (ne=1.553, no=1.544), glass as the other, various metals, and various orientations of the optic axis.

Wendler and Haupt [81] studied the evolution of the LRSPP as a function of structure asymmetry (ε1ε3), showing that the LRSPP cuts off in an asymmetric structure, and that Le as the LRSPP nears cutoff, in agreement with other studies (e.g., [30, 35, 80]). They proposed operating the LRSPP near cutoff, suggesting that an increase in Le of up to 3 orders of magnitude over the LRSPP in a symmetric structure is achievable. However, in subsequent work [48], they considered the excitation of the LRSPP near cutoff by plane waves assuming prism coupling, and they showed that prism loading limited the increase in Le to a factor of about 3 over the LRSPP in the corresponding prism-loaded symmetric case, and to a factor of about 2 over the LRSPP in the corresponding unloaded symmetric case (Fig. 11 of [48]). Interestingly, the measurements of Dohi et al. [35], obtained at the same operating wavelength in a system similar to that modeled [48], are in good agreement with these prism-loaded computations: an increase in Le by a factor of about 3 is apparent for the LRSPP near cutoff compared with the LRSPP of their symmetric case (Fig. 1 of [35]).

Breukelaar and Berini [94] modeled a section of asymmetric metal slab (ε1ε3) placed between two butt-coupled symmetric ones (ε1=ε3), and they computed the insertion loss through the system for end-fire excitation while varying the asymmetry from none (ε1=ε3) through well beyond cutoff of the LRSPP. Radiation spreading through the asymmetric portion was modeled via normal mode decomposition by discretizing the radiation continuum into an appropriate orthonormal basis. The lowest insertion losses were always obtained for no asymmetry (ε1=ε3). This is due to the fact that the end-fire coupling efficiency into the LRSPP decreases as the mode nears cutoff because its fields expand more deeply into the higher-index cladding. Indeed, at cutoff the mode fields extend infinitely into the higher-index cladding, and the end-fire coupling efficiency is zero. Thus, while it is true that Le near cutoff [81], this range extension is not readily accessible owing to difficulties in coupling the mode to sources [48, 94]. At present, the literature suggests no extension [94], or extension by a factor of about 3 [35, 48], for the LRSPP in asymmetric structures compared with in symmetric ones.

Zervas [85] presented computations suggesting that a bound LRSPP could be supported by a thin metal slab (16nm) in a highly asymmetric structure, well beyond the sb cutoff point (see the curve labeled sb in region I of Figs. 2 and 3 of [85]). However, one notes from his computations that the effective index of the mode in the highly asymmetric region is far below the index of one of the claddings (ββ0<1.2<n1=1.462); so the mode is radiative. A subsequent study by Liu et al. [99] ignored the effective index and this consideration, focusing only on the attenuation constant of the sb mode.

Tournois and Laude [90] found negative group velocities for the sb mode in the lossless metal slab (εI=0) when εR becomes similar to εr,1. For metals this condition occurs near the energy asymptote, as is apparent from the computations of Kliewer and Fuchs (Fig. 3 [17]).

As mentioned in Subsection 2.1, the confinement and attenuation of the LRSPP vanish together as the thickness of the metal film is reduced, leading to a trade-off between these two fundamental mode properties (this is apparent from many of the modal studies conducted for the slab, e.g., [80]). Zia et al. [92] reported computations illustrating this trade-off for the metal slab and the metal clads. Berini [96] proposed three figures of merit (FoMs) for 1D waveguides, defined as benefit-to-cost ratios, where three different confinement measures were used as the benefit and attenuation was used as the cost. Closed-form expressions of the FoMs were derived for the single-interface SPP. The FoMs and the quality factor (Q) were used to assess and compare the single interface, the metal slab, and the metal clads, implemented by using Ag and SiO2, over λ0’s ranging from the infrared to the SPP energy asymptote. Preferred λ0’s emerged depending on which FoM was used and thus on how confinement was measured. The largest FoMs were obtained for the LRSPP, but they can also be large for the symmetric mode in the metal clads. Q’s of about 10,000 were found for the LRSPP.

Al-Bader and Imtaar studied the bound [86], leaky [87], and bound hybrid [88] modes of cylindrical structures, comprising a metal film wrapped around a core and surrounded by a cladding. In the case where the cladding is index matched to the core, a long-range mode similar to the sb mode in the slab is supported [86]. They showed that some of the modes in this structure evolve into those of the corresponding metal slab at large radii.

2.6. Rough Metal Films [105, 106]

There are few studies of the effects of roughness on the propagation of the LRSPP, due largely to the arduous task of producing an accurate theoretical treatment. The effects of roughness are that it modifies the LRSPP’s propagation characteristics, outcoupling (scattering) it into free radiation. These effects are of considerable importance to the LRSPP, especially as attempts are made to produce lower-loss waveguides.

Farias and Maradudin [105] computed the effect of roughness on the propagation length of the sb mode supported by a rough Ag film of variable thickness and bounded by vacuum at the optical frequencies of ω=0.94×ωp,Ag (λ0330nm) and ω=0.031×ωp,Ag (λ010μm), where ωp,Ag is the plasma frequency of Ag. The Ag roughness profiles were taken as identical along both surfaces and characterized by an RMS (root mean squared) deviation of 2nm and correlation lengths of 50 and 100nm. They found, as expected, that the propagation length is reduced by roughness, but not very significantly for their chosen (typical) roughness parameters. Extrapolating their results down to a 20nm Ag thickness, one finds that roughness reduces the propagation length by about 10% and 4% at λ0330nm and λ010μm, respectively, compared with the corresponding smooth films.

Paulick [106] constructed a smooth surface model to account for roughness, by introducing an equivalent surface current incorporating one empirical roughness parameter. Results generated by the model were then compared with the experiments of Inagaki et al. [55, 57], yielding encouraging agreement for the dispersion characteristics of the ab and sb modes. He also considered enhanced transmission through an otherwise opaque metal film, in the spirit of [19, 22, 43], but using corrugations instead of prisms to couple the ab and sb modes with free radiation. He found strong transmission at normal incidence through a corrugated free-standing 60nm thick Ag film and demonstrates that the sb mode mediates the transmission, more so than the ab mode.

Modeling roughness as sinusoidal corrugation [56, 58, 59, 60] simplifies the theoretical treatment and seems reasonable for generating approximate estimates (or better) of the effects of roughness on the propagation of the LRSPP and other modes. However, much work remains to be done to determine the range of validity, and indeed the appropriateness, of such models for the LRSPP subject to real roughness profiles.

2.7. Islandized Metal Films [107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122]

It is natural to try very thin metal slabs in order to increase the propagation length. However, as the thickness of a metal film decreases below a threshold value, its (as-deposited, unannealed) optical parameters begin to differ [108, 110, 112, 113, 114, 115] from the bulk values [109, 111]. The main cause is that the volume mass density of metal films typically decreases from the bulk as the thickness is reduced beyond a threshold value because of the formation of voids. Further reduction in thickness eventually leads to a discontinuous (islandized) film. The volume mass density can start decreasing at a thickness of t30nm, and as it does, εR decreases while εI increases. This trend for the permittivity persists as the film turns into a collection of islands if the film is treated as an equivalent continuous plane parallel film and its thickness and permittivity are interpreted as effective optical values. For an islandized metal film in air (or vacuum), as t0, εR goes through 0, changes sign, and hits a peak value before approaching 1, whereas εI hits a peak value then approaches 0; i.e., εr1 as t0 (e.g., [114]). If unmitigated, the main implications of this for the LRSPP are that its attenuation does not drop as rapidly with thickness as suggested by using the bulk permittivity of the metal, and a thickness is eventually reached where the metal permittivity is such that the LRSPP is no longer supported. Annealing treatments postdeposition have a strong impact on the microstructure and thus can significantly improve the quality of a thin metal film [107], so the density problem can be mitigated to some extent. Figure 8 shows trends for the resistivity (ρ) and the relative permittivity (εr=εRjεI) of Au at λ0=632.8nm, measured in situ as a function of Au thickness during vacuum deposition (by thermal evaporation at a rate of 0.02nms onto borosilicate glass substrates held at room temperature); here the bulk values (annealed) are achieved for t15nm [110].

Interestingly, long-range surface modes propagating along islandized metal films bounded symmetrically by dielectrics have been demonstrated [116, 117, 118, 119, 120, 121, 122].

Experiments were reported by Yang et al. [116], where a propagation length of Le=66μm was measured for the long-range mode propagating along an islandized Ag film on quartz covered with index-matching fluid and excited at λ0=632.8nm via prism coupling (the experimental arrangement is sketched in the inset to Fig. 9(a)). Figure 9(a) compares the measured ATR spectrum (crosses) to the fitted theoretical response (solid curve) from which the effective relative permittivity and thickness of the islandized Ag film were extracted [εr,2=0.55j17.19 and t=9.2nm—the relative permittivity follows the trends shown in Figs. 8(b), 8(c)]. Figure 9(b) shows the computed distribution of the z-directed component of the Poynting vector at θ=55.78°, from which it is noted that essentially no energy propagates within the islandized film, explaining the long range of the mode (the field distribution is otherwise similar to that of the sb mode in a continuous film).

Takabayashi et al. [117] studied theoretically long-range modes supported by symmetric ultrathin (<10nm) Ag films at λ0=632.8nm, using the thickness-dependant permittivity measurements for Ag reported in [114] combined with an effective medium theory. They reported that under certain conditions, s-polarized light can excite a surface wave in this structure. In [118], Takabayashi et al. investigated the impact of absorbing claddings in such structures.

Long-range surface mode propagation lengths in the range of 3570μm were measured by Wu et al. [119] for Au, Cu, Al, and Fe islandized films on a glass substrate, covered with index-matching fluid, and excited at λ0=632.8nm via prism coupling.

Takabayashi et al. [121] measured long-range surface mode propagation lengths of 300 and 480μm for islandized Ag films 4 and 2.7nm thick, respectively, on BK7 glass covered with index-matching fluid and excited at λ0=632.8nm by using prism coupling; these propagation lengths are longer by factors of 75 and 120, respectively, than that of the corresponding single-interface SPP.

Kume et al. [122] observed both (TM) p- and (TE) s-polarized long-range modes along a composite layer comprising dispersed and isolated Ag spherical nanoparticles about 4nm in diameter embedded in an SiO2 film, as a function of the composite layer thickness, which was varied from 13 to 47nm. The volume ratio of Ag to the total volume of the SiO2 film was about 0.05, and the composite film was bounded slightly asymmetrically by SiO2 claddings. Modes were excited by using prism coupling at λ0=632.8nm. The longest propagation length measured was 77μm for the p-polarized long-range mode in the 13nm thick composite. They also investigated the effect of prism loading on their responses by varying the thickness of the intervening layer. Theoretical responses to the measurements using a relative permittivity for the composite layer estimated based on Maxwell–Garnett theory (2.624j0.096) agreed reasonably well.

Wood et al. [120] studied the long-range mode propagated by islandized 2nm thick Ni films on SiO2 covered with index-matching fluid and excited via prism coupling at λ0=632.8nm. They then attempted to fit a theoretical response to the measurements in order to uniquely determine the optical effective permittivity and thickness of their Ni layer only to find that degenerate fits (i.e., different combinations of εR, εI, t produce equally good fits). They concluded generally that the thickness and permittivity of films cannot both be determined from theoretical fits to prism coupling experiments conducted with any long-range mode and that the thickness is required in order to determine the permittivity.

Though long propagation lengths are evidently achievable on islandized metal films, it is noted that fabricating such structures reproducibly is challenging and that an islandized film eliminates applications where a continuous metal is essential. However, the ability to support s-polarized waves in such structures is an interesting and potentially useful attribute.

2.8. Long-Range Surface Exciton Polariton[116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134]

Kovacs [26, 123] investigated an unusual system, consisting of a thin continuous Fe film bounded symmetrically by cryolite claddings. What renders the system unusual is that the relative permittivity of Fe at his chosen operating wavelength (λ0=540nm) is εR0 and εI17. Modal computations for semi-infinite claddings revealed that the sb mode had βα and neff>n1 only for the case of thin films (t20nm or less). These inequalities no longer held as t was increased and did not hold for the ab mode at any t. (The corresponding single-interface does not support a purely bound SPP.) Additionally, it was noted for the sb mode that no energy propagates in the Fe film in directions parallel or antiparallel to that of modal propagation (i.e., ±z), in contrast to the LRSPP where energy propagates in the metal film along the antiparallel direction. The existence of this mode was confirmed experimentally via prism coupling at λ0=540nm in a structure consisting of an Fe film 18nm thick bounded by about 550nm of cryolite.

Yang et al. [124] also showed that a thin slab of material satisfying εRεI can support a long-range surface mode when cladded symmetrically, but rather surprisingly, that its range increases as εI increases. Since the condition εRεI is readily met in continuous materials near an excitonic resonance, they termed the mode long-range surface exciton polariton (LRSEP). Experimental excitation of the mode was conducted at λ0=3.391μm via prism coupling to a 45nm thick V film (εr,29j48) deposited onto a quartz substrate and covered with an index-matched fluid. (The effective optical permittivity of islandized metal films can also satisfy εRεI; see Subsection 2.7, Fig. 8 and [108, 110, 112, 113, 114]; so the long-range surface wave propagating along them is often termed an LRSEP, although no excitonic resonances are involved.)

In a subsequent paper, Yang et al. [125] reported useful small-t asymptotic expressions for the long-range surface mode and explored them for various limiting cases of εr,2. Slight asymmetry (εr,1εr,3) and absorption in the claddings were also considered. An expression for the propagation constant of the LRSPP in the symmetric structure (εr,1=εr,3) is given, from which it is observed that α(tλ0)2. They found that long-range surface modes exist in a symmetric structure for almost any value of εr,2, including the case εI=0 and εR<εr,1, which does not support a single-interface SPP. Expressions for the cutoff thickness and cutoff asymmetry (max[εr,1εr,3] and max[εr,3εr,1]) are derived for the LRSPP in slightly asymmetric structures; the expressions exhibit λ0 and λ02 dependencies, respectively, indicating that a larger t is required at longer wavelengths to maintain guidance given an asymmetry, and that the cladding permittivities must be more closely matched at longer wavelengths for a given t. They also discussed the role of the light line in the case of absorbing structures, indicating, as had been previously noted [72, 80], that it does not clearly separate the radiative and nonradiative regions of the dispersion curve; this was also observed in [94]. Prism coupling experiments were conducted at λ0=3.391μm on 43.5nm thick Pd and 50.4nm thick V films deposited onto a quartz substrate with index-matched fluid forming the other cladding. The Pd (εr,2=110j142) and V (εr,2=10j49.3) films were observed to support LRSPP and LRSEP waves, respectively.

At about the same time, Prade et al. [128] produced a study that included consideration of lossless metal slabs bounded by dielectrics where the permittivities satisfy εR<εr,1,εr,3 or εr,3<εR<εr,1 with εR, εr,1, and εr,3 similar in magnitude. They showed ab and sb modes existing for εR<εr,1,εr,3 as long as t remains below a cutoff thickness (recall that the purely bound single-interface SPP is not supported for εR<εr,1). In the asymmetric case (εr,1εr,3) the sb mode has an additional cutoff thickness at smaller t. The ab mode has a negative group velocity. For the case εr,3<εR<εr,1, only the sb mode exists, exhibiting a cutoff thickness at small t and evolving into the single-interface SPP at the εRεr,3 interface with increasing t.

Yang et al. [126] applied the virtual mode treatment [48] to study theoretically prism coupling to the LRSPP and LRSEP. They demonstrated that the perturbation caused by the prism could increase the propagation length of the LRSEP, as opposed to only reducing it as is generally observed for the LRSPP.

Bryan-Brown et al. [127] excited the LRSEP at λ0=1.52μm along Cr films 33.6, 20.9, 17.8 and 11.2nm thick deposited onto quartz substrates and covered by an index-matched fluid. Flat films excited by using prism coupling and corrugated films excited by grating coupling were investigated.

Bryan-Brown et al. [129] investigated at λ0=632.8nm the LRSPP in thick corrugated Pd films and the LRSEP in thin corrugated Pd films both excited by grating coupling. The thickness dependence of the Pd permittivity allowed exploration of both types of wave by using the same material.

Giannini et al. [134] investigated the LRSEP along a thin (t<50nm) amorphous Si layer cladded symmetrically by SiO2. They investigated a few wavelengths of operation but emphasize the ultraviolet (λ0=318 and 375nm) where the relative permittivity of Si satisfies εR<εI. They found that the LRSEP in this structure slightly outperforms the LRSPP in the corresponding Au structure at these wavelengths, by comparing the propagation length, the field extension, and the associated FoM [96] of each wave. Prism coupling experiments were conducted with broadband light and with a laser source at λ0=375nm, on structures comprising a t=13 or 20nm thick amorphous Si layer cladded by SiO2, confirming the excitation of the LRSEP.

Other related studies include those of Crook et al. [130, 131] on an organic thin film, of Takabayashi et al. [132] on a thin Si film, and of Yang and Sambles [133] on indium tin oxide films.

2.9. Nonlinear Interactions [135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168]

The large field enhancement [40] and the long propagation length [28, 29, 30] are the main attributes of the LRSPP motivating interest in nonlinear interactions.

Sarid et al. [135] computed the intensity-dependant propagation constant of the ab and sb modes in a symmetric structure consisting of a Cu film bounded by InSb at λ05μm as a function of the Cu thickness. They found that the power required for a phase shift of π2 over a distance of Le is about 1 order of magnitude lower for the LRSPP at t=15nm compared with the corresponding single-interface SPP.

Stegeman et al. [136] computed the cross sections for copropagating and counterpropagating second-harmonic generation, degenerate four-wave mixing, and intensity-dependant phase shifts, driven by LRSPPs. Ag films cladded symmetrically by CdSe or InSb were considered. Ag thicknesses in the range of 1535nm were found to be optimal for the nonlinear processes considered. Except for copropagating second-harmonic generation, which is limited by the inability to achieve phase matching, they obtain cross sections that are significantly larger than those related to focused Gaussian beams, stating as a reason that a better trade-off between confinement and Le can be achieved for LRSPPs.

Deck and Sarid [137] investigated theoretically second-harmonic generation by LRSPPs in a prism coupling arrangement excited at a fundamental λ0 of 1.06μm, assuming a nonlinear medium (quartz) as one cladding and an index-matched linear medium as the other. They predicted that the intensity of the outcoupled second-harmonic wave would be 2–4 orders of magnitude greater than in the corresponding Kretschmann–Raether and Otto configurations for the same incident field, and they attributed this improvement to the strongly enhanced fields associated with the LRSPP in this arrangement [40].

Quail et al. [138] verified this prediction [137], measuring an outcoupled second-harmonic signal having an intensity that is 2 orders of magnitude larger than in the Kretschmann–Raether and Otto geometries. The LRSPP was excited at a fundamental λ0 of 1.06μm by using prism coupling in a structure consisting of a 13.5nm thick Ag film on an X-cut quartz substrate covered with index-matching fluid, as shown in Fig. 10(a). The outcoupled second-harmonic signal was observed at a 5° offset compared with the angle of the fundamental because of dispersion in the prism. Figure 10(b) compares the measured second-harmonic reflection coefficient R (defined as the ratio of the second-harmonic irradiance to the square of the fundamental irradiance) to that expected for the single-interface SPP. In a subsequent study, Quail and Simon [146] monitored the transmitted second-harmonic signal generated by the LRSPP in a similar experimental arrangement, noting greater generation efficiency.

Stegeman et al. [139] computed the efficiency of second-harmonic generation by two counterpropagating LRSPPs excited at a fundamental λ0 of 1.06μm by prism coupling in a structure consisting of a 15nm thick Ag film on MNA (2-methyl-4-nitroaniline, an organic crystal; see Ref. 15 of [139]) used as the nonlinear cladding and assuming a linear index-matched material as the other cladding. Second-harmonic generation efficiencies of about 104 were predicted.

Moshrefzadeh et al. [140] computed the second-harmonic signal generated by an LRSPP propagating along thin (t=15  nm and t=25nm) Ag films bearing a 0.5nm thick nonlinear adlayer and bounded symmetrically by benzene. The LRSPP was excited at a fundamental λ0 of 1.06μm by prism coupling. An increase in second-harmonic intensity of 105, compared with simple reflection off the corresponding metal surface, was predicted for the 15nm thick Ag case.

Stegeman and Karaguleff [141] investigated theoretically degenerate four-wave mixing via LRSPPs excited by prism coupling at λ0=1.06μm, predicting conversion efficiencies into the degenerate fourth wave of about 10%–50% for an Ag film 15nm thick on a nonlinear substrate (PTS, bis-(p-toluene sulphonate) of 2,4-hexadiyne-1,6-diol; see Ref. 15 of [141]) and covered with a linear index-matched material.

Liao et al. [142] computed the cross sections for second-harmonic generation by counterpropagating waves in dielectric waveguides and Ag slabs supporting LRSPPs. Fundamental λ0’s of 1.06 and 10.6μm were considered, assuming MNA and CdSe as the nonlinear materials, respectively. The Ag slab was bounded symmetrically by the nonlinear material and the dielectric waveguides incorporated the nonlinear material as either the core or the lower cladding. They find the highest cross sections when the nonlinear medium is used as the core of a dielectric waveguide.

Karaguleff and Stegeman [143] conducted a similar study for degenerate four-wave mixing, at λ0=1μm assuming PTS, and at λ0=5.5μm assuming InSb, as the nonlinear materials. They reached essentially the same conclusion as for second-harmonic generation [142], which is that the highest cross sections are obtained when the nonlinear medium is used as the core of a dielectric waveguide. They attributed the difference to the better confinement–attenuation trade-off available in the dielectric waveguides. They also noted that the LRSPP cross section in the corresponding prism-coupled geometry [141] is greater by a factor of about two compared with the freely guided (no prism) LRSPP.

Stegeman and Seaton [144] investigated theoretically the modes supported by the metal slab bounded on one or both sides by media with intensity-dependant refractive indices (n=nL+nI|H|2). They assumed lossless Cu films of thicknesses 50 and 20nm, and InSb (nI<0, self-defocusing) as the nonlinear medium and give results at λ0=5.3μm. They found in this case (nI<0) that the modes approach cutoff with increasing mode power. The details of the approach are different depending one whether one or both claddings are nonlinear, but the sb mode in the thinnest film (i.e., the LRSPP) bounded on both sides by the nonlinear material approaches cutoff most rapidly. Assuming nI>0 (self-focusing) generates a more complex power dependency, including the observation of a maximum in mode power transmission, mode fields developing maxima away from the film, and new modes existing above minimum power thresholds. Stegeman and Seaton searched for TE-polarized SPP’s in these structures (nI>0) but did not find them. However, subsequent work [145] revealed their existence for very thin metal films (t10nm) having a small εR. Ariyasu et al. [150] expanded on this work [144, 145], considering different combinations for the nonlinear claddings, including attenuation.

Mihalache et al. [153, 157] also found TE-polarized SPPs in the self-focusing case, for slightly asymmetric claddings. Boardman and Twardowski [156, 162] studied the interaction between TE- and TM-polarized modes in similar intensity-dependant nonlinear waveguides and considered to some extent the thin metal slab.

Hickernell and Sarid [151] developed a theory for prism coupling to the LRSPP in structures having a metal slab on a substrate exhibiting an intensity-dependant refractive index and covered by an index-matched medium. They found that an intensity 2 orders of magnitude lower than that required for the single-interface SPP is needed to observe bistability via the LRSPP.

Agarwal and Dutta Gupta [152] developed a theory for a multilayer structure on a similar nonlinear substrate and studied bistability with prism-coupled single-interface SPPs (Kretschmann–Raether), and the ab and LRSPP modes in a thin metal slab. They found that LRSPP bistability occurs at much lower intensity thresholds (by at least 1 order of magnitude).

Nunzi and Ricard [148] observed optical phase conjugation using single-interface SPPs and attributed the main nonlinear contribution in their experiments to heating from the metal film (i.e., thermal effects) rather than to field-induced nonlinearities in the media. They made the points that all of the energy coupled into the SPP is converted into heat in the metal film and that the adjacent dielectric region is where nonlinear interactions are sought. They commented that thermal aspects would remain important in comparable experiments conducted with the LRSPP even though the latter exhibits less attenuation. Sambles and Innes [155] raised similar points, emphasizing the need for consideration of thermal issues even when working with the LRSPP.

Yang and Sambles [164] measured, via prism coupling at λ0=514.5nm, optical power-dependant changes in the excitation curve and angle of LRSEPs in a Pd film 4nm thick deposited onto BK7 and bounded on the other side by index-matched fluid. High- and low-power angle scans were conducted, along with power scans at fixed angles. The optical nonlinearities were thermally induced by heating of the Pd film and were deemed to be changes in the index of the matching fluid (thermo-optic effect) and changes in the thickness of the fluid layer (coupling gap).

Quail and Simon [147] observed from modal computations that the sb mode at the second harmonic had the same phase constant as the ab mode at the fundamental for a prescribed Ag thickness in their experimental arrangement. Based on this observation, they demonstrated phase-matched copropagating second-harmonic generation by exciting the ab mode at the fundamental and measuring the prism outcoupled sb mode (LRSPP) at the second harmonic.

Fukui et al. [149] considered the effects of a finite-width beam in prism-coupled second-harmonic generation experiments, computing the spatial profile of the reflected second-harmonic signal for an incident 2mm wide square profile (stepped intensity) beam. The profiles show a global maximum for a prescribed metal film thickness.

Building on this theory, Schmidlin and Simon [161] measured the profile of the reflected second-harmonic signal in the same experimental situation as that reported in [138], but using a 0.2mm wide output slit (moved via a translation stage) and a 0.5mm wide input beam. They deduced the propagation length of the LRSPP (excited at the fundamental) from the measured reflected second-harmonic spatial profile in the region outside the incident beam width.

Chen and Simon [154, 158] studied experimentally and theoretically second-harmonic generation from LRSPPs excited at a fundamental λ0 of 1μm in a corrugated Ag film bounded on both sides by quartz, although only one of the quartz claddings was responsible for the generation of the second harmonic owing to the presence of index-matching fluid at the other Ag/quartz interface. They observed enhanced second-harmonic generation due to the LRSPP but conclude that scattering from the grating grooves significantly limits the possible enhancement compared with flat films in a prism-coupled geometry. Phase matching between the fundamental ab and the second-harmonic LRSPP was also observed in one of the corrugated structures having the appropriate Ag film thickness [158].

Tzeng and Lue [159, 160] studied theoretically second-harmonic generation via prism-coupled excitation of the LRSPP in Ag [159], and Ag, Au, Cu, Al [160] films, bounded by linear dielectrics, where the second harmonic is generated by nonlinearities in the metal (bulk and selvedge regions) and outcoupled by the prism. Electron gas hydrodynamic theory [167] was used to describe the nonlinear response of electrons in the metal. They found an increase in the second-harmonic generation that is 2 orders of magnitude larger for the LRSPP compared with the corresponding single-interface SPP. They also noted effects due to the thickness of the coupling gap. Lue and Dai [166] extended the study to include coupled LRSPPs in structures comprising a pair of Ag slabs bounded on all sides by SiO2.

Simon et al. [163] and Wang and Simon [165] reported the backscattering of the second-harmonic wave from excitation of the LRSPP via prism coupling at a fundamental λ0 of 1.06μm in thin Ag films on quartz, bounded on the other side by index-matched fluid. The measured backscattered second-harmonic signal exhibited a peak in the direction of the incident beam (antispecular) with a slight angular offset (30mrad) due to dispersion in the coupling prism.

Li and Zhang [168] compared theoretically the nonlinear coefficients of the single interface, the metal slab, and the metal clads.

2.10. Biosensors [169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195]

The high surface sensitivity of the single-interface SPP has been heavily exploited in (bio)chemical sensors ever since the initial demonstrations [169]. The conventional and mainstream approach to SPP sensing [169, 170] rests on the Kretschmann–Raether configuration (Fig. 4, case 3), where efficient coupling to the single-interface SPP depends strongly on the thickness and index of an adlayer located at the metal/fluid interface (surface sensing) and on the index of the sensing fluid itself (bulk or refractometric sensing). Various modifications and alternatives to this approach have been proposed over time in the quest to achieve greater sensitivity and lower detection limits. Reviews discussing different SPP sensor architectures and interrogation schemes were published by Homola and co-workers [171, 173] and by Chien and Chen [172].

Some of the alternative approaches proposed involve using the LRSPP instead of the single-interface SPP to perform the sensing function along metal slabs. The typical approach uses a prism-coupled arrangement such as that depicted in Fig. 4, case 1, with the lower cladding (εr,1) being the sensing fluid (usually an aqueous buffer) contained within a flow cell, and the upper cladding (εr,3) being a dielectric that has a refractive index closely matched to that of the sensing fluid. Popular materials for this cladding layer are Cytop or Teflon, which have a refractive index slightly above and slightly below (respectively) that of de-ionized water, so the sensing structures are typically slightly asymmetric. Au is normally used as the sensing surface given its chemical stability and the availability of good surface chemistries for this metal.

The use of the LRSPP in a prism-coupled arrangement was proposed as a sensor by Matsubara et al. [174]. They computed the angular response at λ0=632.8nm for structures comprising Ag as the metal film, bounded by ethanol on one side, and by MgF2 on the other side also in contact with the prism. MgF2 was selected because its index approximately matches that of ethanol. Corresponding Kretschmann–Raether configurations were also modeled. Matsubara et al. measured the angular response of the arrangements in ethanol, demonstrating a narrower response in the case of the LRSPP.

Similar LRSPP structures excited via prism coupling were reported in [178], where Teflon and MgF2 were compared as cladding materials and Au was used for the metal film. The approach was demonstrated in bulk sensing experiments.

A similar structure was reported in [180], where Cytop was selected for the cladding. The approach was demonstrated in bioaffinity sensing experiments on Au spots using an imaging prism-coupled arrangement. An improvement of 20% over the conventional Kretschmann–Raether configuration was claimed.

Slavík and Homola [185] demonstrated bulk sensing using a Teflon-Au-water structure. The optimal thickness of the Au film (24nm) and of the Teflon layer (1200nm) were determined from modeling at λ0=900nm and selected such that the highest coupling and bulk sensitivity would be achieved. Interrogation was conducted by using an LED centered at λ0=830nm and a spectrometer. They reported a bulk sensing detection limit of 2.5×108 and stated that this is the best value reported to date for any bulk sensor based on SPPs. The measured spectral position of the LRSPP dip is shown in Fig. 11 as aqueous sensing fluids of different refractive indices are injected into the sensor. The baseline noise signal is also shown on an expanded scale, from which the noise was deduced to be 1.4pm.

Vala et al. [195] compared a similar Teflon-Au-water structure with a conventional Kretschmann–Raether structure for detecting large analytes such as biotinylated latex beads (through a streptavidin bridge) and bacteria (heat-killed Escherichia coli through antibodies). Cutoff of the LRSPP was noted in the case of latex beads for the test structure having the thinnest Au film. The sensitivity of the LRSPP sensor was found to be about 5.5× greater than the conventional Kretschmann–Raether configurations for the detection of E.coli.

Slavík and Homola [183] considered the Teflon-Au-water and MgF2Au-water structures, optimizing the layer thicknesses (MgF2, Teflon, Au) such that efficient prism coupling could be obtained into both the ab and sb modes of the same structure under either angular or wavelength interrogation. They found for a properly optimized structure that near perfect coupling can be achieved into both modes and verify this experimentally for a Teflon-Au-water structure under wavelength interrogation. They demonstrated bulk sensing and argue that the availability of two sensing modes having different bulk and surface sensitivities is advantageous for removing unwanted perturbations in biosensor applications. Further work on this approach was reported in [184], including noise and cross-sensitivity analyses and biosensing experimentation with IgE. The approach was compared with a two-channel compensated Kretschmann–Raether configuration.

Hastings et al. [189] also considered dual-mode (ab and sb) operation in the Teflon-Au-water structure under wavelength interrogation. They showed that monitoring both resonances allows changes in adlayer thickness and changes in the bulk index of the sensing solution to be monitored separately. Through modeling they found optimal designs that minimize the detection limit for surface and bulk sensing by using a Cramer–Rao lower bound to estimate the smallest detectable shift in the coupling dips. They conducted experiments demonstrating the ability to monitor changes in bulk index and changes in surface coverage, the former by alternating between two buffer solutions and the latter via the biotin-streptavidin system (with biotin immobilized onto the sensor surface). The detection limits for bulk and surface sensing were estimated to be 2.3×105 RIU (refractive index units) and 11pgmm2, respectively. In [190] they investigated the same concept but under angular interrogation and found a reduction in cross sensitivity compared with wavelength interrogation.

Enhanced fluorescence from tagged antibodies pumped with LRSPPs was demonstrated by Kasry and Knoll [181]. The LRSPPs were excited by prism coupling in a Teflon-Au-water structure and the tagged antibodies were adsorbed onto a 30nm thick polysterene spacer layer deposited on the Au surface. Fluorescence intensities about 22 times larger were observed for the LRSPP pump compared with pumping with the single-interface SPP in corresponding experiments. The enhanced fluorescence intensity was attributed to the enhanced field of the LRSPP [40]. The authors also pointed out that the larger penetration depth into the sensing medium of the LRSPP could lead to further enhancement if a thick matrix were used to bind tagged analyte to the sensor along the third dimension (into the sensing medium). In a subsequent paper, Knoll et al. [192] reported the binding of a hydrogel matrix to a Cytop-Au structure and then demonstrated sensing using the LRSPP of free prostate specific antigen to its antibody immobilized in the matrix.

Dostálek et al. [188] compared prism-coupled Cytop-Au-water and Teflon-Au-water structures at λ0=632.8nm. They explored the sensitivity of both structures for bulk and surface sensing and deduced the detection limits from their measured responses and from the width of their reflection dips. Both structures improve on the detection limits of the conventional Kretschmann–Raether configuration, with the Teflon structure being about 14× better for bulk sensing if operated near cutoff, and the Cytop structure being about 2.4× better for surface sensing. They measured the fluorescence intensity of dye pumped by the LRSPP (following [181]) as a function of dye distance from the metal film set by a spacer layer consisting of a protein stack or a thin layer of Cytop. Quenching was noted for a distance of 4nm, maximum intensity was measured for distances of 2040nm, and significantly more fluorescence was measured compared with the conventional Kretschmann–Raether configuration. Their setup for conducting fluorescence studies in this manner is sketched in Fig. 12. They also deposited a series of Au films of thickness ranging from t=15nm to t=45nm on Cytop and on Teflon and extracted the optical parameters of their films by fitting measured ATR spectra to theoretical responses. They observed some substrate dependence in the extracted optical parameters, probably due to differences in the roughness of the starting surfaces, but otherwise observe the same trends in the relative permittivity with decreasing t as discussed in Subsection 2.7. The bulk optical parameters for Au were achieved in their cases at t25nm.

Wang et al. [193] demonstrated a biosensor capable of detecting aflatoxin M1 (AFM1) in milk using a Cytop-Au structure. The sensor detects LRSPP pumped fluorescence emitted from labeled antibodies (Cy5-GAR) bound to the sensor surface following the inhibition immunoassay format (Au/thiol/BSA-AFM1 (where BSA is bovine serum albumin) immobilized onto the sensor followed by detection of aAFM1/Cy5-GaR).

Dostálek et al. [194] proposed a biosensor using a pair of broadside coupled thin Au slabs separated from each other and from the prism (on one side) by thin layers of Cytop. As discussed in Subsection 2.5 (with regards to [74]), coupled thin slabs support supermodes consisting of symmetrical and asymmetrical couplings of ab and sb modes, and when the metals are thin, the two supermodes involving the sb mode are long range. In [194] the symmetric and asymmetric long-range supermodes are excited at different angles of incidence at the same operating wavelength. The modes have different probing depths into the sensing medium; so they exhibit different bulk and surface sensitivities. Thus, by fitting measured ATR spectra involving both supermodes to theoretical responses (computed using the transfer matrix method), the thickness and refractive index of an adlayer can be extracted. Dostálek et al. demonstrated the approach by characterizing hydrogel layers (thickness and index) deposited onto their sensors and by observing the diffusion of BSA into the hydrogels.

Rajan et al. [186] modeled a sensor consisting of a multimode step-index fiber with the cladding removed over a length, whereupon an LRSPP supporting structure is deposited directly onto the core, the structure consisting of a Teflon layer followed by a thin Au film covered with the sensing fluid. The bulk sensitivity of the sensor was determined under wavelength interrogation as a function of structure parameters. In a subsequent paper, Jha et al. [191] studied a similar structure with tapered fiber sections added on either side of the sensing region.

Chen et al. [187] investigated theoretically the temperature stability of prism-coupled LRSPP sensors in a Cytop-Ag-water configuration by assuming a temperature-dependant model for the permittivity of the Ag film. They found that the configuration is thermally stable over a large temperature range (250K), but they ignored the temperature dependence of the prism (SF10), and of Cytop and water (which have large thermo-optic effects).

In the above-described studies, the index symmetry required to ensure propagation of the LRSPP was provided by selecting a cladding material that is closely index-matched to the index of the sensing fluid. An alternative approach involves using a thin high-index layer, which when taken in combination with the low index of the sensing fluid, creates an effective index that closely matches the index of the material on the other side [175]. Such a structure is physically asymmetric but appears symmetric from an effective medium point of view. Sensing using the LRSPP in such a structure has been considered, with coupling provided by a corrugated grating [176, 179], and where one of the claddings comprises two layers, a thin high-index dielectric (Si3N4) layer followed by the sensing medium (air or water), such that the effective index of the combination matches the index of the silica cladding on the other side of the metal film.

A similar idea was applied in [182] to create an LRSPP sensor based on prism coupling, but where a Teflon/Ta2O5 bilayer system was used to match (effectively) the index of the aqueous medium on the other side of an Au film. This approach was demonstrated in bulk sensing experiments.

The LRSPP in Kou and Tamir’s structure [83] was considered theoretically in [64] for sensing by using a corrugated grating as the coupling means. Liao et al. [177] explored theoretically prism-coupled LRSPPs in a multilayer system and commented on the suitability for chemical sensing. (Supporting the metal slab on a 1D finite photonic crystal as discussed in Subsection 2.L [237] or suspending the metal slab as discussed in Subsection 2.4 [55] and Subsection 3.9 [342] represents a further alternative to satisfying the index symmetry requirement for sensing with the LRSPP.)

2.11. Emission and Molecular Scattering [196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217]

The decay of excited molecular emitters directly into SPPs via the near field [196, 197] has been a subject of intense study [198]. Reports involving the LRSPP in this process (and the like) are reviewed here.

Gruhlke et al. [199] observed optical emission mediated by the LRSPP and ab modes in symmetric corrugated Ag films of various thicknesses (1861nm), whereby molecular emitters adjacent to the Ag film excited directly the modes, which were then outcoupled into free radiation by the corrugation. The dispersion of the modes over a broad spectral range (580880nm) was also measured via this emission process. The LRSPP in these experiments was responsible for most of the observed emission.

In a subsequent publication [200], Gruhlke and Hall indicated that in their experiments [199, 200] the excited molecules are on one side of the metal film and the emission is observed on the other side. They emphasized that the process provides a dispersive channel through their otherwise (nearly) opaque metal films (as in studies involving prism coupling [19, 22, 43]). Figure 13 shows the measured radiation spectrum emitted from the symmetric structure sketched at the origin of the polar plot. Fluorescent molecules are located in the lower photoresist layer and are pumped at λ0=514.5nm through the backside at normal incidence. The spectrum is normalized to the intensity measured from a sample that contains only the lower (fluorescent) photoresist layer. The emitted intensity is 30× stronger at λ0=780nm owing to mediation by the LRSPP. Indeed, the fluorescence reradiated by the LRSPP into this peak is 30% of that radiated isotropically (at the same wavelength) in the absence of the metal layer. They stated that field enhanced fluorescence likely had a role to play.

Leung et al. [201] computed the decay rate of a dipole placed 20nm above asymmetrically and symmetrically cladded (free-standing) corrugated gratings. Among all the cases considered, the strongest enhancement of the rate was obtained for coupling into the LRSPP of a 10nm thick free-standing corrugated Ag grating, where the decay rate was about 100× that of a free dipole.

Lenac and Tomaš [202, 203] derived the cross sections for absorption of the sb and ab modes by molecules placed above the metal in a symmetric configuration as a function of t. They found decreasing and increasing cross sections with decreasing t for the sb and ab modes, respectively. They also found larger cross sections at shorter λ0’s. The differences were attributed to differences in modal confinement.

Tomaš and Lenac [204] also derived the cross sections for scattering of the sb mode (β,ω) into the sb mode (β,ω) (as well as other modal combinations) by molecules placed above the metal in a symmetric metal slab as a function of t. They found that the cross section decreases as t decreases and estimated that the LRSPP scattering cross section along an Ag film 10nm thick is 1–2 orders of magnitude smaller than that for scattering between single-interface SPPs. They also commented that the LRSPP cross section would compete with the LRSPP field enhancement in prism-coupled arrangements [40], such that surface-enhanced Raman scattering (SERS) mediated by prism-coupled LRSPPs is not likely to be significantly more enhanced than SERS mediated by prism-coupled single-interface SPPs.

In a subsequent paper [205], Lenac and Tomaš derive the power lost by a molecular dipole to the sb and ab modes of a symmetric metal film as a function of t, with and without prism outcoupling. The dipole was located near and below the metal film within the bottom cladding. Their computations without prism outcoupling (freely guided) showed decreasing and increasing power coupled into the sb and ab modes, respectively, with decreasing t. For an Ag film 15nm thick, about 30× more power is coupled into the ab mode than into the LRSPP at λ0=514.5nm; about 5× more power would be coupled into the corresponding single-interface SPP. However, for a dipole located farther from the metal, the LRSPP is preferentially excited, since its fields penetrate more deeply into the cladding than those of the ab mode. The angular distribution of power (dPdΩ) emitted into the prism by outcoupling from the sb and ab modes, themselves excited by the dipole, was computed, showing that the emission is dominated by the sb mode rather than the ab mode. The computations for the sb mode with decreasing t showed a decrease in the angular width of emission and an increase in the peak of the angular distribution of emitted power (i.e., in max{dPdΩ}). The peak is about 1000× greater for mediation via the LRSPP in an Ag film 15nm thick than for a free dipole in the same medium as the claddings. Computations for mediation via the single-interface SPP in the corresponding (optimized) Kretschmann–Raether configuration yield a peak about 200× greater, so mediation via the LRSPP produces an improvement of about 5×. They also estimate a SERS intensity enhancement of about 30× for mediation via the LRSPP versus the single-interface SPP in prism-coupled geometries. Thus, although the coupling of a dipole to the freely guided LRSPP (no prism) and the molecular scattering cross section of freely guided LRSPP’s [204] are lower than for the corresponding single-interface SPP, the field enhancement associated with prism coupling [40] compensates sufficiently to produce greater and sharper emission peaks for the LRSPP. Subsequent calculations comparing SERS mediated by single-interface SPPs in the Otto geometry with mediation by the prism-coupled LRSPP also yield an enhancement of about 30× in the peak for the LRSPP [206].

Barnes and co-workers have addressed emission extraction through metal films in light emitting diodes (e.g., [198, 207, 208, 209, 210, 211]) for different device architectures and from different perspectives, such as the direct coupling of molecular emitters to SPP modes and the conversion of SPPs into free radiation. The most promising approaches to date involve mediation via the coupled modes of an effectively symmetrical thin metal contact [208, 209, 210, 211], where symmetry is achieved by coating the top of the metal contact with a thin dielectric overlayer of a prescribed thickness, which taken in combination with air yields an effective medium that is index matched to the underlying active medium. Outcoupling of the ab and sb modes to free radiation is achieved via corrugations in the full structure or in the thin dielectric overlayer. The metal contact in these studies is 4355nm thick (Ag).

Chiu et al. [216] compared the measured emission from a two-layer structure consisting of AuAlq3 on photoresist on Si with the emission from a four-layer structure consisting of AuAlq3AuAlq3 on photoresist on Si. The Alq3 layers were 50nm thick, and the Au layers were 20nm thick. Each structure was formed into a 1D rectangular lamellar grating having the purpose of outcoupling the surface plasmons propagating along the structure into free radiation. The structures were pumped by 405nm light, and the Alq3 molecules decay into the modes of the structure including the surface plasmon modes supported therein. Enhanced emission in the range of λ0=500nm to λ0=650nmwas measured from the four-layer structure compared with the two-layer structure and a flat (planar) structure. The enhanced emission was attributed to mediation by LRSPPs. The modes supported by these multilayer structures were not investigated at the operating wavelengths.

Andrew and Barnes [212] demonstrated the transfer of energy between donor and acceptor molecules (dipoles) through thin Ag films, with the transfer being mediated by the ab and sb modes. The Ag film was cladded below by a 60nm thick layer of Alq3-doped polymethyl methacrylate (PMMA, donor) on SiO2, and above by a 60nm thick layer of R6G-doped PMMA (acceptor, where R6G is Rhodamine 6G) , as sketched in Fig. 14(a). The structure is essentially symmetric at the wavelengths of interest. Figure 14(b) shows the measured emission spectrum of an Alq3-doped layer only, and the emission and absorption spectra of an R6G-doped layer only. The emission spectrum of the Alq3-doped layer overlaps strongly with the absorption spectrum of the R6G-doped layer (in the range λ0525   nm to λ0550nm); so, when pumped from the back side (at λ0=408nm), the excited Alq3 molecules can donate their energy to the R6G molecules through interaction with the ab and sb modes of the structure. The R6G molecules then decay spontaneously at λ0575nm, and part of this emission is captured by the optical detection setup aligned with the top of the structure. Figure 14(c) shows the measured spectrum obtained from the structure for the case of a t=60nm thick Ag film (black curve), along with the spectra of two control samples, each having only one type of dipole—donor only (no R6G, blue curve) and acceptor only (no Alq3, red curve). The emission was significantly larger than in the case of the control samples, indicating efficient energy transfer through the Ag film via mediation by the ab and sb modes. The mediation accounted for 70% of the total emission.

Okamato et al. [213] suggested that lasing in the LRSPP in a corrugated grating bounded symmetrically by gain media [4-dicyanomethylene-2-methyl-6- (p-dimethylaminostyryl)-4H-pyran (DCM)-doped Alq3, peak λ0=620nm] could be achieved, by pointing out that the loss of the LRSPP in flat Ag films thinner than 60nm is lower than the available gain in the medium considered. In their concept, standing LRSPP waves would be amplified by stimulated emission and partially outcoupled by the grating forming an output laser beam.

Winter et al. [214] investigated further the concept proposed by Okamoto et al. [213], considering the existence of the ab mode as well as the LRSPP. Photoluminescence measurements on (effectively) symmetric corrugated structures similar to those reported in [210], where the Ag film thickness was varied from 20 to 90nm, show that a significant amount of power is indeed coupled into both the ab and sb modes. They also compute the fraction of total power coupled by a dipole emitting at λ0=620nm, and positioned 20 and 90nm away from a flat symmetrically cladded Ag film, into the ab and sb modes of the structure, as a function of t. For a dipole separation of 20nm and for t=20nm, about 80% of the power is coupled into the ab mode while about 7% couples into the LRSPP. However, for a dipole separation of 90nm and for t=20nm, about 15% of the total power is coupled into the ab mode, and about 15% is coupled into the LRSPP. For larger dipole separations, more power would (proportionally) be coupled into the LRSPP than into the ab mode, a trend consistent with earlier computations [205], owing to the greater extension of the LRSPP mode fields into the cladding. They then estimate the gain available to each mode by ascribing to each a fraction of the total gain taken to be the same as the fraction of total power coupled in from a dipole at a particular location. Taking into account in this manner the gain lost to the ab mode, their results suggest that lasing in the LRSPP would be possible, but an Ag film thinner than about 15nm would be needed.

Wang and Zhou [215] considered the prospects for amplification of LRSPPs in a structure consisting of an Au film on Si and covered with a multilayer system consisting of alternating Si and Er:Si nanolayers. Ignoring the ab mode, they predicted net gain into the LRSPP at λ0=1500nm for Au films thinner than about 20nm.

De Leon and Berini [217] proposed a model for SPP amplification that accounts for the nonuniform gain distribution of a dipolar gain medium pumped at broadside and placed along a symmetric metal slab. The model takes into account four channels for excited state decay (coupling to ab, sb and radiative modes, and coupling to electron–hole pairs in the metal), leading to a position-dependant dipole lifetime. Additionally, the model uses a realistic pump irradiance distribution within the gain medium as computed by using a transfer matrix method. The rate equations for the standard four-level pumping model are then applied locally, with the lifetime and irradiance taking on their position-dependant values, leading to a nonuniform gain distribution. The distribution is then incorporated into a multilayer waveguide mode solver from which mode power gains are computed for the modes of the system. Using this approach, they predict that net amplification of the LRSPP is possible in the visible (λ0=560nm) by using a reasonable concentration of R6G molecules (3mM) and a reasonable pump irradiance (210kWcm2 at λ0=532nm, pulsed) assuming a 20nm thick Ag slab bounded by Cytop on one side and the index-matched gain medium on the other.

2.12. Other Studies [218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245]

Other studies of the LRSPP in the metal slab include investigations involving magnetic materials [218, 219, 220, 233, 236], electro-optic materials [221, 226, 229, 230, 235] and photonic crystals [237, 245], studies of polarizing devices [222, 223, 224, 225, 228, 231, 234] and pulse reshaping devices [227], a study of propagation through gaps in the metal slab [238], and a study of bending out of plane [241]. Electro-optic and filtering devices involving the LRSPP propagating across an array of metal nanowires have been explored [242, 244]. The LRSPP supported by semiconductor heterostructures has been investigated [240]. Approaches to extend the range of the single-interface SPP by involving a large multimode waveguide [232, 243] or by using an anisotropic photonic crystal [239] have been reported.

Sarid [218, 219] modeled the modes supported by a metal film bounded by identical magnetic semiconductor claddings subject to a magnetization field in the plane of the metal film and perpendicular to the direction of propagation of the modes (transverse magnetization). He found that the range of the LRSPP decreases with increasing magnetization owing to the destruction of symmetry in the dielectric claddings. Cutoff thicknesses were noted for the LRSPP.

Hickernell and Sarid [220] investigated LRSPPs in a thin magnetic metal film (Ni) bounded symmetrically by dielectrics under transverse magnetization. They computed the change in the propagation constant of the LRSPP as a function of t due to the magnetization, showing that the change decreases as t decreases. The differential reflectance of a thin Ni film due to the application of a magnetic field was measured by using prism coupling through the excitation angle of the LRSPP. A small magnetically induced modulation was detected.

Sepúlveda et al. [233] studied the metal slab bounded on both sides by magneto-optic dielectric claddings (yttrium iron garnet, YIG), or bounded on one side by YIG and on the other by an index-matched nonmagnetic dielectric. Both configurations were considered under different magnetization directions (transverse, longitudinal). Nonreciprocity was predicted for both the sb and the ab mode in certain cases and was quantified with decreasing t. Their results indicate that nonreciprocal LRSPPs can be obtained, in particular, for transverse magnetizations of opposite direction in the lower and upper claddings for the YIG cladded film, and for both transverse magnetization directions in the case of the YIG/dielectric cladded structure. They also discussed the LRSPP in a ferromagnetic metal film (Co) bounded by dielectrics.

Khurgin [236] studied a similar system, consisting of a thin metal film bounded on one side by a magneto-optic material (bismuth-doped gadolinium iron garnet, Bi:GdIG) and on the other by an index-matched dielectric. He also concluded that nonreciprocal LRSPPs are possible in this structure under transverse magnetization.

Device applications using electro-optic materials include modulators [221, 226, 230] and a tunable filter [229], where the LRSPP is excited via prism coupling in a thin metal film bounded on one side by an electro-optic dielectric, and on the prism side by an index-matched dielectric. The electric field is applied to the electro-optic medium via the metal film and an additional electrode deposited onto its other surface. The narrow width of the LRSPP reflection dip improves the performance of the devices compared with the single-interface SPP.

Liu and Xiao [235] proposed and modeled an electro-optic switch consisting of a lossless metal slab bounded on both sides by an electro-optic material (Ba0.5Sr0.5TiO3, BST). Switching occurs by varying electro-optically the phase (beating) between the ab and the sb mode of the slab and taking as the outputs of the switch the top cladding in isolation and the bottom in isolation.

Konopsky and Alieva [237] reported the excitation of LRSPPs on a thin (5nm) Au film bounded by air on one side and on the other by a finite 1D photonic crystal implemented as a multilayer Ta2O5SiO2 stack on a BK7 prism. Semi-infinite 1D photonic crystals support Bloch surface waves in the bandgap, having fields that oscillate and decay exponentially into the crystal. Thus the full structure (finite 1D photonic crystal, intermediate dielectric layer, metal slab) was designed such that essentially the same LRSPP field distribution was achieved within the metal and air regions as in the corresponding hypothetical air–metal–air structure. An LRSPP propagation length estimated to be about 2 orders of magnitude longer than that of the single-interface SPP in the corresponding Kretschmann–Raether configuration was measured. In subsequent work [245], the authors described a similar structure, shown in Fig. 15, but using an 8nm thick layer of Pd as the slab. The computed ATR angular reflection spectrum is sketched as the red curve in Fig. 15, showing the intensity dip due to coupling to the LRSPP and fringes due to interference between the outcoupled field and the reflected beam (see also Subsection 2.3). They demonstrated sensing of 3% H2 in a N2 atmosphere by using this structure. A finite 1D photonic crystal provides a practical means to support the metal slab for an arbitrary dielectric bounding its other side (air, water, etc.) [237, 245], but the design is specific to the operating wavelength, metal slab (thickness and index), and index of the bounding medium.

The LRSPP has a role to play in polarizers and in polarizing couplers and splitters [222, 223, 224, 225, 231, 234], principally because of the strong coupling that can be achieved with fibers and dielectric waveguides in a broadside arrangement. In [228], specific modes of a dual-mode fiber were selectively excited by coupling to the LRSPP in a structure similar to that of Kou and Tamir [83], and where the LRSPP was excited using prism coupling.

Andaloro et al. [227] studied theoretically the reshaping of pulses on reflection from prism-coupled metal films where either LRSPPs or single-interface SPPs are excited.

Sidorenko and Martin [238] investigated the tunneling of SPPs across a perpendicular gap in the metal slab filled with the background dielectric, for symmetrically and asymmetrically cladded structures, as a function of the gap length and metal slab thickness. Results at λ0=785nm show that the LRSPP on a 40nm thick Au film can tunnel through a 5μm long gap while retaining 80% of its field amplitude. Standing wave patterns in front of the gap are caused by reflection of the LRSPP by the gap. Transmission of the ab mode through the gap is much less efficient and excites the LRSPP on the other side.

Sun [241] investigated bending along metal slabs that are curved out of plane [radius of curvature in the yz plane, Fig. 1(b)]. The metal slab was cladded symmetrically by thin dielectrics, and the structure was bounded by air. The dielectric/air interfaces provide additional confinement to the LRSPP along this direction, allowing low-radiation-loss bends. High transmission levels were computed by using the finite difference time domain method for the LRSPP around 90° bends having radii on the order of the free-space wavelength of operation.

Wu et al. [242] considered a structure where the metal slab was replaced with an array of (10nm thick) metal nanowires, cladded on one side by an electro-optic polymer and on the other by an index-matched glass substrate. They computed ATR angular spectra for the structure under prism coupling, showing a narrower dip compared with a continuous metal slab of the same thickness, due to the excitation of the LRSPP across the wires. Low-loss surface waves can be supported along such a structure, as in discontinuous and islandized films (Subsection 2.7). The narrower dip leads to improved modulator performance compared with, e.g., [221]. In a subsequent study [244] they investigated a similar structure, with the electro-optic polymer replaced by glass, used as a notch filter under prism-coupled wavelength interrogation. They reported filter designs having a 3nm bandwidth and tunable over about 45nm by varying the angle of incidence of the input light.

Plumridge and Phillips [240] considered theoretically the SPPs and the dielectric modes guided by a multiple quantum well heterostructure. The quantum wells are modeled as a quasi-2D electron gas, where the electrons are free to move in the plane of the well as a gas of almost free electrons, but are confined and restricted to intersubband transitions in the perpendicular plane. The main electric field component of the LRSPP is perpendicular to the wells (i.e., not in the plane of the electron gas); so damping is due principally to intersubband transitions (i.e., not to free-electron scattering), which by design can have energies far from that of the LRSPP, leading to lower propagation loss. Structures were modeled by using an anisotropic permittivity for the quantum wells, based on the Drude model for the permittivity components in the plane, and a Lorentz oscillator model for the permittivity along the perpendicular. The model was applied to a GaAsAlGaAs multilayer structure, and the LRSPP (among other modes) was explored in the infrared (λ0=6μm to λ0=20μm). Propagation lengths of many centimeters were predicted.

Lee and Gray [232] proposed a Kretschmann–Raether type of structure for re-exciting single-interface SPPs, whereby the thin metal film is placed directly onto the core of a large multimode dielectric waveguide. The multimode waveguide effectively traps the reradiated light outcoupled by the prism (and normally lost) and redirects it toward the metal film at the proper angle for re-excitation of the single-interface SPP. Simulations confirm the viability of range extension via this approach. Montgomery and Gray [243] further explored the concept and its design space through finite difference time domain simulations and modal analyses.

Krokhin et al. [239] derived the dispersion relation for the SPPs propagated along a thin metal film bounded by vacuum on one side and a strongly anisotropic photonic crystal on the other. They showed for the SPP localized at the metal–crystal interface that its range can be increased by 50% in the infrared, compared with the corresponding isotropic case, by orienting the optical axis of the substrate along the perpendicular to the metal film. The penetration depth of the SPP into the substrate increases with its range.

3. Metal Stripe (w<)

3.1. Modes of the Metal Stripe

The thin metal film of thickness t, finite width w, and relative permittivity εr,2, bounded by optically semi-infinite dielectrics of relative permittivity εr,1 and εr,3, is sketched in front cross-sectional view in Fig. 16 and is henceforth referred to as the metal stripe. The metal stripe is obtained from the metal slab (Fig. 1(b)) by limiting its width. This increase in dimensionality leads to major changes, principally, the creation of lateral confinement and thus of an enriched mode spectrum, and an LRSPP having a lower attenuation than its counterpart in the corresponding metal slab. Another important change is that modal solutions to Maxwell’s equations must be obtained numerically, increasing considerably the analysis effort, whereas the modes of the slab can be derived analytically rather straightforwardly. Despite this difficulty, the metal stripe can be handled by well-established numerical techniques and by some commercial modeling tools, if appropriate care is taken. Theoretical studies using vectorial formulations of the method of lines (MoL), the finite element method (FEM), and the finite difference method (FDM) have been reported. The effective index method (EIM) has also been shown to approximate reasonably well some of the modes, including the LRSPP.

There are four fundamental modes supported by the metal stripe, labeled aab0, asb0, sab0, and ssb0. Given the finite width of the structure, higher-order modes having extrema along x in their field distribution can also be supported. The Ey field component dominates for all modes when wt1; so the modes are TM in character, but not purely TM because all field components including Hz are always nonzero.

The nomenclature adopted extends that used for the slab and describes the Ey field component of the mode: a and s refer to asymmetric and symmetric, respectively, the first position being associated with the horizontal dimension (x) and the second with the vertical one (y); b signifies purely bound (nonradiative), and the superscript counts the number of extrema in the horizontal distribution of Ey, not counting the corner peaks.

The evolution of the modes with dimensions (w,t), materials (εr,1,εr,2,εr,3) and operating wavelength (λ0) is complex, especially for asymmetric structures (εr,1εr,3). The difficulty arises because all modes are supermodes (coupled modes) created from the coupling of elemental corner and/or edge (or finite-width interface) modes, with the selection of specific ones depending on the similarity of their phase constants. Since the elemental modes also change with structure parameters and operating wavelength, the supermodes can at times evolve unpredictably. However, trends have been noted over a range of studies pertaining to symmetric structures (εr,1=εr,3), as discussed in the following paragraphs.

The evolution of the modes as t 0 resembles the evolution of the sb and ab modes of the symmetric metal slab in that all modes eventually become partitioned into either lower-attenuation (ssbm and asbm are sb-like) or higher-attenuation (aabm, sabm are ab-like) modes, as determined by the distribution (symmetric or asymmetric) of Ey along y. This partitioning is readily observed from Fig. 17 in the case of a w=1μm wide stripe (compare Fig. 2). Unlike in the metal slab, the modes in the metal stripe are not asymptotic with the single-interface SPP as w and t increase. Instead, the four fundamental modes are asymptotic and degenerate with an elemental corner mode, and the higher-order modes are asymptotic with elemental edge modes, as is also readily observed from Fig. 17.

The ssb0 mode in the thin symmetric metal stripe is the fundamental long-range mode and, following convention, is termed a LRSPP.

One of the fundamental modes, the ssb0 mode, evolves smoothly and predictably as w, t0 into the vertically polarized TEM wave of the background. Its Ey and Hx fields evolve from being highly localized near the metal corners, as shown in Figs. 18(a), 18(c), to being spread out over the waveguide cross section, as shown in Figs. 18(b), 18(d). (Figure 18 plots the normalized Re{Sz}, where Sz=(ExHy*EyHx*)2 is the complex power density carried by the mode.) The resulting field distribution [Figs. 18(b), 18(d)] can be well matched to Gaussian-like fields, such as those emerging from dielectric waveguides (e.g., single-mode fiber, SMF), leading to efficient end-fire excitation. This modal transformation as w,t0 is accompanied by a reduction in confinement and attenuation, as noted from Fig. 17 [red curve in Fig. 17(b)], due to reduced field penetration into the metal. The ssb0 mode in the thin symmetric metal stripe is the fundamental long-range mode and, following convention, is termed a LRSPP.

The LRSPP in wide metal stripes has an attenuation similar to that of the LRSPP in the corresponding metal slab, but narrowing the width can reduce the attenuation further by orders of magnitude. However, as in the metal slab, confinement must also be traded off against attenuation. Furthermore, it is important for the structure to be symmetric in order for the ssb0 mode to remain purely bound, long range, and well behaved with varying structure parameters and operating wavelengths. The degree of asymmetry that can be tolerated depends principally on the confinement provided by the stripe.

Efficient end-fire excitation of the LRSPP in the metal stripe can be achieved by using a free-space beam in the manner depicted in Fig. 6 or by the polarization-aligned fundamental mode of a SMF, butt coupled directly to the input of the structure as depicted in longitudinal cross-sectional view in Fig. 19(a). Butt coupling can also be achieved with a polarization-maintaining SMF (PM-SMF) or tapered SMF.

One of the other fundamental modes, the asb0 mode, evolves in a similar manner as t0, except that its Ey field develops two extrema along x, and the mode becomes unguided below cutoff dimensions (w,t) that depend on the materials and operating wavelength. This mode, which is fundamental for large w and t, evolves into the first long-range higher-order mode as t0. Long-range modes of orders higher than the asb0 mode may also exist, originating from the mode families ssbm (m>0, odd) and asbm (m>0, even). As observed from Fig. 17, they have cutoff dimensions that increase with mode order m and are long-range only near cutoff.

All modes having the aabm and sabm symmetries (m0) increase in attenuation as t0 and do not couple efficiently with Gaussian-like fields in an end-fire arrangement because Ey is asymmetric along y. The aab0 and sab0 modes are guided for all film dimensions and remain localized near the corners.

In asymmetric structures (εr,1εr,3), true field symmetries exist only with respect to the y axis. Mode fields exhibit symmetriclike or asymmetriclike distributions with respect to the x axis, and localization to either the top or bottom metal–dielectric interfaces. As in the slab, the symmetriclike modes are localized along the interface with the lowest dielectric, while the asymmetriclike modes are localized along the interface with the highest dielectric. The evolution of modes with structure parameters is not obvious, since different elemental modes can merge in and out of a supermode as parameters change. Also, different numbers of extrema may occur along the top and bottom interfaces (they are counted along the interface where the field is localized, and this number is used in the nomenclature). Long-range modes can exist in asymmetric structures but only near cutoff and having perturbed field distributions that compromise excitation in an end-fire arrangement. The long-range modes are localized on the low-index side with fields that extend deeply into the high-index cladding.

3.2. Straight Waveguides [246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282]

The symmetric metal stripe provides confinement in the plane transverse to its longitudinal axis. The stripe can be dimensioned such that the ssb0 mode propagates with low loss (as the LRSPP) and couples efficiently in an end-fire arrangement to TM-polarized Gaussian-like beams (in fiber or free space) while all long-range high-order modes are cut off and any remaining high-loss modes are excited with very low efficiency.

The majority of the experimental work conducted to date has used butt-coupling to SMF to excite the waveguides; this is in contrast to the metal slab (Section 2), where prism and grating coupling are normally used. As mentioned in Subsection 2.1, end-fire coupling is easier to implement than prism coupling, but all modes (including radiative ones) that overlap to some extent with the input fields will be excited; outputs must therefore be interpreted carefully, especially in cases where the input coupling is inefficient. Fortunately, LRSPP butt-coupling excitation efficiencies greater than 90% are readily achievable, rendering the excitation of any other modes (usually) immaterial.

Work conducted on straight waveguides propagating the LRSPP [246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282] is reviewed in this subsection. Passive integrated structures [283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302] are reviewed in Subsection 3.3, but some of the work also reports results on straight waveguides that are discussed here.

Berini [246] studied theoretically the four fundamental bound modes of the symmetric metal stripe (εr,1=εr,3) using the MoL and extended the mode nomenclature of [72] to identify them. The study was conducted at λ0=633nm on a w=1μm wide Ag stripe for a range of t, with the stripe embedded in an optically infinite dielectric background having εr,1=εr,3=4. The constitution of modes from elemental corner and edge modes was discussed. The partitioning of modes with decreasing t into ab-like and sb-like modes was observed. The evolution of the ssb0 mode into the LRSPP, including the extension of its fields from the corners into a Gaussian-like distribution, was described. The need to trade off attenuation versus confinement was noted, end-fire coupling was suggested for exciting the mode, and its use for optical signal transmission was proposed. (In [246], parts (a) and (b) of Fig. 2 were inverted with respect to its caption; this is corrected here as Figs. 18(c), 18(d).)

A subsequent study on symmetric structures [248] investigated via the MoL the fundamental and higher-order modes as a function of stripe dimensions, background permittivity, and operating wavelength. Figure 17 gives the effective index and normalized attenuation of the first eight modes of the stripe (ssb0,asb0,sab0,aab0,ssb1,asb2,aab2,sab1) and of the ab and sb modes of the corresponding slab, and Fig. 18 shows some mode intensity distributions. Cutoff dimensions were noted for the higher-order long-range modes. It was found that decreasing the stripe dimensions (w and t) and the background permittivity, and operating at longer wavelengths, decreased the attenuation and confinement of the LRSPP. MPAs of 0.10.01dBmm were predicted for the LRSPP in the infrared (λ01550nm). It was suggested that the stripe operating in the LRSPP could be used to implement integrated structures such as interconnects, splitters, couplers, and interferometers.

Charbonneau et al. [249] demonstrated propagation of the LRSPP in the metal stripe by measuring output intensity distributions from 8μm wide, 20nm thick, 3.5mm long Au stripes embedded in SiO2. The structures were excited at λ01550nm via end-fire coupling to a standard PM-SMF as sketched in Fig. 19(a). Outputs were captured for various polarization angles of the input light, demonstrating efficient coupling for vertically (TM) polarized light and substantially no coupling for horizontally (TE) polarized light, as shown in Fig. 19(b). The propagation constants of the ssb0 and sab0 modes were also computed via the MoL as a function of t, along with those of the ab and sb modes of the corresponding slab, yielding an MPA of 0.9dBmm for an 8μm wide 20nm thick stripe.

Theoretical studies using the MoL on the bound modes of asymmetric stripes (εr,1εr,3) were reported by Berini [250, 251]. The study in [250] was conducted at λ0=633nm on a 1μm wide Ag stripe for a range of t, with the stripe bounded on both sides by optically semi-infinite dielectric claddings having εr,1=22 and εr,3=1.92. None of the fundamental modes, including the ssb0 and asb0 modes, were found to be long-range in this structure. One of the higher-order modes was long range but only near cutoff, and it had a perturbed field distribution. The subsequent study [251] considered higher-order modes, other widths, and more cases of cladding asymmetry. Modes were found to change character as t was reduced, because elemental modes evolve and merge in or out of supermodes. Long-range modes were again found but only near cutoff and having perturbed field distributions. Other studies involving the (short-range) modes of the asymmetric metal stripe include, for example, [247, 252, 253, 255, 257, 260, 265].

Charbonneau [283] measured the MPA of the LRSPP at λ0=1550nm via the cutback method, as well as its output intensity distribution. The waveguides consisted of 20nm thick Au stripes, of widths 8, 6 and 4μm, embedded in SiO2, and the measured MPAs were 2.4, 1.6, and 1.4dBmm, respectively. The Au stripes in these structures (and in those of [249]) were deposited on a 5μm thick SiO2 lower cladding thermally oxidized from the underlying Si substrate. The upper cladding consisted of a 2μm thick layer of plasma-enhanced chemical vapor deposition SiO2 covered with index-matching fluid. The claddings in these structures were likely slightly index mismatched and insufficiently thick to allow the modes their full expansion, resulting in higher than expected attenuation. However, the trend of decreasing attenuation with decreasing width was observed, as well as long-range single-mode guidance.

It was surmised in [248] that narrowing the width of the stripe would lead to reduced polarization sensitivity. This was confirmed by Berini [254], who modeled via the MoL square cross-section stripes (w=t) in a homogeneous dielectric background, and showed that the ssb0 mode had two degenerate orthogonally polarized counterparts in this structure, with their main transverse electric field component polarized along x (TE polarized) and y (TM polarized). The modes were named ssb,x0 and ssb,y0, respectively, and modeling revealed that they exhibit the same qualitative evolution with decreasing dimensions as the ssb0 mode of the rectangular stripe. MPAs in the range of 30.01dBmm were computed at λ0=1550nm for stripe dimensions ranging from w=t=250nm to w=t=150nm with Au used for the stripe and SiO2 as the background dielectric. Coupling losses to SMF in the range of 0.76dB per facet were computed, with the smallest coupling loss occurring for w=t=250nm and largest one occurring for w=t=150nm. A trade-off between MPA and coupling loss is necessary, and it was suggested that the case w=t=180nm (MPA0.14dBmm, coupling loss 3dB) would provide a good compromise.

Nikolajsen et al. [256] reported insertion loss measurements at λ0=1550nm for the LRSPP in Au stripes of various lengths, 312μm wide and 10nm thick, deposited on 15μm of benzocyclobutene (BCB) spin coated and cured on Si and covered by 15μm of BCB deposited by the same process. They reported MPA values in the range of about 0.60.8dBmm and coupling losses to PM-SMF of about 0.5dB. The vertical and horizontal profiles of the output mode were also measured. The MPA of 0.6dBmm amounts to a 78× increase in propagation length over the corresponding single-interface SPP.

Al-Bader [258] modeled symmetric Ag stripes in Si at λ0=1550nm, using the FDM. The width of the stripe was fixed to w=1μm, and t was varied. The propagation constants of the fundamental modes ssb0, asb0, aab0, sab0, and of the first higher-order mode sab1, were computed and compared with the ab and sb modes of the corresponding slab. He computes an MPA of about 37dBmm for the LRSPP in stripes 1520nm thick.

Boltasseva and co-workers [285, 286] report MPA measurements at λ0=1550nm for 8μm wide Au stripes having t8.5nm to t35nm and cladded on both sides by 1315μm of BCB. The lowest MPA measured among their waveguides was 0.6dBmm for t=15nm. The coupling loss to SMF was measured for t=15nm and found to vary from 0.5 to 1.5dB per facet for w=10μm to w=4μm, respectively. Mode outputs and profiles were measured for various stripe dimensions. The EIM was proposed for modeling the metal stripe, and propagation constants for the fundamental (ssb0) and first three higher-order long-range modes were computed as a function of w for t=10nm.

Charbonneau et al. [287] measured LRSPP mode outputs at λ0=1550nm for 7mm long, 25nm thick Au stripes of various widths (w=2,4,6,8μm) on 20μm of SiO2 on Si and covered with index-matched polymer. The mode outputs captured under identical measurement conditions show reduced mode confinement and attenuation with decreasing w.

Zia et al. [259] applied the EIM to the metal stripe and compared their computed propagation constants for the ssb0, asb0, and sab1 modes with those of Al-Bader [258] over his range of t. Good agreement was achieved for the ssb0 and asb0 modes, but not for the sab1 mode (the authors reported achieving a better agreement with [248] for this mode). They also applied the FDM to extend the comparison to other stripe dimensions (w=0.5μm to w=4μm and t=24,50,100nm), again achieving good agreement with the EIM for the ssb0 and asb0 modes.

Berini et al. [261] measured the MPA and coupling efficiency to PM-SMF of the LRSPP at λ0=1550nm, in waveguides comprising one or many metal stripes, deposited directly (no adhesion layer) onto 15μm of SiO2 on Si, and covered with index-matched polymer. Au stripes 31, 25, and 20nm thick, and Ag stripes 20nm thick, were used to implement the structures. The lowest MPAs measured among the set of Au and Ag stripes were 0.42 and 0.32dBmm (Le1  cm and Le1.4cm, respectively). These MPAs are 93× and 138× lower than those of the corresponding Au and Ag single-interface SPPs, respectively. The largest coupling efficiency measured among the set of Au structures was 98%, corresponding to a coupling loss of 0.09dB per facet. Theoretical results were obtained via the MoL for all of the structures characterized. Theory and experiment agreed to within about 5% for all of the 31 and 25nm thick Au structures, but a thickness-dependant permittivity had to be assumed in order to achieve agreement to within 12% for the 20nm thick Au structures, possibly because films of this thickness are of lower density than the bulk (as discussed in Subsection 2.7).

Charbonneau et al. [288] characterized the LRSPP in 24.4nm thick, 4 and 8μm wide Au stripes on 20μm of sputtered SiO2 on Si and covered by 20μm of sputtered SiO2 (same process). The MPA and coupling efficiency of the LRSPP to SMF were measured at λ0=1525,1550,1588,1620  nm and compared with theoretical expectations (MoL). The MPA was observed to decrease with increasing λ0 as expected, and errors between theory and experiment of 4% to 8% were achieved for the 4μm wide structure, and of 12% to 17% for the 8μm wide structure. The lowest MPA measured was 0.97dBmm for the 4μm wide structure at λ0=1620nm. All measured coupling efficiencies were greater than 90%, approaching 98% for the 8μm wide structure. Horizontal and vertical mode profiles were measured at λ0=1550nm for both waveguides and compared with far-field diffraction-limited theoretical profiles (computed with the FEM) with near perfect agreement being observed.

Leosson et al. [262] characterized at λ0=1550nm narrow (w500to150nm wide) Au stripes t=150nm thick, on 15μm of BCB and covered with 15μm of BCB. The structures were excited via butt coupling to a PM-SMF such that the incident polarization was aligned at 45° to the waveguide axes. Mode outputs and profiles were measured as a function of w through an analyzer (polarizer) aligned either along the vertical (TM) or horizontal (TE) waveguide axes. Figure 20 shows the measured outputs; the stripe aspect ratio wt is indicated in the white boxes for output pairs a, b, and c. Propagation of both long-range ssb,y0 and ssb,x0 modes (TM- and TE-polarized, respectively) was observed for the structure having an almost square cross-section (wt), as shown in output pairs c of Fig. 20. The MPA and coupling loss to SMF of the long-range ssb,y0 mode were measured as a function of w, yielding about 0.5dBmm and 0.5dB per facet in the best cases (w150200nm and w400nm, respectively). The measured MPAs were noted to be larger than the theoretically expected ones [254], and the discrepancy was attributed to solvable fabrication issues.

Degiron and Smith [263] modeled symmetric and asymmetric Ag and Au stripes, using a commercial 3D FEM modeling tool. They investigated the effects caused by rounding the corners of the stripe, concluding that the effects on the LRSPP were negligible. Asymmetric stripes were investigated for a few cases of asymmetry (ε1>ε3) and a few t values. They also modeled roughness as randomly distributed metal cylinders, each cylinder having a random height between 0 and 5nm and a diameter smaller than its height. They reported that the cylinders cause minor perturbations on the propagation constant of the LRSPP, but act nevertheless as subwavelength scatterers, outcoupling the LRSPP into freely propagating radiation.

Hosseini et al. [264] modeled symmetric stripes via the FDM with the eigenvalues and eigenvectors of the propagating modes computed by using the Arnoldi method. They compared their results with those reported in [258], noting good agreement for the ssb0 and asb0 modes.

Boltasseva and Bozhevolnyi [291] investigated the LRSPP in straight waveguides implemented by using 14nm thick Au stripes of width 212μm and cladded on both sides by 15μm of BCB. MPA and coupling loss measurements were carried out on stripes of different widths over the range 1000λ01650nm with the results following expected trends with w and λ0 [248]. The measured MPAs of 10 and 4μm wide stripes at λ0=1550nm were 0.7 and 0.5dBmm, respectively.

Rao et al. [267] measured the MPA and mode profile at λ01550nm of the LRSPP in 15nm thick Au stripes cladded on both sides by 10μm of BCB. The measured MPA of their 8μm wide structure was 2.34dBmm.

Jung et al. [269] modeled square cross-section Au stripes of dimensions ranging from w=t=2005000nm in BCB at λ0=1550nm using the FEM. The propagation constant, mode fields and mode size of the first few modes were computed. They found two degenerate LRSPPs polarized along the x and y axes (ssb,x0 and ssb,y0 [254]) for w=t<300nm, and they computed Le3mm for the case w=t=200nm. They also discussed field symmetries, mode nomenclature, and the evolution of the modes as the square cross-section changes into a rectangular one and then into a larger square one.

Berini [270] via the MoL investigated at λ0=1550nm the effects on the LRSPP of air gaps in various locations adjoining an Au stripe (top, side, and wings) in LiNbO3, finding in general that the gaps were deleterious (as in [75] for the slab), strongly perturbing its mode fields and causing its MPA and confinement to decrease as the gaps become more invasive such that only nanometric gaps could be tolerated. The M2 FoM [96, 271] decreased with increasing gap size, indicating that confinement decreased more rapidly than attenuation. The mode fields developed strong maxima and localization in the gaps, a feature that could be interesting if high-intensity fields in nanometric air gaps are sought, but only if coupling and radiation losses are essentially irrelevant.

Degiron et al. [295] enclosed the metal stripe within the core of a dielectric slab and found that the confinement–attenuation trade-off of the LRSPP was favorably altered. They computed that the LRSPP in this structure can propagate over the same distance (or longer) as the conventional one, but with a smaller mode size, using a significantly thinner metal stripe. The LRSPP in this structure is a hybridized SPP–dielectric waveguide mode.

Buckley and Berini [271] extended the FoMs introduced in [96] to 2D waveguides and applied them to the LRSPP in symmetric metal stripes, comparing different geometries, metals, and operating wavelengths. Depending on which FoM was used, and hence on how confinement was measured, different preferred designs and operating wavelengths emerged. Each of the metals analyzed showed wavelength regions where their performance was best. They also modeled the LRSPP in the metal stripe embedded within the core of a dielectric slab [295] as a function of slab thickness, finding increasing attenuation, decreasing mode size, and decreasing effective index with decreasing slab thickness. All of the FoMs were improved for this structure over those of the conventional LRSPP for a good range of slab thickness.

Berini [272] generated design curves using the MoL for the LRSPP in metal stripes embedded in SiO2. Stripe dimensions within the range 1wμm and 10t100nm were modeled, Au, Ag and Al stripes were compared, the wavelength range covering 1305λ01670nm was considered, and cutoff curves due to index asymmetry were generated. It was found for moderately confining stripes that an index asymmetry of 1 to 3×103 at most could be tolerated before the onset of radiation.

Kim et al. [273] measured the attenuation and coupling losses of the LRSPP propagating along Au stripes (t=14  nm and t=17nm, w=310μm), on 40μm of polymer and covered with the same material. The polymers used were UV-curable ZPU12-450 and ZPU12-460 (fluorinated acrylate, Chemoptics), which have refractive indices of about 1.45 and 1.46, respectively. The measurements were obtained at λ0=1550nm through cutback by using butt-coupled PM-SMFs. They measured decreasing attenuation and increasing coupling losses as the thickness and width of the stripe decreased. They reported an MPA of 0.17dBmm and total coupling losses of 6.8dB for the smallest stripe (w=3μm, t=14nm) in the lower-index polymer; this value of MPA is 131× lower than that of the corresponding single-interface SPP. The large coupling losses indicate that the mode size is larger than the fiber mode. Lower total coupling losses (0.5dB) were measured for wider stripes (w=79μm) of the same thickness. They compared their measurements with computations performed by the MoL. In a subsequent paper, Park et al. [276] reported comparable MPAs (0.14 and 0.2dBmm) and coupling losses for similar Au stripes in ZPU 450 at λ0=1550  nm and λ0=1310nm, respectively.

Salakhutdinov et al. [275] investigated LRSPP propagation along Au stripes (t=10nm, w=510μm) on a thick BCB lower cladding covered by 210μm of BCB, using a scanning near-field optical microscope. The waveguides were excited by butt coupling to PM-SMF over the range of λ0=15001640nm. Salakhutdinov et al. collected aerial scans at various distances above the upper cladding for waveguides having different stripe widths and upper cladding thicknesses. They observed from their scans propagation of the LRSPP and concluded that the scanning near-field optical microscope head was capturing scattered light rather than the evanescent tail of the LRSPP.

Guo and Adato [277] investigated the LRSPP propagating along a metal stripe bounded on both sides by thin low-index dielectric regions of the same width as the stripe, with thick high-index outer claddings bounding the system. They found via modal analysis (film mode-matching method) that increasing the thickness of the low-index regions decreases the attenuation of the LRSPP, increases its size, and pushes it toward cutoff (as in the 1D case [95, 97]). In a subsequent study on a similar structure [281], they reported dispersion curves and other computations for the LRSPP as a function of stripe dimensions and as a function of the thickness and index of the thin dielectric regions, including refractive indices that are above and below that of the outer claddings. They investigated the trade-off between confinement and attenuation, concluding that an improvement can be achieved compared with the conventional structure by adding high-index regions, which is consistent with conclusions reached for the metal stripe embedded in the core of a dielectric slab [295, 271]. They also concluded that adding low-index regions does not improve the trade-off compared with the conventional structure.

Jiang et al. [278] investigated LRSPP propagation along Au stripes (t=12nm, w=49μm) embedded in polymer deposited on 15μm of SiO2 on Si. The polymer used was PFCB (perfluorocyclobutane), which has an index of 1.476 at λ0=1537nm. The upper and lower claddings had the same thickness, which was varied from 3.5 to 13μm (726μm total thickness) from structure to structure. The thinnest claddings do not allow the LRSPP its full expansion, so in these cases the structure performs as a metal stripe embedded in the core of a dielectric slab [295]. The waveguides were excited at λ0=1550nm by a butt-coupled PM-SMF and characterized through cutback. They reported MPAs and coupling losses in the range of 0.20.6dBmm and 0.52.7dB per facet. Their lowest MPA of 0.2dBmm was measured in a 4μm wide stripe with 10μm thick claddings, and is 209× lower than that of the corresponding single-interface SPP (they mention measuring an MPA of 0.16dBmm for the same stripe with thicker claddings). They also characterized Au stripes embedded in the center of a 14μm thick core of PFCB cladded on each side with 6μm of a lower-index polymer (n=1.462). They found for this structure (as for their claddings of limited thickness) that the trade-off between confinement and attenuation is improved, as discussed in [295, 271]. Modal computations were performed by using the FDM, verifying some of their measurements.

Chattopadhyay et al. [279] proposed an approximate modeling approach for computing the modes of 2D plasmonic waveguides. They demonstrated their approach by application to the symmetric metal stripe and compared their results with those reported in [248, 258, 259].

Park et al. [280] described a liftoff process for fabricating metal stripes on a thick polymer lower cladding, and fabricated Ag stripes (t=11nm, w=1.510μm) on 30μm of ZPU 450 (Chemoptics) covered by 30μm of the same material. They reported MPAs in the range of 0.040.4dBmm, and associated mode widths in the range of about 408μm, at λ0=1310nm. The MPA of 0.04dBmm is 1750× lower than that of the corresponding single-interface SPP, but the confinement is extremely weak (mode width >40μm); their more practical structures have MPAs of about 0.08dBmm.

Berini and Buckley [282] compared the convergence and accuracy of the MoL (in-house code) and FEM (commercial code) by computing the propagation constant of modes supported by the metal slab, the metal stripe, and the 90° metal corner. A discretization strategy yielding monotonic convergence was demonstrated for both methods, allowing more accurate results to be extrapolated from the convergence histories. Both methods yielded similar anticipated errors for a comparable minimum discretization spacing, with the FEM being slightly more accurate but the MoL requiring less computational effort. Convergence to within an anticipated error of ±2% was easily achieved with both methods using a minimum discretization of 5nm (except for modes that are highly confined to corners). The percentage difference between the extrapolated results computed from the FEM and MoL convergence histories ranged from 3.75% to 0.012% for the modes of the metal stripe.

Satuby and Orenstein [266] explored theoretically (finite difference beam propagation method) and experimentally 6 and 10μm wide gaps between two thick (400nm) Au films bounded symmetrically with 13μm of BCB at λ0=1550nm. They claimed to observe TE-polarized long-range modes localized in the gap of each structure, but their modeling of the structure reveals effective indices that are lower than the index of the BCB claddings (so the modes are radiative). Pile et al. [274] studied the bound modes supported by this structure, finding no evidence of long-range modes and suggesting that the experimentally observed outputs were bulk waves diffracting off metal edges. In a subsequent paper [268] Satuby and Orenstein observed experimentally propagation at λ0=1550nm of higher-order LRSPPs in 10 and 45μm wide 20nm thick Au stripes bounded by similar claddings (they also investigated a structure similar to that of [266, 274]).

3.3. Passive Integrated Structures [283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302]

The attributes of the metal stripe and the ssb0 mode render them useful as the foundations of an integrated optics technology, and indeed a good deal of work has already been reported toward achieving this goal.

Charbonneau [283] demonstrated at λ0=1550nm various passive elements implemented with Au stripes (w=8μm, t=20nm) in SiO2 (5μm thick thermal SiO2 lower cladding, 2μm thick PECVD SiO2 upper cladding covered with index-matched fluid). The elements demonstrated included S bends of varying radii of curvature, sharp angle bends of different angles, Y junctions as mirrored S bends, Mach–Zehnder interferometers (MZIs), and couplers with a variable spacing between the arms. The minimum bending radius was found to be in the range of 1012mm, and sharp angle bends of 1° produced 0.5dB of radiation loss.

In [287] Charbonneau et al. measured LRSPP mode outputs at λ0=1550nm for 7mm long passive elements including S bends, Y junctions, and couplers of various designs implemented with Au stripes (t=25nm, w=8μm) on 15μm of thermal SiO2 and covered with index-matched polymer. A minimum bending radius of about 12mm was measured.

In a subsequent paper, Charbonneau et al. [288] characterized at λ0=1550nm passive elements operating in the LRSPP and implemented with Au stripes (t=24.4nm, w=8μm) bounded on both sides by 20μm of sputtered SiO2. S bends, Y junctions, couplers, and MZIs were characterized. A minimum bending radius of about 12mm was measured. The experimental results were compared with theoretical results obtained from models constructed for each structure based on decomposition into local modes (including bend modes [284, 290]) and overlap computations. Errors between theory and experiment of about 5% were observed for all of the structures.

Figure 21 collects measured mode outputs at λ01550nm of passive elements operating in the LRSPP and implemented with the metal stripe [283, 287, 288]. Figure 21(a) shows a mosaic of outputs for couplers where the spacing between the parallel stripes is varied from 2μm (lower image) to 8μm (upper image) in steps of 1μm. Figures 21(b), 21(c), 21(d) give outputs for a straight waveguide, an S bend, a Y junction splitter, a MZI, and a sharp angle bend.

Lu and Berini [284, 290] applied the MoL in cylindrical coordinates to model the LRSPP at λ0=633nm along curved Ag stripes of various dimensions (w=0.5, 1μm, t=1015nm) embedded in a dielectric having a refractive index of 2. An absorbing boundary condition was used on the outside (radiating side) of the curve. The 90° insertion and radiation losses, the effective index, mode contours and profiles, and the transition loss to a straight section were computed as a function of the radius of curvature. An optimal radius of curvature minimizing the insertion loss was found, where radiation loss dominates at radii smaller than the optimal radius and propagation loss dominates at radii greater than the optimal radius. The more confining structures led to lower insertion loss bends having a tighter radius of curvature. A stripe having w=1μm and t=15nm yielded about 7dB of insertion loss for a 90° bend at its optimal radius of curvature of about 130μm. Using the same numerical method (MoL in cylindrical coordinates), Berini [272] reported the computed radiation loss of the LRSPP propagating along 90° curved Au stripes (w=4, 8μm, 20t100nm) in SiO2 at λ0=1550nm, and found for moderately confining stripes that radii of curvature in the range of 620mm were needed. Berini and Buckley [282] investigated the convergence and accuracy of this numerical method and found that the absorbing boundary condition used along the radiating side of the curve introduces errors that can further limit the accuracy of the computations. Degiron and Smith [263] modeled the propagation of a well-confined ssb0 mode along a curved stripe as a function of radius of curvature by using a commercial 3D FEM modeling tool.

Boltasseva and co-workers [285, 286] investigated passive elements operating in the LRSPP, reporting measurements at λ0=1550nm for elements implemented with Au stripes (t=15nm) in BCB. Multimode long-range guidance was observed in 40 and 60μm wide stripes, along with twofold and fourfold images for a centrally aligned excitation. S bends, Y junctions, and couplers of various designs, implemented with w=8μm or w=10μm wide stripes were also characterized. They measured a minimum bending radius of about 16mm for the 10μm wide 15nm thick stripe. They also fitted models used in conventional integrated optics to some of their experimental results.

Won et al. [289] demonstrated broadside couplers of various lengths operating in the LRSPP at λ0=1550nm, where 20nm thick 5μm wide Au stripes were deposited one on top of the other, separated by 4μm, as sketched in Fig. 22(a). Polymer (ZPU12-470, Chemoptics) was used as the cladding bounding all stripes. The structures exhibited stronger coupling than edge couplers (where the stripes are deposited on the same level—Fig. 21(a)), yielding a shorter length for total coupling. Broadside and edge couplers were also modeled by using the MoL, in support of their experimentation and conclusions. Figure 22(b) plots the normalized power output from both channels (ports) of a series of couplers as a function of interaction length (L), and Fig. 22(c) shows measured mode outputs for the case L=260μm.

Boltasseva and Bozhevolnyi [291] investigated couplers operating in the LRSPP and implemented by using t=14nm thick Au stripes cladded on both sides by 15μm of BCB. Couplers of various interaction lengths (L) having different separations between stripes (D) were designed with w=8 and 4μm wide stripes. Figure 23(a) shows a sketch of a coupler in top view. Coupling curves were measured, first as a function of interaction length at λ0=1570nm, then over the range 950λ01690nm, demonstrating wavelength multiplexing. Figure 23(b) shows the measured outputs for one of their designs (w=8μm, L=8mm, D=6μm) normalized to the transmittance of a similar straight waveguide, showing E-band light emerging from the direct port and L-band light from the coupled port (the bands are identified as the hashed areas). The structures were excited with a butt-coupled polarization-maintaining photonic crystal fiber carrying either laser light or polarized supercontinuum white light (for the broadband measurements). The measurements were compared with theoretical results generated by using the EIM, with good agreement being achieved.

Kim et al. [292] modeled the LRSPP propagating along stripes that are curved out of plane (radius of curvature in the yz plane), using the MoL formulated in cylindrical coordinates. They computed the field distribution and losses (propagation and radiation) at λ0=1300nm as a function of the radius of curvature for Au stripes of dimensions w=4μm and t=15to30nm embedded in a cladding of index n=1.535. They found that the radius of curvature should be in the range of 220mm to keep radiation losses low.

Liu et al. [293] used the FEM to model couplers comprised of an Au stripe in SiO2 positioned alongside a higher-index dielectric core in the same cladding at λ0=1550nm. They found dimensions allowing efficient coupling between the LRSPP and the TM mode of the dielectric waveguide such that total power coupling can be achieved. They also found that the TE mode of the dielectric waveguide is unaffected by the nearby metal stripe and so propose the device as a polarization splitter. In subsequent papers, Liu et al. [294, 298] investigated theoretically a similar structure consisting of an Au stripe coupled to two dielectric waveguides, one on either side of the stripe, for use as a triple output coupler with a polarization splitting property. In [298] they explored the design space of the structure, including the effects of offsetting the metal stripe relative to the dielectric waveguides finding that this significantly improves the extinction ratio of the coupler.

Degiron et al. [295] found via computations with the FEM that the metal stripe embedded at the center of the core of a dielectric slab could support the LRSPP around tighter bends and with lower insertion loss compared with the conventional structure (no dielectric slab). They reported an insertion loss of about 5dB at an optimal radius of curvature of 2.4mm for an Au stripe w=6μm wide and t=10nm thick embedded in the center of a 1.6μm thick core of BCB bounded on either side by air.

In a subsequent paper [296], Degiron et al. reported insertion loss measurements at λ0=1550nm for 90° bends of varying radii (r) operating in the LRSPP, implemented with Au stripes (t=23, 25nm, w=6.1,6.5,12μm) embedded in BCB and bounded by SiO2 on one side and air on the other. A bend was excited via end-fire coupling to a SMF, and its output was redirected by a turning prism, passed through a polarizer, and captured by a detector array mounted to a microscope (the output power was computed by integrating the measured intensity over the output spot). The structures and the experimental setup are sketched in Figs. 24(a), 24(b). Their measured insertion losses, shown in Fig. 24(c) by squares for a thin BCB layer (b=6.5μm, t=23nm, w=6.1μm) and by diamonds for a thick BCB layer (b=21μm, t=23nm, w=6.5μm), exhibit a minimum at the optimal radius of curvature [284, 290]. A tighter optimal radius and a lower insertion loss are noted for the thin BCB structure (squares) compared with the thick one (diamonds), which is representative of the conventional metal stripe. Theoretical results computed by using the FEM, plotted as the solid curves in Fig. 24(c), are in very good agreement with the measurements. Figure 24(d) shows measured mode outputs from two bends of radii r=7.5 and 1mm in the case of the thin BCB layer (b=6.5μm, t=23nm, w=6.1μm for both); radiation loss along the outside of the bend is evident for r=1mm.

Degiron et al. [299] investigated couplers consisting of a dielectric core (SU-8) coupled to an Au stripe, both embedded in BCB bounded by SiO2 on one side and air on the other. They reduced the thickness of the BCB cladding to match the momentum of the LRSPP in the Au stripe to the fundamental TM mode of the SU8 waveguide and showed that this leads to good coupler performance through an analysis of its supermodes (FEM) and through experimental demonstration at λ0=1550nm. Theoretical projections suggest that 95% power transfer is achievable from the TM mode of the SU8 waveguide to the LRSPP of the Au stripe for light launched into the SU8 waveguide. The structure can be used as an alternative to end-fire excitation of the LRSPP or as a polarization splitter, since TE light launched into the SU8 waveguide is essentially unaffected.

Joo et al. [297] proposed as an LRSPP waveguide an Au stripe (t=20nm, w=5μm) on a thin low-index polymer core (ZPU12-450, Chemoptics) on a thin Au slab (t=20nm), the structure cladded on both sides by a high-index polymer (ZPU12-470, Chemoptics). Conceptually, the structure builds on coupled broadside stripes [289] and slabs [74, 100], and the LRSPP investigated is a coupled symmetric supermode of the Au stripe–slab system. Joo et al. investigated the structure experimentally and theoretically, using the FEM. They showed that the structure can be dimensioned such that the LRSPP is readily excited via end-fire coupling to a SMF. They studied the cutoff characteristics of the LRSPP as a function of the thickness and index of the low-index polymer core, showing that the LRSPP remains supported over a broad range of core–cladding index differences, broader than the index difference of the asymmetric metal stripe, but at the expense of greater attenuation. They demonstrated straight waveguides, an S bend, and a Y junction operating in the LRSPP at λ0=1550nm, commenting that the bending loss may be larger than the symmetric metal stripe.

Xu and Aitchison [301] investigated experimentally discrete diffraction (beam expansion) across an array of coupled parallel Ag stripes (t=20nm, w=5μm, center-to-center stripe separation of 10μm) cladded on both sides by 4μm of SiO2 and operating in the LRSPP. The structure was excited at λ0=1550nm via free-space end-fire coupling, and the output intensity distribution across the array was measured. The output intensity distribution among the waveguides of the array was found to vary as a function of the angle of incidence (in the plane of the structure, xz plane of Fig. 16) of the input beam. They found an angle of incidence for which the intensity out of the outermost waveguides of the array is minimized, thus compensating for discrete diffraction. Modeling of the structure was also conducted by using the EIM in combination with a commercial beam propagation tool, as well as a commercial mode solver.

Buckley and Berini [300] proposed, as an alternative to the metal stripe, a metallodielectric waveguide capable of aggressive bends and long-range propagation. The structure uses a step-index dielectric slab for vertical confinement and a pair of metallic parallel plates disposed alongside the core [Fig. 1(c)] for lateral confinement. They added high-index dielectric plugs near the metal edges to reduce the attenuation. The structure is dimensioned such that all modes that would cause radiation loss in a bend are cut off by the parallel plates. Buckley and Berini modeled the fundamental TE mode of the structure at λ0=1550nm by using the MoL in cylindrical coordinates and showed that the waveguide can be bent to a vanishing radius of curvature (r0) with virtually no loss (0.6dB90°). Low-loss propagation of the fundamental TE mode along straight sections is also possible (1.23dBmm) by flaring out the waveguide width. In a subsequent paper [302], Buckley and Berini further explored the design space of this structure and showed that a similar structure used at microwave frequencies, the nonradiative dielectric waveguide, performs comparatively worse when scaled for use at optical wavelengths.

3.4. Interconnects [303, 304, 305, 306, 307, 308]

The metal stripe and the LRSPP propagating along it have been explored as an interconnect solution for high-speed optical data transmission over short reaches.

Park and co-workers [276, 304] carried out 10Gbit/s optical data transmission measurements at λ0=1550nm via the LRSPP propagating along a straight 14nm thick, 2.5μm wide, 4cm long Au stripe in polymer (ZPU 450, Chemoptics), reporting a power penalty of 2.2dB relative to back-to-back transmission at a bit error rate (BER) of 1012. Ju et al. [303] transmitted 40Gbit/s optical data signals at λ0=1550nm via the LRSPP in a similar straight waveguide, butt coupled to SMF. The waveguide was 4cm long, and its fiber-to-fiber insertion loss was 12dB (0.2dBmm MPA, 2dB coupling loss per facet). They report a power penalty of 0.5dB relative to back-to-back transmission at a BER of 1012. No significant pulse broadening was measured.

Ju et al. [305] summarized results from their previous work [273, 276, 303, 304] and gave additional curves of waveguide performance computed by using the MoL.

Kim et al. [306] demonstrated an optical chip-to-chip interconnect operating in the LRSPP, consisting of a straight 2.5cm long array of four parallel Au stripes (t=14.5nm, w=3μm) embedded in polymer [273, 276], butt coupled to an array of four TM-polarized vertical cavity surface emitting laser (VCSELs) operating at λ0=1310nm on the transmit side and to an array of four photodetectors on the receive side. The coupling tolerance of the VCSEL array to the array of stripes was investigated, yielding 3dB alignment tolerances of about ±5μm for their design. Optical data was transmitted though the interconnect at a rate of 2.5Gbits/s per channel for an aggregate transmission rate of 10Gbits/s. The BER per channel was estimated at 1010.

Lee et al. [307] investigated flexible 6.8cm long interconnects operating in the LRSPP, consisting of an 8nm thick, 3.5μm wide Ag stripe cladded symmetrically by a pair of 10μm thick high-index polymer claddings (n=1.524) followed by a pair of 20μm thick low-index polymer claddings (n=1.514). The index step between the pair of outer claddings adds vertical confinement [95, 295, 271], allowing sharper bends out of the plane [241] than in the case of a single thick cladding [292]. The structures were fabricated on a substrate and then detached, forming a flexible ribbonlike structure. Insertion loss measurements at λ0=1310nm revealed that the out-of-plane bending loss did not change appreciably from the straight value (1113dB) for radii down to 2mm. Figure 25(a) shows the interconnect curved out-of-plane at a radius of 5mm along with its measured mode output in Fig. 25(b); the mode size is 23μm×5μm along the horizontal and vertical directions. They also demonstrated operation of the interconnect with a 90° twist applied about the propagation direction, as shown in Figs. 25(c), 25(d).

Kim et al. [308] reported LRSPP waveguides consisting of Ag (t=14 and 16nm) and Au (t=8nm) stripes, ranging in width from 1.5 to 5μm, cladded on both sides by 30μm of polymer having an index of 1.431 at λ0=1310nm (ZPU13-430, Chemoptics). The measurements reported at λ0=1310nm include MPA, mode size, coupling loss to butt-coupled SMF, and alignment tolerance to a TM-polarized VCSEL. The lowest MPA measured among their waveguides was 0.08dBmm for a 14nm thick 1.5μm wide Ag stripe, and the coupling loss of this waveguide to SMF was 2dB per facet. Optical transmission measurements at λ0=1310nm (2.5Gbits/s) were conducted with the LRSPP propagating along two butt-coupled 5cm long Ag stripes for a total length of 10cm (t=14nm, w=1.5μm), aligned to a TM-polarized VCSEL and a photodetector. The BER achieved was estimated at 1010.

3.5. Bragg Gratings [309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320]

Bragg gratings operating in the LRSPP have been implemented by perturbing the metal stripe over a length, either by changing its width symmetrically (step-in-width), its thickness symmetrically (step-in-thickness), or the claddings symmetrically (step-in-index). Corrugating the stripe or adding bumps near the stripe have also been considered.

Jetté-Charbonneau and co-workers [309, 311] explored step-in-width Bragg gratings, constructed by stepping the width of the metal stripe symmetrically about the longitudinal axis over a length Lg, as shown in top view in Fig. 26(a). The unit cell of period Λ is comprised of stripe segments of width w1 and w2, each of length d1 and d2, as shown in Fig. 26(b). In [311] they demonstrated uniform third-order gratings operating in the LRSPP, where the width of an 8μm wide Au stripe was stepped to a narrower width of 4, 3, 2 or 0μm over a period of 1.6μm. The grating lengths varied from 1 to 5mm. The Au stripes were 20nm thick, patterned by using contact lithography, deposited onto SiO2, and covered with an index-matched polymer. The measured Bragg wavelengths (λB) were near λ0=1544nm, the FWHM reflection bandwidths were in the range of about 0.3 to 1.5nm, and the largest reflectance measured was 66% for a 4.5mm long grating over a 0.3nm bandwidth. The reflectance and bandwidth increased with grating strength. The bandwidth narrowed and the reflectance increased with grating length, then saturated because of attenuation along the structure. The transmittance on and off resonance decreased with grating length for the same reason. A lower transmittance for λ0<λB was evident in the strongest gratings, due to scattering into free radiation, and this asymmetry in the transmittance increased with grating length.

In [309, 315], Jetté-Charbonneau and co-workers characterized similar gratings and proposed and validated a model to represent them. Figure 27 shows the measured transmittance and reflectance spectra of uniform third-order gratings of different length implemented with an Au stripe (t=21.6nm) stepped in width from 8 to 2μm in a 50% duty cycle (d1=d2) over a period of 1.6μm. The inset to Fig. 27(a) shows a measured LRSPP mode output from one of the gratings, and the inset to Fig. 27(b) shows an atomic force microscope (AFM) scan of a grating section. The largest reflectance measured among the gratings tested was 47.4%, the bandwidths ranged from 0.2 to 0.4nm, and the λB’s were near λ0=1544nm. Jetté-Charbonneau and co-workers modeled the gratings as an equivalent dielectric stack where slices of the stack take on the complex effective index computed via the MoL of the corresponding waveguide cross section. Physical measurements of the grating profile on chip were used to construct an accurate representation of the grating using about 75 slices to model one period. Very good quantitative agreement with the principal features of the measured transmittance and reflectance responses was achieved with this model, except for the transmittance for λ0<λB because of radiation losses not being included in the theory. They find that the effective index perturbation in these gratings was about 1.4×103.

Using this model, Jetté-Charbonneau and co-workers produced theoretical responses for step-in-width gratings of various architectures and duty cycles, including first-order uniform, interleaved, and apodized designs, and third-order uniform designs [309, 318]. An 8μm wide 20nm thick Au stripe embedded in SiO2 was assumed as the nominal guiding structure, and the λB’s were positioned near λ0=1550nm. First-order uniform gratings provide the strongest reflectance, 97% over a bandwidth of 0.8nm for gratings a few millimeters long. Third-order uniform gratings provide at most a reflectance of 77% over a bandwidth of 0.3nm. A smaller duty cycle led to a higher reflectance, since the loss of gratings decreases with the duty cycle. Specific λB’s were found to be attainable by using interleaving, and apodized designs lowered the sidelobe levels. Off-resonance insertion losses of a few decibels were predicted.

Boltasseva and co-workers [285, 310, 312, 317] investigated step-in-thickness gratings as sketched in Fig. 26(b), which can also be interpreted as the side view of the grating, with w1 and w2 representing the total stripe thickness. In [312] they demonstrated first-order uniform step-in-thickness Bragg gratings operating in the LRSPP, where the thickness of an 8μm wide, 15nm thick Au stripe was stepped over a period of 500nm to a thickness of 35nm by adding 10nm of Au on both sides of the stripe. Grating lengths ranged from 20 to 160μm. Two metallization–lithography steps were used to make the structures, and the gratings were patterned by using electron-beam lithography. BCB was used as the cladding material. The λB’s were near λ0=1550nm, the bandwidths were about 20nm, and the largest reflectance was about 50% for a 160μm long grating. A lower transmittance for λ0<λB was noted, which was due to scattering into free radiation. An add–drop filter using gratings and stripes arranged in a zigzag pattern was also demonstrated. (In [310] they further investigated this zigzag filter, exploring different angles for the zigzag and gratings of different lengths; a bandwidth of 13nm was measured for one of the designs.) The gratings were represented as a metal slab (w=) having a modulated thickness and were modeled by using the Lippmann–Schwinger equation, which implicitly includes scattering into free radiation. A good correspondence between experimental and theoretical features was noted.

Søndergaard and Bozhevolnyi [314] investigated these gratings further, via the theoretical model of [312]. They computed the transmission, reflection, scattering (into free radiation), and absorption spectra of three grating structures. They find that scattering occurs over the entire spectrum and that it is greatest for λ0<λB. Longer gratings produce more scattering for λ0<λB, and stronger gratings increase the scattering across the entire spectrum, but especially for λ0<λB. Field plots show scattered fields primarily at small angles from the structure in the forward and backward directions and show that the start, end, and central portions of the gratings may scatter strongly depending on the wavelength. In a subsequent paper [316], Søndergaard et al. extended their computations to include more grating designs and more comparisons with experiments, noting a good qualitative agreement between both.

Boltasseva and co-workers [317] investigated a wider design range for these gratings, including thickness steps of 10 to 60nm (half added to each side of the stripe), and duty cycles of 0.25 to 0.75. Figure 28 shows the measured reflectance and transmittance spectra of four uniform first-order gratings implemented with an Au stripe (w=8μm, t=15nm) as a function of the thickness step; the inset to Fig. 28(b) shows an AFM scan of a grating section. Measured bandwidths ranged from 5 to 40nm, and the largest reflectance was 64% for a 160μm long grating. An 80μm long grating had 55% reflectance over about 20nm. Boltasseva and co-workers estimated the effective index perturbation to be 2 to 20×103. They found asymmetry in the transmittance spectrum, and trends with grating strength and length similar to those noted in [311, 312].

Pedersen et al. [319] fabricated via nanoimprinting 8μm wide, 12nm thick straight and corrugated Au stripes buried in Mr-I T85 (nanoimprinting resist). The corrugations had a period of 500nm, were 20nm deep, had different duty cycles, and varied in length from 0.25 to 4mm. Broad dips in transmittance at λ0=1594nm were measured for the corrugated stripes and were found to be deepest for the longest gratings and for a duty cycle of 50%. The measured MPA in straight stripes was about 0.8dBmm at λ0=1500nm.

Mu and Huang [320] investigated theoretically (complex mode-matching method) the propagation of the LRSPP along first-order gratings implemented with a continuous metal slab (w=) but where the cladding index is stepped within one period (step-in-index). They considered a few thicknesses of an Au film and index steps that range from 0.02 to 0.06 above that of SiO2. They predicted reflectance bandwidths of about 2550nm and peak reflectances close to 90% for operation at λ01550nm. They predict lower losses than a comparable step-in-thickness grating [312].

Boltasseva et al. [313] explored the LRSPP propagating along Au stripes augmented with photonic bandgap structures implemented as a 2D array of Au bumps protruding above and below the stripe. The stripes were 1015nm thick, and the bumps had a diameter of 300nm, a height that varied from 90 to 150nm, and were arranged in a 2D triangular lattice having a period in the range from 500 to 600nm. Transmission and reflection spectra were obtained for the LRSPP interacting with arrays in various arrangements, including blocks and defects along certain orientations.

3.6. Thermo-Optic Devices [321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331]

Motivated by the fact that the LRSPP is highly sensitive to asymmetry (e.g., [251]), Breukelaar and co-workers [321, 327] studied the performance of stripes that start out being symmetric and gradually become asymmetric to well beyond the cutoff point of the LRSPP, in order to assess whether cutoff might be suitable for variable attenuation or modulation. Radiation spreading through the structure was modeled via normal mode decomposition, whereby the radiation continuum was represented as a discretized orthonormal basis of radiation modes, and overlaps with end-fire coupled symmetric stripes were used to determine the weighted excitation of the modes. All modes were computed by using the FEM. Radiation loss curves were computed as a function of asymmetry and length for Au stripes in SiO2 at λ0=1550nm, showing that extinction ratios beyond 20dB were possible over moderate lengths (millimeters) for small index asymmetries (2×103) in stripes of moderate confinement. Fiber-to-fiber insertion loss measurements were also obtained for a 4μm wide, 20nm thick, 2.5mm long Au stripe on SiO2 covered with index-matching fluid, as a function of device temperature controlled by a thermoelectric cooler. Index asymmetries were thermally induced via the large difference in the nT of the fluid and SiO2. Measured extinction curves were compared with the theoretical one, with near perfect quantitative agreement being achieved. The curves were linear over a wide range of asymmetry, and an extinction ratio of 16dB was measured for an asymmetry of 2×103. The minimum insertion loss occurred on symmetry, as noted earlier in the case of the slab [94], for the same reasons.

Details of the formulation [321] were given in [329], along with results for more cases. LiNbO3 was also considered as a cladding material. Waveguide design curves (propagation constant and mode size) and radiation loss curves were computed. Measured mode outputs and radiation loss curves for Au stripes of different lengths on SiO2 were given and compared with theory with very good quantitative agreement being noted. It was concluded that the initial level of confinement, the length of the stripe, and the index asymmetry were the primary factors influencing the radiation loss and that, other than setting the initial confinement level, the stripe cross section and the cladding materials (e.g., SiO2 versus LiNbO3) had little to do with the radiative process.

Using the metal stripe to affect the immediate optical environment, and therefore the propagation characteristics of the LRSPP, through, for example, a material effect in the claddings, has stimulated strong interest; means for connecting electrically to the stripe in an optically noninvasive manner were soon devised. Gagnon and co-workers [322, 323, 330], used arms of the same width and thickness as the waveguide stripe to connect the latter to contact pads, and they isolated the stripe electrically by introducing 1μm long gaps as depicted in Fig. 29(a). The effect of the arms and the gaps on the optical insertion loss was found to be negligible.

Gagnon and co-workers described various thermo-optic devices operating in the LRSPP, including variable optical attenuators (VOAs), switches, tunable filters, and tunable external cavity lasers, where the upper and lower claddings in the immediate vicinity of the stripe are heated by passing current along the stripe [323]. They considered structures where both claddings have the same nT (e.g., positive in the case of glasses or negative in the case of polymers), and where they have nT’s of opposite sign (e.g., glass on one side and polymer on the other). The thermo-optic performance of straight stripes, MZIs, Y-junction splitters, couplers, and Bragg gratings was considered. Monitoring the temperature of the stripe through changes in resistivity was also discussed, providing means for controlling the temperature of the chip or for detecting local heating due to the propagation of the LRSPP along it.

Gagnon and co-workers constructed VOAs configured as an electrically connected and straight 15nm thick Au stripe [Fig. 29(a)] deposited on 15μm of SiO2 on Si and covered with index-matched polymer [322, 323, 330]. The stripe widths were 4, 6, and 8μm, the heated length varied from 0.84to4.44mm, and the overall length was 7mm. Electrical contact with the pads was achieved by probing. The attenuation mechanism is radiation loss due to thermally induced index asymmetry driven by the passage of current and commensurate heating of the stripe. Figures 29(b), 29(c), 29(d), 29(e) show a sequence of LRSPP outputs for a 6μm wide stripe measured at λ0=1550nm as a function of dissipated electrical power in the stripe (I2R). An extinction ratio of about 20dB was achieved with a dissipated electrical power of 222mW in an 8μm wide stripe having a 4.44mm heated length. Figure 29(f) shows the measured extinction ratio for two stripe widths as a function of the dissipated electrical power density Pde. Response times of 60μs (fall time) and a few milliseconds (rise time) were measured. The electromigration limit of stripes was estimated experimentally to be 112GAm2 by monitoring over a short period of time (minutes) the resistance of stripes subjected to increasing levels of current. The VOAs were driven at a maximum current density equal to about half of this value without any visible or measurable (electrical, optical) degradation in the stripes. The resistivity of stripes was measured as a function of the drive current and temperature, and the simultaneous use of a stripe as a thermal monitor was discussed and demonstrated. Thermal modeling was conducted by using the FDM, revealing that a temperature increase near the stripe of at least 35°C was readily achievable with current densities well bellow the electromigration limit. Computed thermal contours plotted over half of an 8μm wide stripe are shown in Fig. 29(g); evidently, a very good overlap with the optical mode was achieved.

Nikolajsen et al. [325] reported similar VOAs, consisting of an 8μm wide, 15nm thick Au stripe on 15μm of BCB on Si covered by 15μm of BCB; 10μm long gaps were used to isolate the stripe. The VOAs characterized were 10mm long and had a heated stripe length in the range of 36mm. A 30dB extinction ratio was measured at λ0=1550nm with about 100mW of electrical drive power and a 0.5ms response time. Devices were tested over 1470λ01610nm, showing reasonable uniformity (2dB). The index of BCB decreases in proportion to its temperature; so as heating is induced and progresses, the effective index of the LRSPP decreases, eventually reaching cutoff.

Leosson et al. [262] also investigated this VOA concept but using narrower thicker Au stripes in BCB. They measured extinction ratios at λ0=1550nm of 45dB with 35mW of electrical drive power in a 1.6mm long device with a 1mm long heated section. In a subsequent paper [331], Leosson et al. reported improved devices implemented with 1 and 2mm long electrically contacted square cross-section (w=t=180nm) Au stripes cladded on both sides by 12μm of BCB. They reported fiber-to-fiber on-state insertion losses of about 515dB and polarization-dependant loss values of about 1.25dB for λ0 in the range of 15251625nm. Their best VOA was 2mm long and produced about 30dB of extinction, with 60mW of dissipated electrical power, and a polarization-dependant loss that remained within about ±5dB over the full attenuation range. Horizontal profiles of the long-range ssb,x0 and ssb,y0 modes were measured and compared with far-field diffraction-limited theoretical profiles (computed with the FEM) with excellent agreement being achieved.

Park and Song [328] reported a similar VOA consisting of a 4μm wide, 20nm thick, 10mm long Au stripe on 15μm of polymer (ZPU 450 Chemoptics) and covered by 15μm of the same polymer. The stripe was not contacted, but an overlying resistive 8mm long heater was used, causing an asymmetric thermal distribution along the vertical axis of the device as verified through modeling, and thus a strong index asymmetry that induces mode cutoff and radiation. A measured extinction ratio of 30dB was obtained at λ0=1550nm with 100mW of electrical drive power. A 3ms response time was measured for a 20dB extinction ratio.

Nikolajsen et al. [324] demonstrated a thermo-optic VOA and a thermo-optic switch based on a MZI and a coupler, respectively, implemented by using 8μm wide, 15nm thick Au stripes in BCB; 10μm long isolation gaps were used. The VOA was 20mm long, had a heated stripe length of 5.7mm, and an arm separation of 250μm. As shown in Fig. 30(a), deep extinction was measured at λ0=1550nm for a drive power of Pπ=8mW. The switch was 15mm long and had a coupled stripe separation of 4μm. Heating one stripe of the coupler over the interaction length resulted in switching, with a 20dB extinction ratio being achieved for a drive power of 66mW, as shown in Fig. 30(b). The response time of both devices was 0.7ms.

Bozhevolnyi et al. [326] exploited the dependence of resistivity on temperature to monitor the power carried by the LRSPP along 15nm thick, 8μm wide, 10mm long Au stripes embedded in BCB. The power absorbed by the stripe due to the propagation of the LRSPP caused its temperature to increase, thus increasing its resistance as monitored in a Wheatstone bridge configuration. The bridge was implemented by using similar stripes to mitigate environmental effects. A linear response was measured for LRSPP powers in the range of about 0.25 to 50mW at λ0=1550nm. A sensitivity of a few microwatts was estimated, and their wavelength response was investigated over the range λ0=1520nm to λ0=1580nm.

3.7. Electro-Optic Devices [332, 333, 334, 335, 336]

Berini et al. [332] explored direct wafer bonding (fusion) as an approach to fabricate metal stripes in cladding materials that are not readily deposited. The approach was applied with Pyrex and z-cut LiNbO3 claddings. The structures consisted of a thin Au stripe deposited into a shallow trench etched into one of the claddings, to which another cladding of the same material was directly bonded. In some cases, the claddings were thinned by wafer grinding and polishing to 1020μm thick layers. The MPA of the LRSPP in an 8μm wide 20nm thick Au stripe in Pyrex was measured at λ01550nm and found to be about 2.5× larger than theoretical expectations. Electro-optic LRSPP cutoff measurements were made on LiNbO3-cladded Au stripes, and the results compared favorably with theoretical expectations [329], indicating that the LiNbO3 claddings retained their bulk electro-optic properties.

Mattiussi et al. [335] described in detail the fabrication of these structures [332] for the case of z-cut LiNbO3 claddings and gave results of physical characterization conducted on completed structures and on structures that underwent intermediate processing steps. The main processing steps consisted of etching a shallow trench on the surface of a LiNbO3 wafer via ion beam milling, deposition and liftoff of Au stripes into the trenches, direct bonding LiNbO3 to LiNbO3, grinding and polishing thick LiNbO3 layers down to 15μm, and direct bonding a LiNbO3 stack to a Si wafer through intermediate layers of SiO2. All processing occurred at low temperature (<300°C) to preserve the embedded Au stripe and mitigate potential problems due to the difference in the coefficient of thermal expansion of LiNbO3 and Si. Edge breakaway and point defects in LiNbO3 layers were noted after the polishing process, and point defects were noted after the lithography process. Figure 31(a) shows a scanning electron microscope (SEM) cross section of a finished device, and Fig. 31(b) shows an optical microscope image of a device in top view. The inset to Fig. 31(b) shows the measured LRSPP output at λ01550nm of a 4mm long device where the Au stripe (w=2μm, t=20nm nominally) was buried at about the midpoint of a 25μm thick LiNbO3 stack.

Jetté-Charbonneau et al. [336] developed a polishing process to produce high-quality end facets on these heterogeneous devices [335]. The process successfully removed much of the damage caused by dicing and led to a significant reduction in fiber-to-fiber insertion loss, ranging from 4.7 to 9.1dB less loss per waveguide, attributed to 2.44.6dB less loss per facet. The LRSPP insertion loss was measured at λ01550nm on 2mm long structures comprising a 1.2 or 1.3μm wide 20nm thick Au stripe buried in the middle of a 25μm thick stack of z-cut LiNbO3.

Berini et al. [334] considered parallel or antiparallel crystal orientations for the z-cut LiNbO3 claddings and investigated the implementation of various LRSPP structures theoretically and experimentally. The main theoretical findings were that an MPA of 1dBmm or less was achievable by using Au stripes of reasonable dimensions (0.51μm wide, 2040nm thick); low overlap loss (<1dB) to large and small modes was achievable for the same stripe thickness; radii of curvature in the range of 1030mm were required for stripes having a moderate confinement, first-order step-in-width gratings having a reflectance of 0.9, a bandwidth of 0.75nm, and electro-optically tunable over a 2.9nm range were achievable; and electro-optically induced index asymmetry of about 4×104 was sufficient to cut off weakly confined LRSPPs. Measured optical insertion losses for 2mm long straight structures varied from 10 to 17dB, which is somewhat higher than theoretical expectations. Low-frequency electro-optic mode cutoff measurements produced extinction ratios of 12dB and a linear transfer characteristic.

Kim et al. [333] explored structures where a thin dielectric slab waveguide having a core composed of an electro-optic polymer was modified by depositing a pair of thin Au stripes (w=4μm or w=) of various separations on top of the bottom cladding. Modes were supported in the gap between the stripes, with vertical confinement provided by the core–cladding index step and horizontal confinement provided by the metal stripes. (This structure is a metal-cladded dielectric waveguide, which differs significantly from those investigated in [266, 274]). A long-range TM mode was observed in a multimode structure. Thermo-optic variable attenuation and electro-optic phase modulation were also observed in some structures.

3.8. Active Structures [337, 338, 339, 340]

Nezhad et al. [337] investigated theoretically the propagation of SPPs along metal structures adjacent to gain media. They computed, using the FEM, that the LRSPP in a 40nm thick Ag slab bounded on both sides by semi-infinite InGaAsP (εr,1=εr,3=11.38) could propagate with no loss at λ0=1550nm if the claddings provide a gain of about 360cm1 (156dBmm). For a 0.4μm wide 40nm thick Ag stripe in the same background they found that a gain of about 180cm1 (78dBmm) is needed for lossless LRSPP propagation, and they noted that this is about one order of magnitude less than required for the corresponding single-interface SPP. They also computed the gain required from a thin layer, 50175nm thick, located within one of the InGaAsP claddings, as a function of its proximity to the Ag stripe. For a layer adjoining the stripe they found a required gain in the range of about 7001800cm1 and pointed out that such gain is available from a stack of quantum wells (for example). They showed that the required gain increases monotonically as the layer moves away from the stripe.

Alam et al. [338] investigated theoretically at λ0=1550nm an Ag stripe on a 50nm thick Al0.3Ga0.18In0.52As barrier (n=3.35) followed by five 8nm thick Al0.12Ga0.12In0.76As quantum wells (n=3.49), each separated by 16nm thick Al0.3Ga0.18In0.52As barriers on a semi-infinite InP (n=3.17) substrate and covered with a finite-thickness superstrate index matched to the barriers. They investigated the effects caused by changing the stripe dimensions and the thickness, index, and loss of the superstrate, finding a good design such that the LRSPP is supported with an MPA of 10dBmm and a good overlap with the quantum wells. For a superstrate with no loss they found a required gain of about 400cm1 (174dBmm) for lossless propagation of the LRSPP in their structure. The high-index finite-thickness superstrate taken in combination with air is roughly and effectively index matched to the quantum wells, barriers, and lower-index InP substrate on the other side of the Ag stripe.

Jetté-Charbonneau and Berini [339] demonstrated an external cavity laser using a TE-polarized InP gain chip coupled to a step-in-width Bragg grating operating in the LRSPP. The gain chip had a high-reflection coating on one end facet, to form one end of the lasing cavity, and a length of PM-SMF butt coupled to its other end facet. The other end of the PM-SMF was polarization aligned and butt coupled to a Bragg grating defining the other end of the lasing cavity. The grating was a 5mm long third-order uniform periodic step-in-width design similar to those discussed in [311, 315] (Au on SiO2 covered with index-matched polymer), providing a 10% reflectance over a 0.2nm bandwidth (FWHM) centered at λB=1544.1nm with 14dB of insertion loss on resonance. The onset of lasing occurred at a threshold current of 57mA, and the maximum output power was about 3dBm at λB1544nm. The total cavity length was about 20cm (length of the PM-SMF), so lasing occurred in many longitudinal modes, but single-mode lasing is feasible for shorter cavity length. The TM-to-TE polarization extinction ratio of the laser output was 35dB.

Ambati et al. [340] investigated experimentally a metal stripe (20nm of Au on 2nm of Cr, w=8μm) cladded on both sides by Er-doped glass. The structure was fabricated via wafer bonding, as in [332]. The optical pump (λ0=1480nm) and probe (λ0=1532nm) were combined by a fiber multiplexer and injected into the structure via a butt-coupled SMF, thus exciting LRSPPs as copropagating pump and probe waves. The output at the probe wavelength was extracted by using a butt-coupled SMF and a fiber demultiplexer. The fiber-to-fiber insertion loss of an 8mm long structure, measured at the probe wavelength without pumping, was 39dB. The measured insertion loss decreased as the pump power increased, dropping by 1.73dB for a continuous-wave pump power of 266mW. Experiments conducted with pulsed pump and probe signals attribute the loss reduction to stimulated emission into the LRSPP.

3.9. Biosensors [341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355]

Charbonneau et al. [345] reported surface sensing experiments conducted with the LRSPP propagating along MZIs implemented by using Au stripes on SiO2 and covered with index-matched oil. BSA was deposited on MZIs via microspotting [341], either covering the entire MZI or only a portion of one arm. The wavelength response of the MZIs was measured near λ0=1550nm, and a wavelength shift of 10nm was obtained for an MZI having a partially covered arm relative to uncovered and fully covered MZIs, a shift comparable with the response of conventional prism-coupled single-interface SPP sensors under wavelength interrogation [172]. A 3.8nm thick adlayer of BSA accounted for the observed shift, as determined by modeling by using the MoL.

Tencer et al. [341] developed a technique for depositing and confining small amounts of solution on a flat hydrophilic substrate using the capillarity of a flat high surface free energy guide positioned slightly above. Interfacial forces strongly confined the solution between the guide and the substrate, and the solution followed the movement of the guide over the surface to specific thin Au features thereupon. The thermodynamic background of the method was given, and its application to coat one arm of Au MZIs with BSA was demonstrated. AFM measurements were used to verify BSA coverage on the stripes.

Tencer et al. [343] conducted an AFM study of Au stripes on SiO2 covered with BSA adsorbed from phosphate buffer solutions, finding that BSA forms an adlayer of average thickness of 2nm. Comparisons with an adsorption model suggested the adsorption of one monolayer followed by denaturation and flattening. The BSA coated stripes had higher roughness measures (RMS, average and peak to valley) than a similar virgin stripe, and the most affected measure was the peak-to-valley roughness, reflecting the nonuniformity of adsorption, possibly due to the formation of aggregates.

Tencer and Berini [349] described an electrochemical method to selectively desorb thiol self-assembled monolayers from gold surfaces separated by tens of micrometers on a substrate. The potentials of both surfaces were controlled independently with a multichannel potentiostat because the resistance between adjacent surfaces can be much lower in electrolyte than the resistance between one of the surfaces and the counter electrode, and both reductive and oxidative thiol desorption may occur. Desorption potentials were determined for 1-dodecanethiol-based self-assembled monolayers in phosphate buffer, phosphate-buffered saline, and NaOH. Desorption was verified via contact angle measurements. The method should be transferable to electrically contacted MZIs [e.g., Fig. 32(c)] in order to chemically differentiate its arms, with a receptor chemistry applied to one (the sensing arm) and a blocking chemistry applied to the other (the reference arm).

Berini et al. [342] reported a membrane waveguide capable of propagating LRSPPs in any gaseous or liquid environment, consisting of a large-area free-standing ultrathin dielectric membrane upon which thin metal stripes were deposited, and where the environment (gaseous or liquid) was allowed to surround the structure, in effect becoming the claddings. As long as the membrane was not too invasive optically, the ssb0 mode propagating along the stripe retained the essential characteristics of the LRSPP with slight localization along the top surface of the stripe opposite the membrane. Si3N4 membranes 0.3×3mm2 and 20nm (100 atoms) thick, clamped around their perimeter to the underlying Si substrate, supporting 25nm thick, 5μm wide Au stripes, were fabricated and characterized at λ0=1310nm. The measured MPA of the LRSPP in air and in a liquid having an index close to water was 3.6 and 10dBmm, respectively, which agreed with theory (MoL) to within 7%. The excitation of the LRSPP was accomplished by using prism coupling via the top surface because the waveguide end facets were not accessible. Mode outputs were obtained for a membrane cut in half by using a focused ion beam, as shown in Figs. 32(a), 32(b).

In a subsequent paper, Berini et al. [350] explored theoretically the design space of the membrane waveguide, considering Au on a thin Cr or Ti adhesion layer as the stripe, Si3N4 or SiO2 as the membrane, vacuum or H2O as the background, and three operating wavelengths λ0=632.8,1310,1550  nm. Good thicknesses were found to be in the range of t=1530nm for the stripe and 1530nm for a Si3N4 membrane or 20100nm for a SiO2 membrane. Computations revealed that the LRSPP in such structures had a moderate MPA of 2to12dBmm at λ0=1310nm, good confinement, and a reasonable range extension factor of 3 to 25 when in vacuum or H2O. The adhesion layer was found to modestly impact the MPA of the LRSPP, since the latter develops localization along the opposite metal surface away from the adhesion layer. Structures were fabricated as Au on Cr stripes (25 or 20nm thick) on free-standing (20 or 30nm thick) large area Si3N4 membranes. Propagation of the LRSPP was observed and characterized in air, in H2O, and in optical fluids of similar index at λ0=632.8 and 1310nm. The measurements reported include an optical streak, mode outputs and MPAs. Errors between measured and theoretical (MoL) MPAs were below 7% for all of the structures tested.

Berini et al. [348] described the fabrication of these membrane waveguides [342, 350] and gave results of physical characterization conducted on completed structures and on structures that underwent intermediate processing steps. The main fabrication steps consisted of timed deep reactive ion etching and TMAH (tetramethylammonium hydroxide) back-side etches to release the membranes, and bilayer liftoff photoresist and metal evaporation processes to define metal stripes and features on the front side. They reported optical, SEM, and AFM images, ellipsometry measurements, and membrane segmentation by focused ion beam. Mechanical probing using a tipless AFM probe revealed that the membranes routinely sustain 3μN of point force without shattering. Figure 32(c) shows a microscope image of a fabricated electrically contacted MZI on a membrane.

Charbonneau and Berini [346] investigated techniques for broadside coupling to LRSPPs and demonstrated them by measuring MPAs along membrane waveguides in air and in fluid. Input coupling was achieved by using a high-index right-angle prism placed in close proximity to the membrane waveguide and launching an input beam such that it struck its base close to the 90° corner (to minimize reradiation of the LRSPP into the prism—see Subsection 2.3). Output coupling using a similar (mirrored) arrangement was investigated. A simple alternative output coupling technique was also devised using a tipless AFM probe placed in contact with the stripe to generate out-of-plane scattering, which was then captured by a nearby multimode fiber. The output coupling was reproducible as the AFM probe and its multimode fiber were moved along the stripe to generate cutback measurements, and so measured MPAs were in very good agreement with theoretical ones. Out-of-plane scattering caused by micrometer-sized particles on the stripe was also investigated. The stability of the experimental setup was assessed and found to be about 0.01dB peak-to-peak over a few minutes at constant temperature by using a reference optical signal.

Charbonneau et al. [344] proposed a broadside excitation technique using a PM-SMF cleaved at a steep angle and positioned near the top surface of the structure to be excited such that the slow mode of the fiber couples evanescently to the LRSPP propagating on it. The technique is analogous to prism coupling except that it is more easily implemented because there is only one element to manipulate and align (the PM-SMF). They demonstrated the technique at λ0=1310nm by exciting the LRSPP along membrane waveguides in fluid, observing a streak as the LRSPP propagated, and measuring its MPA by cutback, using an AFM probe with a multimode fiber for output coupling. The measured MPAs agreed very well with the theoretical ones.

Tencer and Berini [351] described an approach for integrating microfluidic channels and optical input–output coupling means with the membrane waveguide. The solution envisaged consisted of clamping a pair of glass chips with etched channels on either side of the membrane such that the membrane forms a common wall between the channels, and accurately controlling the spacing between the top chip and the metal stripe such that prism coupling of incident light to the LRSPP can occur along its bottom surface. The spacing could be set by a metal ring deposited around the membrane, also serving as a fluidic seal. Tencer and Berini computed the pressure drop required along the channels to drive a laminar flow of 60μlmin as a function of channel cross section and length. They also computed the deflection of the membrane as a function of pressure difference across the membrane, concluding that the difference should be minimized for reliable operation.

Fong et al. [353] described the fabrication of membrane waveguides using Cytop as the membrane material. Cytop has a low index (n1.34), slightly above that of H2O, so membranes can be made considerably thicker (350400nm) and possibly more robust than if made with Si3N4 (1530nm) or SiO2 (20100nm), while remaining optically not too invasive. The main process steps developed include spin coating and curing thin Cytop layers, depositing Au stripes and features (without an adhesion layer) on Cytop via evaporation and liftoff, and applying a TMAH etch through a Si3N4 back-side mask to release the membranes. Fabricated structures had a released Cytop membrane thickness of about 400nm, bearing Au stripes (t=25nm, w=5μm) and components such as MZIs.

In a subsequent paper [354], Fong et al. investigated the deflection and failure of Cytop membranes subjected to a pressure difference applied across the membranes. The membranes tested had a thickness of about 400nm, widths that ranged from 170 to 600μm, and lengths of 5mm (much greater than their widths). A membrane under test was sealed to a custom chuck having a pinhole, and a pressure difference was applied by changing the volume of air below the membrane by using a manual syringe. The pressure difference was measured by using a manometer, and the membrane deflection was measured by using an interferometric optical profilometer. The Young’s modulus and the residual stress in the membranes were extracted from a simple 1D model fitted to the measured pressure-deflection curves. Cytop membranes having widths less than 250μm withstood pressure differences of at least 30kPa while deflecting by 1020μm.

As an alternative to membrane structures, Daviau et al. [355] fabricated Au stripes (t=32nm to t=36nm, w=5.5μm) and integrated components on a thick (>8μm) Cytop lower cladding intended for use with an index-matched aqueous solution used as the upper cladding. The Cytop lower cladding was deposited by using a multilayer spin-coat–cure process, and the Au stripes and features were defined (without an adhesion layer) via electron-beam evaporation and liftoff. Physical characterization, consisting of optical, SEM and AFM inspections and of Cytop index and thickness measurements, was conducted on structures that had undergone intermediate process steps and on finished structures. Dicing was found to produce optical-quality end facets. The LRSPP was excited in finished structures covered with an index-matched glycerol solution (11% in de-ionized H2O) at λ0=1310nm by butt coupling to a PM-SMF. The MPA of the LRSPP measured through cutback was in very good agreement with theory (FEM), and mode outputs were of very good quality.

Daviau et al. [352] described a broadside excitation technique using a tapered PM-SMF positioned in physical contact with the top surface of the metal stripe such that the slow mode of the fiber couples through partial modal overlap with the LRSPP propagating thereon. The technique was inspired from [344] except that it used an off-the-shelf tapered fiber. They demonstrated the technique at λ0=1310nm by exciting the LRSPP along Au stripes on Cytop [355] covered with index-matched aqueous buffer and by measuring the MPA via cutback. The measured MPAs agreed well with theory.

Berini [347] assessed theoretically the potential of various surface plasmon waveguides for bulk and surface (bio)chemical sensing, anticipating their use in a MZI sensor. The sensitivity of a generic MZI implemented with attenuating waveguides (e.g., Fig. 21(e)) was derived, revealing that maximum sensitivity occurs when the sensing length is set equal to the propagation length of the mode used. The MZI sensitivities for bulk and surface sensing were then found to be proportional to the ratio of the corresponding waveguide sensitivity (bulk or surface) to its normalized attenuation, so maximizing a ratio leads to preferred waveguide designs and operating wavelengths. The propagation constant, sensitivities, and ratios were determined for modes in 1D surface plasmon waveguides, such as the SPP in the single-interface [Fig. 1(a)], the sb mode in the metal clads [Fig. 1(c)] and the sb mode in three variants of the metal slab [Fig. 1(b)] consisting of a free-standing metal slab, a metal slab on a substrate index-matched to the sensing solution (e.g., [180, 185, 188, 355]), and a metal slab on a thin free-standing dielectric membrane (e.g., [342]). Au was assumed as the metal, H2O as the sensing solution, and adlayers representative of biochemical matter were placed at all metal/H2O interfaces. Operating wavelengths spanning the range 600λ01600nm were considered. It was found that the surface sensitivity in the thin metal claddings was 100× larger than in the single interface, whereas that in the thin metal slab was 5× smaller; but the ratio of surface sensitivity to normalized attenuation was 10× larger in the thin metal slab than in the single interface. Also, the bulk sensitivity in the thin metal clads was 3× larger than in the single interface, whereas that in the thin metal slab was slightly smaller; but the ratio of bulk sensitivity to normalized attenuation was 10× larger in the thin metal slab than in the single interface. It was concluded that the LRSPP in thin metal slabs was very competitive for both bulk and surface sensing using an MZI, given the superior ratios of waveguide sensitivity to normalized attenuation. Preferred wavelengths for surface sensing were found to be near the short-wavelength edge of the Drude region, where detection limits of about 0.1pgmm2 were predicted.

4. Prospects for Applications

It is the attributes of a technology that guide it toward applications. But it is competitiveness versus other technologies, on the basis of performance, cost, and size, and other considerations such as market size, time to market, and capital requirements, that determine the level of interest for a particular application. Performing a competitiveness evaluation is nontrivial but necessary for any application that is seriously considered. Doing this exhaustively goes beyond the scope of this paper. But the attributes that make LRSPPs competitive for certain applications are outlined and discussed in the subsections that follow.

4.1. Competitive Context

The single-interface SPP and dielectric waveguide modes are the main (established) competition for the LRSPP. Compared with the single-interface SPP, the LRSPP is less attenuated [28, 29, 30, 248], and because of this exhibits a narrower excitation linewidth and a larger field enhancement in a prism-coupled setup [40], but is less confined (smaller neffn1 and larger mode size). The single-interface SPP is TM polarized, as is the LRSPP in the slab and stripe, but the square cross section stripe supports TM and TE LRSPPs [254, 262]. Both are surface waves. The LRSPP derives its competitive edge over the single-interface SPP primarily from its lower attenuation.

Dielectric waveguides support essentially bulk waves, and compared with the LRSPP can provide more confinement for less attenuation and a similar or larger field enhancement in a prism-coupled setup [44]. Confinement in dielectric waveguides comes for free, meaning with essentially no attenuation (in principle and in practice for technologies like SiO2 on Si). But confinement in any SPP waveguide is always accompanied by the cost of attenuation [96]. Applications must therefore rely on other attributes to achieve competitiveness. The presence of the metal is a fundamental distinction, having implications for fabrication, device architecture and chemical interaction, as highlighted below, and is the main feature from which the LRSPP can derive a competitive edge.

The LRSPP is complementary to the symmetric mode of the metal clads [Fig. 1(c)] and 2D variants thereof, in that the waves capture end points in the confinement–attenuation trade-off [96]. Different applications might be targeted altogether by these waves, but if they do target the same application, then the former (LRSPP) relies on length for a competitive edge and the latter (metal clads) on confinement. Interestingly, both can lead to improved sensor performance compared with the single-interface SPP in the Kretschmann–Raether geometry [347].

4.2. Nonlinear Optics

The field enhancement and long propagation length of the LRSPP offer improved nonlinear optical interactions over reflection from flat surfaces, over single-interface SPPs in the Otto and Kretschmann–Raether geometries, and over some focused beams in bulk media [136, 137, 138]. However, dielectric waveguides, where the core is used as the nonlinear medium, present stiff competition, since they provide a better confinement–attenuation trade-off than the LRSPP [142, 143]. Also, absorption and heating in the metal may cause thermal nonlinearities to dominate over certain field-based ones [148], which is troublesome given the large fields needed for nonlinear interactions and thus the typically high intensity of the incident beam. These points explain in part why research on nonlinear optics using LRSPPs (and other SPPs) appears to have waned.

4.3. Biosensors

Optical biosensing is dominated by surface plasmons, particularly the single-interface SPP on Au in the Kretschmann–Raether geometry [169, 170], as can be observed from the large number of optical biosensing studies reported using this technology in any given year (e.g., [356]). The technological reasons for this dominance include good sensor performance (sensitivity, detection limit), the ability to integrate microfluidics, and importantly, the availability of good surface chemistries for Au (e.g., [357]), which are necessary for interfacing the sensor to the (bio)chemical world. The convergence of all of these requirements is essential in a biosensor and may explain in part why dielectric waveguides have yet to make significant inroads into this application space, even though they offer good sensitivity [358]. Other reasons for the dominance of the single-interface SPP include the fact that this technology was early to market, and user-friendly instruments have been available for about 15  years [170]. But the approach is nearing maturity, and further substantive improvement seems difficult to achieve.

The LRSPP is less surface sensitive than the single-interface SPP because the mode overlap with a thin adlayer is lower (e.g., [347]). This is due to its greater spatial extent and to the fact that it is symmetric; so only half of it interacts with the adlayer. But it is overall sensitivity, detection limit, and the rejection of interference (background fluctuations, nonspecific bindings) that really matter, so LRSPPs may lead to better biosensors via their other attributes.

For instance, the LRSPP in the metal slab exhibits a very narrow resonance (coupling) width in a prism-coupled arrangement; so the location of the resonance can be tracked with higher accuracy, and intensity changes are larger near the resonance, features that may more than compensate for the lower surface sensitivity to yield a larger overall sensitivity [185]. The larger field enhancement [40] is advantageous for fluorescence-based sensing [181]. The LRSPP in the metal stripe can propagate along integrated optic structures, such as long MZIs [288], potentially leading to greater overall sensitivity [345, 347]. Also, the ability of the MZI to reference out common interferences and (in principle) nonspecific bindings potentially leads to a lower detection limit. The larger penetration depth of the LRSPP into the sensing medium offers an advantage in that larger analyte (e.g., bacteria) can be sensed [195]. Also, a receptor matrix (e.g., receptor molecules in Dextran) deposited on the metal and extending into the sensing medium increases the binding capacity per unit area, compensating for the lower surface sensitivity [192]. A clear drawback, however, is that index symmetry must be ensured at all times, which leads to increased sensor complexity and/or to tighter constraints on the sensing fluid in terms of composition and temperature. But promising solutions to this problem have been proposed [180, 185, 237, 342, 352], and recent experiments pointing to improved biosensor performance are encouraging.

4.4. Emission, Surface-Enhanced Raman Scattering, and Lasing

The extraction of light from emissive devices through metallic contacts is a problem attracting considerable research effort given its practical importance, especially for organic light emitters, where certain architectures position one or two metallic contacts above and/or below the active region. In such cases, a significant amount of power can be coupled directly from the emitting medium into the SPP modes of these contacts, and unless recovered, represents a loss channel reducing the efficiency of the devices. Both coupled modes of the slab (sb and ab) have an important role to play in this process and in improving the performance of such devices. Using symmetric (or effectively symmetric) corrugated metal slabs appears to be a promising avenue [200, 204, 211].

An improvement in SERS intensity mediated via the LRSPP is also potentially at hand [206], although this prediction has apparently not yet been verified experimentally.

Although the gain available from certain media (e.g., semiconductors and dyes) is larger than the attenuation of the LRSPP, it is still unclear whether net amplification and oscillation (lasing) in this mode is possible. The challenge with lasing in the LRSPP is that the ab mode (slab) or the aabm and sabm modes (stripe) are always supported and more tightly confined, and thus will deplete a portion of the gain region nearest the metal through spontaneous emission and amplified spontaneous emission. Recent computations [214, 217] suggest that these challenges can be overcome in dipolar gain media (dyes), and initial experiments conducted in Er-doped glass are encouraging [340]. If net amplification of the LRSPP were possible, then better biosensors (at least) might result, as well as unforeseen applications. Whether better lasers and amplifiers would be enabled is unknown, but at least a greater degree of polarization is expected from the output [339].

4.5. Interconnects

The basic task of an optical interconnect is to confine and transport electromagnetic energy over a prescribed distance with the lowest possible loss while allowing high-speed optical signaling. High interconnect packing density with low crosstalk is also desirable in certain prospective applications such as on-chip interconnects. Relevant interconnect length scales are meters for board-to-board interconnects, centimeters for chip-to-chip or board level interconnects, millimeters for on-chip global and clocking interconnects, and micrometers for transistor-to-global (on chip) interconnection. As the length scale diminishes, the packing density increases. Except for interconnects requiring very high packing density, the dielectric waveguide (optical fiber or other) seems to satisfy the general requirements very well, especially at longer length scales.

The lowest MPAs reported to date for the LRSPP propagating along a metal stripe of reasonable confinement all cluster around 1dBcm [261, 291, 278, 280] at λ01310  nm and λ01550nm. So the LRSPP in the metal stripe might challenge other schemes in certain short-reach (centimeters) medium-density (40 waveguides per mm width) applications [303]. Competitive features include single (long-range) mode operation, the ability to transmit electrical signals along the same structure, and the fact that buried metal stripes can be fabricated very inexpensively via, for example, evaporation and liftoff of metal and spin-coated or sputtered claddings. The packing density could be increased relatively easily by stacking waveguides vertically along the perpendicular axis (i.e., along y in Fig. 16). Attaching connectors to the waveguides or aligning them to sources and detectors remains an important part of the cost equation, but the relaxed alignment tolerances of larger-sized LRSPPs could be very helpful in this respect (e.g., [329, 306]). The fact that the LRSPP in the stripe is TM polarized only may or may not be a problem, depending on whether one has control over the transmit portion of the interconnection. Alternatively, polarization-insensitive LRSPPs along square cross-section metal stripes could be used [254, 262].

At the other end of the trade-off scale, the metal clads and 2D variants thereof might be suitable for extremely short very high-density interconnections such as transistor-to-global interconnection [11, 12, 359].

4.6. Integrated Optics

Passive integrated optics is dominated by dielectric waveguides because they provide low fiber-to-fiber insertion loss and polarization independence with adequate confinement. These are crucial requirements for many applications, especially in optical fiber communications. Planar SiO2 waveguides on Si are particularly well suited.

An attractive feature of integrated optics with the LRSPP is the low cost of fabrication, where only one metal formation cycle (e.g., lithography, metal deposition, liftoff) is required for fabricating all elements. Another attractive point is the ability to define metal stripes and features down to the critical dimension of the litho process. This may be difficult to do with etched core dielectric waveguides because of limitations in producing vertical walls and the need to infill trenches and gaps between cores with upper cladding material.

Accurate fabrication leads to very high-quality Y junctions and highly reflective (>90%) narrowband (<0.5nm) step-in-width Bragg gratings [318]. Also, very deep extinction is possible in inteferometric structures such as the MZI because they can be fabricated accurately and the TM-only nature of the structure eliminates unwanted interference occurring with cross-polarized light.

Integrated optics with LRSPPs fits very well with sensing applications, particularly biosensing, where Au waveguides are advantageous given the large user base working on this material and given mature and stable surface chemistries available for Au (as pointed out in Subsection 4.3). Integrated elements might also find applications in interconnects and thermo-optic devices.

4.7. Thermo-Optic and Electro-Optic Devices

The embedded metal slab or stripe is a feature of central importance to thermo-optic or electro-optic devices in that it can also be used as the heating element by passing current through it, or as an electrode for applying electric fields. Combining the heating and LRSPP guiding functions, for example, leads to an excellent overlap between thermal and optical contours [330, 324], and in an optimized design may reduce the electrical power consumption compared with conventional thermo-optics with dielectric waveguides.

5. Concluding Remarks

The LRSPP has appeared in a large number of studies, either as the focal point or peripherally within another context. The studies involving the LRSPP range from the fundamental to the applied and span a very wide landscape including modal studies, prism coupling, field enhancement, corrugated gratings, material characterization, roughness, islandized metal films, nonlinear interactions, biosensors and biosensing, molecular scattering and SERS, transmission through opaque films and emission extraction, fluorescence enhancement, amplification and lasing, waveguides and interconnects, integrated optics (bends, couplers, Y junctions, etc.), Bragg gratings, thermo-, electro- and magneto-optics and associated devices such as VOAs, switches, and modulators.

Despite the breadth and vigor of the research conducted to date with LRSPPs, much remains to be uncovered, and the scope for investigations is broad. Topics involving the LRSPP needing and warranting further study include amplification and lasing, waveguides and integrated optics, corrugated and Bragg gratings, roughness, fluorescence enhancement, emission extraction, SERS, thermo- and electro-optic (bio)chemical sensing, and fabrication techniques. The prospects for applications in biosensing and thermo- or electro-optic devices are bright.

6. Addendum [360, 361, 362, 363, 364, 365, 366, 367, 368]

Additional works involving the LRSPP have been reported since this review was written [360, 361, 362, 363, 364, 365, 366, 367, 368]. They include a proposal for a sensor based on the excitation of the LRSPP by a long-period grating defined in the core of a dielectric waveguide placed in proximity and parallel to a thin Au slab [360]; a proposal for a sensor based on integrating a Bragg grating and a microfluidic channel with a Au stripe coupled to a thin Au slab and operating in the LRSPP as a coupled symmetric supermode of the Au stripe–slab system[364] (building on [297]); a scheme for tracking the LRSPP coupling angle in a prism-coupled sensor where light outscattered in transmission is detected and used to control an angle-scanning piezomirror [366]; a study of the LRSPP propagating along a Pd2Si stripe embedded in a Si slab bounded by air at mid- to far-infrared wavelengths [363]; an investigation of the decay of dipoles into the ab and sb (LRSPP) modes of a conformally corrugated Ag grating, including gratings where the ab mode is suppressed [361]; the quantum mechanical description of LRSPP excitation in a prism-coupled metal slab [362]; a demonstration of LRSPP-assisted transmission of nonclassical light (squeezed vacuum states) along an Au stripe buried in BCB [365]; a proposal for a Schottky contact detector consisting of a symmetric CoSi2 stripe buried in Si capable of detecting LRSPPs at infrared wavelengths (below the bandgap of Si) [367]; and an investigation of SPP and LRSPP amplification in planar metallic structures incorporating dipolar gain media (R6G in solution) [368].

Appendix A: Alphabetical List of Acronyms

  • 1D   One dimensional  
  • 2D   Two dimensional  
  • AFM   Atomic force microscope  
  • ATR   Attenuated total reflection  
  • BER   Bit error rate  
  • BCB   Benzocyclobutene  
  • BSA   Bovine serum albumin  
  • EIM   Effective index method  
  • DCM   4-Dicyanomethylene-2-methyl-6- (p-dimethylaminostyryl)-4H-pyran  
  • FDM   Finite difference method  
  • FEM   Finite element method  
  • FoM   Figure of merit  
  • FWHM   Full width at half-maximum  
  • LRSEP   Long-range surface exciton polariton  
  • LRSPP   Long-range surface plasmon polariton  
  • MoL   Method of lines  
  • MPA   Mode power attenuation  
  • MNA   2-Methyl-4-nitroaniline  
  • MZI   Mach–Zehnder interferometer  
  • PFCB   Perfluorocyclobutane  
  • PMMA   Polymethyl methacrylate  
  • PM-SMF   Polarization-maintaining single-mode fiber  
  • PTS   bis-(p-Toluene sulphonate  
  • Q   Quality factor  
  • RMS   Root mean squared  
  • R6G   Rhodamine 6G  
  • SEM   Scanning electron microscope  
  • SERS   Surface-enhanced Raman scattering  
  • SMF   Single mode fiber  
  • SPP   Surface plasmon polariton  
  • TE   Transverse electric  
  • TEM   Transverse electromagnetic  
  • TM   Transverse magnetic  
  • TMAH   Tetramethylammonium hydroxide  
  • VCSEL   Vertical-cavity surface-emitting laser  
  • VOA   Variable optical attenuator  
  • YIG   Yttrium iron garnet  

Tables and Figures

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Table 1. Model Properties of SPP Waveguides

 

Fig. 1 (a) Single interface between a metal (εr,2) and a dielectric (εr,1) supporting a bound SPP. (b) Metal slab (εr,2) of thickness t bounded by semi-infinite dielectrics (εr,1,εr,3) supporting two bound SPP modes (ab,sb). (c) Dielectric slab (εr,1) of thickness t bounded by semi-infinite metals (εr,2) supporting a symmetric bound mode (other modes not shown). The distribution of the main transverse electric field component of the modes is shown as the red curves over the cross section of each structure. Propagation occurs along the +z axis (perpendicular up from the page). Adapted from Fig. 1 of [96].© 1981 Optical Society of America.

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Fig. 2 Normalized phase and attenuation constants of the ab and sb modes supported by an asymmetric metal slab at λ0=632.8nm, assuming Ag for the metal εr,2=(0.0657j4)2 with εr,1=1.52 and εr,3=1.552. Adapted from Fig. 2 of [30]. © 1981 American Physical Society.

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Fig. 3 Normalized dispersion curves of the sb and ab modes propagating along a lossless metal film modeled as a Drude metal and bounded symmetrically by semi-infinite vacuum claddings for three normalized thicknesses U=0.1,1.0,2.0; ωp is the plasma frequency of the Drude model. The light line in vacuum is indicated as the dashed line. Adapted from Fig. 2 of [17]. © 1969 American Physical Society.

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Fig. 4 Prism coupling technique for exciting SPPs. Case 1: εr,3=εr,1,sb mode (LRSPP) excited at a smaller angle of incidence θ than the ab mode [19, 27]. Case 2: t=, single-interface SPP excited along the εr,3|εr,2 interface (Otto configuration [18]). Case 3: s=0, single-interface SPP excited along the εr,2|εr,1 interface (Kretschmann–Raether configuration [23]). Case 4: εr,1εr,3, single-interface SPP along εr,2|εr,1 interface excited at a smaller angle θ than the single-interface SPP along the other (εr,3|εr,2) interface (Abelès and Lopez–Rios configuration [25]).

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Fig. 5 Reflectance of p-polarized light at λ0=632.8nm versus angle of incidence at the base of the prism θ for an Ag film about 49nm thick bounded by cryolite layers. Dips in the reflection at θ=47° and 50° are due to coupling with the sb and ab modes, respectively. The dip at small angle (θ33°) is due to coupling with a TM guided mode in the bottom cryolite cladding. Adapted from Fig. 8 of [27]. © 1978 National Research Council of Canada.

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Fig. 6 End-fire coupling technique for exciting SPPs. Adapted from Fig. 20 of [80]. © (1986) American Physical Society.

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Fig. 7 (a) Prism (TaFD9) coupling to the LRSPP by using a finite-width input beam; the oil is index matched to the Pyrex substrate. (b) Measured intensity profile at the observation plane: λ0=632.8nm, w=1.27mm, s=1.35μm, t=16nm, Le=274μm (Lew=0.2157). Adapted from Figs. 2 and 3(b) of [42]. © (1985) Elsevier B.V.

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Fig. 8 (a) Resistivity ρ and (b), (c) relative permittivity εr=εRjεI of Au at λ0=632.8nm, measured in situ as a function of Au thickness during vacuum deposition (by thermal evaporation at a rate of 0.02nms onto borosilicate glass substrates held at room temperature). Adapted from Figs. 3(a) and 4 of [110]. © (1977) Institute of Physics.

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Fig. 9 (a) Measured ATR spectrum for an islandized Ag film on a substrate and covered with index-matching fluid. Inset, experimental arrangement. The measured results (crosses) are compared with a fitted theoretical response (solid curve). (b) Computed distribution of the z-directed component of the Poynting vector at θ=55.78°. Adapted from Figs. 2 and 3 of [116]. © (1991) American Physical Society.

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Fig. 10 (a) Prism-coupling arrangement for second-harmonic generation (2ω) through excitation of the LRSPP at the fundamental (ω). (b) Second-harmonic reflection coefficient R as a function of the angle of incidence θ of the input beam: dots, measurements (LRSPP); solid curve, theoretical (LRSPP); dashed curve, theoretical (single-interface SPP). Adapted from Figs. 1 and 2 of [138]. © 1983 American Physical Society.

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Fig. 11 Spectral position of the LRSPP dip as aqueous sensing fluids of different refractive indices are injected into the sensor. The baseline noise signal is shown on an enlarged scale. Adapted from Fig. 5 of [185]. © (1985) Elsevier B.V.

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Fig. 12 Setup for measuring fluorescence emitted through the backside and pumped by the prism-coupled LRSPP. Adapted from Fig. 1 of [188]. © (2007) Springer Science + Business Media LLC.

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Fig. 13 Normalized radiation spectrum emitted from the symmetric structure sketched at the origin of the polar plot. The dashed lines identify angles of emission for specific wavelengths. Fluorescent molecules are located in the lower photoresist layer and are pumped at λ0=514.5nm from the back side at normal incidence. The fluorescence is collected from the top. Adapted from Fig. 2 of [200]. © 1988 American Institute of Physics.

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Fig. 14 (a) Structure investigated and distribution of the Ey field component of the sb and ab modes supported. (b) Emission spectrum of the Alq3-doped layer only, and emission and absorption spectra of the R6G-doped layer only. (c) Emission spectrum collected from the top of the structure when pumped at λ0=408nm from the back (black curve), and emission spectra collected from control samples (no R6G, blue curve; no Alq3, red curve). The thickness of the Ag film is t=60nm. Adapted from Figs. 1(a), 1(d), and 2(b) of [212]. © 2004 Science/AAAS.

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Fig. 15 Pd film bounded by air on one side and, on the other, by a finite 1D photonic crystal on a prism. The input and reflected beams are sketched in magenta. The LRSPP and its outcoupled (reradiated) field are sketched in red. The computed ATR angular reflection spectrum is sketched as the red curve, showing the intensity dip due to coupling to the LRSPP, and fringes due to interference between the outcoupled field and the reflected beam. Adapted from Fig. 1(a) of [245]. © 2009 Optical Society of America.

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Fig. 16 Metal stripe (εr,2) of thickness t and width w bounded by semi-infinite dielectrics (εr,1,εr,3). The direction of mode propagation is along the +z axis, which is directed up out of the page. Adapted from Fig. 1 of [251]. © 2001 American Physical Society.

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Fig. 17 (a) Normalized phase and (b) attenuation constants of modes supported by symmetric metal slab (w=) and stripe (w=1μm) waveguides at λ0=633nm, assuming Ag for the metal (εr,2=19j0.53) and εr,1=εr,3=4. Adapted from Fig. 2 of [248]. © 2000 American Physical Society.

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Fig. 18 Contour and 3D plots of Re{Sz} of the ssb0 mode for w=1μm. (a) t=80nm, (b) t=20nm, (c) t=100nm, (d) t=40nm. All other parameters are the same as in Fig. 17 (λ0=633nm, εr,2=19j0.53 and εr,1=εr,3=4). The outline of the metal film is shown as the rectangular dashed contour. Adapted from Fig. 2 of [246], © 1999 Optical Society of America, and Fig. 7 of [248], © 2000 American Physical Society.

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Fig. 19 (a) Longitudinal cross-sectional view of an optical fiber butt coupled to the input of the metal stripe to excite the LRSPP (red). A polarization-maintaining SMF is often used. (b) Sequence of LRSPP outputs measured at λ0=1550nm from an 8μm wide, 20nm thick, 3.5mm long Au stripe embedded in SiO2 for angles of incident polarization ranging from 0° (TM polarization) to 90° (TE polarization). The green vertical arrowheads identify the location of the stripe. Adapted from Fig. 2 of [249]. © 2000 Optical Society of America.

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Fig. 20 Measured LRSPP mode outputs at λ0=1550nm for three waveguides, each comprising a low-aspect-ratio (wt) Au stripe (t=150nm) in BCB. Linearly polarized light aligned at 45° from the vertical axis is end-fire coupled to the input of the waveguides, and the outputs are viewed through an analyzer aligned along the vertical (TM) axis (top sequence) or the horizontal (TE) axis (bottom sequence). a, Output pairs for wt=1.4; b, output pairs for wt=1.2; c, output pairs for wt=1.0. Adapted from Fig. 1 of [262]. © 2006 Optical Society of America.

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Fig. 21 Measured mode outputs at λ01550nm of various passive elements operating in the LRSPP and implemented by using 8μm wide, 20nm thick Au stripes on SiO2 (upper cladding not shown) [283, 287, 288]. (a) Mosaic of outputs for edge couplers where the spacing between the parallel stripes is varied from 2μm (lower image) to 8μm (upper image) in steps of 1μm. (b) Output of a straight waveguide. (c) Output of an S bend. (d) Output of a Y-junction splitter. (e) Output of a MZI. (f) Output of a sharp angle bend. Adapted from [13]. © 2008 American Institute of Physics.

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Fig. 22 (a) Sketch of a broadside coupler implemented with Au stripes (t=20nm, w=5μm) deposited one on top of the other (D=4μm) and embedded in polymer. (b) Measured outputs of a series of couplers operating in the LRSPP at λ0=1550nm as a function of interaction length (solid curves are fitted); (c) measured mode outputs for the case L=260μm. Adapted from Figs. 1 and 3 of [289]. © 2006 American Institute of Physics.

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Fig. 23 (a) Edge coupler in top view implemented with Au stripes (t=14nm, w=8μm) in BCB. (b) Measured outputs of a coupler operating in the LRSPP over the range 950λ01690nm. The outputs are normalized to the transmittance of a similar straight waveguide. The O–U telecommunications bands are identified as the hashed areas. Adapted from Figs. 6 and 10 of [291]. © 2006 IEEE.

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Fig. 24 (a) Au stripe of width w and thickness t, embedded at the center of a BCB core of thickness b, bounded by SiO2 on one side and air on the other. (b) Experimental setup. (c) Insertion loss of 90° bends operating in the LRSPP as a function of radius of curvature. The measurements are shown by squares (b=6.5μm, t=23nm, w=6.1μm) and diamonds (b=21μm, t=23nm, w=6.5μm), and the solid curves plot the associated theoretical results. (d) Measured LRSPP mode outputs from two 90° bends of radii r=7.5mm and r=1mm (b=6.5μm, t=23nm, w=6.1μm for both); the image on the right is saturated to show the radiation loss on the outside of the bend. Adapted from Figs. 1, 2, and 3 of [296]. © 2008 American Physical Society.

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Fig. 25 6.8cm long Au stripe (t=8nm, w=3.5μm) in flexible ribbonlike polymer claddings (a) curved out of plane at a radius of 5mm, and (c) twisted 90° along the direction of propagation. The associated measured LRSPP mode outputs at λ0=1310nm are shown in (b) and (d); the mode size is roughly 23μm wide by 5μm high. Adapted from Fig. 5 of [307]. © 2009 Optical Society of America.

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Fig. 26 Top view of a step-in-width Bragg grating implemented by using a metal stripe. (a) Grating of length Lg, and (b) unit cell of period Λ showing segments of width w1 and w2, each of length d1 and d2. Part (b) can also be interpreted as the side view of a step-in-thickness grating with w1 and w2 representing the total stripe thickness [312]. Adapted from [309] and Fig. 1 of [311]. © 2005 Optical Society of America.

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Fig. 27 Measured transmittance and reflectance of four uniform third-order gratings of different length (Lg) implemented with an Au stripe (t=21.6nm) stepped in width from w1=8μm to w2=2μm over a period of Λ=1.6μm (d1=d2, 50% duty cycle). The inset to (a) shows a measured LRSPP mode output from a grating, and the inset to (b) shows an AFM scan of a step-in-width section. Adapted from [309] and Figs. 8 and 9 of [315]. © 2006 IEEE.

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Fig. 28 Adapted from Figs. 2 and 4 of [317]. © 2006 IEEE. Measured reflectance and transmittance of four uniform first-order gratings implemented with an Au stripe (w=8μm) stepped in thickness from t=15nm to t=15nm+δ over a period of Λ=0.5μm (45% duty cycle). The inset to (b) shows an AFM scan of a step-in-thickness section.

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Fig. 29 (a) Electrically contacted and isolated metal stripe. (b)–(e) Mosaic of LRSPP mode outputs measured at λ0=1550nm from a straight stripe (w=6μm, t=15nm) thermo-optic VOA. The electrical power dissipated in the stripe (I2R) is indicated in milliwatts on each image. (f) Extinction ratio as a function of dissipated electrical power density Pde for 2 VOAs of different width and a (heated) length of 4440μm. (g) Computed temperature increase due to the passage of current along a metal stripe (half of the calculation domain is shown). Adapted from [322, 330]. © 2006 IEEE.

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Fig. 30 (a) Measured response of an electrically contacted thermo-optic MZI (sketched in inset) operating in the LRSPP at λ0=1550nm as a function of electrical power (I2R) dissipated in the stripe (w=8μm, t=15nm). (b) Switching characteristics of a thermo-optic coupler (inset) operating in the same manner. The other insets show measured outputs for two switching states. Adapted from [324]. © 2004 American Institute of Physics.

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Fig. 31 (a) SEM cross section of a diced and polished wafer-bonded LiNbO3 device having a total cladding thickness of about 32μm. The bonding interface between the top and bottom LiNbO3 claddings is seamless. The 20nm thick Au stripe, which cannot be seen at this magnification, is buried at interface between the claddings within the dotted yellow oval. (b) Optical microscope image of a device in top view. Inset, measured output of a 4mm long device where the Au stripe (w=2μm, t=20nm nominally) is buried at about the midpoint of a 25μm thick LiNbO3 stack. Adapted from Figs. 9 and 10 of [335]. © 2007 American Vacuum Society.

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Fig. 32 (a) Microscope image of half a membrane waveguide obtained by cutting a full one with a focused-ion beam. The structure consists of a 20nm thick Si3N4 free-standing membrane supporting a 25nm thick 5μm wide Au stripe. (b) Measured LRSPP output from a cut membrane waveguide in air at λ0=1310nm, as viewed through an analyzer aligned parallel to the transverse electric field. (c) Stitched microscope image of an electrically contacted Mach–Zehnder interferometer on a free-standing Si3N4 membrane. The membrane is 30nm thick and about 300μm wide by 2900μm long. The metal stripes are 5μm wide and 20nm thick. Adapted from Fig. 4 of [342], © 2007 American Chemical Society, and Fig. 7 of [348], © 2008 American Vacuum Society.

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335. G. Mattiussi, N. Lahoud, R. Charbonneau, and P. Berini, “Fabrication of long-range surface plasmon-polariton waveguides in lithium niobate on silicon,” J. Vac. Sci. Technol. A 25, 692–700 (2007). [CrossRef]  

336. S. Jetté-Charbonneau, N. Lahoud, R. Charbonneau, G. Mattiussi, and P. Berini, “End-facet polishing of surface plasmon waveguides in lithium niobate,” IEEE Trans. Adv. Packag. 31, 479–483 (2008). [CrossRef]  

337. M. P. Nezhad, K. Tetz, and Y. Fainman, “Gain assisted propagation of surface plasmon polaritons on planar metallic waveguides,” Opt. Express 12, 4072–4079 (2004). [CrossRef]   [PubMed]  

338. M. Z. Alam, J. Meier, J. S. Aitchison, and M. Mojahedi, “Gain assisted surface plasmon polariton in quantum wells structures,” Opt. Express 15, 176–182 (2007). [CrossRef]   [PubMed]  

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341. M. Tencer, R. Charbonneau, and P. Berini, “Confinement and manipulation of droplets on hydrophilic surfaces using a flat high surface energy guide,” Lab Chip 7, 483–489 (2007). [CrossRef]   [PubMed]  

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349. M. Tencer and P. Berini, “Toposelective electrochemical desorption of thiol SAMs from neighboring gold surfaces,” Langmuir 24, 12097–12101 (2008). [CrossRef]   [PubMed]  

350. P. Berini, R. Charbonneau, and N. Lahoud, “Long-range surface plasmons along membrane-supported metal stripes,” IEEE J. Sel. Top. Quantum Electron. 14, 1479–1479 (2008). [CrossRef]  

351. M. Tencer and P. Berini, “Design of microfluidic channels separated by an ultra-thin free standing dielectric membrane,” Microfluid. Nanofluid. 6, 17–26 (2009). [CrossRef]  

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364. Y. H. Joo, S. H. Song, and R. Magnusson, “Long-range surface plasmon-polariton waveguide sensors with a Bragg grating in the asymmetric double-electrode structure,” Opt. Express 17, 10606–10611 (2009). [CrossRef]   [PubMed]  

365. A. Huck, S. Smolka, P. Lodahl, A. S. Sørensen, A. Boltasseva, J. Janousek, and U. L. Andersen, “Demonstration of quadrature-squeezed surface plasmons in a gold waveguide,” Phys. Rev. Lett. 102, 246802 (2009). [CrossRef]   [PubMed]  

366. V. N. Konopsky, D. V. Basmanov, E. V. Alieva, D. I. Dolgy, E. D. Olshansky, S. K. Sekatskii, and G. Dietler, “Registration of long-range surface plasmon resonance by angle-scanning feedback and its implementation for optical hydrogen sensing,” New J. Phys. 11, 063049 (2009). [CrossRef]  

367. C. Scales, I. Breukelaar, and P. Berini, “Surface-plasmon Schottky contact detector based on a symmetric metal stripe in silicon,” submitted to Opt. Lett..

368. I. De Leon and P. Berini, “Modeling surface plasmon-polariton gain in planar metallic structures,” submitted to Opt. Express.

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