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We provide an overview of Fano resonance and plasmon induced transparency (PIT) as well as on plasmons coupling in planar structures, and we discuss their application in sensing and enhanced spectroscopy. Metal-insulator-metal (MIM) structures, which are known to support symmetric and anti-symmetric surface plasmon polaritons (SPPs) arising from the coupling between two SPPs at the metal-insulator interfaces, exhibit anticrossing behavior of the dispersion relations arising from the coupling of the symmetric SPP and the metal/air SPP. Multilayer structures, formed by a metal film and a high-index dielectric waveguide (WG), separated by a low-index dielectric spacer layer, give narrow resonances of PIT and Fano line shapes. An optimized Fano structure shows a giant field intensity enhancement value of 106 in air at the surface of the high-index dielectric WG. The calculated field enhancement factor and the figure of merit for the sensitivity of the Fano structure in air can be 104 times as large as those of the conventional surface plasmon resonance and WG sensors.
© 2016 Optical Society of America
1. Introduction
The coupling of resonances is of upmost importance in many physical systems. For example, the magnificent 509 m tall skyscraper Taipei 101, which we had the chance to visit during the ICNP2016 conference in Taipei, has a 680 tons steel ball placed at its top floors to counter balance possible mechanical movements; e.g. vibrations, that might be caused by strong winds, to damp the oscillation of the building and to enhance its mechanical stability. Indeed, the phenomenon of resonance – be it mechanical, acoustic or electromagnetic one – is a characteristic of many types of classical and quantum systems. Free electrons driven by electromagnetic light, for example surface plasmon polaritons (SPPs), are no exception in this regard. In this paper, we will discuss the mutual coupling of SPPs, and the interaction of a SPP with an electromagnetic mode excited in a planar waveguide. The observations are made in a metal-insulator-metal (MIM) structure for SPPs coupling, and in a layered structure of a metal film and a dielectric WG separated by a dielectrics spacer layer (Fig. 1). The coupling of such resonances, e.g. interference effects owing to interacting resonances, brings about interesting physical phenomena. For example, anticrossing of dispersion curves is observed when coupling between SPPs takes place; and the coupling between a SPP and a waveguide mode leads to the Fano resonance. The latter has generally been regarded as a feature entirely specific to quantum systems; however, wavefunction interference phenomena are also ubiquitous in classical optics. Fano resonance, which can be theoretically described by coupled harmonic oscillators [1,2], occurs in many systems, such as plasmonic nanostructures [3–15] and metamaterials [16–21]. We will discuss, in succession, the coupling of SPPs and anti-crossing behavior observed in MIM structures and experimental observation of the Fano line shapes in planar multilayer systems, which do not require the use of nanofabrication techniques. We will go on to discuss the giant field intensity enhancement (FE) that can be generated in a planar Fano structure and its possible use in enhanced spectroscopy and sensing.
Fig. 1 (a) MIM structure and supported SPP modes. (b) Metal/Spacer/WG structure supporting the coupling of SPP and PWG modes.
2. Plasmons Coupling in MIM Structures
SPPs are collective oscillations of free electrons in a metal that are driven by electromagnetic waves; e.g. light; and they are bound to an insulator-metal (I/M) interface and propagate along this interface, and fade away from it exponentially [22–28]. When a metal film is sandwiched from each side by a semi-finite insulator, the SPPs travelling at the I/M interfaces couple through degenerate dispersion when the metal is sufficiently thin (~100 nm) to allow coupling to occur and leads to symmetric and anti-symmetric SPP modes; i.e., S-SPP and AS-SPP, respectively [22–24,28–30]. The AS-SPP propagates for long distances along the I/M interface and penetrates deeper in the insulator, and it is referred to as long range SPP (LR-SPP) [31–33]; the optical excitation of which leads to enhanced sensitivity in surface plasmon resonance sensors; i.e. SPR sensors [34–37]. Besides, IMI structures, MIM structures support S-SPP and AS-SPP as well [28–30,38–42]. The latter should persist even when the insulator is ultra-thin (thickness close to zero)) [40,43]; thereby MIM structures have been intensively studied for realizing nanoscale plasmonic waveguides [44] and negative refraction of light [45].
Recently, tuning the dispersion curves of SPPs has gained increasing interest owing to the possibilities of controlling near-field light at the nano-cogent environment of structured metal. Coupled SPP modes may lead to anti-crossing, around the crossing zone, of folded dispersion curves [24,46–50], and researchers studied the coupling of SPPs with, for example, localized surface plasmons at nanostructured metals [51,52], as well as excitons at quantum dots [53–55] and fluorescent chromophores [55–58].
Next, we give evidence of the coupled-mode nature of SPP modes and the anticrossing behavior of their dispersion curves in layered MIM structures. Besides SPPs, MIM structures can support waveguide modes; e.g. transverse electric (TE) modes, similar to those observed in Fabry-Perot cavities [59,60]. Note that in those cavities, the metal layers are semi-infinite. The experiments we preformed on layered MIM structures of Ag and PMMA are angular and wavelength interrogation in attenuated total reflection (ATR) in a Kretschmann geometry. MIM structures were prepared by evaporating a ~45 nm thick Ag film on a cleaned glass substrate, followed by spin coating a ~220 nm thick PMMA layer, and another ~45 nm thick Ag film was evaporated on top of the PMMA layer. Angular ATR spectra as well as calculated electric-field profile (not shown) suggest that coupling of SPPs occurred in our MIM structure, and the wavelength ATR scan (not shown) allowed for the derivation of the dispersion curves [61]. Figure 2 shows that anti-crossing of the dispersion curves clearly occurs due to the coupling of the Ag/Air-SPP and S-SPP modes, and agrees fairly well with theoretical dispersion curves; a feature which may help develop novel optical devices based on MIM structures (vide infra). Next, we discuss the coupling of SPP and a waveguide mode that result in PIT and Fano resonance.
Fig. 2 (a) Calculated dispersion curves of SPPs and TE0 supported by the MIM structure which is shown as an inset in the top left corner of the figure. In this figure the Ag layers are semi-infinite, and the light lines for air and PMMA are indicated by dashed lines. (b) Obsevation of anticrossing between the S-SPP and Ag/Air-SPP modes in the MIM structure which is indicated at the top of the figure. Scatters are experimental data and full lines are theoretical calculation of the dispersion curves of SPPs. Reproduced with permission from Ref. 61.
3. Plasmon-Waveguide Mode Coupling: Fano Resonance and PIT
Eventhough Fano resonance has been regarded as a feature specific to quantum systems and has been observed in atomic physics together with electromagnetically induced transparency (EIT) [62,63], recently, Fano- and EIT-like resonances in plasmonic nanostructures witnessed intensive studies, and they are rationalized by the coupling between dark and bright resonances [64], and they present potential for sensing applications (vide infra) [65] - EIT in plasmonic systems is referred to as PIT [16] - and recently, PIT and Fano resonance have been observed in multilayer structures of a planar waveguide (PWG) deposited on a metal-dielectric stack in a Kretschmann configuration [66]. Such a structure is simple to prepare since it does not require nanofabrication processes. We performed numerical simulations that established a clear analogy between our optical system and a system of coupled oscillators, and revealed the true nature of the resonances; i.e. the coupling of the electromagnetic modes in our plasmonic planar structure, namely the PWG mode and the SPP at the metal-dielectric interface [67]. Such a coupling leads to narrow Fano and PIT resonances; a feature which may increase the sensing capability of refractive index changes by two orders of magnitude versus that of conventional SPR sensing.
The multilayer system; e.g. SPP-PWG hybrid samples, is a combination of a metal-dielectric interface that supports SPP modes and a stack of three dielectrics that supports PWG modes. The layered structures samples were prepared as follows: a ~45 nm thick film of Ag was vacuum evaporated on a SF10 glass substrate, and a fluoropolymer Cytop film was deposited on top of the Ag layer by spin-coating from a Cytop solution of ~6 wt. %. To complete the sample, a PMMA film was spin coated on top of the Cytop film from toluene solution with a PMMA concentration of ~7 wt.%. The thicknesses of the Cytop and PMMA films were controlled by the spin coating speed. The thicknesses and dielectric constants of the films were estimated by fitting theoretical ATR spectra with the experimental ones.
Experimental evidence of PIT and Fano line shapes in ATR spectra of planar multilayer systems can be seen in Fig. 3. The multilayer structure was put in contact with a SF11 glass prism (60°) with an index matching oil. In Fig. 3(a), an ATR spectrum obtained for an SPP-PWG hybrid sample with a Cytop intermediate layer at 632.8 nm wavelength is shown. A salient feature in the observed spectrum is the appearance of a very narrow asymmetric line shape around 55° denoted as TM0F. We also see a dip corresponding to the TM1 PWG mode at 50.32°. Figure 3(a) demonstrates that the experimental spectrum of the SPP-PWG hybrid sample exhibiting the asymmetric line shape can be reproduced fairly well by the EM calculation, and the asymmetric line shape can fit to a Fano line shape function (Fig. 3(b)). The experimental results agree fairly well with the results of the EM calculations, and the physical origin of the appearance of the Fano line shapes is unambiguously identified by the coupling between the broad SPP mode and narrow PWG mode.
Fig. 3 (a, b) Fano and (c) EIT-like line shapes in ATR spectrum for prism/Ag/Cytop/PMMA structure with PMMA waveguide of height (a, b) d = 920 nm and (c) d = 803 nm. Reproduced with permission from Ref. [68].
Figures 3(a) and 3(c), as well as other ATR Spectra [66,67] (not shown), demonstrate clearly that the Fano resonance and the TM1 PWG mode shift to lower angles, as the PMMA WG thickness, d, decreases. In Fig. 3(c), the line shape of the sharp resonance which is located near the middle of the broad dip approaches that of EIT’s [1,62,63] or PIT’s [16] line shapes, which are characterized by a sharp peak at the middle of a broad resonance band. The giant FE, which can result from the Fano resonance, is discussed next.
4. Giant Field Enhancement for Sensing and Spectroscopy
Sensing is one of the most widely studied topics in the field of PIT and Fano resonance, and it is developing rapidely. Indeed, theoretical predictions showed a large sensitivity and figure of merit (FOM) for refractive index sensing for ring/disk nanocavities [69], plasmonic nanorices and nanobelts [70] and MIM coupled to resonators [71], and so on [72–75], with sensitivities and FOMs much larger than that of conventional SPR in some cases. This interest is driven by the development of high-sensitivity cost effective sensors.
In our recent work [76], we discussed theoretically the effect of resonance ATR line shapes, on the sensitivity to the bulk refractive index changes and FE of SPP-PWG structure in aqueous environment. It was demonstrated that the SPP-PWG structure can be optimized based on losses in the dielectric layers to achieve the maximum values of sensitivity and intensity enhancement. The optimal configurations with low loss spacer and WG layers exhibit deep and narrow resonances that result in a huge sensitivity. The sensitivity of ~105-fold higher than that of conventional SPR [77,78], and WG-SPR and guided-mode [79] sensors was estimated by FOM for s- and p- polarizations. Sharp resonances are accompanied by the giant FE of 107-fold on the surface of the WG.
The giant FE of the Fano resonance and PIT owing to the SPP-PWG hybrid structure is very much suited for applications. In our opinion, besides biosensing, enhanced Raman scattering and fluorescence spectroscopy are the major potential applications of the SPP-PWG structures. Such planar structures do not require nanofabrication processes, and alleviate the problem of fluorescence quenching [80] because the fluorophore sits far away – more than a micron away – from the metal surface. Figure 4 shows the (x, z)-plane, z is perpendicular to the structure’s plane, electric FE spatial distribution for four planar resonance structures that support propagating modes in air. The resonance excitation of the modes is performed by a p-polarized plane wave at the wavelength of 632.8 nm under oblique incidence. The electric field distribution at the resonance conditions was calculated using 2 × 2 transfer matrix method [81]. The FE factor is calculated as a ratio of the intensity of total electric field to the electric field intensity of the incident wave for a particular position.
Fig. 4 Maps of electric FE factor at resonance conditions for the experimental structures that support (a) SPP mode, (b) coupled S-SPP and SPP modes; (c) experimental; and (d) theoretical optimized structure that support coupled SPP and WG modes.
The spatial distribution of the FE for a conventional SPR structure is shown in Fig. 4(a). The structure is a 47-nm thick Ag layer attached to a BK7 glass prism. The structure supports excitation of a SPP mode propagating along the metal-insulator interface. We used the values of refractive indices for BK7 glass found in a database [82], for Ag from Ref [83]. The intensity distribution cross-section is demonstrated for the incidence angle of 43.038°. The intensity of electric field on the surface of the structure is enhanced by a factor of 1.2 × 102. The intensity-sensitivity of bulk refractive index changes of the conventional SPR structure, estimated by a FOM defined in Ref [76], is 1.2 × 102 RIU−1.
The spatial distribution of the FE for a MIM structure is shown in Fig. 4(b). The MIM structure consists of a BK7 glass prism, a Ag layer, a PMMA film, and covering Ag layer. The refractive indices of the materials and the thicknesses of the layers are taken from our previous experimental work [61]. The MIM structure supports an SPP mode at the Ag/air interface. The resonance excitation of the SPP mode for the incidence angle of 42.56° is characterized by the surface intensity enhancement of a factor of 1.0 × 102. The FOM for the MIM structure is estimated as 1.4 × 102 RIU−1.
Figures 4(c) and 4(d) illustrate the intensity distribution for electric field of the experimental and theoretically optimized SPP-PWG hybrid structures, respectively. The considered SPP-PWG hybrid structure consists of a SF11 prism, Ag, Cytop, and PMMA layers. The structure supports an SPP mode at the Ag/Cytop interface and a PWG mode in the Cytop/PMMA/air waveguide. The coupling of the modes in the Cytop layer results in a narrow Fano resonance in the reflectivity spectrum. The properties of the Fano resonance depend strongly on the parameters of the structure. The parameters of the experimental structure are taken from our experimental work [68]. The structure was optimized to demonstrate a Fano resonance, which could be easily observed; a feature that resulted in a low FE and sensitivity. The intensity distribution across the experimental structure is shown in Fig. 4(c) for the incidence angle of 55.272° which corresponds to the maximal FE at the structure surface in the Fano resonance region shown in Figs. 3(a) and 3(b). In addition, the field penetration depth is lower as compared to the previous structures due to the higher propagation constant of the excited mode. The field which is mainly localized in the PMMA waveguide decays exponentially from the center.
The calculated maximum FE in air at the surface of the optimized SPP-PWG hybrid structure achieves 1.3 × 106 (Fig. 4(d)). For the dielectrics in the optimized structure, we used the following refractive indices, 1.488 + i1.0 × 10−8 for PMMA and 1.346 for Cytop. The field distribution is obtained for the incidence angle of 52.875406729°. The thicknesses of Ag, Cytop and PMMA layers are 40 nm, 2000 nm, and 500 nm, respectively. Changes (not shown) in calculated ATR spectra, corresponding to an angular shift of 1.32 × 10−6 deg. of the resonance spectrum, can be easily observed for the optimized SPP-PWG hybrid structure due to the increase in the ambient refractive index of 1.0 × 10−6 RIU. The angular width and height of the Fano line shape in the reflectivity spectrum are w = 1.38 × 10−6 deg. and h = 0.349, respectively. The sensitivity by intensity is estimated by the FOM of 3.4 × 105 RIU−1. Such values unambiguously and clearly demonstrate the huge potential of Fano-type SPP-PWG hybrid structures for ultra-sensing and enhanced spectroscopy.
5. Conclusions
The work discussed in this paper has important implications in the field of nanophotonics, including the possibility of tuning the optical properties in plasmonic devices based on the control of dispersion relations in MIM structures, and the potential of ultra-sensing and giantly enhanced spectroscopy using PIT and Fano resonances in SPP-PWG hybrid structures. We hope that researchers of the nanophotonics and plasmonics communities will adopt the study discussed in this paper for their future work.
Acknowledgments
Partial support to this work from an Osaka University International Joint Research Promotion Program, the Handai project, is acknowledged.
References and links
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