1. Introduction

Surface plasmon-polaritons (SPPs) are transverse-magnetic (TM) surface electromagnetic waves coupled with the collective oscillation of electrons on a metal-dielectric interface [1]. Plasmonic waveguides and related functional components with highly confined modes (subwavelength lateral confinement) have shown great potential of application in ultra-compact integrated circuits with large bandwidth as well as fast data transferring speed, which overcome the shortages of limited data processing speed of integrated electronic circuits and the diffraction-limited field confinement in traditional integrated optical circuits [2–5]. In recent years, various types of plasmonic waveguides have been developed and investigated, such as metal stripes [6], nanoparticle chains [7], nanowires [8], grooves [9], wedges [10], slot waveguides [11], and the dielectric-loaded surface plasmon-polariton waveguides (DLSPPWs) [12]. Among these SPP waveguides, DLSPPW consisting of a dielectric stripe deposited on a metallic film has attracted increasing interests due to its good mode confinement (lateral field confinement by the dielectric stripe in addition to the intrinsic subwavelength vertical confinement of the SPPs at the metal-dielectric interface), relatively low propagation loss, and the comparably simple planar fabrication process [12–15].

In previous works [12–15], the properties of DLSPPWs have been well studied, including the dispersion relations and field distributions of the confined modes, the propagation and bending losses, and some functional applications. However, few works have dealt with the efficient excitation of SPP modes in the DLSPPWs, such as the coupling of free-space propagating light to the waveguide mode. The direct use of some traditional excitation methods is not so straightforward. For example, the prism-coupling method (in Kretschmann configuration) has been commonly used for efficient excitation of SPPs on planar metal surface under oblique incidence [16]. But it is not readily adapted to integrated circuit because an off-chip coupling element (i.e., the prism) is involved and the excited SPPs are usually not focused to couple to the DLSPPW. To achieve the end-fire coupling, Gosciniak [17] et al. employed a single-mode fiber to illuminate the end facet of a DLSPPW, but it requires fine alignment of the fiber tip to the small area (μm² scale) of the DLSPPW facet. Another method is to use microscope objective to focus light onto the facet of DLSPPW [18–20]; but it still has the alignment problem because the adjustment of the overlapping of the μm-size focused light spot with the subwavelength waveguide mode of the DLSPPW is also very difficult. Therefore, it is the motivation of our work to design an integrated SPP launcher for the DLSPPW to achieve high coupling efficiency, under the illumination of external light source.

Recently, various plasmonic lens structures have been proposed for exciting and focusing SPPs on metal-dielectric interface by use of the interference of SPPs [21–25]. It is shown that plasmonic lens consisting of ring slits perforated in metallic film can efficiently couple free-space propagating light into a sub-diffraction-limit focusing spot of SPPs. In this paper, we propose a semi-circular plasmonic lens functioning as an integrated SPP launcher for DLSPPW. The input facet of the DLSPPW is placed in the focal plane of the plasmonic lens so that the excited and focused SPPs can be efficiently coupled to the waveguide mode of the DLSPPW. The coupling performance is analyzed theoretically and numerically, which shows that high coupling efficiency can be achieved by matching the profile of the focused SPP field with the DLSPPW mode in this geometry. By adding multiple semi-circular slits, the output power can be further improved. Furthermore, the DLSPPW launcher is found dependent on the incident angle as well as the polarization of the illuminating light. Therefore, by proper design, the structures may function as SPP switches and multiplexers, which have potential applications in plasmonic circuitry. These properties will be investigated in detail in the following sections.

Note that, in the whole work, we assume backside illumination for the structure (i.e., the incident light is from the substrate side). This is to avoid the crosstalk between the incident field and the excited SPPs, so that the whole process of exciting, focusing, coupling, and waveguiding of the SPPs can be observed clearly. Otherwise, if the incident light is from the front side and the light spot is not small enough to be far away from the DLSPPW, the light would be a source of noise by exciting SPPs directly on the end of the DLSPPW via scattering [26]. But, if the spot and the plasmonic lens are far from the DLSPPW, the propagating loss of the SPPs as well as the total device size would increase, so that the coupling efficiency of the SPPs into the DLSPPW mode would decrease, which is not expected. So, the backside illumination is preferred.

2. Geometry and principle of the device

The schematic geometry of the integrated plasmonic semi-circular launcher for DLSPPW is shown in Fig. 1(a) . The working wavelength is chosen as λ ₀ = 1.55 μm without loss of generality. One or several semi-circular slits with 300 nm width are perforated into a 200 nm thick silver film (with dielectric constant of ε _Ag= −129.1+3.283i at λ ₀ = 1.55 μm) deposited on a silica substrate (with n _silica = 1.5) to function as the plasmonic focusing lens. A dielectric (e.g., polymer with n _polymer = 1.5) stripe is fabricated directly on the silver surface to form the DLSPPW, whose input facet is in the focal plane (yz plane) of the semi-circular plasmonic lens. The geometric aspect ratio of the polymer stripe is chosen reasonable, with width of 500 nm and height of 600 nm [15], with which the DLSPPW has good mode confinement property at this wavelength and is achievable with standard nanofabrication techniques such as electron-beam lithography.

 

Fig. 1 (a) Geometry of the proposed integrated plasmonic semi-circular launcher for DLSPPW. (b) Top view of the plasmonic lens with a single semi-circular slit. (c) Cross section of the DLSPPW waveguide.

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The principle of the DLSPPW launcher is described below. Since the silver film thickness is much larger than skin depth, the incident light cannot penetrate through the film except in the region where the slits are perforated. Therefore, when light illuminates the structure from the back side, SPPs can be excited on the air-silver interface via scattering of the incident light on the slits. With proper arrangement of the slit spacing, the SPPs excited by adjacent slits may get constructive interference when propagating on the air-silver interface, which leads to an intense focal spot at the center of the input facet of the DLSPPW [25]. If the spatial field distribution of the focal spot could closely match the DLSPPW mode, then high coupling efficiency of the SPPs into the waveguide mode could be achieved [27].

For the convenience of our analysis below, we define three planes as shown by the dashed rectangles in Fig. 1(a): an input plane (in xy plane) covering the plasmonic lens area, a focal plane (in yz plane) at the focusing center of the plasmonic lens and containing the input facet of the DLSPPW, and an output plane (in yz plane) containing the output facet of the DLSPPW. Then by calculating and comparing the fields and power flows in the three planes, we can evaluate the coupling performance of the SPP launcher.

3. Coupling performance of the SPP launcher

First we consider a simple plasmonic lens consisting of only one semi-circular slit, as shown in Fig. 1(b), where r _in = 2 μm and r _out = 2.3 μm are the inner radius and outer radius of the slit, respectively. To begin with, we analyze the focusing property of the plasmonic semi-circular lens and the fundamental mode in the DLSPPW separately, by considering each element alone. The simulation was performed with commercial three-dimensional finite-element method software COMSOL MULTIPHYSICS. Figure 2(a) shows the calculated time-averaged power flow distributions in both the input plane and the focal plane under linearly polarized light (with electric field vector parallel with x axis) at backside normal incidence. Since only TM-polarized light component can excite SPPs, it is reasonable to see that the strongest (weakest) excitation of SPPs takes place at the center (ends) of the semi-circular arc where the slit is perpendicular (parallel) to the x axis. Figure 2(b) shows the time-averaged power flow distribution of the fundamental mode in the DLSPPW. The two fields in Figs. 2(a) and (b) resemble each other by viewing their profiles in the focal plane, especially the confinement on the silver-air surface in the vertical direction and the maximum intensity at the center. This implies that efficient coupling of the focused SPPs into the DLSPPW mode may be achieved. The coupling efficiency can be estimated by the overlapping integral below [28],

 

Fig. 2 Simulated field distribution of time-averaged power flow in the considered structures. (a) Field distributions in both the input plane and focal plane (the inset) for a stand-alone semi-circular plasmonic lens. The arrow indicates the x-polarized incident light. (b) Field distribution of the fundamental mode in a stand-alone DLSPPW. The inset shows the field distribution in the focal plane. (c) Field distribution in the whole structure including both the SPP launcher and the DLSPPW. (d) Top view (in xy plane) of the field distribution in (c).

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Then we performed simulation for the whole structure containing both the SPP launcher and the DLSPPW. Note that in numerical modeling we terminate the output plane with absorption boundary condition to approximate the semi-infinitely long DLSPPW. Figures 2(c) and (d) present the field distribution in the structure. As can be seen, highly confined field (in both vertical and lateral directions) appears in the focal plane of the plasmonic lens and then propagates in the DLSPPW, meaning that most of the energy of SPPs excited in the input plane can be focused and coupled into the waveguide. Therefore, the plasmonic lens serves as an efficient SPP launcher that transfers energy from far-field light source to localized SPP mode in the DLSPPW.

In order to study the coupling efficiency more quantitatively, we need to calculate the integrated power flow in the three defined planes, i.e., P _inc in the input plane over an area of 2r _out×r _out,P _focus in the focal plane over an area of 1.5×1μm², and P _out in the output plane over an area of 1.5×1μm² after the coupled SPPs propagate 7μm away in the DLSPPW. Then the conversion efficiency of incident light to SPPs can be characterized by η _spp=P _focus/P _inc=1.36%, which is relatively low, meaning that only a small portion of the incident energy is transferred to the focused SPPs on the air-silver interface. This is reasonable because the scattering excitation of SPPs via a slit or a defect is very weak [29] and the backside illumination further decreases the excitation efficiency. However, if we consider the coupling efficiency of the focused SPPs to the DLSPPW mode, we can obtain η′ _mode=P _out/P _focus=61.3%. Note that the calculated coupling efficiency includes the intrinsic SPP propagation loss in the DLSPPW. If we take into account the propagation loss by exp(2k ₀ n″L), where L=7μm is the propagation distance between the focal plane and output plane and n″ is the imaginary part of the calculated effective refractive index of the fundamental DLSPPW mode (which is solved as n _eff=n′+in″=1.248+0.002733i), then the corrected coupling efficiency η _mode=71.59%, which agree with our theoretical prediction by Eq. (1). It shows that the plasmonic semi-circular lens can indeed act as an efficient SPP launcher for DLSPPW. Moreover, if we consider visible wavelength and neglect the contribution of creeping wave [30] at this wavelength, even higher coupling efficiency can be obtained.

So far, we have considered only a single semi-circular slit and, hence, from a practical point of view, it is natural to think about improving the output power flow by increasing the number of slits to have constructive interference of SPPs between them [24,25]. In principle, if the radial distance between the slits is chosen properly to match the parallel (in xy plane) wavevector component of the incident light so that the constructive interference condition is satisfied, the output power can be readily increased by adding additional semi-circular slits and until the radius of the outermost semi-circular slit is greater than the propagation length of the SPPs [31]. The semi-circular slits are arranged concentric as shown in Fig. 1 (a), with the radial distance between the adjacent slits as λ _spp (λ _spp is the wavelength of SPPs on the air-silver interface, which is calculated as ${\lambda }_{\text{spp}}={\lambda }_0\sqrt{\left({\epsilon }_{\text{Ag}}+{\epsilon }_{\text{air}}\right)/{\epsilon }_{\text{Ag}}{\epsilon }_{\text{air}}}=1.544\text{μm}$in this case). In Fig. 3 , we calculated the time-averaged power flow integrated in the output plane P _out and the DLSPPW coupling efficiency η _mode with respect to the number of semi-circular slits; the inset shows the power flow distribution for a SPP launcher with four semi-circular slits. It is seen that the integrated power flow in the output plane already increases by one order of magnitude when the number of slits increases to four, while the coupling efficiency of the focused SPPs to the DLSPPW mode remains the same (i.e., η _mode=71.59%). This means that higher power flow can be coupled into the DLSPPW just by increasing the number of slits.

 

Fig. 3 Normalized time-averaged power flow integrated at the output plane P _out and the DLSPPW mode coupling efficiency η _mode with respect to the number of semi-circle slits. The inset shows the power flow distribution for an SPP launcher with four semi-circular slits.

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4. Tunable SPP coupling by modulating the incident angle and polarization

Having seen that the plasmonic semi-circular lens can be used as an efficient integrated SPP launcher for DLSPPW under linearly polarized light at normal incidence, in the following, we proceed to analyze how the coupling performance can be tuned by changing the incident angle and polarization, which introduces a phase shift to the excited SPPs emitted from the semi-circular slits.

We first incline the x-polarized incident light in the yz plane by an angle θ with respect to the z axis as shown in Fig. 4(a) . A phase delay of the incident wavefront arriving at the circumference of the semi-circular slit arises due to the presence of the in-plane wavevector component k _inc,y=k ₀ sinθ, where k ₀ is the wavenumber in free space. Since SPPs are excited only in the radial direction (i.e., perpendicular to the tangent of the slit), the phase delay of the incident wave also affects its radial component, which leads to a phase shift of the excited SPPs on the circumference of the slits. Consequently, the interference of the phase-shifted SPPs propagating from different parts of the semi-circular slit towards the circle center would produce a shift of the focal spot along the y axis. Simulation results show that the focal spot can be moved upward or downward by 1.13μm along the y axis on the air-silver interface if θ is changed, for example, to +20 or −20 degrees, respectively. This property may be utilized to achieve active switching between different DLSPPWs. For example, if we place three DLSPPWs with their input facets spaced by 1.13μm in the focal plane, then the SPPs could be launched into different DLSPPWs simply by changing the incident angle, as shown in Figs. 4(b)-(d), with coupling efficiency of 60.79%, 71.58% and 60.79% respectively. Note that although we have inclined the upper and lower DLSPPWs by 15 degrees with respect to the central one to minimize their cross-coupling, there is still some slight coupling into the neighbor waveguides. Nevertheless, the switching function is demonstrated unambiguously.

 

Fig. 4 (a) Geometry of an incident-angle-switching SPP launcher for multiple DLSPPWs. (b)-(d) Simulated time-averaged power flow distribution on the air-silver surface of the device under x-polarized light with incident angle θ = +20°, θ = 0°, and θ = −20°, respectively.

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Furthermore, we would like to check the dependence on polarization. As is known, left- (LCP) or right-circularly polarized (RCP) light can naturally introduce phase change in its wavefront [32]. Thus, if the illumination is LCP or RCP wave, the focusing spot in the focal plane of the semi-circular launcher may also shift, even under normal incidence. By simulation, we found a shift of the focal spot by about 600nm in y direction upward or downward, depending on the RCP or LCP illuminations, respectively, as shown in Fig. 5(b) . Therefore, we can also utilize this property to achieve switchable SPP launching for different DLSPPWs (but under normal incidence in this case), as shown in Fig. 5(a). Two DLSPPWs are symmetrically placed with respect to the x axis with their input facets in the focal plane and spaced by a distance of 600nm. The two DLSPPWs are also rotated by 15 degree to reduce the cross-coupling. The calculated time-averaged power flow distributions on the air-silver surface are shown in Figs. 5(c) and (d) with coupling efficiency of 56.43%. Again, the principle of switchable launching is verified, although there is still little cross-coupling noise between the DLSPPWs.

 

Fig. 5 (a) Geometry of a polarization-switching SPP launcher for multiple DLSPPWs. (b) Simulated power flow distribution in the focal plane on the silver surface for LCP (dotted line) and RCP (solid line) illuminations. The insets show the power flow distribution in the xy plane on the silver surface for the two cases without including the DLSPPWs. (c) and (d) are the simulated time-averaged power flow distribution in xy plane on the silver surface for LCP and RCP illuminations, respectively, by including the DLSPPWs.

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5. Conclusion

We have proposed and analyzed the integrated SPP launchers for DLSPPW based on the plasmonic semi-circular lens, which can convert far field light to SPPs and then focus and couple the SPPs efficiently into the DLSPPW. Numerical simulations show that high coupling efficiency can be achieved via the highly matched spatial field distribution of the SPP focal spot with the DLSPPW mode in the focal plane. The coupled power flow into the DLSPPW can be further improved by adding multiple semi-circular slits. Furthermore, it is found that selective/switchable launching of SPPs into different DLSPPWs can be realized by simply changing either the incident angle or polarization. These properties can be utilized to realize integrated SPP switches or multiplexers, which may have potential applications in plasmonic circuitry and biosensing.