1. Introduction

Surface plasmon polaritons (SPPs) are propagative electromagnetic waves highly confined to the interface between a metal and a dielectric [1]. This strong confinement, together with a resonant enhancement of SPP fields with respect to the exciting light field enables applications as surface plasmon resonance (SPR) sensors [2] or highly miniaturized photonic circuitry [3, 4]. However, a major drawback of SPPs is their rather short propagation length of typically a few tens of µm in the visible spectral range due to ohmic losses in the metal. A possible solution to this problem is the combination of (virtually lossless) dielectric waveguide modes for long-range light field propagation and SPP elements enabling highly confined local light field manipulation. According coupling geometries were investigated in the context of integrated SPR sensors [2, 5], integrated waveguide polarizers [6] and electro-optical waveguide modulators [7]. Here, we aim at the direct imaging of this coupling effect to analyze in detail the underlying effects. Therefore, we first introduce a hybrid waveguide system built from a metal-clad dielectric waveguide and a metal interface and analyze its properties in terms of an extended layer system. Then, we focus on the laterally resolved characteristics of the coupling of the dielectric and the plasmonic waveguide. We corroborate our experimental results with numerical simulations.

2. Extended layer system

 

Fig. 1. (Color online) Schematics of a metal-clad (a), a plasmonic (b) and a coupled metalclad/plasmonic waveguide (c). n and d denote the refractive index and thickness of the involved layers as explained in the text.

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We start with the analysis of a metal-clad waveguide as schematically shown in Fig. 1(a). A dielectric layer (refractive index n_f, thickness d_f) on a dielectric substrate (refractive index n_s) is covered by an opaque metal layer. By calculating the Fresnel factors of this layer system and retrieving the according solutions [8] we deduce the dependency of the effective mode index N (for definition see e.g. [9]) on the thickness d_f. For the calculation we use a vacuum wavelength of 514 nm, a glass substrate (n_s=1.505), the polymer SU8 (refractive index n_f=1.577) as waveguide material and silver (n_Ag=0.13+3.05i) as clad metal. The result for TM polarization (i.e. polarized in the xz-plane as defined in Fig. 1(b)) is shown in Fig. 2. The TM₀ mode is the SPP mode with a maximum field strength at the metal/dielectric interface, while the higher indexed modes have their maximum field strength inside the dielectric layer. The effective mode index of the TM₀ mode for d_f=0 is given by

where ε_s=n ² _s and ε_Ag is the real part of the dielectric function of silver. When including a SU8 layer, the effective mode index depends on its thickness, ranging from 1.73 (SPP at a silver/glass interface) to 1.84 (SPP at a silver/SU8 interface). The effective mode indices for the higher indexed modes range between the refractive indices of glass and SU8 (n_s<N_TMx<n_f with x=1,2,3,…).

 

Fig. 2. (Color online) Effective mode index N for the TM₀, TM₁, TM₂ and TM₃ modes as a function of the thickness of the SU8 layer d_f as depicted in Fig. 1(a) and for the TM_0′ mode as a function of d_c as depicted in Fig. 1(b), calculated for a wavelength of 514 nm. TM₀ and TM_0′ are SPP modes, TM₁, TM₂ and TM₃ are dielectric modes. For coupling the TM_0′ to the TM₁ mode at an effective mode index of 1.54 the necessary values of d_f and d_c can be read from the graph as 700 nm and 90 nm, respectively (dashed green lines).

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Next we aim at coupling the TM₀ (SPP) and TM₁ (dielectric) mode which requires a configuration allowing to match their respective effective mode indices. In an intermediate step we consider the geometry depicted in Fig. 1(b), i.e, a silver/SiO₂/air multilayer ( $n_{{\mathrm{SiO}}_2}=1.46$ ) as opposed to the silver/SU8/glass multilayer system in Fig. 1(a). This geometry sustains a SPP mode (TM_0′) that is characterized by a lower effective mode index as compared to the TM₀ mode (Fig. 2).

The combination of the geometry shown in Fig. 1(a), employed as a dielectric TM₁ waveguide, with the geometry shown in Fig. 1(b), employed as a TM_0′ or SPP waveguide, results in the layer system depicted in Fig. 1(c). In this geometry, the appropriate (and mutually independent) choice of the thicknesses d_f and d_c allows to match the effective refractive indices of the two guided modes. (The dashed green lines in Fig. 2 show how to read the values for the thicknesses from the graph for coupling at an effective mode index of 1.54.) In other words, the TM₁ mode mainly propagating in the SU8 layer on one (lower) side of the metal is coupled to a SPP mainly propagating on the other (upper) side of the metal. The strength of the mode coupling is controlled by the thickness of the metal layer.

For closer analysis we consider the layer system glass substrate/700 nm SU8/50 nm Ag/85nm SiO ₂ and calculate its dispersion relation, again using the method described in [8]. As plotted in Fig. 3(a) we find an anti-crossing like behavior of the two involved modes around a wavelength of 500 nm, a clear indication of mode coupling. For wavelengths shorter than this coupling wavelength the red and black curves represent the SPP (TM₀ mode) and the dielectric (TM₁) mode, respectively, whereas for larger wavelengths this assignment is inversed. For the sake of clarity, the solid and dashed blue lines illustrate the uncoupled modes. While in principle these could be individually recovered in the calculation by increasing the thickness of the silver layer, this would modify the properties of the individual modes so that the coupling condition could not be maintained. We thus chose to plot the dispersion curves for two different layer systems, each sustaining only one of the two modes whose characteristics are not changed as compared with the coupled system. These layer systems are SU8 substrate/50 nm Ag/85 nm SiO ₂ /air and glass substrate/700nm SU8/50 nm Ag/SiO ₂ superstrate for the SPP and the TM₁ mode, respectively. Figures 3(c)–(e) show the normalized field intensities for the uncoupled (c, d) and the coupled modes (e) at the coupling wavelength (500 nm). Note the field enhancement at the metal surface with respect to the field strength in the dielectrics which is evident in (e).

 

Fig. 3. (Color online) Calculated dispersion relations (a), propagation lengths L (1/e ² of the intensity) (b) and magnetic field intensity profiles at a wavelength of 500 nm (c)–(e). Red and black lines plot the coupled modes of the layer system as depicted in (e), the full and dashed blue lines plot the uncoupled SPP and TM₁ modes, as depicted in (c) and (d), respectively.

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Figure 3(b) shows the wavelength dependent intensity propagation length L (1/e ² of the intensity) of the coupled modes. The damping of the propagation is evidently dominated by losses of the SPP. For wavelengths below the coupling wavelength the propagation length is low for the mode represented by the red line because it is SPP-like, whereas for wavelengths above the coupling wavelength the propagation length increases as the mode turns to TM₁ type. At the coupling wavelength the propagation length for both modes is identical. The value of the coupling wavelength can be tuned mainly by changing the thickness of the SiO₂ layer (or by using dielectrics with different refractive indices). The strength of the coupling between the modes is mainly affected by the thickness of the metal layer. Stronger coupling generates a larger index gap at the coupling wavelength.

 

Fig. 4. (Color online) Grey scale plot of the calculated reflectance against wavelength and effective mode index (a) of the layer system sketched in (b): Glass substrate/700 nm SU8/50nm Ag/85nm SiO ₂ /100 nm Air/SF18 superstrate (glass prism)

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For retrieving experimental data corresponding to our theoretical considerations about the dispersion relation of an extended layer system we use angle resolved reflectance spectroscopy, which allows to probe directly the optical mode structure in the multilayer systems of interest. We prepared the layer systems by successive deposition of a 700nm thick SU8 (MicroChem, Newton, MA) layer by spin casting from solution and baking following the manufacturers instructions, a 50 nm silver layer by thermal evaporation and finally a 85 nm thick SiO₂ layer by electron beam evaporation onto a cleaned glass substrate. For the measurements the sample surface was mechanically pressed against a high index glass prism (SF18, n=1.734 at a light wavelength of 514 nm). Thereby, an air gap between the prism and the SiO₂ layer (maintained mainly due to dust particles) enables optical coupling to the multilayer structure [10], see Fig. 4(b).

Calculated reflectance data, retrieved by applying the Fresnel expressions to our multilayer are shown in the gray scale plot in Fig. 4. The dispersion relations of the coupled modes appear as local reflection minima, i.e., dark areas in the plot. For comparison the two uncoupled modes as shown in Fig. 3(a) are additionally plotted as the blue lines. The slight difference in the position (reflectance minima are shifted to longer wavelengths compared to the uncoupled modes) is caused by the presence of the glass prism needed for the reflection measurements. As the effective mode index N is directly related to the angle of incidence φ in the reflection measurement, N=n_Prism sin φ, a vertical cross-cut of the plot corresponds to the measured angle resolved reflectance acquired at a fixed wavelength.

The three angle resolved reflectance curves shown in Fig. 5(a) were measured with TM polarized light at three different light wavelengths 457 nm, 488nm and 514 nm. We find excellent quantitative agreement with the calculated curves in Fig. 5(b). In fact, the only parameter unknown from the experiment was the thickness of the air gap between the SiO₂ layer and the prism which therefore had to be fit. Best agreement with the experimental data was achieved for a value of 100 nm. Slight deviations between measured and calculated data may originate from the laterally varying thickness of the air gap and differences in the optical constants between the tabulated values used in the calculations (taken from Ref. [11]) and those of the silver layers used in the experiment. We conclude that our experiments clearly corroborate the theoretical findings of mode coupling in the investigated metal/dielectric multilayer structure.

 

Fig. 5. (Color online) Experimental (a) and calculated angle resolved reflectance curves of the layer system defined in Fig. 4(b); φ is the angle of incidence inside the SF18 prism; for calculations the width of the air gap was set to 100 nm.

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3. Laterally resolved measurements

We now turn to the experimental demonstration of this coupling effect by direct imaging. In analogy to an all-dielectric directional coupler the light field propagating in the metal/dielectric waveguide system is expected to perform lateral oscillations between the two waveguides. To observe this experimentally we prepared samples as sketched in Fig. 6(e). One half of the sample (left) consists of a purely dielectric waveguide (glass substrate/700nm SU8/85 nm SiO ₂) while the other half (right) is built from the coupled dielectric/plasmonic system as discussed above. A shadow mask was used for Ag evaporation defining the edge of the metal film onset (blue arrow in Fig. 6(e)) which is smeared out over typically 2µm.

Light is injected in the dielectric waveguide by edge coupling using a microscope objective [12] and propagates toward the metal edge. The parameters for the layer systems are identical to those discussed above (Fig. 4). To visualize the distribution of the optical field on top of the metal layer (mainly originating from the SPP-mode), about half a monolayer of Rhodamine 6G molecules was thermally evaporated on top of the whole sample. These fluorescing molecules convert a part of the optical near field to red-shifted light which is imaged using a microscope setup (including an edge filter) coupled to a CCD camera [13]. Figures 6 (a)–(c) show images acquired at excitation wavelengths of 458 nm, 488nm and 514 nm, respectively. Again, the blue arrow marks the onset of the coupled waveguide. (The curvy features on the metal edge are caused by defects of the shadow mask used in the evaporation process.) In all cases, we clearly observe modulations in the intensity along the direction perpendicular to the metal edge (maxima are marked by the green arrows). These oscillations are indicative of lateral oscillation of the energy between the SPP and the TM₁ mode.

The periods ΔL of the observed modulations are plotted in Fig. 6(d). For comparison we deduced the expected coupling length theoretically. To this end we applied the calculated difference of the effective mode indices ΔN for the two coupled modes at the respective wavelengths λ (see Fig. 3(a)) to the calculation of their beat i.e., coupling length $\Delta L=\frac{\lambda }{\Delta N}$ . This beat length reaches a maximum for the coupling wavelength which is 500nm in the considered case. Analogous to a dielectric directional coupler we expect the optical power to be completely transferred between the two waveguides only if the system is driven at the coupling wavelength.

 

Fig. 6. (Color online) Fluorescence microscope images for different excitation wavelengths ((a) 458 nm, (b) 488 nm, (c) 514 nm)) of the sample sketched in (e). Light is injected into the left end face (red arrow) and is guided to the edge of the metal film (blue arrow) which is the position from where the coupled waveguide system extends to the right. The red dots indicate the fluorescing dye molecules. The green arrows in (a)–(c) mark the intensity maxima. (b) and (c) share the same length bar with (a). (d) shows the coupling lengths ΔL as retrieved from the images (circles), compared with the according theoretical values (crosses).

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The fluorescing molecules on top of the sample mainly probe the field of the SPP-like mode. In order to retrieve information about the TM₁ like mode we included Rhodamine 6G molecules as well inside the SU8 waveguide by adding the molecules to the SU8 dilution before spin casting. To detect the fluorescence light emitted from inside the SU8 layer we imaged the sample through the glass substrate (bottom view). Some exemplary results of these measurements are shown in Figs. 7(a), (b), (d) and (e).

This figures show two different samples, one optimized for mode coupling at an excitation wavelength of 514nm (glass substrate/700nm SU8/55 nm Ag/90 nm SiO ₂) and one with strongly supressed coupling due to a smaller SiO₂ thickness (glass substrate/700 nm SU8/55 nm Ag/30 nm SiO ₂). From the fluorescence microscope images (Fig. 7(a),(b)) and the intensity crosscuts (c) of the non-coupled waveguide sample we find that the optical power remains in the TM₁ mode propagating from left to right. In top view the right half appears black (i.e., no intensity) because the fluorescence of the SU8 layer is shielded by the metal layer from detection, whereas in bottom view the whole image appears bright. The propagation of the mode is obviously only affected by the edge of the metal layer (Fig. 7(b)) which is probably due to scattering. For the coupled case, on the other hand, the top view image (Fig. 7(d)) looks quite different, though similar to the coupled waveguide sample shown in Fig. 6(b). There are however two main differences. First, the dielectric waveguide region (left half of Fig. 7(d)) appears bright due to the molecules inside the SU8 layer. Second, there is no beating of the coupled modes because in this case the coupling length is larger than the propagation length of the modes which means that the optical power couples from the dielectric waveguide mode to the SPP-like mode and is absorbed by the metal before it can couple back. This interpretation is further evidenced by the bottom view in Fig. 7(e), where the optical power in the SU8 guide quickly fades away to the right hand side of the metal edge. For quantitative illustration, Figs. 7(c), (f) plot cross-cuts along the horizontal directions of Figs. 7(a), (b), (d) and (e).

 

Fig. 7. (Color online) Fluorescence microscope images of two different samples, one designed for coupled the other one designed for non-coupled wave guiding as viewed from top and bottom ((a), (b) and (d), (e), respectively). (c) shows crosscuts through images (a) (blue line) and (b) (black line), (f) shows crosscuts through images (d) (blue line) and (e) (black line). Fluorescing molecules are deposited on top of the sample as well as dispersed in the SU8 layer. The insets sketch the paths of the optical power.

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Finally, we investigate samples which are laterally structured in two dimensions, reducing the metal layer extension and hence the coupled waveguide region to a circular area defined by shadow mask evaporation. Figure 8(e) shows a sketch of the geometry in top and side view. Again, light is injected into the end face of the dielectric waveguide using a microscope objective and the propagation of the mode is visualized by Rhodamone 6G molecules evaporated on top of the sample and embedded in the SU8 layer as described above. Figures 8 (a)–(d) show the resulting fluorescence microscope images. In all images the light field propagates from left to right. As the coupled waveguide system was optimized for an excitation wavelength of 514nm (glass substrate/700nm SU8/50 nm Ag/90 nm SiO ₂) in (a) and (c) the optical power couples to the SPP mode which can be seen as bright sickle shaped area of the metal disk. The diameters of the metal disks which are 75µm in the case of (a) and 20µm for (c) are indicated by the blue arrows. Behind the metal disk (right part of the image) remains a dark region which can be interpreted as the shadow of the metal disk since the guided light is absorbed by the metal. Figures 8(b) and (d) show the fluorescence images for the TE polarized mode. In that case no SPP mode can be excited and the dielectric mode propagates below the metal disk almost unhindered. The presence of the dark regions around the circular metal waveguide as observed in (a) and (b) is yet unclear. As it can be observed in a conventional reflection type fluorescence microscope as well it is most likely due to fluorescence quenching.

 

Fig. 8. (Color online) Fluorescence microscope images (a)–(d) of samples with a geometry depicted in (e). The diameter of the silver disk is 75µm for (a) and (b) excited with TM and TE polarized light, respectively and 20µm for (c) and (d) again forTM and TE polarization. The blue arrows in (a) and (c) indicate the diameter of the disks, the red arrows in (e) the position and direction of the in coupled light.

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These results illustrate the possibilities of laterally structured coupling geometries of dielectric and SPP waveguides. As an application one can think of miniaturized waveguide polarizers as realized with the 20µm disk shown in Figs. 8(c) and (d).

4. Discussion

We have demonstrated a concept for coupling dielectric waveguides to plasmonic waveguides theoretically and experimentally by direct imaging the lateral oscillations of the guided optical power between the two involved modes. Possible applications could exploit the strong difference in the spatial profile of the electromagnetic field between a dielectric and a plasmonic mode. In the dielectric mode, the field is distributed in the core, whereas the plasmonic field is concentrated at the metal/dielectric interface (Figs. 3(c) and (d)). As a SPP can thus be seen as a light concentrator it can be used to enhance the interaction of light with matter, as it is done for instance in surface plasmon resonance sensing [2]. On the other hand, the propagation length of SPPs is rather short and not useful for macroscopic light transport. The system discussed here could be seen as a hybrid dielectric/plasmonic platform for enhanced light/matter interaction: Light injected into an integrated dielectric waveguide propagates for several centimeters and is at a certain position converted to a SPP in order to enhance the interaction with matter. This could be for sensing applications as well as for plasmonic functionalities as reflection [14], focusing [15] or modulation [16] which have been demonstrated in the last decades. Finally, the SPP couples back to the dielectric mode carrying the light to further applications or a detector.

Our study aimed at the proof-of-principle rather than to optimize the coupling system. It should be noted that in the blue/green spectral band which we have chosen here for sake of experimental convenience (readily available evaporable dyes) SPP damping is rather strong. The according losses could be strongly reduced by choosing the red part of the spectrum, as illustrated in Fig. 9. Compared to a coupling wavelength of 510nm (Fig. 9(a)) the propagation lengths are increased for a coupling wavelength of 750nm (Fig. 9(b)), leading to reduced losses per coupling cycle below 40%.

 

Fig. 9. (Color online) Propagation length L and coupling length ΔL of the coupled waveguide system for the coupling wavelengths 510 nm (a) and 750 nm (b). The values were calculated from dispersion diagrams corresponding to the curves shown in Fig. 3(a).

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