1. Introduction

Surface plasmon polaritons (SPP) result from the coupling between the propagation of electromagnetic waves and the oscillation of the conduction electrons at metal surfaces [1,2]. Such coupling requires the propagation constant of SPP to be larger than that of the electromagnetic wave in free space. This results in the confinement of the electromagnetic field at metal surfaces, as well as the challenge of exciting SPP with electromagnetic waves in free space. The confinement of SPP at optical frequencies and the possibility of manipulating its propagation with subwavelength structures on metal surfaces offer a great potential in communication and sensing applications. Therefore, the excitation of SPP on metal surfaces at desired locations becomes the first challenge for the applications of SPP, and it has inspired an intense and continuous effort to develop compact and effective artificial structures to couple light in free space and its SPP on metal surfaces [3–9].

The aim of the development of the structure for launching SPP has been focused on the directional coupling of SPP on metal surfaces, and the compactness of the device suitable for subwavelength scale control of SPP. Most of the SPP launching structures reported in the literature consist of a grating structure [10–14] or nano-slit accompanied with auxiliary structures such as a second neighboring groove [15–18], or an array of regular periodic grooves [19]. For the case of a slit with auxiliary structures, the auxiliary structures break the symmetry of the system, thus leading to directional coupling of SPP. For the drive of device miniaturization, the approach of making slit/groove with asymmetric sub-structures has also been investigated [20–25], and has been proved to be an effective approach for coupling the SPP waves. To date, the majority of these slit structures were fabricated with focus ion beam (FIB) lithographic tools. Although FIB is superb in defining the lateral dimensions and positions of the designed structure in nanoscale by simply removing locally the full thickness of the metallic film deposited on the substrate at desired location, it is intrinsically inadequate for making planer sub-structures by removing partial thickness of the film due to the fact that ion bombardment of the film results in substantial roughness on the final surfaces [20–21]. This would potentially leads to lesser control of the vertical dimension of the structure as well as loss of signal due to scattering of SPP from such surface roughness. Furthermore, FIB tools are not quite suitable for scale-up production nor are they as accessible to general researchers. Therefore, it is beneficial for the applications of SPP waves to develop methods of fabricating asymmetric nano-groove/slit structures that can achieve the high lateral precision required for the directional coupling of SPP but the circumvent the limitations of the FIB lithographic tools.

In this report, we present our results of directional coupling of SPP with asymmetric slit structures that we design and fabricated with electron beam lithography (EBL) and glancing angle deposition technique (GLAD) [26]. EBL provides the spatial resolution needed for lateral precision of the slit size and location, and GLAD of Ag films implements the asymmetric structure of the slit with smooth surfaces. We illuminated the slit with a focused 532nm laser beam and characterized the intensities of SPP excited on the Ag/air interface with near field scanning optical microscopy (NSOM). We found that by varying the width of the overall slit structure we can achieve directional coupling to launch SPP on either side of the slit, with the optimal extinction ratio of 79000 ± 18000. We also conducted numerical simulations of the coupling of SPP with our slit structures using finite difference time domain method (FDTD). Our simulation qualitatively reproduces the experimental results. Detailed analysis of the simulated E-field distribution and the time-averaged Poynting vector distribution in the slit indicates that SPP excited on the Ag surface of the sub-slit structure plays an important role in shaping the energy flow of the incident light, which leads to the directional coupling of SPP we observed.

2. Experiment and simulation

2.1 Sample fabrication

Figure 1(a) shows the design of the asymmetric slit structure and the scheme of coupling the incident laser beam to SPP on the air/silver interface. The description of the fabrication methods follows. We first spin-coated a layer of PMMA film on top of an ITO-coated glass substrate. The thickness of the PMMA film t_PMMA was controlled with the spin rate. Before e-beam exposure, the PMMA film was soft-baked at 180 °C for 5 minutes. We then patterned an array of slit structure on the PMMA film with EBL as shown in Fig. 1(b). Finally, we applied GLAD method with a 50° incident angle for the Ag flux to deposit a layer of Ag film with t_Ag∼100 nm on top of the PMMA film in vacuum with a thermal evaporator. After Ag deposition, the sample was gently annealed at 140 °C in air for 8 min. Figure 1(b) shows the scanning electron microscopy (SEM) image of the slit array. Each slit is 4 µm long with the width w_p varied from λ/8 to 18λ/8 in unit of λ/8, where λ ( = 500 nm) is the wavelength of the SPP on Ag/air interface excited by 532 nm wavelength laser beam. The horizontal distance between neighboring slits is 30 µm, and their vertical spacing is 10 µm from edge to edge. Figure 1(c) shows the SEM image of the structural details of the asymmetric slit with overall width (w_p) of 960 nm. It can been seen that within the slit there is a sub-planer pad that breaks the symmetry of the structure, leaving a narrow air gap on the right side of the slit structure (w_S). For ease of description, in this paper we refer to the left hand side of the slit, where the Ag film is continuous from the top to the bottom pad, as the “left side,” and the opposite side, where a gap opening remains in the Ag film, as the “right side.” Figure 1(d) shows the atomic force microscopy (AFM) height line profile of the same slit. It is clear that surface roughness of the Ag pad in the slit structure is comparable to that of the pristine Ag film, and edges of the features are well defined. Note that for slits whose overall width w_P is smaller than 240 nm the shadowing effect from the GLAD deposition resulted in the absence of the Ag pad inside the slit. The Ag film only decorates the left side wall of the slit. Besides the overall width w_P of the slit structure, we also explored the effect of the PMMA film thickness t_PMMA on the performance of the slits by varying t_PMMA from ∼200 nm to 300 nm.

 

Fig. 1. Sample design and characterization. (a) Schematics of the asymmetric slit design and the scheme for coupling the incident light to SPP on the Air/Ag interface. The dashed arrow at the top indicates the orientation of the incoming Ag flux during the glancing angle deposition of the Ag film on the sample. (b) The SEM image of the array of asymmetric slits fabricated on an Ag film. The horizontal spacing between neighboring grooves is 30um. (c) SEM image of a 960 nm (w_P) wide slit. The vertical length of the slit is 4um. (d) AFM height line profile extracted from the AFM image (insert) scanned from the slit structure shown in (c). The RMS surface roughness of the Ag film is 8.6nm on the top surface, and 6.8nm on the Ag pad in the slit.

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2.2 Excitation and characterization of SPP intensity distribution

We excited SPP on the Air/Ag interface with a 532 nm wavelength laser beam illuminating the slit. The sample was placed on the sample stage of a NSOM system (Nanonics Multiview 2000 NSOM system). We illuminated the slit with the laser beam focused by a 10x objective lens from the backside of the sample, as indicated in Fig. 1(a). The total power of the laser beam measured at the sample position is 100 µW, and the diameter of the laser spot is about 4um. The polarization of the laser beam was set to be perpendicular to the slit edge. An NSOM tip with 200 nm aperture was used to scan the top surface of the sample in tapping mode to collect the near field signal of SPP and to characterize the surface morphology simultaneously. We started scanning the sample at a distance 2 µm away from the slit edge to avoid scanning over the slit structure because of the tip instability presumably resulted from the strong interaction between the tip and the incident light directly transmitted through the slit. We further extracted intensity line profiles from the NSOM images to estimate the SPP intensities exited with the slits.

2.3 Numerical simulation

To understand the origin of the dependence of the SPP intensities on the slit structure, we carried out 2-dimensional finite difference time domain method (FDTD) [27] calculations to simulate the interaction between the incident light and the slit structures. We compared the simulated electric field intensity |E|² on the surface to the SPP signal intensity measured from the experiment. We also calculated the time-averaged Poynting vector distribution in the slit structure according to the results of the simulation.

3. Results

Figure 2 shows the results of the NSOM measurement and the intensity line profiles extracted from the NSOM images of the SPP exited with slit structures on the sample with t_Ag= 101 nm and t_PMMA = 302 nm. Figures 2(a) and 2(b) show the NSOM images of the SPP intensity (I_SPP) distribution on the left side and the right side of the 510 nm wide slit, respectively. It is clear that SPP was preferentially coupled toward the left side. The line profiles extracted from the images in Figs. 2(a) and 2(b) are shown in Figs. 2(c) and 2(d), respectively. It is clear that I_SPP decay exponentially with distance. Figures 2(e) and 2(f) show the I_SPP distributions of a wider slit, whose width is 680 nm. Again, the coupling is directional, and for this slit it is toward the right. The intensity line profiles show while I_SPP expands over 20 um on the right side of the slit,but on the left side I_SPP dramatically decayed to the level of background noise over the range of 6 um. Further increasing the slit width to 890 nm, the coupling of SPP is again toward the right as shown in Figs. 2(i) and 2(j), and the corresponding intensity line profiles are shown in Figs. 2(k) and 2(m), respectively. Figure 2(n) shows the summary plot of I_SPP measured at a distance of 6 um from the edges of the slit on both sides as a function of the slit width w_p. For w_p smaller than 400 nm, I_SPP are comparable on both sides with a local maximum occurs at slit width of 370 nm. Above 400 nm, a local maximum occurs at w_p = 510 nm for I_SPP toward the left (I_SPP,L), while a broad local minimum occurs for I_SPP toward the right (I_SPP,R), leading to the directional coupling of the SPP waves toward the left. As w_p further increases, I_SPP,L becomes quite small, and I_SPP,R varies quasi-periodically with w_p reaching local maxima at 690 nm and 890 nm. This results in the directional coupling of the SPP waves toward the right for these slits. To make contact with the literature, where I_SPP,Land I_SPP,R at distances about 20 or 30 µm away from the slits are compared and is expressed in terms of the extinction ratio I_SPP,R / I_SPP,L, we calculated the extinction ratio with the background subtracted SPP signal intensities at 15um away from the slit edge, and the results are shown in Fig. 2(m). The ratio reaches a value of 79000 ± 18000 for optimal right coupling at slit width of 690 nm. This results from the rather fast decay of the left propagating SPP wave down to noise level, as shown in Fig. 2(g). For the optimal left coupling scenario, a moderate extinction ratio of 0.2 was obtained for the slit with width of 510 nm. The results shown in Fig. 2 demonstrate that by choosing an appropriate slit width w_p the asymmetric slit structure fabricated with EBL and GLAD of Ag film allows the coupling of incident laser beam to SPP on the Ag surface toward the left or right as desired, with an optimal extinction ratio near 8×10⁴ for the right coupling.

 

Fig. 2. Near field scanning optical microscopy images of SPP intensity distribution near the slits. (a), (b) are the NSOM images scanned from the area on the left side and the right side of the slit with w_p = 510 nm, respectively. Similarly (e) and (f) are the images scanned from both sides of 690 nm slit, and (i) and (j) from 890 nm slit. The color scale in (a) applies to all images. (c), (d), (g), (h), (k), and (m) are intensity line profiles (solid curve) extracted from the section in between the horizontal blue lines in the images right above. The dash curves are the results of fitting the data with the function I_SPP(x)= I_B+A·e ^-(x-x0)/λ . (n) I_SPPmeasured at positions 6 um from the edge of the slit as a function of slit width w_p, The red and blue filled circles are the results for the left and the right sides of the slit, respectively. The dashed curves are for visual guidance. (m) The ratio of I_SPP,R /I_SPP,L plotted as a function of slit width w_p for experiment (filled squares) and simulation (open squares). The error bars of the experimental extinction ratio are covered by the symbols.

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To understand the origin of the directional coupling of SPP with the asymmetric slits we fabricated, we carried out FDTD simulations for the interaction between the incident light and the slit structures. We modeled each slit as an infinitely long slit and performed two-dimensional simulations. The incident light was modelled as a plane wave with its polarization normal to the slit (transverse-magnetic field configuration). Figure 3(a) shows the distribution of the electric field intensity |E|² in a cross-sectional view of the 510 nm wide slit structure. It is clear that the |E|² intensity near the Ag surface on the left hand side of the slit is much stronger than that on the right hand side, i.e. the slit couples SPP toward the left. Figures 3(b) and 3(c) shows the cross-sectional view of the |E|² distribution of 690 nm and 930 nm slit structures, respectively. It is clear that these two wider slits couple the SPP waves toward the right. Figure 3(d) plot the |E|² intensities of the SPP waves on both sides estimated at 6 um from the slit edges. Compared to the experimental results in Fig. 2(n), the simulation qualitatively reproduces the directional coupling of the SPP waves of the asymmetric slits with w_p ≥ 400 nm, and the optimal slit widths for the directional coupling agrees with the experiment. Furthermore, the slit width dependence of the |E|² for the right-propagating SPP wave show quasi-periodic behavior, with the period roughly equal to 250 nm, which is half of the SPP wavelength the Ag/air interface from the 532 nm laser beam. The suggests that the SPP wave excited by the laser beam on the Ag structures in the slit plays an important role in the directional coupling of the SPP on the top Ag surface. The extinction ratio I_SPP,R / I_SPP,L is also calculated with |E|² intensities at 15 um away from the slit edges, and for the purpose of comparison it is shown in Fig. 2(m). It is clear that the simulation reproduces the experiment qualitatively. In the simulation, for optimal left coupling with w_p = 510 nm, the ratio can reach as low as 0.007, and over 200 at w_p = 690 nm for the right coupling.

Besides nearfield analysis, it has been reported that the energy flux flow of the electromagnetic waves in term of the Poynting vector distribution has also revealed intriguing insight about the excitation of SPP with metallic nanostructures [28–29]. Figure 4 compares the instantaneous distribution of the simulated E-field vector and the time-averaged Poynting vector distributions in the slit structures with optimal directional coupling widths. For the narrow slit in Fig. 4(a), where the left wall of the PMMA slit was coated with Ag films and has negligible bottom pad structure, the incident light interacts with the bottom of the Ag film on the sidewall and excited SPP waves, which results in a near field whose polarization is the same as that of the incident light. The Poynting vector distribution shown in Fig. 4(b) indicates that while the energy flux of the incident light mainly flows upward in the slit, however the amplitude of the flow is strongly concentrated near the left wall of the slit and is nearly zero around the edge of the Ag film at the top of the right wall of the slit. Therefore, the slit couples the incident light to the left-propagating SPP waves.

 

Fig. 3. Simulated E-field intensity distribution of a plane wave incident at the asymmetric slit structure. (a), (b) and (c) are the cross-sectional view of the |E|² distribution for slip width w_p = 510 nm, 690 nm, and 930 nm, respectively. The dashed line segments marks the material interfaces. (d) The summary plot of the simulated |E|² intensity at the Air/Ag interface and at 6um from the slit edge as a function of w_p. The red and blue filled circles are the |E|² intensity estimated from the left and the right side of the slit, respectively. The green filled circles are the number of nodal points of the x-component of the E-field that appears to the top surface of Ag pad in the slit in the simulation. The dashed curves are for visual guidance.

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Fig. 4. Simulated instantaneous E-field vector distribution and time-averaged Poynting vector distribution in the slit structure. (a), (c) and (e) are the E-field vector distribution for the slits with w_p = 510 nm, 690 nm, and 930 nm, respectively. The color map in each panel represents the E_x-component of the E-field. The color scale in panel (a) applies to (c) and (e). (b),(d) and (f) are the time-averaged Poyning vector distribution of the slits with w_p = 510 nm, 690 nm, and 930 nm, respectively. The color map in each panel represents the magnitude of the Poynting vector, and the color scale in (b) applies to (d) and (f).

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Figures 4(c) and 4(d) show markedly different distributions of the E-field and the Poynting vector for a wider slit. In Fig. 4(c), the width of the bottom Ag pad is nearly half of the overall slit width. The incident light excited SPP on the surface of the Ag pad. The distribution of the E-field vector shows that the polarization of the E-field is mainly in the z-direction in the region above the Ag pad, which is perpendicular to that of the incident light. The time dependence of the E-field vector shows that E-field behaves like standing waves along the x-direction in the region above the Ag pad but remains a propagating wave along the + z-direction in the region above the slit opening. This leads to nearly zero amplitude of the time-averaged Poynting vector distribution near the left side of the slit, as shown in Fig. 4(d), and the concentrated energy flux near the edge of the Ag film on top of the right wall of the slit. Therefore, the slit couples the incident light to the right propagating SPP waves. The SPP waves excited on the Ag pad seemingly forced the polarization of the E-field in the region above it to be predominantly in the z-direction, thus alternated the propagation of the light waves into the x-direction. The Ag film on the left wall reflected such waves and resulted into standing wave like E-field distribution and the nearly zero Poynting vector distribution. This is quite different from the cases where the nano-grooves/slits are confined with metallic sidewalls [25,30]. There, the SPP mainly couples with the waveguide modes or a superposition of the waveguide modes propagating vertically in the grooves [25]. In our case the slits are confined with Ag sidewall on the left and mainly the PMMA sidewall on the right. This asymmetry in material composition makes the near field associated to the SPP excite on the Ag sidewall to shape the configuration of the E-field in the slit, thus the time-averaged Poynting vector distribution. The shifting of the intensified Poynting vector strength leads to the directional coupling of SPP on the top Ag surface.

Further increasing the overall slit width increases the width of the bottom Ag pad, leading to the expansion of the standing wave like region inside the groove. We note that there are nodal points of the x-component of the E-field occurs to the surface of the bottom Ag Pad. The number of nodal point increases with the slit width as shown in Fig. 3(d), and it can be seen that optimal right coupling of SPP waves occurs when a new nodal point appears. Figures 4(e) and 4(f) show, respectively, the E-field and the time averaged Poynting vector distribution of a slit structure right after the third nodal point appears. It is clear that the Poynting vector distribution near the right side of the groove is nearly the same as that of Fig. 4(d), which also corresponds to the appearance of a new nodal point. This coincidence further confirms the role of the SPP excited on the Ag pad plays a dominant role in the directional coupling of SPP toward the right of the slit.

We further investigated the effect of the PMMA film thickness in our design. Figure 5(a) shows the summary plot of the simulated SPP wave intensities as a function of slit width w_P for various PMMA film thickness with a Ag film of t_Ag = 120 nm. It is clear that all the plots bare the similar trends: an optimal slit width for left coupling of the SPP waves occurs to a smaller slit width for each film thickness (except for the case of t_PMMA = 180 nm), followed by multiple optimal slit widths for the right coupling of the SPP waves. It is also clear the as the film thickness t_PMMA increases the corresponding slit width for optimal directional coupling increases. Figure 5(b) shows the comparison between the measured SPP intensities coupled with slits fabricated on ∼100 nm thick Ag films over a 204 nm thick PMMA film, and those shown in Fig. 2(n), where the PMMA film thickness is 302 nm. It is clear that the optimal left coupling and the first optimal right coupling slit width all occur at smaller widths for the case of 204 nm thick PMMA film. Therefore, the trend of our experimental results agrees with the simulation. This demonstrated that the PMMA film thickness can be used as one of the design parameter for optimal coupling of SPP waves toward the desired direction with the incident light of selected wavelengths.

 

Fig. 5. Effect of PMMA film thickness on SPP coupling of the asymmetric slit structures (a) Simulated E-field intensities |E|² at 6 μm from the slit edges on the left side (red filled circle) and on the right side of the (blue filled circle) slit plotted as a function of slit width w_p for various PMMA film thickness as labeled. The Ag film thickness is 120nm. (b) SPP intensities measured with NSOM as a function of slit width w_p for slits fabricated with t_PMMA = 204 nm, and t_Ag=101nm. The red (blue) filled circles represent the SPP signals measured 6 μm from the left (right) edge of the slit. For ease of comparison, the results shown in Fig. 3(n) is replotted here with open circles and dashed curves. The dashed arrow indicates the shift between corresponding features of both curves. The solid and dashed curves in (a) and (b) are for visual guidance.

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4. Conclusion

We presented an asymmetric slit structure design for directional coupling of SPP on Ag films that is suitable for fabrication with EBL and GLAD of Ag films. The slit structure consists of an Ag sidewall on one side, whose base extends into a smooth Ag pad for wider slits, and a PMMA sidewall on the other side. We fabricated the asymmetric slit structures and characterized the SPP coupling to the incident 532nm laser beam with NSOM measurements. Our results demonstrated directional coupling of SPP on the Ag film with the direction of the coupled SPP tunable with the slit width, and the optimal extinction ratio near 8 × 10⁴ for the right coupling of SPP has been achieved. We carried out simulation of the interaction between the incident light and our asymmetric slit structure. The simulation reproduced the experiment qualitatively. The detailed comparison between the simulated the E-field and the time averaged-Poynting vector distributions inside the slit revealed the physical insight of the directional coupling of the SPP waves with our asymmetric slits. For narrow slits the incident light passes the slit and excites SPP on the Ag sidewall, leading to coupling of the SPP wave toward the side of slit with Ag sidewall. For wider slits, the incident light excites SPP on the bottom Ag pad inside the slit and causes the incident light wave in the region above the pad to propagate in horizontal direction forming a standing wave like field distribution presumably due to interference with the waves reflected from the Ag sidewall. This results in null time-averaged Poynting distribution in the region above the Ag pad but an intensely concentrated distribution near the PMMA side wall, leading to coupling of the SPP waves toward the PMMA side of the slit. We further examined the effect of the PMMA films thickness on the performance of the directional coupling of our asymmetric slits, with experiment and simulation. Both results indicate that varying the PMMA film thickness does not change the coupling of the SPP waves with the slits qualitatively. The film thickness can be used as a control parameter to fine tune the slit width for desired coupling of the SPP waves.