1. Introduction

Surface plasmon polaritons (SPPs) are electromagnetic waves that propagate along metal-dielectric interface and are coupled to the free electrons in the metal. They may be exploited to realize highly integrated photonic circuits [1–3], owing to the capability to miniaturize the sizes of photonic devices into subwavelength scales. However, before such applications coming true, it is essential to generate SPPs effectively and flexibly. For instance, unidirectional SPP launchers have attracted great research interest [4–10], which can excite SPPs to a unique propagation direction. Furthermore, bidirectional dichroic SPP splitters have also been proposed [11–15], which are capable of generating and splitting SPPs at two different wavelengths into opposite directions. For example, by adding two gratings with different periods on the opposite sides of a nanoslit, SPPs at two different wavelengths corresponding to the grating periods can be guided into desired directions [11, 12]. However, these additional gratings increase the device size significantly (>10 μm), which are undesired for high density integration. A compact SPP splitter was realized by coating an asymmetric nanoslit with a dielectric film [13]. The shortcoming is the greatly decreased SPP propagation length and device flexibility due to the dielectric film coating. Utilizing different SPP reflecting properties of nanogrooves with different dimensions, a simple plasmonic structure consisting of a pair of parallel nanogrooves with different widths was also suggested to act as a dichroic SPP splitter [14]. But the splitting ratios (defined as the ratio between the launched SPP intensities to the two opposite directions) are quite low, which are only 1:2 and 3:1 at the two splitting wavelengths. Recently, another design of SPP splitter has been proposed, which is based on a composite cavity structure [15]. However, the measured splitting ratios (1:5 and 6:1) are much lower than numerical predictions (1:24 and 23:1), because the high fabricating accuracy required by this complex composite structure was not easy to satisfy in the real experiment.

In this letter, we propose to utilize an asymmetric T-shape nanoslit to realize a compact dichroic SPP splitter. T-shape nanoslits have been used in some plasmonic studies such as plasmon-induced transparency [16], nanofocusing [17], electromagnetic enhancement [18] and multiband plasmonic absorber [19]. This structure is relatively easy to fabricate and does not require a quite high fabricating accuracy. Here, we show that, because of the SPP interferences in the asymmetric T-shape nanoslit, the intensities of the SPPs generated to the left and right directions can be manipulated nearly independently by changing the right and left groove widths, respectively. Based on such effects, a dichroic SPP splitter with high splitting ratios of 31:1 and 1:12 at splitting wavelengths of 680 nm and 884 nm are numerically presented with a structure’s lateral dimension of only 1200 nm. Moreover, further experimental results match well with the simulations.

2. Analyses and simulations

The proposed asymmetric T-shape nanoslit is schematically shown in Fig. 1(a), consisting of a conventional nanoslit (width of w_slit) in immediate contacting with two nanogrooves of different widths (w_G1 and w_G2) in a 450-nm-thick gold film. When p-polarized light (magnetic vector parallel to the slit) illuminates the structure from the back side with normal incidence, eigenmodes in the lower-part nanoslit are excited and such modes can generate two SPPs propagating along the bottom of the two nanogrooves in opposite directions. These SPPs are reflected by the two metal walls at the edges of the T-shape nanoslit, and will interfere with each other. This means that the upper part of the asymmetric structure acts as a SPP cavity. SPPs in the cavity also partly scatter into SPPs propagating along the front metal surface at the two metal walls. Basically, the intensities of the left-going and right-going SPPs on the front metal surface are proportional to the total intensities of the left-going and right-going SPPs in the cavity, respectively. Considering the left-going SPPs in the cavity, they mainly come from the interference between two components. One is the directly excited left-going SPPs from the lower nanoslit, and the other is the directly excited right-going SPPs from the lower nanoslit after being reflected by the right metal wall, as schematically shown in Fig. 1(b). The phase difference between these two interfering components can be expressed as:

 

Fig. 1 (a) Schematic of the proposed asymmetric T-shape structure and geometrical parameters. (b) Schematic diagram of the generation progress of the left-going SPPs.

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One thing should be pointed out is that, in the above analysis, SPP reflections are considered for only once for simplification, which corresponds to a first-order approximation. This simplification is reasonable considering the low SPP reflectance at a shallow metal wall [15]. Although multiple reflections of SPPs do introduce higher-order corrections to the results, the main conclusions of the above analysis are not affected. Another simplification is that only SPPs are consider, whereas the electromagnetic fields radiated by the nanoslit can be viewed as a combination of SPPs and quasi-cylindrical waves (CWs) within short distances. Because the wave vector of CWs is nearly the same as that of SPPs on the single gold-air interface [13], CWs almost do not affect the phase differences in the interferences but only affect the absolute field amplitudes. Therefore, the above simplified model can predict the main properties of the proposed T-shape structure, which is well verified by the following rigorous numerical simulation results.

To testify the above analysis, we carry out numerical simulations by the finite element method (FEM) with Comsol Multiphysics. In the simulations, the slit width and the groove depth are fixed to w_slit = 180 nm and h = 150 nm, respectively. The permittivity of the gold as a function of the wavelength was taken from the literature [20], and expanded using the method of interpolation. The simulated structure was illuminated from the bottom of the nanoslit. After calculating the total electromagnetic field distribution, we evaluated the launched SPP intensity by integrating the Poynting vector over a 200-nm-high observation window on the front metal surface which is 10 μm away from the source. Then, the SPP generation efficiency to one side η was defined as the ratio between the launched SPP intensity of the T-shape structure and the launched SPP intensity of a reference nanolit structure without the nanogrooves. Figure 2(a) displays the calculated SPP generation efficiency to left (η_L) as a function of the right groove width w_G2, with the left groove width fixed at w_G1 = 350 nm and the incident wavelength at λ = 830 nm. The SPP interference behavior is clearly identified, and the period referring to w_G2 is about 405 nm which is quite close to λ_spp/2 = 407 nm. This agrees well with the previous analysis. In addition, η_L can decrease to nearly zero with proper w_G2, which means that the proposed T-shape nanoslit is able to effectively suppress the SPP intensity to a certain propagation direction.

 

Fig. 2 (a) SPP generation efficiency to the left (η_L) as a function of the right groove width w_G2, with the left groove width fixed at w_G1 = 350 nm and the incident wavelength at λ = 830 nm. Extinction ratios η_L/η_R (black lines) and η_R/η_L (red lines) as functions of the wavelength with (b) w_G1 = 400 nm and w_G2 = 500 nm, 550 nm, 600 nm, and (c) w_G2 = 650 nm and w_G1 = 400 nm, 450 nm, 500 nm. (d) SPP generation efficiencies η_L (black line) and η_R (red line) as functions of the wavelength with w_G1 = 420 nm and w_G2 = 600 nm. The corresponding power flow distributions with w_G1 = 420 nm and w_G2 = 600 nm at splitting wavlengths of (e) λ = 680 nm and (f) λ = 884 nm.

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To demonstrate the SPP splitting capability of the asymmetric T-shape nanoslit, further simulations have been made with changing the incident wavelength. First, the left groove width is fixed at w_G1 = 400 nm, and the right groove width is set to w_G2 = 500 nm, 550 nm and 600 nm, respectively. The calculated extinction ratios η_L/η_R and η_R/η_L as functions of the wavelength are displayed by the black and red lines in Fig. 2(b). High values of η_L/η_R and η_R/η_L are clearly observed at different wavelengths, which indicate that the asymmetric T-shape nanoslit can work as an efficient dichroic SPP splitter. Moreover, it can be seen that, the splitting wavelength to the right direction evidently shifts to the longer wavelength as w_G2 becomes larger, while the splitting wavelength to the left remains nearly the same. Similarly, if the left groove width is altered and the right groove width is fixed, the splitting wavelength to the left changes accordingly, while the splitting wavelength to the right keeps nearly unchanged, as illustrated by Fig. 2(c). Thus, the splitting wavelengths to the left and to the right can be adjusted nearly independently and conveniently for the proposed SPP splitter. These simulation results are in good accordance with the previous analysis. To present the SPP splitting behavior more intuitively, the calculated SPP generation efficiencies to the left (η_L) and to the right (η_R) as functions of the incident wavelength are shown in Fig. 2(d) with typical groove widths of w_G1 = 420 nm and w_G2 = 600 nm. The launching direction change of the generated SPPs with the incident wavelength is clearly observed. SPPs primarily propagate to the left near λ = 680 nm with a maximal extinction ratio as high as about η_L/η_R = 31:1, and SPPs mainly propagate to the right around λ = 884 nm with a maximal η_R/η_L of about 12:1. The corresponding power flow distributions at these two splitting wavelengths are displayed in Fig. 2(e) and Fig. 2(f), respectively.

3. Experimental results

Experimentally, the asymmetric T-shape nanoslit was fabricated using a focused ion beam (FIB) in a 450-nm-thick gold film which was evaporated on a glass substrate with a 30-nm-thick titanium adhesion layer. At first, a 20-μm-long nanoslit (width of 180 nm) was etched through the gold film by using a relatively long FIB etching time. Then, two 10-μm-long nanogrooves with different widths were etched partly into the gold film together by using a relatively short FIB etching time. The two nanogrooves are in immediate contact with the lower half of the single nanoslit, forming the T-shape structure. Hence, the upper-half single nanoslit acts as an in-chip reference and the lower-half structure is the proposed SPP splitter. Figure 3(a) shows a scanning electron microscope (SEM) image of the experimental structure. Two gratings with periods of 800 nm lying symmetrically on the two sides of the slit with a distance of 15 μm are designed to scatter SPPs. So the far-field detected scattered signals can give a direct measurement on the relative intensities of the evanescent SPPs. The measured geometrical parameters are about: w_G1 = 420 nm, w_G2 = 600 nm, w_slit = 180 nm and h = 150 nm.

 

Fig. 3 (a) SEM image of the experimental structure. (b) Measured splitting ratios (scatters) of the proposed SPP splitter at different wavelengths and corresponding simulation results (lines). Typical CCD images displaying the scattered light signals from the nanoslit and the decoupling gratings at the splitting wavelengths of (c) λ = 700 nm and (d) λ = 880 nm.

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In the measurement, the structure was normally illuminated from the back side using a p-polarized laser beam (Ti: sapphire laser, wavelength tunable in the [700, 950] nm range) with a radius of about 100 μm. Light scattered from the front metal surface was collected by an objective and then imaged onto a charge coupled device (CCD). At the incident wavelength of λ = 700 nm, it is observed that the lower half of the right grating is quite dark [Fig. 3(c)], which reveals that the generated SPPs primarily propagate to the left. The measured splitting ratio η_L/η_R reaches 13:1. At λ = 880 nm, the lower half of the left grating become dark [Fig. 3(d)], which indicates that the generated SPPs mainly propagate to the right. The measured splitting ratio η_R/η_L is 12:1. These phenomena well consist with the previous analysis and simulation results. As a contrast, for the upper-half reference structure of the single symmetric nanoslit, the left grating is always as bright as the right one. The wavelength dependences of the splitting ratios of the proposed SPP splitter were also measured, and the results are shown by the scatters in Fig. 3(b). Although the optimal SPP splitting to the left predicted by the simulations was not experimentally observed due to the limitation of the available wavelength of the laser source, it can still be seen that the experimental results well match the simulations [lines in Fig. 3(b)] in the measured wavelength range.

4. Conclusion

In summary, we have proposed a dichroic SPP splitter by using an asymmetric T-shape nanoslit. Simulations and experiments demonstrated that such structure was capable of generating and splitting SPPs of two different wavelengths to opposite directions, which was a direct result of SPP interferences in the asymmetric T-shape nanoslit. High splitting ratios (η_L/η_R) of 13:1 at λ = 700 nm and 1:12 at λ = 880 nm were experimentally achieved with a splitter’s lateral dimension of only 1200 nm, which were in good accordance with the simulations. Moreover, the proposed dichroic SPP splitter showed good flexibility in adjusting the splitting wavelengths and was easy to fabricate. So such a compact device with high performance may have wide applications in highly integrated plasmonic circuits.