1. Introduction

Surface plasmon polaritons (SPPs) are electromagnetic waves coupled to collective electron oscillations on the surface of a metal. SPPs offer unique properties, including high field confinement and strong field enhancement beyond the diffraction limit [1, 2]. This remarkable capability opens unique prospects for the design of nano optical integrated circuits [3–9].

One of the main components of optical circuits based on SPPs is the plasmonic waveguide (PWG). Especially, the symmetrical slab PWG (a thin metal film embedded in dielectrics) is a good candidate for real applications, because of the ease of fabrication due to the planar structure. For the symmetrical slab PWG, the SPPs on the upper and lower metal-dielectric interfaces are coupled with each other, and form long-range SPPs (LRSPs) or short-range SPPs (SRSPs), depending on the symmetry of the electromagnetic fields [10–12]. The LRSPs have comparatively lower loss and can be applied to transmission lines [13–15], optical modulators [16,17] and optical amplifiers [18,19]. On the other hand, although the SRSPs have much higher propagation loss, unique phenomena including nanoguiding [20–22] and superfocusing [23] can be realized.

The two SPP modes are usually excited by using a grating coupler [24], a prism coupler [25] or and an end-fire method [26] by one input light. However, since the control of the field distribution of SPP modes is nearly impossible with the ordinary methods, the excitation control including excitation efficiency modulation and mode selection has not been achieved until now. This problem has prevented the further development of LRSP and SRSP applications.

The excitation efficiency of LRSPs and SRSPs will depend on the symmetry of the electromagnetic fields formed by the input light. We have already showed the theoretical analysis of the excitation of SPPs using two input lights for controlling the symmetry of the field distribution in a previous work [27]. When an input coupler is illuminated by two beams, the symmetry of the field of an excited SPP mode is greatly dependent on the phase difference. This method has a high potential for the excitation control of SPP modes in symmetrical slab PWGs.

In this paper, we report the first experimental demonstration of the excitation control of LRSPs by two incident lights. By changing the phase difference or the intensity ratio between the two input signals, the excitation efficiency of the SPP modes in the PWG can be controlled, resulting in the strongly modulated signal of the LRSPs at the output. These results show that our excitation method can be applied to a plasmonic direct modulator and a plasmonic logic gate circuit.

2. Basic concept of selective excitation

Our excitation method is based on the control of the symmetry of the electromagnetic fields. In symmetrical slab PWGs, SPP modes are divided into two modes, LRSPs and SRSPs, based on the symmetry of the magnetic field distribution: the LRSPs and SRSPs show symmetrical and antisymmetrical field distribution, respectively (Fig. 1 Inset). We control these field distributions by the phase difference Δϕ of the two incident beams’ magnetic field, and change the excitation efficiency of the two SPP modes, as shown in Fig. 1.

 

Fig. 1 Selective excitation of LRSPs (a) and SRSPs (b) by two incident beams. The excitation of the SPP modes significantly depends on the phase difference between the two beams. Inset: the schematic diagram of the magnetic field distributions H_x of LRSPs (a) and SRSPs (b).

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When the film edge of the PWG is illuminated by two beams from the upper and lower sides, the symmetry of a SPP mode depends on the phase difference between the two beams. Figure 2 shows the finite–difference time–domain (FDTD) analyses of the SPP excitation by two input lights (wavelength 635 nm, same intensity and z–axis polarization) in SiO₂–Ag–SiO₂ structure (Ag thickness 30 nm). In the case of Δϕ = 0, the field distribution (E_y) shows symmetry, resulting in a strong LRSP excitation (Fig. 2(a)). On the other hand, in the case of Δϕ = π, an antisymmetrical field is formed, and the SRSPs are thereby excited selectively (Fig. 2(b)). These results show that the excitation of the SPP modes strongly depends on Δϕ. The excitation control can be achieved based on this mechanism.

 

Fig. 2 The field distributions (E_y) of the SPP modes formed by two incident beams with Δϕ = 0 (a), and Δϕ = π (b) in the FDTD simulation. The PWG structure consists of a thin Ag film (thickness 30 nm, indicated by the white line) embedded in SiO₂. The film edge is illuminated by two beams from the upper and lower sides, with polarization of the electric field along the z–axis.

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In principle, the concept based on two incident beams can be applied to the excitation control of both LRSPs and SRSPs. However, in the case of SRSPs, it is very difficult to demonstrate the excitation control, due to its much higher propagation loss. In contrast, since LRSPs have comparatively lower propagation loss, it is easy to observe the output signal. Therefore, LRSPs are the mode suitable for the demonstration. In this research, we experimentally show the excitation control, focusing on LRSPs.

3. Fabrication and experimental setup

Because symmetrical slab PWGs consist of a metal film embedded in dielectrics, the SPP imaging based on a near–field microscopy [28–30] cannot be used to observe the SPP propagation. Instead, a taper structure as an output coupler [31] is one of the ways to achieve the observation of SPP signals; we observe SPP signals as scattered light at the taper tip of the PWG. This method makes it easy to observe the LRSP signals in the symmetrical slab PWG, and is also very suitable for our experiments.

The geometry of the symmetrical slab PWG is shown in Fig. 3(a). The PWG is fabricated on a glass substrate covered in SiO₂. The thickness of SiO₂ (2 μm) is sufficiently larger than half of the beam width of the LRSP. To fabricate the patterned Ag film, the substrate is first coated with a layered stack consisting of a positive electron beam resist (ZEP520A) and a conductive polymer (ESPACER 300Z). The PWG structure is patterned in the electron beam resist layer with electron beam lithography. After removing the conductive polymer layer and the exposed resist, a 30 nm thick Ag film is evaporated directly on the substrate. The remaining resist is then stripped in a liftoff process. Finally, the substrate is coated with an index-matched polymer (GA700H, n = 1.46) of the thickness 10 μm.

 

Fig. 3 (a) Schematic of a symmetrical slab PWG. The Ag slab is 30 nm thick, and is embedded between a SiO₂ layer (2 μm thick) and an index-matched polymer layer (10 μm thick). (b) Optical microscope image of the fabricated symmetrical slab PWG.

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An optical microscope image of the PWG is shown in Fig. 3(b). The width of the PWG is 5 μm, and the triangularly shaped tapered structure starts at a distance of 5 μm from the edge. The taper structure has a base width of 5 μm and a length of 16 μm (taper angle 17.8°). The length between the edge and the tip (21 μm) is significantly larger than the propagation length of the SRSPs (∼ 1 μm). Therefore, only LRSPs (propagation length ∼ 42 μm) can reach the tip and be observed.

Figure 4 shows the schematic of the experimental geometry. The laser beam (wavelength 635 nm) is split into two beams (intensity I₁, I₂) by a beam splitter (BS). The phase difference between the two beams is controlled using the delay line of a piezo actuator (resolution 10 nm) in one of the beam paths. Moreover, the intensity ratio I₂/I₁ between the two beams can be varied by a neutral density (ND) filter. The two beams are focused onto the edge of the PWG from the upper and lower sides by using objectives (50, NA = 0.55), with the polarization of the electric field along the z–axis. The signal from the tip is recorded by a complementary metal oxide semiconductor (CMOS) detector.

 

Fig. 4 Experimental setup configuration. The laser beam (wavelength 635 nm) is split into two beams (intensity I₁, I₂) at BS. Then the two beams are focused onto the input edge of the PWG from the upper and lower sides.

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4. Results and discussion

Figure 5 shows the experimentally measured scattering intensity from the tip as a function of the phase difference Δϕ between the two incident beams (I₂/I₁ = 1). As the phase difference Δϕ is monotonically increased, the scattering intensity varies in an oscillatory manner between a maximum (Δϕ = 0, 2π, 4π, · · ·) and a minimum (Δϕ = π, 3π, 5π, · · ·) value. The ratio of the maximum to minimum intensity is 5.7, corresponding to a modulation depth of (max – min)/max = 0.82. The maximum modulation depth at the output occurs when the intensities of the two input lights are equal to each other (I₂/I₁ = 1). These results are in close agreement with the FDTD simulations for the fabricated waveguide dimensions.

 

Fig. 5 Scattering intensity from the tip as a function of the phase difference between the two incident beams. The red dots and black dashed-dotted line represent experiments and FDTD simulations, respectively.

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The optical images and the simulated field distributions for the Δϕ = 0 and Δϕ = π are shown in Fig. 6. A clear difference is noticeable between Δϕ = 0 and Δϕ = π in experiments. For the Δϕ = 0, the strong scattering from the tip can be observed (Fig. 6(a)). In contrast, for the Δϕ = π, the scattering from the tip is very weak (Fig. 6(b)).

 

Fig. 6 The selective excitation of LRSPs. (a, b) The experimentally observed scattering from the tip (shown by the dashed circle) for the case of Δϕ = 0 (a) and Δϕ = π (b). (c, d) The field distributions (|E|², on the Ag surface) of SPP modes excited by two beams with Δϕ = 0 (c) and Δϕ = π (d), in the FDTD simulation. The color scale is the same for both figures.

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The dependence of the output signals on the phase difference can be explained through a variation in the excitation efficiency of SPP modes. In the case of Δϕ = 0, the excitation efficiency of LRSPs is significantly higher than that of SRSPs, because of the field distribution formed by the two incident beams, as shown in Fig. 2(a). Furthermore, propagation of the LRSPs to the tip can be obtained in the simulation (Fig. 6(c)). Therefore, the selectively excited LRSP reaches the tip, with low loss, and is observed as a strong output signal (Fig. 6(a)). On the other hand, for the Δϕ = π, only SRSPs show high excitation efficiency by forming an antisymmetrical field (Fig. 2(b)). As shown in Fig. 6(d), although SRSPs with high excitation efficiency can be observed near the edge (input), they cannot reach the tip and never contribute to the scattering at the tip, because of high propagation loss. Only a minute amount of LRSPs excited simultaneously with the SRSPs at the edge is observed as an output signal in the case of Δϕ = π. Therefore, the output signal is very weak (Fig. 6(b)) compared with the case of Δϕ = 0. Similarly, at other phase differences, the excitation efficiency of LRSP and SRSP will vary, depending on the formed field distribution, resulting in the modulated output signal as shown in Fig. 5.

Considering the symmetry of the field distribution, the output signal can also be modulated by changing the intensity ratio I₂/I₁ between the two input beams. Figure 7 shows the experimentally measured scattering intensity from the tip as a function of I₂/I₁, for the phase difference Δϕ = π. As the intensity ratio I₂/I₁ is increased from 0 to 1, the output intensity gradually decreases, which is in good agreement with the FDTD simulations. The lowest intensity (at I₂/I₁ = 1) is less than half of those observed by one beam excitation (that is I₂/I₁ = 0).

 

Fig. 7 Scattering intensity from the tip as a function of the intensity ratio between the two incident beams, for the phase difference Δϕ = π. The red dots and black dashed-dotted line represent experiments and FDTD simulations, respectively.

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This phenomenon can also be understood as excitation efficiency depending on the field distribution. For the I₂/I₁ = 1 and Δϕ = π, an antisymmetrical field is formed (Fig. 2(b)), resulting in the low excitation efficiency of the LRSPs. However, if the intensity of one side beam decreases, the antisymmetry is broken because the intensity of SPPs excited at the upper and lower metal–dielectric interfaces is different and mismatched. Therefore, additional LRSPs will be excited from the complicated field distribution caused by decreasing I₂/I₁, and some output signals will thereby be observed even if Δϕ = π. The difference of the minimum value at the I₂/I₁ = 1 between the experiments and simulations can also be due to the disorder of field distribution caused by imperfections in the fabrication of the input edge.

The experiments presented in Fig. 5 and Fig. 7 reveal that two incident beams can control the excitation of LRSPs. To our knowledge, this is the first report about experimental demonstration of the excitation control of SPP modes. In the excitation method analyzed here, it is possible to modulate the excitation efficiency of LRSPs by controlling the phase difference between two input lights. If the phase difference is fixed to π, the control of the LRSP excitation by the intensity ratio is also realized. These functions lead to active plasmonic devices [32] including modulators, switching and logic gates based on LRSPs.

In addition, although we focused on LRSPs in symmetrical slab PWGs in this research, the excitation of SPP modes in other PWGs, i.e. asymmetrical slab PWGs and metal gap PWGs, can be controlled by two incident beams. The excitation method analyzed here can be applied to these waveguides, and they will be a powerful platform for the active plasmonics.

5. Conclusion

We have demonstrated experimentally that the excitation of LRSPs can be controlled by two incident beams. We have shown the LRSPs modulated by the phase difference or the intensity ratio between the two beams. These results indicate that the excitation control can be applied to active plasmonic devices including modulators, switching and logic gates based on LRSPs. We expect that our findings will further highlight the wide photonic functionality made available by SPPs.