In 1998, Ebbesen et al. reported extraordinary optical transmission (EOT) in the subwavelength metal structures with periodic hole arrays^[1,2] for the first time. Since then, extensive research on the transmission in subwavelength structures has been carried out^{[3–15" target="_self" style="display: inline;">–15]}. People have studied EOT phenomena in different aperture arrays such as circles, rectangles, ellipses, and triangles. In addition, the EOT in some special subwavelength structures such as groove arrays and bullseye structures has also caused widespread concern due to their easy processing and high transmission. Based on the theoretical and experimental studies, EOT has been widely employed in selective lenses, optical switches, enhanced nonlinearity, and other novel sensors^{[15–23" target="_self" style="display: inline;">–23]}.

Although the physical mechanism of EOT is not completely clear, it has been recognized that the shape and size of the hole, the period of the groove, the material of the film, and the refractive index of the environment have a significant effect on the transmission characteristics. Once a structure and the parameters of the structure are proposed, the transmission characteristics of the structure are fixed. It is impossible to achieve dynamic regulation of their transmission continuously. People have to etch a variety of samples with different parameters for different requirements.

In this Letter, we propose a strategy to adjust the transmission of a subwavelength metal structure by employing external light. Because the bullseye structure^[24] is a typical subwavelength structure and it has been widely applied in many fields^[16,17] such as selective lens and novel sensor, we use it as an example to verify the validity of this solution.

As shown in Fig. 1, we design a bullseye structure on a silicon dioxide substrate. The whole structure covers an area with a 300 nm thickness. A hole with a radius of 150 nm is located in the center of the film surrounded by a groove with a depth of 60 nm and a period of 600 nm.

Fig. 1. Cross section of the bullseye structure (a) x-z cross section (elevation view) and (b) x-y cross section (top view).

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As shown in Fig. 2, we immerse the bullseye in carbon disulfide (CS2), which is known as a typical nonlinear medium with a relatively larger nonlinear refractive index. In the external light field, the total refractive index n of CS2 is expressed as^[25]n=n0+n22|E2|=n0+γI,(1)where n0 is the linear refractive index that is 1.6276, n2 is nonlinear refractive parameter, E is the peak electric field (cgs), and I denotes the irradiance (MKS) of the laser beam within the sample. γ and n2 are related through the conversion formula n2(esu)=(cn0/40π)γ(m2/W), where c(m/s) is the speed of light in vacuum, at a wavelength of 800 nm, and γ is 2.1×10−7μm2/W^[26]. From Eq. (1), we can see that the refractive index of CS2 will vary with the intensity of the controlling light. Here we use a plane light with a wavelength of 800 nm and a power of 105–106W as the controlling light to adjust the refractive index of the CS2.

Fig. 2. Schematic diagram of the regulation strategy.

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Using the finite-difference time-domain (FDTD) method, we simulate the transmission of the structure for a signal light (from 600 nm to 1300 nm) at five different controlling lights with power densities of 0W/μm2, 2.38×105W/μm2, 4.76×105W/μm2, 7.14×105W/μm2, and 9.52×105W/μm2, which make the nonlinear refractive index of CS2 increase up to 0 RIU, 0.05 RIU, 0.1 RIU, 0.15 RIU, and 0.2 RIU, respectively. The corresponding transmission characteristics of the bullseye structure obtained are shown in Fig. 3.

Fig. 3. Transmission spectra of the signal light under different powers of controlling light.

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In Fig. 3, we find that when there is no controlling light the transmission spectra have two peaks; the first one is at 930 nm, and the second one is at 1097 nm. Compared with the 660 nm measured by Lezec et al. in air instead of CS₂^[27], obviously, the transmission peaks redshift because the structure was immersed in CS2. When the controlling light with the power density of 2.38×105W/μm2 is introduced, the first peak redshifts to 949 nm, and the second to 1162 nm. As the power density of the controlling light increases further to 4.76×105W/μm2, 7.14×105W/μm2, and 9.52×105W/μm2, the first peak shifts to 967 nm, 1006 nm, and 1046 nm and the second peak shifts to 1133 nm, 1151 nm, and 1165 nm. In order to know how these peaks change with the power density of the controlling light, we plot the wavelength of the first peak as a function of power of the controlling light in Fig. 4.

Fig. 4. Wavelength of the primary transmission peak under different powers of controlling light.

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From Fig. 4 we can see that the wavelength of the first peak (γpeak) increases linearly with the power density of the controlling light, following γpeak=94.715I+928.768. Hence, we can tune the transmission spectrum of the signal light continuously by adjusting the power of the controlling light. Thus, a tuneable nano-device is realized.

Generally, the mechanism of the EOT phenomenon can be considered as the coupling of surface plasmon resonance (SPR) and local surface plasmon (LSP)^[6]. The incident light generates the diffraction wave in the subwavelength structure that satisfies the phase condition, thus excites SPR and enhances transmission at a specific resonance wavelength^{[24" target="_self" style="display: inline;">–4]}. At the same time, the resonance of the local waveguide affects the central wavelength and the peak of transmission spectrum. The redshift of the transmission spectrum can be explained by the interaction between incident light in a medium and surface plasmon on a metal surface. In this Letter, the dielectric constant of the nonlinear medium effectively increased with the power of the controlling light. In this condition, the incident signal photons with lower energy can satisfy the resonance condition and realize the coupling with surface plasmon. So the positions of the resonance peaks shifted to longer wavelengths.

In addition, multiple peaks in the transmission spectrum can be considered as the dominating effect of surface plasmon and local surface plasmon, respectively. The transmission spectra of both modes are nonlinearly related to the permeability of the medium^[5]. Therefore, when the third-order magnetic permeability of carbon disulfide was changed by the controlling light, the transmission peaks dominated by the two resonance modes exhibited different transmittances. So, the height of peaks in the transmission spectrum varied irregularly with the power of the controlling light.

As discussed above, plane light can realize a tuneable device. However, in the view of application, the laser is the best choice. Usually, the transverse mode of the laser pulses was nearly Gaussian. Hence, we further simulated the transmission of the structure under the laser as the controlling light. In this case, the nonlinear refractive index of CS2 will show a transverse Gaussian distribution n=n0+γIexp[−σ(x2+y2)],(2)where x and y are coordinate parameters, I is the center power of the Gaussian beam, and σ is a characteristic parameter of a Gaussian beam (herein, we chose σ=0.2). The spatial distribution of the refractive index of CS2 under the Gaussian beam is shown in Fig. 5.

Fig. 5. X axis distribution of the refractive index.

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By using FDTD, we simulated the transmission spectra under the Gaussian controlling light with the center power density of 0W/μm2, 2.38×105W/μm2, 4.76×105W/μm2, 7.14×105W/μm2, and 9.52×105W/μm2 in Fig. 6.

Fig. 6. Transmission spectra of the signal light under different powers of controlling light.

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In Fig. 6, with the increasing controlling light power, the first transmission peak wavelength redshifts from 930 nm to 949 nm, 966 nm, 984 nm, and 1008 nm, and the second peak from 1097 nm to 1109.53 nm, 1121.83 nm, 1130.94 nm, and 1139.04 nm. In addition, as shown in Fig. 7, the first peak also increases linearly with the increasing power density of the controlling light following γpeak=79.267I+928.893.

Fig. 7. Wavelengths of the primary transmission peak under different powers of controlling light.

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To summarize, a strategy to adjust the transmission of a subwavelength metal structure by employing external light was proposed. Specifically, we immersed the bullseye structure in a nonlinear medium and employed a controlling light to change the refractive index of the medium to adjust the wavelength of the transmission peak of the structure. By using FDTD, we verify the feasibility of our scheme. It is necessary for us to carry out experimental studies of the design in the future. In fact, we think the strategy can also be used in other structures. Furthermore, we infer that other forms of external fields such as electric fields, magnetic fields, and thermal fields may be used to adjust the transmission characteristics of subwavelength metal structures effectively via appropriate design. More research can be conducted.