# Numerical Study of a Polarization Selective Visual Optical Switch
## 3 Results and Discussions
### The Influence of the Number of Metal Strips on the Enhanced Optical Transmission  
Considering the special function of the metal strip in the polarization direction of the incident light, a composite structure of the metal strip and the hollow circular hole is constructed. As shown in Figure 2a, the polarization direction of the electric field of the incident light is changed when there is no metal strip in the hollow circular hole, and the transmittance remain stable. Generally speaking, the resonance mode in the circular hole is mainly the SPPs resonance mode, and the primary factor affecting the transmission peak shift is the period \(P\) of the structure [26]. In addition, due to the special symmetry of the circular hole, the polarization direction of the incident light has no effect on the structure. As shown in Figure 2b-d, different number of metal strips are added to the hollow circular hole. When the polarization direction of the incident light changes from parallel to perpendicular to the _X-axis_, the results show that the transmission peak shifts obviously. So far, in order to unrestricted display the color rendering effect of materials, we invert the transmission spectrum of FDTD simulation into CIE1931 color coordinate map, and calculate the color coordinate points on an excellent space map [27]:  
\[X=k\!\!\!\sum_{\lambda}T(\lambda)I(\lambda)x^{\prime}(\lambda) \tag{1}\]  
\[Y=k\!\!\!\sum_{\lambda}T(\lambda)I(\lambda)y^{\prime}(\lambda) \tag{2}\]  
\[Z=k\!\!\!\sum_{\lambda}T(\lambda)I(\lambda)z^{\prime}(\lambda) \tag{3}\]  
\[k=100/\!\!\sum_{\lambda}I(\lambda)z^{\prime}(\lambda) \tag{4}\]  
\[x=X/(X+Y+Z) \tag{5}\]  
Figure 1: Structural cross-sectional diagram of the unit structure in the _X-Y_ plane. \(R\) represents the circular structure radius; \(H\) is the thickness of the Al; \(L\) and \(W\) are the length and width of the metal strip; \(W\)(1–5) are the distance between metal strips; \(P_{x}\) and \(P_{y}\) are the periods; As follows: \(H\) = 50 nm; \(L\) = 100 nm; \(W\) = 10 nm; \(P_{x}\) = \(P_{y}\) = 200 nm; \(W_{1}\) = 75 nm; \(W_{2}\) = 30 nm; \(W_{3}\) = 80 nm; \(W_{4}\) = 30 nm; \(W_{5}\) = 35 nm; (**a**) Hollow circular hole; (**b**) one metal strip; (**c**) two metal strips; (**d**) three metal strips; the metal strips are symmetrically distributed along the center of the circular hole. \[\mathrm{y}=\mathrm{Y}/(\mathrm{X}+\mathrm{Y}+\mathrm{Z}) \tag{6}\]  
where the \(T(\lambda)\) is the transmission spectrum we detected; \(I(\lambda)\) is the spectrum of the incident light source (D65); And \(x^{\prime}(\lambda)\), \(y^{\prime}(\lambda)\), \(z^{\prime}(\lambda)\) represent the tristimulus value. The wavelength ranges are 400 nm to 700 nm, which basically covers the visible light ranges. And \((x,y)\) obtained from Equations (5) and (6) is the chromaticity coordinates of the transmission spectrum. As shown in the illustration in Figure 2b-d, materials under different conditions present different colors. As shown in the figure, by changing the number of metal strips in the hollow circular hole, the different colors in the visible light range can be obtained. In addition, it is found that when the polarization direction of the incident electric field is 0\({}^{\circ}\) and 90\({}^{\circ}\), there is a huge difference in the transmittance at a specific wavelength. This is exactly how the POS works. In other words, by rotating the polarization direction of the electric field of the incident light, the metal strip can be controlled to participate in resonance mode, thus the incident light can be turned on and off. Furthermore, when the resonance mode changes in the structure, the transmission peak of the visible light band shifts, which leads to the color change of the material surface. Take advantage of this point, we can construct a visual POS, that is to use the color change to directly characterize the different working states of the switch.