## 4 Micropolarizer Array Design  
### Grating Model Establishment  
The micropolarizer array is composed of several polarizers with different polarization directions. The fabrication method based on metal micro/nano grating is selected to design the micropolarizer array, and the design parameters that will affect the performance of the micropolarizer array are considered [13; 14].  
Figure 2 is a schematic diagram of the principle of rectangular subwavelength metal grating. The light wave incident on the grating can be decomposed into transverse magnetic wave (TM wave) and transverse electric wave (TE wave), which are perpendicular to each other. TM wave is the component whose vibration direction is perpendicular to the grating direction. The TE wave is the component whose vibration direction is parallel to the grating direction. The main transmittance is the transmittance of the TM wave.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Operating Wavelength** & **Caliber** & **Focal Length** & **Field Angle** & **Resolution Ratio** \\ \hline
8–12 \(\upmu\)m & 80 mm & 96 mm & 9.17\({}^{\circ}\) & 0.25 m @ 1 km \\ \hline \end{tabular}
\end{table}
Table 2: Design index of the optical system.  
Figure 1: Design of long-wave infrared polarization optical system. (**a**) Optical system structure diagram, (**b**) MTF curve.  
The simulation software Lumechanical FDTD is used for simulation, and the wavelength range of incident light is 8-12 \(\upmu\)m. Figure 3 shows the simulation structure of a periodic polarization grating. When the incident light is the normal incidence, the boundary conditions are set as periodic boundary conditions.  
According to the equivalent medium theory [15], when the grating period is far less than the incident wavelength, the grating with periodic structure can be regarded as a layer of uniform medium. For TE and TM polarized light, the equivalent refractive index of the grating is as follows:  
\[n_{TE}=\sqrt{DC(n_{1}+ik_{1})^{2}+(1-DC)(n_{1}+ik_{1})^{2}} \tag{12}\]  
\[n_{TM}=\sqrt{\frac{(n_{1}+ik_{1})^{2}+(n_{2}+ik_{2})^{2}}{DC(n_{2}+ik_{2})^{2}+ (1-DC)(n_{1}+ik_{1})^{2}}} \tag{13}\]  
where \(DC\) is the duty ratio of the grating (the ratio of the grating width to the period); \(n\), \(k\) are, respectively, the refractive index and extinction coefficient of the material, and also the real part and imaginary part of the refractive index. Subscripts 1 and 2, respectively, represent the grating material and the material in the grating gap. When the grating gap material is air, \(k_{2}=0\). At the same time, in order to simplify the calculation, the metal is regarded as a perfect conductor, i.e., \(k_{1}\) tends to infinity. The equivalent refractive index of TE and TM polarized light is simplified as follows:  
\[n_{TE}=ik_{1}\sqrt{DC} \tag{14}\]  
\[n_{TM}=n_{2}(1-DC)^{\frac{1}{2}} \tag{15}\]  
Figure 3: Raster simulation model: (**a**) thumbnail, (**b**) detailed.  
Figure 2: Schematic diagram of rectangular subwavelength metal grating principle.  
The refractive index of the simplified metal grating has only an imaginary part for TE polarized light, which is equivalent to a metal film. Most of the TE polarized light is reflected and absorbed, but only a small amount of light is transmitted; for TM polarized light, only the real part can be regarded as the medium layer. The grating has weak absorption for TM light, and most TM polarized light is transmitted.  
The extinction ratio is expressed as:  
\[ER=10\times\log_{10}\left(\frac{n_{TM}}{n_{TE}}\right) \tag{16}\]