# Ultra-Compact Digital Metasurface Polarization Beam Splitter via Physics-Constrained Inverse Design
## 3 Results and Discussion  
To verify the viability and reasonability of our model, the device performance was simulated via three-dimensional finite-difference-time-domain (3D FDTD) simulation, utilizing the Lumerical FDTD Solutions 2020 R24(r) software. The input and output ports were set as 2-\(\mu\)m-wide waveguides and the maximum meshing step was set as 10 nm. A DFT monitor was placed 8 \(\mu\)m behind the output ports to obtain the field strength distribution. Figure 4a,b shows the simulated light propagation in the designed PBS when the mixed input light is emitted from the input port of the device. It can be clearly seen from the figure that the incident light with a mixture of the TE mode and TM mode is introduced into the PBS element through the left port, and as light propagates along the \(x\)-axis inside the device, the separating distance of different polarizations increases, resulting in a large distance difference along the \(y\)-axis. The light of different polarization modes ultimately focuses on the different output ports' efficiency. A quantitative evaluation of the performance of the metasurface PBS device is shown in Figure 4c,d, which demonstrates a high performance of the device over the entire 80 nm wavelength range. At a 1550 nm wavelength, the insertion loss (IL) of the TE mode reaches 0.706 dB, while the IL of the TM mode is 0.809 dB. The extinction ratio (ER) is defined as the ratio of the power of a matched mode to another mode in the corresponding output port. According to the results shown in the figure, the calculated ERs for the TE output port and TM port of the device are 12.59 dB and 10.76 dB at 1550 nm wavelength, respectively. It can be seen from the figure that when operating at shorter wavelengths, the output efficiency of the TE mode is relatively higher, while that of the TM mode performs the opposite. The reason is that the metasurface layer exhibits a relatively larger difference in the equivalent refractive index when operating at longer wavelengths. Figure 3: Design pipeline for the metasurface layer. wavelengths, resulting in a stronger deflection effect, thus the propagation directions of the two modes are deflected by a larger angle in the device. A simulation shows that both the TM and TE modes have low ILs (<0.731 dB for TE mode and <0.873 dB for TM mode) and low ERs (10.5-15 dB) over a broad wavelength band of 80 nm, thereby covering the C-band (1530-1565 nm), which shows the potential of the device to be used together with the WDM on-chip system to further improve the link capacity. Since manufacturing defects, which usually lead to the deterioration of the device performance, are unavoidable in practical applications, we simulated the device performance under different fabrication errors to verify whether the device has good tolerance. We first simulated the possible under-etching and over-etching conditions during the etching process, and the simulation results show that the device can tolerate a variation in etch depth of up to \(\pm\)20 nm, as shown in Figure 5a-d. ILs of both polarization modes fall less than 0.34 dB from the peak value over the entire 80 nm width band, while the reduction of ERs is up to 2.95 dB. We noticed that, whether under-etched or over-etched, the separation efficiency of the device for TM-polarized light fluctuates greatly, while TE-polarized light is almost unaffected. This is consistent with our previous setup where the equivalent refractive index of the TE mode hardly varies with the structure of the metasurface layer. Figure 4: The simulated normalized transmission spectra with detected mode profiles for (**a**) TM mode and (**b**) TE mode. E-field profiles of the propagation along the device for (**c**) TM mode and (**d**) TE mode. To elucidate the tolerance of our device to small changes in device geometry, we simulated the device behavior under irregular etching conditions. Considering the outer proximity effect during the etching process, an etched shape close to a round hole is used to replace the ideal square etched air hole.