# Compensation Method for Polarization Mixing in the Homodyne Interferometer
## 4 Conclusions  
Through the theoretical calculation and analysis of interference signals, the influence of the PBS in the interferometer part on nonlinearity is determined to be embodied in polarization mixing, whereas the effect of the PBSs in the detection part on the nonlinearity is the unequal separation of optical intensity. The DC offsets and unequal AC amplitudes caused by the PBSs in the detection  
Figure 4: The comparison of nonlinearity before and after adoption of the high-quality polarizer: the red solid curve—after adoption of the high-quality polarizer.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Polarizer** & \(\varepsilon\)**before Correction** & \(\varepsilon\)**after Correction** \\ \hline P\({}_{1}\) & 0 & 0.01 \\ P\({}_{2}\) & 0 & 0.01 \\ \hline \end{tabular}
\end{table}
Table 2: The extinction ratio \(\varepsilon\) before and after correction of Jones matrices.  
part can be easily eliminated by adjusting the gains of the detector. However, this approach does not work for the polarization mixing caused by the PBS in the interferometer part. In this regard, the nonlinear error caused by the polarization mixing of the PBS in the interferometer part is analyzed, and an optical configuration to compensate for the polarization mixing caused by the PBS in the interferometer part is proposed. By placing two high-quality polarizers at the end of the interferometer part, the unwanted s- and p-polarized components are isolated by the polarizers, thereby suppressing the inherent polarization mixing of the homodyne interferometer. The nonlinearity is reduced from approximately 4.5 nm to 0.045 nm, which is a decrease of two orders of magnitude, by integrating other compensation methods such as gain correction, compared with using only gain adjustment. The residual error is mainly due to the imperfection of the polarizer.  
Compared with the existing studies, we focus on the compensation of the polarization mixing of imperfection of the PBS, which is difficult to correct. In our proposed solution, polarization mixing caused by imperfection of the PBS is isolated by the polarizers with a high extinction ratio in the optical layout; thereby, the inherent nonlinear error of the homodyne interferometer is reduced. In a future experiment, all of the optical components in the optical layout should be considered. DC offsets and unequal AC amplitudes that are induced by the other optical components except the PBS can be reduced first through fine adjustment and improved components. Then, the nonlinear errors can be further corrected by our proposed optical layout of compensation and combination with gain adjustment.  
All work in relation to this paper was accomplished by all authors' efforts. Conceptualization, Q.H. and C.W.; methodology, C.W.; simulation and visualization, X.D., R.C., L.Z., R.L. and H.L.; writing the paper, C.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China (Grant No. 51875163, 51705123), National Key Research and Development Program of China (Grant No. 2019 YFB2004900) and Anhui Provincial Natural Science Foundation (Grant No. 1908085 QE201).  
The authors acknowledge the financial support from National Natural Science Foundation of China (Grant No. 51875163 and 51705123), National Key Research and Development Program of China (Grant No. 2019 YFB2004900) and Anhui Provincial Natural Science Foundation (Grant No. 1908085 QE201).  
The authors declare no conflict of interest.