Wave-optical Analysis of the Effects of Mirror Misalignment and Aperture in a Four-mirror Ring Resonator

A full-wave analysis of resonant modes in optical applications based on optical resonators, such as optical gyroscopes and semiconductor lasers, requires solving Maxwell’s equations under specific boundary conditions. Numerical methods such as the finite element method and finite-difference timedomain (FDTD), are commonly used to solve Maxwell’s equations. However, their computational costs increase exponentially with system size, making it nearly impossible to analyze extremely large optical systems. To address this problem, a recently novel method based on FDTD has been proposed for the analysis of large-scale systems. However, this approach has only been demonstrated in systems with Nfold symmetry. In this paper, we apply the method to more general systems without folding symmetry, while accounting for aperture and mirror misalignments. We also optimize the aperture size and mirror alignment, which are crucial for suppressing higher-order optical modes and reducing magnetic field effects in optical ring laser gyroscopes. To this end, the Q-degradation of the four-mirror ring resonator was investigated according to the apertures and misalignment. By conducting simulations, one can determine the minimum aperture size that preserves the fundamental mode of the resonator while suppressing higher-order optical modes and obtain essential information about the mirror alignment by analyzing the degradation of the Q-factor caused by mirror misalignment.