Resonant mode calculation method for extremely large-scale optical ring resonators

To analyze the resonant modes of optical devices such as optical gyro-sensors and semiconductor lasers, Maxwell's equations need to be solved. Widely used numerical methods are the finite element method (FEM) and the finite-difference time-domain (FDTD) method. However, when optical systems are significantly larger than the operating wavelength, applying these methods becomes practically infeasible due to the exponential increase in computational resources and simulation time. In this study, we propose a novel FDTD-based method to obtain the optical modes of large-scale optical systems, by setting the calculation area as the region where most of the light field is formed, dividing it into computationally feasible subdomains, and sequentially compute the field along the direction of light propagation. We have verified the proposed method by applying it to the calculation of resonant modes of 3-mirror ring resonators, which are used in ring laser gyro-sensors. In solving this problem, we also utilize transformation optics so that a non-rectangular subdomain is mapped to the rectangular-shaped subdomain with spatially varying refractive index distribution. Our method is expected to be useful for the improvement of device performance in large-scale optical systems in which the electromagnetic field propagates mainly around a simple closed path.