Time-domain modeling of nonlinear counter-propagating wave dynamics in reflective microring resonators

We present a one-dimensional finite-difference time-domain model that analyzes nonlinear counter-propagating wave dynamics in reflective microring resonators for integrated microcomb generation. The proposed method captures real-time field interactions with high temporal resolution in complex cavity configurations, eliminating the need for mean-field approximations or periodic boundary conditions. By directly solving the modified generalized nonlinear Schrödinger equation, the model reveals key phenomena, including bright soliton formation in anomalous dispersion, symmetry breaking, and crystallized dark pulse emergence in normal dispersion. This computationally efficient framework addresses limitations in existing methods, enabling detailed exploration of nonlinear photonic structures across diverse time scales and guiding the design of next-generation integrated frequency comb sources.