Theoretical Study on Dual-Comb Generation and Soliton Trapping in a Single Microresonator with Orthogonally Polarized Dual Pumping

Microresonator-based optical frequency combs (known as microcombs or Kerr combs) have a large repetition frequency ranging typically from 10 to 1000 GHz, which is compatible with fast-scanning applications, including dual-comb spectroscopy and LiDAR. In this research, we numerically study dual-comb generation and soliton trapping in a single microresonator, whose two transverse modes are excited with orthogonally polarized dual pumping. The simulation model is described by using coupled Lugiato-Lefever equations (LLEs), which take account of cross-phase modulation and the difference in repetition frequencies. The numerical simulation calculates the dual-comb formation in a microresonator, whose microcombs propagate as soliton pulses and cause soliton trapping depending on the parameters. In the simulation, a trapped soliton is seeded by one of the original solitons in two transverse modes. In addition, we introduce an analytical solution for trapped solitons in coupled LLEs using a Lagrangian perturbation approach and clarify the relation between the parameters. Revealing the conditions of dual-comb soliton generation and soliton trapping is helpful in terms of optimizing the conditions for causing or avoiding these phenomena.