Engineering Resonant Peaks of Valley Photonic Crystal Ring Resonators for Optical Comb Generation

The spectral line density of an optical frequency comb (OFC) generated in a microring resonator is fixed by the free spectral range (FSR), and hence by the resonator size: the dense combs required for spectroscopy, optical clocks, and high-capacity communications conventionally demand centimeter-scale cavities, in direct conflict with photonic integration. Here, we propose a route around this FSR–footprint trade-off using topological ring resonators (TRRs) built on a silicon valley photonic crystal (VPC) platform. Evanescently coupling two identical TRRs, an optical analog of quantum tunneling in a double-well potential, deterministically splits each resonance into a doublet of supermodes (Rabi splitting), doubling the spectral line density within a fixed bandwidth while the parallel two-ring layout occupies orders of magnitude less chip area than a single conventional ring of equivalent effective FSR. A coupled-mode-theory model quantitatively captures the splitting observed in full-wave 3D finite-difference time-domain (FDTD) simulations, and the topological protection of the valley edge states preserves the doublet against lattice disorder; a fabrication-tolerance analysis shows the splitting varies by only a few percent for nanometer-scale gap errors. Nonlinear simulations based on the coupled nonlinear Schrödinger equation indicate that the doubled supermode grid translates directly into a denser comb, increasing the generated line count from 48 to 122 under identical Kerr-only pumping conditions. An explicit nonlinear-loss budget, including two-photon and free-carrier absorption, bounds these results for silicon at 1550 nm and identifies mid-infrared silicon and TPA-free platforms such as silicon nitride as physically realistic implementations. This design study establishes coupled topological resonators as a compact, disorder-tolerant architecture for high-density comb generation, which can potentially be experimentally demonstrated.