Analytical Model of Dual-Pumped Kerr Micro-Resonators for Variable Free Spectral Range and Composite Frequency Comb Generation

We develop an analytical model to understand the generation of tunable free spectral range frequency comb (FC) and composite FC using two competing phenomena, namely nondegenerate four-wave mixing (FWM) and intensity-dependent modulation instability (MI) in dual-pumped micro-resonator configurations. Our analytical approach is based on the popular four-wave model. The MI rate at the onset, corresponding to the most susceptible frequency component that conditionally accompanies threshold-less comb generation in case of dual pump, is derived. Based on the analytical model, the mutual interplay of nondegenerate FWM and threshold intensity-dependent MI is investigated in detail for the comb generation process, and their regions of operations are clearly demarcated. The proposed analytical model provides a deterministic and quick estimation of micro-resonator parameters for generating a variety of FCs while avoiding the computationally intensive route of solving the Lugiato-Lefever equation. A close agreement between the analytical and numerical simulation is found.