By using nonlinear coupled mode equations, we numerically investigated the generation of a Kerr comb in a normal dispersion microcavity system, where mode coupling between two cavity modes is present. In contrast to previous studies, our model is rigorous in which we fully considered the mode coupling between two modes. We investigated the phase matching condition to obtain the suitable parameters needed to form a free-spectral-range (FSR)-selectable comb. Our calculations are in good agreement with existing experimental results, and enable us to obtain a good understanding of the phenomenon; moreover our model also allows us to reveal new phenomena. We investigated 1-FSR comb generation in detail and found that randomly oscillating behavior will appear when detuning is scanned, which has never before been clearly observed. This modeling approach will be a powerful tool that will assist dispersion engineering for Kerr comb generation and the frequency tuning needed to generate a deterministic mode-locked comb.
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