Abstract

Within the framework of vertically coupled silicon nitride (${{\rm{Si}}_3}{{\rm{N}}_4}$) resonators characterized by 220 GHz free spectral range driven by a continuous wave laser at 1.55 µm for Kerr comb generation, severe issues may arise in the design of achromatic critically coupled resonators because of the difficulty in designing dispersion-free access couplers with controlled coupling factor over a large spectral bandwidth. As a consequence, numerical simulations of Kerr frequency comb in these structures may drastically differ from reality if frequency dependence of the access coupler’s properties is not taken into account in the simulated model. In order to address this issue, we have developed a numerical model that takes into account the frequency dependence of the access coupler coefficients and remains valid even for the simulation of low $Q$ factor resonators. Field propagation within the ring is described by nonlinear Schrödinger equation. The novelty of this model lies in the computation of a complex-valued, frequency-dependent coupling transfer function between a resonant ring and underlying access waveguide that models frequency-dependent dispersion and losses in the access-coupling region of the resonator. Based on simulation results, we discuss the differences observed in Kerr comb generation in resonators with three different coupler designs initially intended to yield critical coupling over the largest achievable bandwidth.

© 2019 Optical Society of America

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