Numerical Investigation of Parametric Frequency Dependence in the Modeling of Octave-Spanning Kerr Frequency Combs

A generalized Lugiato-Lefever equation in frequency domain for the modeling of Kerr frequency combs, including full-order frequency dependence of all parameters, is derived and solved without sacrifice of computational time. The proposed model shows high accuracy and efficiency in simulations, agreeing well with previous reports. Based on the proposed model, the influence of parametric frequency dependence is systemically investigated by generating octave-spanning combs in a silicon-nitride micro-ring-resonator with an air slot. The device is dispersion-tailored for broadband comb generation, and its parameters are strongly dependent on frequency. When considering three kinds of parametric influence separately, we reach the following conclusions. The frequency dependent propagation constant determines whether the dispersive wave is generated, matching well with the phase-matching condition. Besides, the frequency dependence of effective area and nonlinear refractive index can both introduce spectral blue-shift. Combining full-order frequency dependence of the three parameters together, a dispersive wave sideband emerges and this phenomenon has never been reported. Our work reveals that full-order frequency dependence of all parameters can be considered with high computational efficiency, which enables precise prediction of dispersive wave frequency for f-2f self-referencing and opens up more reliable avenues for the understanding of Kerr frequency comb generation, especially octave-spanning cases.