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.

中文翻译：

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倍频程克尔频率梳建模中参数频率相关性的数值研究

在不牺牲计算时间的情况下，导出并求解了用于 Kerr 频率梳建模的频域中的广义 Lugiato-Lefever 方程，包括所有参数的全阶频率相关性。所提出的模型在模拟中显示出高精度和高效率，与之前的报告非常吻合。基于所提出的模型，通过在具有空气槽的氮化硅微环谐振器中生成倍频程跨度梳，系统地研究了参数频率依赖性的影响。该器件为宽带梳状生成量身定制，其参数强烈依赖于频率。当分别考虑三种参数影响时，我们得出以下结论。频率相关的传播常数决定是否产生色散波，与相位匹配条件匹配良好。此外，有效面积和非线性折射率的频率依赖性都会引入光谱蓝移。将三个参数的全阶频率依赖性结合在一起，出现了色散波边带，这种现象从未被报道过。我们的工作表明，可以以高计算效率考虑所有参数的全阶频率依赖性，从而能够精确预测 f-2f 自参考的色散波频率，并为理解克尔频率梳的产生开辟了更可靠的途径，尤其是跨倍频程的情况。将三个参数的全阶频率依赖性结合在一起，出现了色散波边带，这种现象从未被报道过。我们的工作表明，可以以高计算效率考虑所有参数的全阶频率依赖性，从而能够精确预测 f-2f 自参考的色散波频率，并为理解克尔频率梳的产生开辟了更可靠的途径，尤其是跨倍频程的情况。将三个参数的全阶频率依赖性结合在一起，出现了色散波边带，这种现象从未被报道过。我们的工作表明，可以以高计算效率考虑所有参数的全阶频率依赖性，从而能够精确预测 f-2f 自参考的色散波频率，并为理解克尔频率梳的产生开辟了更可靠的途径，尤其是跨倍频程的情况。