论文标题
具有二次非线性微孔子的耦合模式理论
Coupled-mode theory for microresonators with quadratic nonlinearity
论文作者
论文摘要
我们使用Maxwell的方程来得出几种描述多模式基本场相互作用的模型，以及其在具有二次非线性和准阶段匹配的环微孔子中的第二个谐波。我们演示了如何通过田间信封的傅立叶变换来计算输入非线性极化响应的多模式三波混合总和。具有任意配置文件的准阶段匹配光栅无缝地纳入了我们的模型中。我们还介绍了几个级别的近似级别，以说明非线性系数的分散，并演示如何将耦合模式方程式减少到具有自我固定项的Invelope Lugiato-Lefever方程。 $χ^{（2）} $诱导的级联的Kerr非线性的估计值，在不完美的相匹配方面，将其置于固有的KERR效应上，这是多个数量级。
We use Maxwell's equations to derive several models describing the interaction of the multi-mode fundamental field and its second harmonic in a ring microresonator with quadratic nonlinearity and quasi-phase-matching. We demonstrate how multi-mode three-wave mixing sums entering nonlinear polarisation response can be calculated via Fourier transforms of products of the field envelopes. Quasi-phase-matching gratings with arbitrary profiles are incorporated seamlessly into our models. We also introduce several levels of approximations allowing to account for dispersion of nonlinear coefficients and demonstrate how coupled-mode equations can be reduced to the envelope Lugiato-Lefever-like equations with self-steepening terms. An estimate for the $χ^{(2)}$ induced cascaded Kerr nonlinearity, in the regime of imperfect phase-matching, puts it above the intrinsic Kerr effect by several orders of magnitude.
