Integrated, monolithic nonlinear cavities are of great interest in both classical and quantum optics experiments due to their high efficiency and stability. However, a general analytic theory of classical three-wave mixing in such monolithic systems, including both linear and nonlinear regions with arbitrary finesse and non-zero propagation losses, is a challenging task. Here, we derive such a model for any three-wave mixing process (second harmonic, sum frequency and difference frequency generation) under the sole assumption of low single-pass conversion efficiency. We demonstrate remarkable agreement between the presented model and the experimentally obtained highly complex second-harmonic spectrum of a titanium-indiffused lithium niobate waveguide cavity that includes both a linear and nonlinear section. We then show the effect that reversing the linear and nonlinear regions has on the output spectrum, highlighting the importance of system design. Finally, we demonstrate that the model can be extended to include the effect of phase modulation applied to the cavity.

由于其高效率和稳定性，集成的单片非线性腔在经典和量子光学实验中都引起了极大的兴趣。然而，在这种单片系统中，包括具有任意精细度和非零传播损耗的线性和非线性区域的经典三波混频的一般分析理论是一项具有挑战性的任务。在这里，我们在低单通转换效率的唯一假设下为任何三波混频过程（二次谐波、和频和差频生成）推导出这样的模型。我们证明了所提出的模型与实验获得的钛扩散铌酸锂波导腔的高度复杂的二次谐波谱之间的显着一致性，其中包括线性和非线性部分。然后我们展示了反转线性和非线性区域对输出频谱的影响，突出了系统设计的重要性。最后，我们证明该模型可以扩展到包括应用于腔的相位调制的影响。