Frequency‐dependent nonlinear process in microresonators is widely acknowledged, but there is no theory available to calculate the conversion efficiency for each resonance of the ring, except for the phase‐matching one. Similarly for azimuth‐dependent nonlinear process in birefringent rings, there is a lack of theory to analysis the conversion efficiency for each azimuth of the ring. Consequently, it leads to old‐fashioned or ill‐considered coupling position and inefficient energy conversion in birefringent microrings. Here, the study introduces spatio‐temporal coupled‐mode equation to describe mode spatial properties in the cavity, compensating for the deficiency of temporal coupled‐mode equation in describing sophisticated responses. By this equation, it is found that over a wide frequency range, the extremely strong second‐harmonic generation of TE modes can be achieved at different azimuth under different pumps in an X‐cut lithium niobate microring, as proved by a 440 000%/W conversion efficiency in a non‐poling ring recently. This theory is important for realizing an efficient entangled quantum light source, for example. Meanwhile, it will provide new ideas and guidelines for design and applications of monolithic birefringent photonic integrated circuits with high energy efficiency.

中文翻译：

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双折射微环中的时空非线性理论

微谐振器中与频率相关的非线性过程已被广泛认可，但除了相位匹配谐振之外，没有可用的理论来计算环的每个谐振的转换效率。类似地，对于双折射环中的方位角相关的非线性过程，缺乏理论来分析环的每个方位角的转换效率。因此，它导致双折射微环中耦合位置过时或考虑不周以及能量转换效率低下。在此，研究引入时空耦合模式方程来描述腔内的模式空间特性，弥补了时间耦合模式方程在描述复杂响应方面的不足。通过该方程发现，在很宽的频率范围内，X切割铌酸锂微环中的不同泵浦下的不同方位角可以实现极强的TE模二次谐波产生，440 000%/最近非极化环中的 W 转换效率。例如，该理论对于实现高效的纠缠量子光源非常重要。同时，也将为高能效单片双折射光子集成电路的设计和应用提供新的思路和指南。