Mohajan Jewel, Chao Pengning, Jin Weiliang, Molesky Sean, Rodriguez Alejandro W
Opt Express. 2023 Dec 18;31(26):44212-44223. doi: 10.1364/OE.513565.
Recent advances in fundamental performance limits for power quantities based on Lagrange duality are proving to be a powerful theoretical tool for understanding electromagnetic wave phenomena. To date, however, in any approach seeking to enforce a high degree of physical reality, the linearity of the wave equation plays a critical role. In this manuscript, we generalize the current quadratically constrained quadratic program framework for evaluating linear photonics limits to incorporate nonlinear processes under the undepleted pump approximation. Via the exemplary objective of enhancing second harmonic generation in a (free-form) wavelength-scale structure, we illustrate a model constraint scheme that can be used in conjunction with standard convex relaxations to bound performance in the presence of nonlinear dynamics. Representative bounds are found to anticipate features observed in optimized structures discovered via computational inverse design. The formulation can be straightforwardly modified to treat other frequency-conversion processes, including Raman scattering and four-wave mixing.
基于拉格朗日对偶性的功率量基本性能极限的最新进展，正被证明是理解电磁波现象的有力理论工具。然而，迄今为止，在任何力求高度符合物理实际的方法中，波动方程的线性都起着关键作用。在本论文中，我们将当前用于评估线性光子学极限的二次约束二次规划框架进行推广，以纳入在泵浦未耗尽近似下的非线性过程。通过在（自由形式的）波长尺度结构中增强二次谐波产生这一示例性目标，我们展示了一种模型约束方案，该方案可与标准凸松弛相结合，以在存在非线性动力学的情况下限制性能。发现代表性边界能够预测通过计算逆设计发现的优化结构中观察到的特征。该公式可以直接修改以处理其他频率转换过程，包括拉曼散射和四波混频。
