多层纳米光子学中作为边值问题的非线性麦克斯韦方程
Nonlinear Maxwell's Equations as a Boundary Value Problem in Multilayer Nanophotonics
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中文总结 AI 辅助
本文提出结合转移矩阵法与迭代格林函数法的统一框架，将线性多层响应作为边界条件纳入非线性边值问题自洽求解，经两个示例验证，可关联纳米光子设计与超快非线性动力学。
中文摘要 AI 辅助
计算复杂纳米光子结构中的强场、宽带非线性现象仍然存在困难，因为这需要同时处理非微扰动力学、脉冲过程和结构复杂性。本文介绍了一种统一框架，将转移矩阵方法与迭代格林函数方法相结合。线性多层响应作为边界条件被纳入非线性边值问题中，随后自洽求解，自然适配宽光谱和任意非线性。该框架通过透明和共振区域的两个示例进行验证：第一个示例展示了二次谐波产生中的脉冲光谱调制，仅通过全结构宽带处理才能捕捉；第二个示例展示了泵浦-探测实验中激子-极化激元的完整动力学演化，通过统一模拟重现。该框架将纳米光子设计与超快非线性动力学直接关联起来。
英文摘要
Calculating strong-field, broadband nonlinear phenomena in complex nanophotonic structures remains difficult because it requires simultaneous handling of non-perturbative dynamics, impulsive processes, and structural complexity. Here, we introduce a unified framework that combines the transfer matrix method with an iterative Green's function approach. The linear multilayer response is incorporated as boundary conditions into a nonlinear boundary value problem, which is then solved self-consistently, naturally accommodating broad spectra and arbitrary nonlinearity. The framework is validated with two examples in the transparent and resonant regimes, respectively. The first demonstrates an impulsive spectral modulation in second harmonic generation that is captured only by a full-structure broadband treatment. The second demonstrates the entire dynamical evolution of exciton-polaritons in a pump-probe experiment reproduced by a unified simulation. This framework directly links nanophotonic design with ultrafast nonlinear dynamics.
