论文标题
黑盒耦合模式理论：一个从头算框架，用于建模开放，有损和分散谐振器的电磁相互作用
Black-Box Coupled-Mode Theory: An Ab Initio Framework to Model Electromagnetic Interactions of Open, Lossy, and Dispersive Resonators
论文作者
论文摘要
时间耦合模式理论（TCMT）提供了一个简单而功能强大的平台来建模和分析电磁谐振器系统。然而，限制性的假设和与麦克斯韦方程式缺乏严格的联系限制了TCMT配方的一般性和鲁棒性。本文中，我们介绍了黑框耦合模式理论（BBCMT），这是一种从麦克斯韦方程和准标准模式（QNM）理论开发的一般AB始于CMT框架，用于模拟分散，有损和开放谐振器的电磁相互作用。通过采用Poynting和共轭互惠定理来将BBCMT开发启用，以将QNM严格归一化并计算其扩展系数。我们的新型QNM分析方法允许对谐振器汉密尔顿基质的定义来表征模式的电磁相互作用，能量存储和吸收。独特的是，BBCMT框架可以通过将谐振器散射场作为对背景结构的扰动来捕获谐振器的非谐振散射和吸收，从而考虑到所需的准确性 - 模拟性折价，可以灵活地选择其扰动。 BBCMT建模复杂性可以通过将谐振系统的用户定义子组件作为黑盒进行进一步调整，因为黑盒仅通过其输入输出传输特性描述。除了BBCMT公式之外，我们还提出了两个引理，以反向工程工程，从计算出或测量的远场光谱中逆转建模参数。此外，我们介绍了控制理论的信号流图，以说明，解释和求解BBCMT方程。为了证明BBCMT的有效性和普遍性，我们比较了两个等离子纳米词系统的BBCMT和TCMT预测，以有限差分时间域模拟，并发现BBCMT结果是更好的匹配。在某些约束和近似值下，BBCMT减少了TCMT或空腔扰动理论。
Temporal coupled-mode theory (TCMT) provides a simple yet powerful platform to model and analyze electromagnetic resonator systems. Nevertheless, restrictive assumptions and lack of rigorous connection to Maxwell's equations limit the TCMT formulation's generality and robustness. Herein, we present the Black-box Coupled-Mode Theory (BBCMT), a general ab initio CMT framework developed from Maxwell's equations and quasinormal mode (QNM) theory to model the electromagnetic interactions of dispersive, lossy, and open resonators. BBCMT development is enabled by employing Poynting's and conjugated reciprocity theorems to rigorously normalize QNMs and calculate their expansion coefficients. Our novel QNM analysis approach allows the definition of a resonator Hamiltonian matrix to characterize the modes' electromagnetic interactions, energy storage, and absorption. Uniquely, the BBCMT framework can capture a resonator's non-resonant scattering and absorption by treating the resonator scattered fields as a perturbation to those of a background structure, which can be flexibly chosen considering the desired accuracy-simplicity trade-off. BBCMT modeling complexity can be further adjusted by treating user-defined subcomponents of a resonator system as black-boxes described only by their input-output transfer characteristics. Beyond the BBCMT formulation, we present two lemmas to reverse-engineer the modeling parameters from calculated or measured far-field spectra. Moreover, we introduce the signal flow graphs from control theory to illustrate, interpret, and solve the BBCMT equations. To evince BBCMT's validity and generality, we compare the BBCMT and TCMT predictions for two plasmonic nanoresonator systems to finite-difference time-domain simulations and find BBCMT results to be a much better match. BBCMT reduces to TCMT or cavity perturbation theory under certain constraints and approximations.
