Perrin Mathias
Opt Express. 2016 Nov 28;24(24):27137-27151. doi: 10.1364/OE.24.027137.
We derive a quasi-normal mode theory for three-dimensional scatterers, taking care to remove an hypothesis of weakly dispersive materials implicitely used in previous works. In our approach, the normalized modes remain unchanged, but the analytic expansion coefficients onto the set of QNM are modified. In particular, we take into account in a simple way the non-orthogonality of the modes, and we set up a rigourous frame, to treat the case where several QNMs are excited. Eventally, the complex concept of PML integration, previously introduced, becomes unnecessary, even to compute the QNM mode volume. Besides, crossover integrals of QNM fields over the whole space can now be written rigourously, as integrals on the finite volume of the scatterer, without surface terms.
我们推导了三维散射体的准正态模理论，特别注意去除先前工作中隐含使用的弱色散材料假设。在我们的方法中，归一化模式保持不变，但在准正态模集合上的解析展开系数会被修改。特别是，我们以一种简单的方式考虑了模式的非正交性，并建立了一个严格的框架来处理多个准正态模被激发的情况。最终，先前引入的复杂的完全匹配层（PML）积分概念变得不再必要，甚至在计算准正态模模式体积时也是如此。此外，现在可以严格地将准正态模场在整个空间上的交叉积分写成散射体有限体积上的积分，而没有表面积分项。
