Sauvan Christophe, Wu Tong, Zarouf Rachid, Muljarov Egor A, Lalanne Philippe
Opt Express. 2022 Feb 28;30(5):6846-6885. doi: 10.1364/OE.443656.
The scattering of electromagnetic waves by resonant systems is determined by the excitation of the quasinormal modes (QNMs), i.e. the eigenmodes, of the system. This Review addresses three fundamental concepts in relation to the representation of the scattered field as a superposition of the excited QNMs: normalization, orthogonality, and completeness. Orthogonality and normalization enable a straightforward assessment of the QNM excitation strength for any incident wave. Completeness guarantees that the scattered field can be faithfully expanded into the complete QNM basis. These concepts are not trivial for non-conservative (non-Hermitian) systems and have driven many theoretical developments since initial studies in the 70's. Yet, they are not easy to grasp from the extensive and scattered literature, especially for newcomers in the field. After recalling fundamental results obtained in initial studies on the completeness of the QNM basis for simple resonant systems, we review recent achievements and the debate on the normalization, clarify under which circumstances the QNM basis is complete, and highlight the concept of QNM regularization with complex coordinate transforms.
共振系统对电磁波的散射由系统的准正则模（QNMs），即本征模的激发所决定。本综述探讨了与将散射场表示为激发的QNMs叠加相关的三个基本概念：归一化、正交性和完备性。正交性和归一化使得能够直接评估任何入射波的QNM激发强度。完备性保证了散射场可以如实地展开为完整的QNM基。这些概念对于非保守（非厄米）系统并非微不足道，自70年代的初步研究以来推动了许多理论发展。然而，从广泛且分散的文献中很难理解它们，尤其是对于该领域的新手而言。在回顾了关于简单共振系统QNM基完备性的初步研究中获得的基本结果之后，我们综述了最近的成果以及关于归一化的争论，阐明QNM基在何种情况下是完备的，并强调复坐标变换下QNM正则化的概念。
