Normalization, orthogonality, and completeness of quasinormal modes of open systems: the case of electromagnetism [Invited]

Sauvan, Christophe, Wu, Tong, Zarouf, Rachid, Muljarov, Egor A. ORCID: https://orcid.org/0000-0002-2878-4148 and Lalanne, Philippe 2022. Normalization, orthogonality, and completeness of quasinormal modes of open systems: the case of electromagnetism [Invited]. Optics Express 30 (5) , pp. 6846-6885. 10.1364/OE.443656

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Abstract

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.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Physics and Astronomy
Publisher:	Optical Society of America
ISSN:	1094-4087
Date of First Compliant Deposit:	9 March 2022
Date of Acceptance:	28 January 2022
Last Modified:	14 Nov 2023 23:24
URI:	https://orca.cardiff.ac.uk/id/eprint/148182

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