Many nanophotonic systems are strongly coupled to radiating waves, or suffer significant dissipative losses. Furthermore, they may have complex shapes which are not amenable to closed form calculations. This makes it challenging to determine their modes without resorting to quasi-static or point dipole approximations. To solve this problem, the quasi-normal modes (QNMs) are found from an integral equation model of the particle. These give complex frequencies where excitation can be supported without any incident field. The corresponding eigenvectors yield the modal distributions, which are non-orthogonal due to the non-Hermitian nature of the system. The model based on quasi-normal modes is applied to plasmonic and dielectric particles, and compared with a spherical multipole decomposition. Only with the QNMs is it possible to resolve all features of the extinction spectrum, as each peak in the spectrum can be attributed to a particular mode. In contrast, many of the multipole coefficient have multiple peaks and dips. Furthermore, by performing a multipolar decomposition of each QNM, the spectrum of multipole coefficients is explained in terms of destructive interference between modes of the same multipole order.
David A. Powell, "Resolving nanophotonic spectra with quasi-normal modes
(Conference Presentation)," Proc. SPIE 9921, Plasmonics: Design, Materials, Fabrication, Characterization, and Applications XIV, 99211B (Presented at SPIE Nanoscience + Engineering: August 31, 2016; Published: 9 November 2016); https://doi.org/10.1117/12.2237428.5161456650001.
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