Leaky Modes of Solid Dielectric Spheres

Abstract

In the absence of external excitation, light trapped within a dielectric medium generally decays by leaking out, and also by getting absorbed within the medium. We analyze the leaky modes of solid dielectric spheres by examining solutions of Maxwell's equations for simple homogeneous, isotropic, linearly dispersive media that admit complex-valued oscillation frequencies. We show that, under appropriate circumstances, these leaky modes constitute a complete set into which an initial electromagnetic field distribution inside a dielectric sphere can be expanded. We provide the outline of a completeness proof, and also present results of numerical calculations that illustrate the close relationship between the leaky modes and the resonances of solid dielectric spherical cavities.

19 pages, 9 figures, 24 equations, 28 references, one Appendix. (There exists some overlap with the corresponding conference paper, "Leaky Modes of Dielectric Cavities," by M. Mansuripur, M. Kolesik, and P. Jakobsen, Proceedings of SPIE 9931, 99310B~1:20 (2016); also available at arXiv:1610.00045.)

References in corpus (11)

• Modes and Mode Volumes of Leaky Optical Cavities and Plasmonic Nanoresonators
• Resonant state expansion applied to three-dimensional open optical systems
• Quasimodal expansion of electromagnetic fields in open two-dimensionnal structures
• Resonant state expansion applied to two-dimensional open optical systems
• Resonant-state expansion of dispersive open optical systems
• Resonant state expansion applied to planar waveguides
• A roundtrip matrix method for calculating the leaky resonant modes of open nanophotonic structures
• Probabilistic Interpretation of Resonant States
• Resonant-state-expansion Born approximation with a correct eigenmode normalisation
• Natural modes and resonances in a dispersive stratified N-layer medium
• Resonant-state-expansion Born approximation for waveguides with dispersion

Cited by in corpus (6)

• Light interaction with photonic and plasmonic resonances
• Normalization, orthogonality and completeness of quasinormal modes of open systems: the case of electromagnetism
• Modal Expansion of the Scattered Field: Causality, Non-Divergence and Non-Resonant Contribution
• Light propagation and magnon-photon coupling in optically dispersive magnetic media
• Multiple-Order Singularity Expansion Method
• Quasinormal modes expansions for nanoresonators made of absorbing dielectric materials: study of the role of static modes