Non-uniqueness of the Quasinormal Mode Expansion of Electromagnetic Lorentz Dispersive Materials

Abstract

Any optical structure possesses resonance modes and its response to an excitation can be decomposed onto the quasinormal and numerical modes of discretized Maxwell's operator. In this paper, we consider a dielectric permittivity that is a N-pole Lorentz function of the pulsation $\omega$. We propose a common formalism and obtain different formulas for the modal expansion. The non-uniqueness of the excitation coeffcient is due to a choice of the linearization of Maxwell's equation with respect to $\omega$ and of the form of the source term. We make the link between the numerical discrete modal expansion and analytical formulas that can be found in the literature. We detail the formulation of dispersive Perfectly Matched Layers (PML) in order to keep a linear eigenvalue problem. We also give an algorithm to regain an orthogonal basis for degenerate modes. Numerical results validate the different formulas and compare their accuracy.

arXiv comment11 figures, 21 pages

References in corpus (14)

• Light interaction with photonic and plasmonic resonances
• Rigorous modal analysis of plasmonic nanoresonators
• Resonant state expansion applied to three-dimensional open optical systems
• Quasinormal mode solvers for resonators with dispersive materials
• Quasimodal expansion of electromagnetic fields in open two-dimensionnal structures
• Resonant-state expansion of dispersive open optical systems
• Quasinormal-mode modeling and design in nonlinear nano-optics
• Resonant-state expansion for open optical systems: Generalization to magnetic, chiral, and bi-anisotropic materials
• Riesz-projection-based theory of light-matter interaction in dispersive nanoresonators
• Modal Expansion of the Scattered Field: Causality, Non-Divergence and Non-Resonant Contribution
• Photonics in highly dispersive media: The exact modal expansion
• Quasinormal-mode analysis of grating spectra at fixed incidence angles
• Intrinsic multipolar contents of nanoresonators for tailored scattering
• Completeness and divergence-free behavior of the quasi-normal modes using causality principle

Cited by in corpus (6)

• Normalization, orthogonality and completeness of quasinormal modes of open systems: the case of electromagnetism
• Modal analysis of electromagnetic resonators: user guide for the MAN program
• Exact Maxwell evolution equation of resonators dynamics: temporal coupled-mode theory revisited
• A continuous family of Exact Dispersive Quasi-Normal Modal (DQNM) Expansions for dispersive photonic structures
• Resonance expansion of quadratic quantities with regularized quasinormal modes
• Quasinormal modes expansions for nanoresonators made of absorbing dielectric materials: study of the role of static modes