Modal Expansion of the Scattered Field: Causality, Non-Divergence and Non-Resonant Contribution

Abstract

Modal analysis based on the quasi-normal modes (QNM), also called resonant states, has emerged as a promising way for modeling the resonant interaction of light with open optical cavities. However, the fields associated with QNM in open photonic cavities diverge far away from the scatterer and the possibility of expanding the scattered field with resonant contributions only has not been established. Here, we address these two issues while restricting our study to the case of a dispersionless spherical scatterer. First, we derive the rigorous pole expansion of the $T$-matrix coefficients that link the scattered to the incident fields associated with an optical resonator. This expansion evinces the existence of a non-resonant term. Second, in the time domain, the causality principle allows us to solve the problem of divergence and to derive a modal expansion of the scattered field that does not diverge far from the scatterer.

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Cited by in corpus (14)

• Normalization, orthogonality and completeness of quasinormal modes of open systems: the case of electromagnetism
• Quasinormal-mode modeling and design in nonlinear nano-optics
• Efficient near-field to far-field transformations for quasinormal modes of optical cavities and plasmonic resonators
• Generalized Drude-Lorentz Model Complying with the Singularity Expansion Method
• Quasinormal mode expansion of optical far-field quantities
• Nanophotonic resonance modes with the nanobem toolbox
• Non-uniqueness of the Quasinormal Mode Expansion of Electromagnetic Lorentz Dispersive Materials
• First-order perturbation theory for material changes in the surrounding of open optical resonators
• Dynamical quasinormal mode excitation
• Multiple-Order Singularity Expansion Method
• Extending completeness of the eigenmodes of an open system beyond its boundary, for Green's function and scattering-matrix calculations
• Quasinormal modes expansions for nanoresonators made of absorbing dielectric materials: study of the role of static modes
• A scalar product for the radiation of resonant modes
• Gaussian regularization for resonant states: open and dispersive optical systems