Modal expansion of the scattered field: Causality, nondivergence, and nonresonant contribution

Abstract

Modal analysis based on the quasinormal modes (QNMs), 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 QNMs in open photonic cavities diverge far away from the scatterer and the possibility of expanding the scattered field with only resonant contributions 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 nonresonant 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.