Two tractable models of non-stationary light scattering by subwavelength particles and their application to Fano resonances

TL;DR

This paper introduces two analytical models to describe dynamic light scattering by subwavelength particles, explaining complex phenomena like Fano resonances and sharp scattering spikes with high accuracy.

Contribution

The paper presents two new tractable analytical models based on coupled-mode theory and normal modes for non-stationary light scattering, validated against numerical simulations.

Findings

Models accurately predict sharp scattering spikes near pulse edges.

Dynamic effects linked to interference of fast and slow modes are explained.

Application to Fano resonances demonstrates model effectiveness.

Abstract

We introduce two tractable analytical models to describe dynamic effects at resonant light scattering by subwavelength particles. One of them is based on generalization of the temporal coupled-mode theory, and the other employs the normal mode approach. We show that sharp variations in the envelope of the incident pulse may initiate unusual, counterintuitive dynamics of the scattering associated with interference of modes with fast and slow relaxation. To exhibit the power of the models, we apply them to explain the dynamic light scattering of a square-envelope pulse by an infinite circular cylinder made of $GaP$, when the pulse carrier frequency lies in the vicinity of the destructive interference at the Fano resonances. We observe and explain intensive sharp spikes in scattering cross section just behind the leading and trailing edges of the incident pulse. The latter occurs when the incident pulse is over and is explained by the electromagnetic energy released in the particle at the previous scattering stages. The accuracy of the models is checked against their comparison with results of the direct numerical integration of the complete set of Maxwell's equations and occurs very high. The models' advantages and disadvantages are revealed, and the ways to apply them to other types of dynamic resonant scattering are discussed.