Universal tractable model of dynamic resonances and its application to light scattering by small particles

TL;DR

This paper introduces a simple, universal model for describing transient resonance effects in complex systems, simplifying their dynamics to a few driven oscillators, and demonstrates its effectiveness in light scattering by small particles.

Contribution

The paper presents a novel, tractable approximation method for transient resonance phenomena applicable across various systems, validated by light scattering simulations.

Findings

Model accurately describes sharp spikes in light scattering

Excellent agreement with numerical simulations

Applicable to many types of resonances

Abstract

If the duration of the input pulse resonantly interacting with a system is comparable or smaller than the time required for the system to achieve the steady state, transient effects become important. For complex systems, a quantitative description of these effects may be a very difficult problem. We suggest a simple tractable model to describe these phenomena. The model is based on approximation of the actual Fourier spectrum of the system by that composed of the superposition of the spectra of uncoupled harmonic oscillators (normal modes). The physical nature of the underlying system is employed to select the proper approximation. This reduces the dynamics of the system to tractable dynamics of just a few driven oscillators. The method is simple and may be applied to many types of resonances. As an illustration, the approach is employed to describe the sharp intensive spikes observed in the recent numerical simulation of short light pulses scattered by a cylinder in the proximity of destructive Fano interference [Phys. Rev. A., vol. 100, 053824 (2019)] and exhibits excellent agreement with the numerics.