Perturbative Born theory for light scattering by time-modulated scatterers

TL;DR

This paper develops a perturbative theoretical framework for light scattering by time-modulated particles, deriving explicit scattering matrix expressions and analyzing inelastic scattering phenomena in resonant dielectric structures.

Contribution

It introduces a first-order Born approximation approach for dynamic electromagnetic scattering, relating it to static modes and demonstrating control over inelastic channels in resonators.

Findings

Inelastic scattering amplitudes depend on overlap integrals of static modes.

Modal orthogonality can suppress inelastic scattering channels.

Resonant structures can enhance inelastic scattering via high-Q modes.

Abstract

We present a theoretical framework for electromagnetic scattering by particles with a permittivity that is periodically varying in time, based on a perturbative approach. Within this framework, we derive explicit expressions for the scattering matrix of the dynamic system in a first-order Born approximation, relating it directly to the corresponding static problem. We show that inelastic scattering amplitudes are governed by overlap integrals between static modes at the input and output frequencies. Using this insight, we analyze scattering from a time-modulated, isotropic, dielectric sphere and a high-permittivity dielectric cylinder, and demonstrate how modal orthogonality can suppress inelastic channels, while appropriate tuning of geometric parameters can significantly enhance them. In particular, we show that cylindrical resonators support strong inelastic scattering when resonance-to-resonance optical transitions, induced by the temporal variation, involve a high-Q supercavity mode. Comparison with full time-Floquet calculations confirms that the first-order Born approximation remains quantitatively accurate for modest modulation amplitudes and provides clear physical intuition for frequency conversion and resonance-mediated scattering processes in time-modulated photonic resonators.