Temporal coupled-mode theory for Fano resonance in light scattering by a single obstacle

TL;DR

This paper develops a temporal coupled-mode theory to describe Fano resonance in light scattering by single obstacles, applicable to small or symmetric systems, validated through simulations and used to design structures with tailored optical properties.

Contribution

It introduces a simple coupled-mode formalism for Fano interference in light scattering, applicable to small and symmetric obstacles, and demonstrates its utility in designing specific optical responses.

Findings

The theory accurately models Fano resonance line shapes.

Numerical simulations validate the theoretical predictions.

Designed structures exhibit strong absorption with weak scattering at the same frequency.

Abstract

We present a theory for Fano interference in light scattering by individual obstacle, based on a temporal coupled-mode formalism. This theory is applicable for obstacles that are much smaller than the incident wavelength, or for systems with two-dimensional cylindrical or three-dimensional spherical symmetry. We show that for each angle momentum channel, the Fano interference effect can be modeled by a simple temporal coupled-mode equation, which provides a line shape formula for scattering and absorption cross-section. We validate the analysis with numerical simulations. As an application of the theory, we design a structure that exhibits strong absorption and weak scattering properties at the same frequency.