Poles of the Scattering Matrix: An Inverse Method for Designing Photonic Resonators

TL;DR

This paper introduces a novel inverse design method for photonic resonators by analyzing the poles of the scattering matrix, enabling the creation of structures with high quality factors and multiple resonances.

Contribution

The authors develop a new mathematical framework that efficiently designs photonic structures with high-Q resonances by targeting the poles of the scattering matrix.

Findings

Designs subwavelength structures with Q > 500

Spectral cross sections match Fano lineshapes

Method is computationally efficient and versatile

Abstract

We develop and implement a new mathematical and computational framework for designing photonic elements with one or more high-$Q$ scattering resonances. The approach relies on solving for the poles of the scattering matrix, which mathematically amounts to minimizing the determinant of the Fredholm integral operator of the electric field with respect to the permittivity profile of the scattering element. We apply the method to design subwavelength gradient-permittivity structures with multiple scattering resonances and quality factors exceeding 500. We also find the spectral scattering cross sections are consistent with Fano lineshapes. The compact form and computational efficiency of our formalism suggest it can be a useful tool for designing Fano-resonant structures with multiple high-$Q$ resonances for applications such as frequency mixing and conversion.