Inverse Design in the Complex Plane: Manipulating Quasi-Normal Modes

TL;DR

This paper introduces two novel methods for directly controlling the complex frequencies of quasi-normal modes in materials, enabling precise manipulation of their spectral properties for advanced optical design.

Contribution

It presents an eigen-permittivity approach and a perturbation theory method for targeted manipulation of quasi-normal modes in the complex plane.

Findings

Successfully shifts quasi-normal mode frequencies to desired values

Provides a systematic approach for inverse design of optical structures

Enables precise spectral control of resonant modes

Abstract

Utilising the fact that the frequency response of a material can be decomposed into the quasi-normal modes supported by the system, we present two methods to directly manipulate the complex frequencies of quasi-normal modes in the complex plane. We first consider an `eigen-permittivity' approach that allows one to find how to shift the permittivity of the structure everywhere in order to place a single quasi-normal mode at a desired complex frequency. Secondly, we then use perturbation theory for quasi-normal modes to iteratively change the structure until a given selection of quasi-normal modes occur at desired complex frequencies.