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

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.