# First-order perturbation theory for material changes in the surrounding of open optical resonators

## TL;DR

This paper extends first-order perturbation theory for open optical resonators to include changes in the surrounding medium, enabling more accurate predictions of resonance shifts and linewidths.

## Contribution

It introduces a novel extension of the perturbation theory to the surrounding medium, complementing existing internal modifications.

## Key findings

- Theory successfully applied to metallic nanosphere and photonic crystal slab
- Retrieves known normalization condition as a side result
- Provides accurate first-order estimates of resonance changes

## Abstract

The single-mode approximation of the resonant state expansion has proven to give accurate first-order approximations of resonance shifts and linewidth changes when modifying the material properties inside open optical resonators. Here, we extend this first-order perturbation theory to modifications of the material properties in the surrounding medium. As a side product of our derivations, we retrieve the already known analytical normalization condition for resonant states. We apply our theory to two example systems: A metallic nanosphere and a one-dimensional photonic crystal slab.