# Indifferent electromagnetic modes: bound states and topology

## TL;DR

This paper explores electromagnetic modes at zero energy in Maxwell's equations, revealing topologically influenced states that are insensitive to local material changes and have applications in non-Hermitian media.

## Contribution

It introduces a Dirac-like formulation of Maxwell's equations to identify zero-energy electromagnetic modes governed by topology, with implications for designing reflectionless and absorptive media.

## Key findings

- Zero-energy electromagnetic modes depend only on asymptotic material parameters.
- Topological properties influence mode asymmetry and behavior.
- Potential applications include reflectionless materials and perfect absorbers or lasers.

## Abstract

At zero energy the Dirac equation has interesting behaviour. The asymmetry in the number of spin up and spin down modes is determined by the topology of both space and the gauge field in which the system sits. An analogous phenomenon also occurs in electromagnetism. Writing Maxwell's equations in a Dirac-like form, we identify cases where a material parameter plays the role of energy. At zero energy we thus find electromagnetic modes that are indifferent to local changes in the material parameters, depending only on their asymptotic values at infinity. We give several examples, and show that this theory has implications for non-Hermitian media, where it can be used to construct permittivity profiles that are either reflectionless, or act as coherent perfect absorbers, or lasers.