# Optical manifestations of domains with constant topological charge density

## TL;DR

This paper explores how constant topological charge density domains in chiral materials influence electromagnetic phenomena, revealing boundary effects and modifications to wave behavior due to the chiral anomaly.

## Contribution

It demonstrates that the chiral anomaly affects electromagnetic boundary conditions and modifies wave refraction and radiation spectra in domains with constant topological charge density.

## Key findings

- Modified Fresnel equations for constant-$ heta$ domains
- Brewster's angle depends on $ heta$ value
- Transition radiation spectrum is enhanced at finite $ heta$

## Abstract

Domains of finite topological charge density can exist in chiral materials and chiral matter. Spatial and temporal variation of the average topological charge density, represented by the $\theta$-field, induces anomalous currents that are responsible for the chiral magnetic effect, the anomalous Hall effect and other phenomena that are intimately related to the chiral anomaly. We consider domains with constant average topological charge density. We argue that even though the Maxwell equations in the bulk are not altered, the chiral anomaly manifests itself by the way of the boundary conditions. This is illustrated by several examples. The first example deals with the refraction of plane electromagnetic wave on a surface of a constant-$\theta$ domain. We derive the modified Fresnel equations and discuss the effect of the chiral anomaly on the amplitude and polarization of the reflected and transmitted waves. In particular, we argue that the Brewster's angle is sensitive to the value of $\theta$. In the second example we compute the spectrum of the transition radiation at high frequencies and show that it is enhanced at finite $\theta$.