# Topological non-Hermitian origin of surface Maxwell waves

## TL;DR

This paper reveals that surface Maxwell waves at media interfaces have a topological origin linked to the helicity operator, with their properties characterized by a Z4 invariant, offering new insights into wave physics and metamaterials.

## Contribution

It introduces a topological classification of surface Maxwell waves based on the helicity operator's spectrum, extending topological concepts to non-Hermitian wave physics in optics.

## Key findings

- Surface Maxwell waves are topologically protected by a Z4 invariant.
- The helicity operator's non-Hermitian nature is key to the topological classification.
- Additional Z2 indices distinguish TE and TM polarization zones.

## Abstract

Maxwell electromagnetism, describing the wave properties of light, was formulated 150 years ago. More than 60 years ago it was shown that interfaces between optical media (including dielectrics, metals, negative-index materials) can support surface electromagnetic waves, which now play crucial roles in plasmonics, metamaterials, and nano-photonics. Here we show that surface Maxwell waves at interfaces between homogeneous, isotropic media described by real permittivities and permeabilities have a purely topological origin explained by the bulk-boundary correspondence. Importantly, the topological classification is determined by the helicity operator, which is generically non-Hermitian even in lossless optical media. The corresponding topological invariant, which determines the number of surface modes, is a Z4 number (or a pair of Z2 numbers) describing the winding of the complex helicity spectrum across the interface. Moreover, there is an additional pair of non-topological Z2 indices, which describe zones of the TE and TM polarizations at the phase diagram of surface modes. Our theory provides a new twist and insights for several areas of wave physics: Maxwell electromagnetism, topological quantum states, non-Hermitian wave physics, and metamaterials.

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Source: https://tomesphere.com/paper/1901.00346