Topological non-Hermitian origin of surface Maxwell waves

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 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 number (or a pair of numbers) describing the winding of the complex helicity spectrum across the interface. 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.

Quantum and semiclassical exceptional points of a linear system of coupled cavities with losses and gain within the Scully-Lamb laser theory

“…Now, by combining Eqs. (32) and (33), and using the operatorsâ † j , j = 1, 2 instead of the operatorÔ, one obtains the following solution for the TTCF,…”

Perspective on topological states of non-Hermitian lattices

“…Today, this has shifted to non-Hermitian Hamiltonians regarded as an effective description of, for example, open quantum systems [24,25], where the finite lifetime introduced by electronelectron or electron-phonon interactions [26][27][28], or disorder [29], is modeled through a non-Hermitian term, or in the physics of lasing [30][31][32][33][34]. An additional source of momentum in this field comes from the study of systems where the quantum mechanical description is used after mapping to a Schrödinger-like equation, as in systems with gain and loss (as found in optics and photonics [35][36][37][38]), surface Maxwell waves [39], and topoelectrical circuits [40,41].…”

Chiral Maxwell waves in continuous media from Berry monopoles

“…where f = (E, H) T and is the 6 × 6 matrix associated to the curl part of the equations and does not depend of ω; here (S i ) αβ = i iαβ is formed out of the totally antisymmetric rank 3-tensor and is an element of a spin-1 SU (2) algebra 14,24 . Since at finite frequency the equations in (5) are implied by Eq.…”