Origin of folded bands in metamaterial crystals

TL;DR

This paper investigates the origin of folded bands in metamaterial crystals, revealing their connection to PT-symmetry in non-Hermitian wave equations and explaining the appearance of complex-frequency solutions.

Contribution

It demonstrates that the spectral features in metamaterial crystals are linked to PT-symmetry, providing a new understanding of band folding and complex solutions.

Findings

Real spectra correspond to PT-symmetric solutions

Complex-frequency solutions emerge with broken PT symmetry

Folded bands are explained by non-Hermitian PT-symmetric wave equations

Abstract

Recently it has been found numerically that the spectra of metamaterial crystals may contain pairs of bands which disappear inside the Brillouin zone. We observe that the wave equations for such systems are essentially non-Hermitian, but PT -symmetric. We show that the real-frequency spectra correspond to PT -symmetric solutions of the wave quation. At those momenta in the Brillouin zone where apparently no solutions exist, there appear pairs of complex-frequency solutions with spontaneously broken PT symmetry.