Brillouin-zone definition in non-reciprocal Willis monatomic lattices

TL;DR

This paper analytically defines the Brillouin zone in non-reciprocal Willis monatomic lattices, revealing that non-reciprocity shifts zone boundaries but keeps the zone area constant, affecting wave propagation characteristics.

Contribution

It provides the first analytical quantification of Brillouin-zone shifts in non-reciprocal Willis lattices, including one-dimensional and square lattice extensions.

Findings

BZ boundaries shift with non-reciprocity in 1D lattices

BZ width remains constant despite non-reciprocity

Asymmetric dispersion diagrams have unequal wavenumber ranges

Abstract

Brillouin-zone (BZ) definition in a class of non-reciprocal Willis monatomic lattices (WMLs) is analytically quantified. It is shown that BZ boundaries only shift in response to non-reciprocity in one-dimensional WMLs, implying a constant BZ width, with asymmetric dispersion diagrams exhibiting unequal wavenumber ranges for forward and backward going waves. An extension to square WMLs is briefly discussed, analogously demonstrating the emergence of shifted and irregularly shaped BZs, which maintain constant areas regardless of non-reciprocity strength.