$\mathcal{PT}$ symmetry and anti-symmetry by anti-Hermitian wave coupling and nonlinear optical interactions

TL;DR

This paper explores how anti-Hermitian wave coupling and nonlinear optical interactions can realize and observe $\\mathcal{PT}$ symmetry and anti-symmetry in optical systems, highlighting their ubiquity and different definitions of parity.

Contribution

It introduces a general framework for observing $\\mathcal{PT}$ symmetry in optics via anti-Hermitian coupling and nonlinear interactions, including new definitions of parity.

Findings

$\\mathcal{PT}$ symmetry observed in anti-Hermitian coupled systems

Different parity definitions reveal additional $\\mathcal{PT}$ symmetric states

Examples include modulation instability and optical parametric amplification

Abstract

Light propagation in systems with anti-Hermitian coupling, described by a spinor-like wave equation, provides a general route for the observation of anti parity-time ($\mathcal{PT}$ ) symmetry in optics. Remarkably, under a different definition of parity operator, a $\mathcal{PT}$ symmetry can be found as well in such systems. Such symmetries are ubiquitous in nonlinear optical interactions and are exemplified by considering modulation instability in optical fibers and optical parametric amplification.