Odd-time reversal $PT$ symmetry induced by anti-$PT$-symmetric medium

TL;DR

This paper introduces an optical coupler with odd-time reversal $PT$ symmetry, revealing unique properties and nonlinear mode behaviors in an anti-$PT$-symmetric medium, including stable polarization-based states.

Contribution

It presents the first realization of an optical system with odd-time reversal $PT$ symmetry and explores its linear and nonlinear mode properties.

Findings

Symmetry-protected degeneracy of linear modes

Realization of a coherent polarization-based switch

Existence of stable nonlinear $PT$-conjugate mode pairs

Abstract

We introduce an optical system (a coupler) obeying parity-time ($PT$) symmetry with odd-time reversal, $T^2=-1$. It is implemented with two birefringent waveguides embedded in an anti-$PT$-symmetric medium. The system possesses properties which are untypical for most physical systems with the conventional even-time reversal. Having symmetry-protected degeneracy of the linear modes, the coupler allows for realization of a coherent switch operating with a superposition of binary states which are distinguished by their polarizations. When a Kerr nonlinearity is taken into account, each linear state, being double degenerated, bifurcates into several distinct nonlinear modes, some of which are dynamically stable. The nonlinear modes are characterized by amplitude and by polarization and come in $PT$-conjugate pairs.