Nonparaxial electromagnetic Bragg scattering in periodic media with PT symmetry

TL;DR

This paper analytically investigates nonparaxial electromagnetic Bragg scattering in PT-symmetric periodic media, revealing complex wave dynamics, energy exchange regimes, and nonreciprocal behavior across symmetry-breaking transitions.

Contribution

It provides exact solutions beyond the paraxial approximation for PT-symmetric lattices, detailing the regimes of symmetry breaking and associated wave dynamics.

Findings

Identified three regimes of wave behavior based on symmetry breaking.

Derived analytic solutions for Maxwell's equations in complex periodic media.

Showed nonreciprocal, unidirectional evolution characteristic of PT-symmetric systems.

Abstract

The evolution of a pair of resonant Bragg modes through a medium characterized by a complex one-dimensional $\mathcal{PT}$-symmetric periodic permittivity is thoroughly investigated. Analytic solutions of Maxwell's equations are derived beyond the paraxial approximation to investigate the periodic energy exchange that occurs between the Bragg modes for the Hermitian lattices as well as for complex lattices. Three regimes defined by the symmetry breaking point are discussed: below it, above it and at it. These regimes are determined by the existence of four real eigenvalues in the symmetric phase, which collide and coalesce into a pair at the breaking point. Above the critical value each member of the pair bifurcates into a pair of complex values. Therefore, the complex lattice reveals a variety of wave dynamics depending on the gain/loss balance. In all regimes of the transition the signature of $\mathcal{PT}$-symmetric systems is present, as the evolution is always nonreciprocal and unidirectional.