Exceptional contours and band structure design in parity-time symmetric photonic crystals

TL;DR

This paper explores how parity-time symmetric photonic crystals with specific periodicities can undergo thresholdless PT transitions, enabling advanced control over their band structures and resulting in novel optical phenomena.

Contribution

It introduces a $ extbf{k} ullet extbf{p}$ perturbation theory for multidimensional PT-symmetric systems and demonstrates new band structure effects in photonic crystals.

Findings

Thresholdless PT transitions induce significant band structure modifications.

Control over supercollimation and superprism effects in photonic crystals.

Unidirectional optical behavior achieved through PT symmetry.

Abstract

We investigate the properties of multidimensional parity-time symmetric periodic systems whose non-Hermitian periodicity is an integer multiple of the underlying Hermitian system's periodicity. This creates a natural set of degeneracies which can undergo thresholdless $\mathcal{PT}$ transitions. We derive a $\mathbf{k} \cdot \mathbf{p}$ perturbation theory suited to the continuous eigenvalues of such systems in terms of the modes of the underlying Hermitian system. In photonic crystals, such thresholdless $\mathcal{PT}$ transitions are shown to yield significant control over the band structure of the system, and can result in all-angle supercollimation, a $\mathcal{PT}$-superprism effect, and unidirectional behavior.