Conservation relations and anisotropic transmission resonances in one-dimensional PT-symmetric photonic heterostructures

TL;DR

This paper explores the unique optical properties of one-dimensional PT-symmetric photonic structures, revealing generalized unitarity relations, anisotropic transmission resonances, and their relation to PT-symmetry breaking.

Contribution

It introduces generalized unitarity relations for complex 1D PT-symmetric structures and identifies anisotropic transmission resonances as signatures of PT-symmetry and its breaking.

Findings

Existence of anisotropic transmission resonances with unit transmission and zero reflection from one side.

Generalized unitarity relations linking scattering matrix elements.

Transmission resonances can occur at PT-symmetry breaking points.

Abstract

We analyze the optical properties of one-dimensional (1D) PT-symmetric structures of arbitrary complexity. These structures violate normal unitarity (photon flux conservation) but are shown to satisfy generalized unitarity relations, which relate the elements of the scattering matrix and lead to a conservation relation in terms of the transmittance and (left and right) reflectances. One implication of this relation is that there exist anisotropic transmission resonances in PT-symmetric systems, frequencies at which there is unit transmission and zero reflection, but only for waves incident from a single side. The spatial profile of these transmission resonances is symmetric, and they can occur even at PT-symmetry breaking points. The general conservation relations can be utilized as an experimental signature of the presence of PT-symmetry and of PT-symmetry breaking transitions. The uniqueness of PT-symmetry breaking transitions of the scattering matrix is briefly discussed by comparing to the corresponding non-Hermitian Hamiltonians.