Optical Reciprocity Induced Symmetry of the Scattering Eigenstates in Non-$\cal PT$-Symmetric Heterostructures

TL;DR

This paper uncovers a new symmetry relation of the scattering matrix in optical heterostructures derived from reciprocity, revealing a quasi-transition akin to PT-symmetry breaking and providing evidence of exceptional points even without gain.

Contribution

It introduces a novel symmetry relation of the scattering matrix based on optical reciprocity, independent of Hermiticity or PT symmetry, and demonstrates its use in identifying exceptional points.

Findings

Identifies a new symmetry relation of the scattering matrix from optical reciprocity.

Reveals a quasi-transition similar to PT-symmetry breaking in non-Hermitian systems.

Provides evidence of exceptional points without gain or traditional PT signatures.

Abstract

The scattering matrix $S$ obeys the unitary relation $S^\dagger S=1$ in a Hermitian system and the symmetry property ${\cal PT}S{\cal PT}=S^{-1}$ in a Parity-Time (${\cal PT}$) symmetric system. Here we report a different symmetry relation of the $S$ matrix in a one-dimensional heterostructure, which is given by the amplitude ratio of the incident waves in the scattering eigenstates. It originates from the optical reciprocity and holds independent of the Hermiticity or $\cal PT$ symmetry of the system. Using this symmetry relation, we probe a quasi-transition that is reminiscent of the spontaneous symmetry breaking of a $\cal PT$-symmetric $S$ matrix, now with unbalanced gain and loss and even in the absence of gain. We show that the additional symmetry relation provides a clear evidence of an exceptional point, even when all other signatures of the $\cal PT$ symmetry breaking are completely erased. We also discuss the existence of a final exceptional point in this correspondence, which is attributed to asymmetric reflections from the two sides of the heterostructure.