Exceptional points of degeneracy and $\cal{PT}$-symmetry in photonic coupled chains of scatterers

TL;DR

This paper explores exceptional points of degeneracy in non-Hermitian photonic coupled chains, revealing new types of degeneracies and their conditions, with implications for advanced light control and photonic device applications.

Contribution

It demonstrates the existence of second- and fourth-order EPDs in coupled scatterer chains, including under conditions where $\ ext{PT}$-symmetry is not required, expanding understanding of degeneracies in photonic systems.

Findings

Second-order EPD associated with $\ ext{PT}$-symmetry in coupled chains.

Fourth-order EPD at the band edge with gain and loss balance.

$\ ext{PT}$-symmetry is not necessary for EPD realization.

Abstract

We demonstrate the existence of exceptional points of degeneracy (EPD) of periodic eigenstates in non-Hermitian coupled chains of dipolar scatterers. Guided modes supported by these structures can exhibit an EPD in their dispersion diagram at which two or more Bloch eigenstates coalesce, in both their eigenvectors and eigenvalues. We show a second-order modal EPD associated with the parity-time ($\cal{PT}$) symmetry condition, at which each particle pair in the double chain exhibits balanced gain and loss. Furthermore, we also demonstrate a fourth-order EPD occurring at the band edge. Such degeneracy condition was previously referred to as a degenerate band edge in lossless anisotropic photonic crystals. Here, we rigorously show it under the occurrence of gain and loss balance for a discrete guiding system. We identify a more general regime of gain and loss balance showing that $\cal{PT}$-symmetry is not necessary to realize EPDs. Furthermore, we investigate the degree of detuning of the EPD when the geometrical symmetry or balanced condition is broken. These findings open unprecedented avenues toward superior light localization and transport with application to high-Q resonators utilized in sensors, filters, low-threshold switching and lasing.