Spectral Distribution of Exceptional Points in Lattices with Localized Loss

TL;DR

This paper investigates how the geometry of finite waveguide arrays influences the existence and stability of exceptional points caused by localized loss, revealing parity-dependent spectral behaviors and guiding optical structure design.

Contribution

It provides analytical and numerical insights into the parity effect on exceptional points in finite non-Hermitian lattices, a novel understanding in the field.

Findings

Exceptional points depend on array parity (even vs. odd).

Parity effect leads to distinct spectral behaviors.

Guidelines for designing optical structures with controlled EPs.

Abstract

We explore the existence and stability of exceptional points (EPs) in finite waveguide arrays subject to single-site dissipation. We show that the EP landscape is dictated by a geometry-dependent parity effect, leading to strictly distinct spectral behaviors for arrays with even versus odd numbers of waveguides. Through analytical derivation and numerical analysis, we define the conditions under which these singularities emerge and evolve. Our findings clarify the mechanisms of symmetry breaking in finite non-Hermitian lattices, offering new guidelines for the design of robust optical structures that exploit or avoid exceptional points.