Diffraction-free beam propagation at the exceptional point of non-Hermitian Glauber Fock lattices

TL;DR

This paper demonstrates the construction of diffraction-free localized beams in non-Hermitian Glauber Fock lattices at the exceptional point, combining analytical solutions and numerical methods to identify conditions for non-diffracting propagation.

Contribution

It provides a closed-form eigenstate solution at the exceptional point and a numerical approach to find lattices supporting non-diffracting beams.

Findings

Eigenstates at the exceptional point are analytically derived.

Non-diffracting beams are constructed in finite NGF lattices.

Numerical methods identify other lattices supporting diffraction-free propagation.

Abstract

We construct localized beams that are located at the edge of a non-Hermitian Glauber Fock (NGF) lattice made of coupled waveguides and can propagate for a long distance without almost no diffraction. Specifically, we calculate the closed-form of the eigenstates at the exceptional point of a semi-infinite NGF lattice composed of waveguides which are coupled in a unidirectional manner. We use the closed-form solution to construct the non-diffracting beams in finite NGF lattices. We provide a numerical approach to find other lattices that are capable of supporting non-diffracting beams at an exceptional point.