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

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.

Quasi-stationary solutions in non-Hermitian systems

“…We explore quasi-stationary states with continuum spectrum in a finite lattice with open boundary conditions. They are not truly stationary but stay stationary in the time scale of a typical experiment in photonics systems [43,44]. We discuss that the transition from the eigenstates to quasistationary states is dramatically non-perturbative.…”

Quantum transport in non-Markovian dynamically-disordered photonic lattices

“…We choose this particular photonic structure because its closed dynamics is effectively described by the unitary evolution of a displaced quantum harmonic oscillator [18], as experimentally demonstrated in [20,21]. In addition, physics of nonlinear [22] and non-Hermitian systems [23,24] can also be studied using such photonic devices. Thus far, there is a lack of theory accounting for the interaction of GF lattices with non-dissipative noisy environments.…”