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

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