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A non-unitary transformation leading to a Hatano-Nelson problem is performedon an array of equally-spaced optical waveguides. Such transformation producesa non-reciprocal system of waveguides, as the corresponding Hamiltonian becomesnon-Hermitian. This may be achieved by judiciously choosing an attenuation(amplification) of the injected (or exciting) field. The non-Hermitiantransport induced by such transformation is studied for several cases andclosed analytical solutions are obtained. The corresponding non-HermitianHamiltonian may represent an open system that interacts with the environment,either loosing to or being provided with energy from the exterior.

Non-Hermitian propagation in equally-spaced Hermitian waveguide arrays