Spectral Mixing, Skin Localization, and Linear Optical Response in Dissipative Photonic Lattices

Abstract

We study the linear optical response of a finite dissipative Hatano--Nelson photonic lattice. The response between selected input and output ports is resolved into a phase-coherent intensity and an incoherent modal-weight contribution using the biorthogonal Green function. Their comparison isolates interference among non-Hermitian modal residues, while a response-weight entropy and the associated participation number $\Neff$ quantify how broadly the measured signal is distributed over the complex modes. The numerical results show that loss broadens the modal distribution, periodic-boundary spectral winding increases modal participation, and onsite disorder reduces it. Time-domain quantum-walk dynamics independently display the drift and right-edge accumulation produced by non-reciprocal hopping under open boundaries. A parameter map in the $(g,W)$ plane, supplemented by disorder-ensemble averages, identifies a finite-size crossover in which $\Neff$ responds to disorder before the response-weighted center is displaced from the skin boundary. The analysis applies to coupled waveguides, microring arrays, driven cavity lattices, and other linear photonic platforms with loss, gain, or non-reciprocal coupling.