Bistable responses of Fabry–Perot cavities and optical arrays in the presence of diffraction and diffusion are studied both analytically and numerically. The model is a pair of nonlinear Schrödinger equations coupled through a diffusion equation. The numerical computations are based on a split-step method, with three distinct characteristics. In these diffusion-dominated arrays with weak diffraction, this study demonstrates that focusing nonlinearity can improve the response characteristics significantly. The primary results of the study are that (1) for diffusion-dominated media a small amount of diffraction is sufficient to alter optical bistability significantly; (2) focusing nonlinearities enhance optical bistability in comparison with defocusing nonlinearities; (3) in diffusion-dominated media these focusing–defocusing effects are quite distinct from self-focusing behavior in Kerr media; (4) in the presence of diffraction the response of the array can be described analytically by a reduced map, whose derivation can be viewed as an extension of Firth’s diffusive model to include weak diffraction; (5) this map is used to explain analytically certain qualitative features of bistability, as observed in the numerical experiments; and (6) optimal spacing predictions are made with a reduced map and verified with numerical simulations of small all-optical arrays.
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