Focusing-defocusing effects for diffusion-dominated bistable optical arrays

Bistable responses of Fabry-Perot cavities and optical arrays in the presen ce of diffraction and diffusion are studied both analytically and numerical ly. The model is a pair of nonlinear Schrodinger equations coupled through a diffusion equation. The numerical computations are based on a split-step method, with three distinct characteristics. In these diffusion-dominated a rrays with weak diffraction, this study demonstrates that focusing nonlinea rity can improve the response characteristics significantly. The primary re sults of the study are that (1) for diffusion-dominated media a small amoun t 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 m edia; (4) in the presence of diffraction the response of the array can be d escribed analytically by a reduced map, whose derivation can be viewed as a n extension of Firth's diffusive model to include weak diffraction; (5) thi s map is used to explain analytically certain qualitative features of bista bility, as observed in the numerical experiments; and (6) optimal spacing p redictions are made with a reduced map and verified with numerical simulati ons of small all-optical arrays. (C) 1999 Optical Society of America [S0740 -3224(99)00107-1].