Diffraction effects on diffusive bistable optical arrays and optical memory

Bistable responses of Fabry-Pérot cavities and all-optical arrays, in the presence of weak diffraction and strong 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. This bistable nonlinear system, with strong diffusion and weak diffraction, behaves very differently than dispersive bistability with Kerr nonlinearity. Nevertheless, focusing nonlinearity can improve its response characteristics significantly. For example, it is found that hysteresis loops are much wider when nonlinearity is self-focusing than when nonlinearity is self-defocusing. For self-defocusing nonlinearity, strong diffraction can close a hysteresis loop completely. Because of strong diffusion, refractive index distributions are smoothed versions of intensity distributions. This weakens the nonlinear behavior of the system. By approximating the refractive index by a constant, the model is reduced to a discrete map. This reduction incorporates diffraction into a nonlinear response function, allowing diffractive effects to be studied analytically, and shown to agree well with more extensive numerical simulations. Optical arrays are also studied numerically. Because of weaker diffractive crosstalk and a wider "operation gap" between "on" bits and "off" bits, an array with focusing nonlinearity allows finer packing than with self-defocusing nonlinearity. Using the reduced map, optimal packing densities of optical arrays are estimated.