Abstract

The salient question which arises when light is coupled via a grating or a prism into a waveguide exhibiting an intensity-dependent refractive index is whether switching occurs with or without bistability under appropriate detuning conditions. There are two prevailing theories. In the first¹, a plane wave input is assumed leading to a uniform optically induced index change in the coupling region. In the second², a finite width incident beam is assumed and the growth of the guided field under the coupler leads to an index change proportional to the local guided wave intensity. The first approach leads to optical bistability under certain detuning conditions, whereas the second results in switching only. Although it is known that plane wave analyses are inadequate when dealing with linear-nonlinear interfaces, bistability has been observed experimentally with nonlinear prism couplers³. Fundamentally the finite beam theoretical approaches are unable to predict bistability because no longitudinal feedback is included. Recently we showed that when non-locality is introduced into the optically induced refractive index change, longitudinal feedback occurs and bistability is predicted for the growing mode case⁴. However, the model used for the non-locality was artificial and resulted only in qualitative predictions. In this paper the nonlocality is modelled by the same equation used to describe heat transfer and carrier diffusion, leading to a quantitative estimate of the minimum diffusion length required for bistability.

© 1989 Optical Society of America