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Europhysics Letters (EPL)

Dispersive Optical Bistability with Diffusion: A Scaling Law

Denis L. Weaire, Conor O’Carroll, C Wickham

Published Jan 1, 1989• 5 citations
Publisher

Abstract

Using elementary finite difference methods the response of a Fabry-Perot cavity is investigated for the case of dispersive nonlinearity, with diffusion of the carriers responsible for the nonlinearity. Results are consistent with those of other workers in this field and are extended over a wider range, exposing a simple scaling law for the switch-up power.

DOI
10.1209/0295-5075/8/1/005

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Using elementary finite difference methods the response of a Fabry-Perot cavity is investigated for the case of dispersive nonlinearity, with diffusion of the carriers responsible for the nonlinearity. Results are consistent with those of other workers in this field and are extended over a wider range, exposing a simple scaling law for the switch-up power.
The influence of transverse effects on optical bistability in Fabry-Perot cavity filled with saturable absorber was numerically investigated. A simple model of singlet absorption was used on numerically solving the relationships between the input and output light fields. The proposed model corresponds well to organic compounds considered as novel optical materials with third-order optical nonlinearities. The proposed optically bistable systems were demonstrated for two organic dyes of fluorescein and rhodamine 6G dispersed in transparent solid matrices. Their optically bistable behaviour was anticipated considering the homogeneous and Gaussian distribution of light energy in the radial direction. Most notable cases are discussed related to the changes of the Gaussian beam radii, positive feedback conditions in the Fabry-Perot cavity and considering linear and nonlinear absorption parameters of the organic media. The simulation results enabled us to establish numerically thresholds of Fabry-Perot mirror reflectance and Gaussian beam radius for both nonlinear organic materials, above which absorptive optical bistability can occur. The results can be helpful in design of optical switches for all-optical communication networks.
The system we analyze has the structure of a planar optical waveguide containing a multiple quantum well, with the planes of the wells parallel to the direction of propagation. We consider the two different configurations of a Fabry-P\'erot cavity and distributed-feedback device. The optical nonlinearities are described by means of the first-principles theory developed by Haug, Koch, Schmitt-Rink, and co-workers, generalized to include the finite width of the wells. The dynamics of the system is described by the equations that govern the evolution of the two counterpropagating fields, coupled with the carrier-density equation, and accompanied by the appropriate boundary conditions. The steady-state behavior is analyzed as a function of the control parameters of the system for the case of a GaAs/${\mathrm{Al}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$Gax{\mathrm{Ga}}_{\mathit{x}}Gax​As/AlAs structure. The system develops bistability even when the input field is in resonance with the excitonic peak, but the phenomenon becomes more pronounced in the detuned configuration. The hysteresis cycles obtained in the case of distributed-feedback device turn out to be competitive with those displayed by the Fabry-P\'erot system.