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Journal of the Optical Society of America B

Model for mirrorless optical bistability in multiple-quantum-well GaAs/GaAlAs due to induced absorption

Y. Q. Li, Joseph W. Haus, C. M. Bowden, C. C. Sung

Published Sep 1, 1986• 8 citations
Publisher

Abstract

The temperature dependence of the band gap as a function of the local intensity is taken into consideration for the propagation of light in the multiple-quantum-well structure, GaAs/GaAlAs. With appropriate boundary conditions for heat conduction as well as the field, we derive the conditions for bistability that are due to this mechanism. Analyses of the system parameters in connection with experimental data are also given.

DOI
10.1364/josab.3.001206

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The temperature dependence of the band gap as a function of the local intensity is taken into consideration for the propagation of light in the multiple-quantum-well structure, GaAs/GaAlAs. With appropriate boundary conditions for heat conduction as well as the field, we derive the conditions for bistability that are due to this mechanism. Analyses of the system parameters in connection with experimental data are also given.
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Heat conduction and propagation of the electromagnetic field as well as temperature-dependent absorption are considered in a model for mirrorless optical bistability. The effects of temperature and laser-frequency detuning are calculated and discussed. It is shown that the multiple bistability of output intensity as a function of input intensity can be induced and controlled by the temperature boundary conditions. It is emphasized that changes in these boundary conditions determine the details of the transmission characteristics.
The multiple quantum well structure, GaAs/GaAIAs, displays room temperature optical bistability at very low switching powers in various conditions through the temperature variation and the external voltage across the sample.1,2 We have constructed detailed models to calculate these effects. Coupled Maxwell’s equations and the heat conduction equation are solved to demonstrate how the red shift of the band gap leads to absorptive bistability. The spatial variation of the external field strength is a typical PIN junction and the experimental values of the absorption coefficient are used to obtain the bistability properties as a function of the incident frequency and the biased external voltage. The results based on the actual material constants are in good agreement with the experimental data without adjustable parameters. We also extend the previous work on the stability analysis in the mean-field approximation to this system involving complicated boundary conditions with the propagation effects.
It is shown theoretically that optical bistability will exist in a material whose optical absorption is more than linearly proportional to the degree to which the material is excited. No cavity or external feedback is required. The underlying principle of this bistability appears to be a generalization of several previous independent discussions of mirrorless bistabilities in specific physical systems. This bistability and associated differential gain are demonstrated experimentally using a thermal nonlinearity in a GaAs/GaAlAs multiple-quantum-well semiconductor. Theory and experiment show good agreement.
Longitudinal spatial effects in the nonlinear medium are analyzed in a model for mirrorless optical bistability due to induced absorption that treats heat conduction, electromagnetic field propagation, and temperature-dependent absorption. We consider two specific cases: the temperature-induced shift of the absorption peak of bound I2 excitons in CdS single crystals and the temperature-induced shrinkage of the band gap in GaAs/GaAlAs quantum-well material. For both cases it is shown that the inhomogeneous spatial distribution of the nonlinear absorption profile along the direction of propagation of the electric field undergoes a first-order-like phase transition commensurate with the transition of the output intensity from one value to another for fixed input intensity. Stability conditions are presented for the steady states of the output intensity as a function of the input intensity for the cases treated. There is a multiplicity of bistability curves, and the stability analysis produced the expected branches of stable solutions.
The temperature distribution in a GaAs/(Al,Ga)As multiple quantum well structure was measured with high lateral and temporal resolution while passing through the characteristic hysteresis loop of a thermally induced absorptive optical bistability. In a pump and probe beam experiment, the local transmission spectra of the quantum well structure were recorded and the temperature distribution in the sample was deduced from the spectral positions of characteristic exciton resonances. These resonances remain sufficiently sharp even far above room temperature to guarantee an accuracy of better than 3 K The experiment was conducted under both steady-state and dynamical conditions. The steady-state results were compared with numerical calculations, showing good agreement. The dependence of the relative width of the characteristic hysteresis on the environmental temperature of the bistable sample was investigated. A simple relaxation-time model of the bistability was shown to describe nicely the observed behaviour if the bleaching of the lowest exciton resonance due to high laser intensities is considered. Based on this dependence, a miniature temperature-sensing device using an optical fibre to guide the laser beam is presented.