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Journal of the Optical Society of America B

Longitudinal spatial inhomogeneities in intrinsic optical bistability due to induced absorption

Charles M. Bowden, Chi C. Sung, Joseph W. Haus, J. M. Cook

Published Jan 1, 1988• 7 citations
Publisher

Abstract

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.

DOI
10.1364/josab.5.000011

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Using the nonlinear oscillator model as a prototype medium exhibiting intrinsic optical bistability, we investigate the inhomogeneous absorption of the electromagnetic field. The forward- and backward-field amplitudes and diffraction effects are retained in the mathematical description. Analytic results are given in the limit of plane-wave propagation under steady-state conditions. The transmitted and reflected intensity exhibit a structure that is determined by the spatial inhomogeneity of the absorption in the longitudinal direction. The transmitted intensity has a structure that is dependent on the length of the medium. The reflected intensity has an interference structure from light reflected at the front surface and the internal boundary separating a high-polarization from a low-polarization branch. A degenerate-four-wave-mixing experiment is predicted to be a very sensitive probe of the internal boundary and the interference between the forward and backward field. The phase-conjugate signal develops large oscillations as the input field is varied. Numerical results for diffraction effects are also given, and we find that the plane-wave results for the center of the beam remain reliable down to Fresnel numbers of order unity and in media that are smaller than the linear absorption length.
Dynamical transient response and longitudinal spatial evolution of the first-order phase transition are presented for intrinsic optical bistability of a system of interacting spatially distributed, coherently driven two-level atoms. It is shown that a discontinuity in the nonlinear dielectric function is established internal to the medium due to transient response to a coherent, externally applied, time-dependent driving field, following the attainment of a critical value for the input intensity. If the externally applied field intensity reaches the steady state, beyond the critical value, the discontinuity of the nonlinear dielectric function in the medium reaches a stable stationary condition and forms a spatial boundary between states of high and low polarization in the medium. Thus it is shown that intrinsic optical bistability corresponds to a spatial as well as a temporal first-order phase transition in light-matter interactions, far from thermodynamic equilibrium, where the spatial boundary between different phases is established by transient dynamical response to the incident field.
In this contribution the systematic analysis of the steady-state absorptive optical bistability in a thin semiconductor film is given. The heat-conductivity equation with corresponding two-point boundary conditions is solved numerically and the analytical approximation of the switching intensity is given based on the theorem about lower bounds for critical parameters in nonlinear boundary-value problems. The influences of diffusion and of spatial inhomogenities of the excitation profiles in the sample on the input-output characteristic are analyzed in detail. The transverse nonuniformity of the system leads to a condition for the existence of bistability that differs significantly from the well known case of a spatially homogeneous excitation of the medium. The critical slowing down phenomenon is discussed analytically and compared to previous experimental results.
Mirrorless optical bistability has been established in CdS1 and in multiple quantum well (MQW) GaAs structures2. The mechanism responsible for the bistable behavior in these semiconductors is the coupling between the temperature distribution and the electric field intensity in the sample. In these semiconductors, the mechanism is simple enough that a quantitative analysis should be possible. However, a successful model of bistability in these systems must await a careful experimental analysis of the thermal boundary conditions3. With this caveat we have proceeded with the theoretical development. Steady-state results for CdS and MQW GaAs are presented.
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.