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TRANSVERSE BEAM PROFILE VARIATIONS IN AN INDUCED ABSORBER.

S. W. Koch, E. M. Wright

Published Apr 26, 1987• 0 citations
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Abstract

For a system showing intrinsic optical bistability due to an absorption which increases with increasing excitation density, we investigate the transverse beam profile variations assuming that longitudinal diffusion over the sample length is enough to exclude formation of longitudinal kinks.1 The general features of our results apply to induced absorption in semiconductors and to other diffusive nonlinear mechanisms.2

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Transverse beam-profile variations are investigated for a system which shows cavityless optical bistability due to increasing absorption. Coupled transport equations for the light field and the excitation density are derived and solved numerically for the case of an optically thin sample, where longitudinal density variations can be neglected and where diffusion of the excitation is the dominant transverse coupling mechanism. Assuming a Gaussian input beam, the increasing absorption is shown to cause substantial profile modifications when the medium undergoes the transition from low to high absorption. The formation of spatial ring structures is predicted and it is shown that transverse carrier diffusion plays an important role in determining both the steady-state and the temporal response of the system.

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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.

Journal of Nonlinear Optical Physics & Materials•Jan 1, 1994•3 citations
For a system showing intrinsic optical bistability due to an absorption which increases with increasing excitation density, we investigate the transverse beam profile variations assuming that longitudinal diffusion over the sample length is enough to exclude formation of longitudinal kinks.1 The general features of our results apply to induced absorption in semiconductors and to other diffusive nonlinear mechanisms.2
Transverse beam-profile variations are investigated for a system which shows cavityless optical bistability due to increasing absorption. Coupled transport equations for the light field and the excitation density are derived and solved numerically for the case of an optically thin sample, where longitudinal density variations can be neglected and where diffusion of the excitation is the dominant transverse coupling mechanism. Assuming a Gaussian input beam, the increasing absorption is shown to cause substantial profile modifications when the medium undergoes the transition from low to high absorption. The formation of spatial ring structures is predicted and it is shown that transverse carrier diffusion plays an important role in determining both the steady-state and the temporal response of the system.
Koch et al.1 have solved for the laser light intensity and the excitation density as a function of time and space (in the beam direction) in a semiconductor doped glass that exhibits increasing absorption2 optical bistability under pulsed operation. A kink in the excitation density that propagates as a discontinuity in the beam direction and manifests itself as a sawtooth variation in the output intensity is predicted. Gibbs et al.3 reported the first experimental observation of kinks in a sharp cut color filter. Kinks that are an emphatic illustration of the local nature of increasing absorption optical bistability are presented. Furthermore, kinks demonstrate an intrinsic dissimilarity between increasing absorption optical bistability and bistability dependent upon external feedback, where a longitudinal discontinuity cannot occur. If the input is an increasing ramp, then the front part of the sample reaches the condition, carrier density, and temperature, for switching down before the remainder, whose light intensity is reduced by absorption in the front. The discontinuity in the excitation density develops as a consequence of competition between transverse thermal conduction and heating of the sample by increasing absorption in the shielded back part of the sample. The number of discontinuities is limited by the pulse rise time, sample length, and conduction time, which scale as the square of the beam radius.
Recently, we predicted1) that partial sample switching can occur in a system showing resonatorless optical bistability due to induced absorption. For an increasing intensity of the incident light, a stepwise propagation of the kink in the excitation profile takes place. In the meantime, the corresponding modulation of the transmitted light has been observed in sharp-cut color filters2). Here, we present an in-depth study of the structure, formation and motion of the kinks. We supplement and expand our original numerical investigations1) by detailed analytical studies. We show that the kink profile may be approximated by a soliton structure if the diffusion of the excitation density is taken into account. Furthermore, we present some simple estimates for the kink propagation.
Koch et al.1 have solved the transport equations for the light intensity and the excitation density for a system that exhibits increasing absorption2 optical bistability. Under pulse operation a kink in the excitation density is predicted, which moves discontinuously in the beam direction and causes a saw-tooth variation in the transmitted intensity. Herein is reported the first observation of these kinks which emphasize the local nature of increasing absorption optical bistabillty. Kinks illustrate well the intrinsic difference between increasing absorption optical bistability and optical bistability that depends on external feedback, where a longitudinal discontinuity cannot occur.
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.