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Transverse effects in increasing absorption optical bistability

Brian P. McGinnis, Ewan M. Wright, S. W. Koch, Nasser N. Peyghambarian

Published May 21, 1990• 0 citations
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Abstract

Theoretical modeling of increasing absorption optical bistability in thin semiconductors has predicted the appearance of transverse spatial rings in the transmitted intensity profiles of an incident Gaussian laser beam.1 The formation of this ring is due to nonuniform switching of the semiconductor in response to the varying beam profile.

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•Apr 26, 1987•0 citations

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Journal of Applied Physics•Mar 15, 1993•6 citations
Theoretical modeling of increasing absorption optical bistability in thin semiconductors has predicted the appearance of transverse spatial rings in the transmitted intensity profiles of an incident Gaussian laser beam.1 The formation of this ring is due to nonuniform switching of the semiconductor in response to the varying beam profile.
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.
A transverse optical bistability is defined here as a bistability that would not occur with a plane-wave input, i.e., it depends crucially upon the radial variations in the input. Such bistabilities are characterized by much more pronounced changes in transverse profiles than in total transmission. An optical cavity is not required, making such systems good candidates for continuous wave studies of delayed-feedback instabilities which require a round-trip time longer than the medium response time. Trapping bistability and diffraction-free-encoding bistability are two limiting cases of transverse optical bistabilities. Trapping bistability occurs only for a long self-focusing nonlinear medium and arises from self-trapping of a single beam with a single feedback mirror or from cross trapping of two counterpropagating beams. In the diffraction-free-encoding case, diffraction is negligible through the portion of the nonlinear medium performing the encoding, but it is significant through any remaining medium and in the free-space propagation to the mirror and back. This paper is organized as follows: The physics of transverse optical bistabilities is summarized in Section I. Theoretical models are presented in Section II. A thin-sample-encoding (TSE) rings model is defined and shown not only to predict transverse bistability but also to account for the interference rings observed to accompany TSE bistability; it also yields delayed-feedback instabilities with a rich bifurcation sequence. Transverse bistability using a short length of sodium vapor is reported under TSE and DFE conditions in Section III. Recently it was discovered that TSE bistability has been seen only when the feedback beam is displaced from the input by about one beam diameter at the sodium. It remains to be determined just how much the nonconcentric feedback assists the concentric bistability predicted by the TSE rings model. A delayed-feedback instability with a period of twice the round-trip time is also seen.
Absorptive switching and transverse structures in resonatorless optical bistability in bulk ZnSe is observed upon exciting the sample at the Urbach edge. The switching is due to nonlinear absorption induced by a temperature tuning of the band gap. We have modeled such behavior by numerically solving for the intensity, carrier density, and temperature, including both longitudinal and transverse fluctuations. Simulations show that both longitudinal and transverse heat diffusion are necessary in producing specific structures, as well as in determining the time of switching. During switching, the experiment and theory illustrate for the intensity profile the formation of a local minima on axis (hole) followed by a local maxima on axis and local minima off axis (rings). Such beam distortions and bistable switching are the result of the spatial and temporal dynamics and positive feedback existing among the absorption and heating.