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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Interplay between heat diffusion and self-focusing in absorptive optical bistability

F. Pereira, Michael Scott Belsley, José R. Salcedo

Published May 20, 1996• 0 citations
Publisher

Abstract

We used a modified form of the Z-scan technique to study the various factors influencing bistability in a semiconductor doped glass filter. A strong self-focusing effect was observed and an estimate of the corresponding n2 coefficient is obtained. A systematic modeling of absorptive bistability in a semiconductor doped glass, including both longitudinal and transverse heat diffusion as well as the effects of self-focusing, is presented and compared with experimental observations.

DOI
10.1117/12.240540

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We used a modified form of the Z-scan technique to study the various factors influencing bistability in a semiconductor doped glass filter. A strong self-focusing effect was observed and an estimate of the corresponding n2 coefficient is obtained. A systematic modeling of absorptive bistability in a semiconductor doped glass, including both longitudinal and transverse heat diffusion as well as the effects of self-focusing, is presented and compared with experimental observations.
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We have characterized the transverse spatial dependence of the real and imaginary parts of the complex nonlinear refractive index of a semiconductor doped glass filter, which exhibits absorptive bistability. Using the Z-scan technique, combined with an interferometric measurement of the integrated optical thickness, we are able to fit the observed experimental data assuming a quadratically varying transverse temperature profile in the sample. The transverse variations in the nonlinear refractive index do not scale directly with the size of the incident beam, but exhibit marked asymmetries depending on whether the incident beam is converging or diverging.
We have characterized the transverse spatial dependence of the real and the imaginary parts of the complex nonlinear refractive index of a semiconductor-doped glass filter that exhibits absorptive bistability. Using the Z-scan technique combined with an interferometric measurement of the integrated optical thickness, we are able to fit the observed experimental data, assuming a quadratically varying transverse temperature profile in the sample. The transverse variations in the nonlinear refractive index do not scale directly with the size of the incident beam but exhibit marked asymmetries that depend on whether the incident beam is converging or diverging.
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.
We present a simple experiment which demonstrates the main features of intrinsic optical bistability obtained through thermally induced shifts in the band edge of semiconductor particles embedded in a glass matrix. This readily demonstrates how nonlinear optical effects can be used to transmit information, providing an instructive introduction to the main concepts of optical computing. Several possible extensions of the experiment suitable for advanced independent research projects are discussed.
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.