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Physical Review A

Effects of transverse diffusion on increasing absorption bistability

S. W. Koch, Ewan M. Wright

Published Mar 1, 1987• 18 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.35.2542

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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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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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Longitudinal Effects in Increasing Absorption Optical Bistability

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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.

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The steady-state bistability and the evolution of the field envelope of a ring-cavity optical-bistable system including the effect of the transverse radiation field and the effect of an inhomogeneously broadened atomic medium are studied by means of the mean-field approximation and dressed-mode theory in this paper. Our study shows that the bistable region enlarges with an increase of the ratio ${\mathit{r}}_{0}$/${\mathit{w}}_{0}$ (${\mathit{r}}_{0}$ is the radius of the cylindrical atomic sample and ${\mathit{w}}_{0}$ the beam waist of the Gaussian beam), and decreases with increasing width of the inhomogeneously broadened line. The transverse-field effect has more impact on the magnitude of the bistable region than the inhomogeneous broadening under certain conditions. In the case of two unstable modes, the evolution of the field envelope before reaching the stable oscillation regime differs remarkably from that in the case of the plane-wave approximation with a homogeneously broadened atomic medium.

Physical Review A•Aug 1, 1991•5 citations
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.
Transverse effects are known to play a central role in nonlinear-optical systems.Since experiments are generally performed with lasers with finite transverse dimensions, the transverse nature of the field must be considered.Experimental evidence, for example, indicates that mechanisms in the form of diffusive and diffractive coupling within the medium, free-space diffraction, or some combination of these, can create transverse structures which are important in optical bistability and self-focusing/defocusing.In particular, transverse coupling is attributed to such phenomena as radial dependence of the switch up times of bistable loops, spatial hysteresis, and the formation of solitary waves in passive systems.The dynamical effects of free-space diffraction in a unidirectional ring cavity containing a thin resonant absorber driven by an external coherent signal is considered.Minimal focusing effects exist in this system by incorporating a thin medium whose width is small compared to the cavity length and Raleigh range.There is no restriction on the medium response time relative to the round trip time; i.e. the time-dependent polarization is not adiabatically eliminated from the equations of motion.Free-space diffraction effects are isolated and diffraction and diffusive coupling within the medium is negligible.In this model where free-space diffraction is the dominant mechanism for changing the field profile in the system, shifting, deformation, and radial variation of the bistable loop and spatial hysteresis is attributed to an inherent dispersion induced by the free-space diffraction.
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.
The steady-state bistability and the evolution of the field envelope of a ring-cavity optical-bistable system including the effect of the transverse radiation field and the effect of an inhomogeneously broadened atomic medium are studied by means of the mean-field approximation and dressed-mode theory in this paper. Our study shows that the bistable region enlarges with an increase of the ratio r0{\mathit{r}}_{0}r0​/w0{\mathit{w}}_{0}w0​ (r0{\mathit{r}}_{0}r0​ is the radius of the cylindrical atomic sample and w0{\mathit{w}}_{0}w0​ the beam waist of the Gaussian beam), and decreases with increasing width of the inhomogeneously broadened line. The transverse-field effect has more impact on the magnitude of the bistable region than the inhomogeneous broadening under certain conditions. In the case of two unstable modes, the evolution of the field envelope before reaching the stable oscillation regime differs remarkably from that in the case of the plane-wave approximation with a homogeneously broadened atomic medium.