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Journal of the Optical Society of America B

Transverse effects in intrinsic optical bistability

Michael Scalora, Joseph W. Haus

Published Sep 1, 1989• 12 citations
Publisher

Abstract

Electromagnetic wave propagation with one transverse dimension is investigated in a medium whose response is modeled by a nonlinear oscillator. We report results with transverse effects due to diffraction, which are controlled by varying the Fresnel number. We find that diffraction does not significantly reduce the bistable intensity characteristics either for the center of the beam intensity or in the intensity integrated across the transverse coordinate, although in the latter case the contrast is reduced; bistable behavior is found to persist even for a Fresnel number of order unity, and the switching intensity is not affected by the Fresnel number. These results are explained by simple physical arguments.

DOI
10.1364/josab.6.001714

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Transverse effects in intrinsic optical bistability

Michael Scalora, Joseph W. Haus, C. M. Bowden

A nonlinear oscillator model is used as a prototypical medium for intrinsic optical bistability.1 The phenomenon of intrinsic optical bistability is so named because the medium does not require the optical feedback of a cavity. In this model we retain dispersive effects and introduce a diffractive coupling of the electromagnetic field amplitude. The threshold of the optical bistable device is insensitive to the Fresnel number, which determines the coupling between field amplitudes at different transverse positions.2 This is useful for obtaining reproducible operating characteristics of an array of devices. The medium can be introduced inside a cavity to understand the role of dispersive and diffractive effects in a more fundamental way. The threshold intensity is again insensitive to the Fresnel number. Furthermore, we observe instabilities in the cavity configuration, but no chaotic solutions were found. The periodic instabilities are sensitive functions of the Fresnel number.

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Absorptive, dispersive, and diffractive effects are studied in a nonlinear ring-cavity configuration containing an intrinsically bistable medium modeled generically by a nonlinear oscillator. The output intensity is shown to exhibit steady-state and periodic characteristics for constant input intensity, but no chaotic solutions are found. We find that the plane-wave analysis is inconsistent with the inclusion of diffraction effects and that periodic output characteristics are affected even for Fresnel numbers of order 1000. Our results are contrasted with previously reported experimental and theoretical work.

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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.

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Transverse effects in switching of bistable Fabry–Perot etalons filled with a saturable medium

Ulf Olin, Olof Sahlén

A systematic variation of the Fresnel number has been performed when solving the nonlinear wave equation for a Fabry–Perot étalon filled with a saturable medium and including unsaturable background absorption. We show that the optimum Fresnel number for absorptive and defocusing bistability in media such as CdS, using the nonlinearity due to the bound exciton resonance, can be considerably greater than one and that bistability is completely lost for tight focusing.

Journal of the Optical Society of America B•Mar 1, 1987•18 citations
Electromagnetic wave propagation with one transverse dimension is investigated in a medium whose response is modeled by a nonlinear oscillator. We report results with transverse effects due to diffraction, which are controlled by varying the Fresnel number. We find that diffraction does not significantly reduce the bistable intensity characteristics either for the center of the beam intensity or in the intensity integrated across the transverse coordinate, although in the latter case the contrast is reduced; bistable behavior is found to persist even for a Fresnel number of order unity, and the switching intensity is not affected by the Fresnel number. These results are explained by simple physical arguments.
A nonlinear oscillator model is used as a prototypical medium for intrinsic optical bistability.1 The phenomenon of intrinsic optical bistability is so named because the medium does not require the optical feedback of a cavity. In this model we retain dispersive effects and introduce a diffractive coupling of the electromagnetic field amplitude. The threshold of the optical bistable device is insensitive to the Fresnel number, which determines the coupling between field amplitudes at different transverse positions.2 This is useful for obtaining reproducible operating characteristics of an array of devices. The medium can be introduced inside a cavity to understand the role of dispersive and diffractive effects in a more fundamental way. The threshold intensity is again insensitive to the Fresnel number. Furthermore, we observe instabilities in the cavity configuration, but no chaotic solutions were found. The periodic instabilities are sensitive functions of the Fresnel number.
Absorptive, dispersive, and diffractive effects are studied in a nonlinear ring-cavity configuration containing an intrinsically bistable medium modeled generically by a nonlinear oscillator. The output intensity is shown to exhibit steady-state and periodic characteristics for constant input intensity, but no chaotic solutions are found. We find that the plane-wave analysis is inconsistent with the inclusion of diffraction effects and that periodic output characteristics are affected even for Fresnel numbers of order 1000. Our results are contrasted with previously reported experimental and theoretical work.
Abstract : The interaction of a light beam with matter has varying degrees of dependence on the transverse profile of the beam. Two topics are considered here. The first topic, superfluorescence, involves the coherent emission generated by an initially inverted two-level medium. Calculations in the past have included either quantum fluctuations in the initial conditions or transverse effects, but never both. The calculations presented here include both transverse effects and quantum fluctuations. The results of the theoretical calculations are in good agreement with previous experimental results, both quantitatively in terms of time delay averages and distributions and also qualitatively in terms of pulse shapes. The second topic considered, optical bistability, involves devices which exhibit two stable output light intensities (a high and a low branch) over a limited range of input light intensities. Simulations performed here show the effect of diffraction, measured in terms of the Fresnel number, on how much of the device becomes bistable. It was found that for small Fresnel number cases, the entire device become bistable. For high Fresnel number cases, only part of the device becomes bistable while the rest of the device remains low transmitting. The results of an experiment performed are consistent with the simulations. (Author)
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.