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Stability analysis for absorptive optical bistability in a Fabry-Pérot cavity

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  • van Wonderen, A.J.
  • Douwes, B.J.
  • Suttorp, L.G.

Abstract

A stability analysis is performed for absorptive optical bistability in a medium of arbitrary absorption coefficient, which is contained in a Fabry-Pérot cavity with non-ideal mirrors. In order to describe this system we use a hierarchical set of equations which is obtained from Maxwell-Bloch theory by expanding the polarization and population inversion in slowly varying harmonics. We reduce the stability problem to two pairs of coupled differential equations for the amplitudes and the phases of the space-dependent deviations of the forward and the backward electric field envelopes. The coefficients of these equations depend on the stationary inversion fields for which a representation in terms of Chebyshev polynomials depending on the electric field envelopes is given. The influence of a truncation of the Bloch hierarchy on the instabilities is studied numerically in the uniform-field limit.

Suggested Citation

  • van Wonderen, A.J. & Douwes, B.J. & Suttorp, L.G., 1989. "Stability analysis for absorptive optical bistability in a Fabry-Pérot cavity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 157(2), pages 907-932.
    • Handle: RePEc:eee:phsmap:v:157:y:1989:i:2:p:907-932
    DOI: 10.1016/0378-4371(89)90073-3
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