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AIP conference proceedings

The effects of diffraction, dispersion, and transient propagation on optical bistability in a one-directional ring cavity

F. P. Mattar, Jiří Teichmann, Yves Claude, C. Goutier

Published Jan 1, 1987• 0 citations
Publisher
DOI
10.1063/1.36848

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We report the transient nonadiabatic generalization of Bonifacio-Lugiato1 cw nonlinear ring cavity optical bistability (NRCOB) with mirrors that ensure the necessary feedback. A semiclassical formalism is adopted, consisting of a paraxial wave equation coupled to the two-level sharp-line density matrix which includes detuning and relaxation times in conjunction with boundary conditions at the mirrors. The existing super-fluorescence finite difference code2 with radial variations of the Beer length has been modified to simulate the NRCOB with the free space propagation between the mirror treated with a finite Hankel series.3
Pioneered by Moloney and collaborators [1], transverse effects of nonlinear passive systems in a ring cavity have been the object of extensive study. Analytical investigations with diffractive coupling in one transverse dimension have demonstrated [1] that static and dynamic transverse structures occur in this system. Extension of the mean-field dispersive model developed from optical bistability to include diffraction [2] independently demonstrated qualitatively similar features, again in one transverse dimension. Investigations in two transverse dimensions have been largely confined to numerical studies by the Moloney group [1], showing for gaussian beam illumination ring structures which develop through azimuthal instability to a pattern of spots which typically execute a slow chaotic motion with a progressive loss of symmetries.
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.