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Optica Acta International Journal of Optics

Bistable Behaviour of a Detuned Fabry-Perot Etalon with a Gaussian input Spatial Profile under Self-focusing and Defocusing Conditions

J. V. Moloney

Published Nov 1, 1982• 20 citations
Publisher

Abstract

Bistable operation of an initially detuned Fabry-Perot etalon with a spatially varying transverse input is studied numerically. Non-linear medium propagation effects are accounted for explicitly. Fast Fourier transforms are used to treat beam diffraction, providing a computationally efficient numerical algorithm. Steady state bistable loops are computed for a Fresnel number close to unity, under both self-focusing and defocusing conditions. Beam diffraction causes earlier switch-on in the defocusing case.

DOI
10.1080/713820780

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Bistable operation of an initially detuned Fabry-Perot etalon with a spatially varying transverse input is studied numerically. Non-linear medium propagation effects are accounted for explicitly. Fast Fourier transforms are used to treat beam diffraction, providing a computationally efficient numerical algorithm. Steady state bistable loops are computed for a Fresnel number close to unity, under both self-focusing and defocusing conditions. Beam diffraction causes earlier switch-on in the defocusing case.
The non-linear wave-equation has been solved numerically for a Fabry-Perot etalon, assuming a cylindrical symmetric gaussian input beam, a local mixed dispersive and absorptive saturable nonlinearity and an additional nonsaturable background absorption term. The role of focusing has been systematically investigated for both absorptive and dispersive bistability. Whole-beam switching occurs under tight focusing conditions. But, in the case of defocusing and absorptive bistability, a further reduction of spotsize results in loss of the hysteresis characteristics. Thus, thisposes a restriction on the minimum spotsize and, hence on the minimum input power, for bistable operation.
In this work, the external switching dynamics of a Fabry-Perot etalon are studied via optical bistability system simulation. The simulated set-up of this investigation consists of two laser beams; the first beam is continuous (CW) which is considered as a biasing beam and capable of holding the bistable system for a certain range, which we are interested in, from a point that is very close self-switching to a point where the switching is unachievable. The second beam is modulated by passing the first beam through an acousto-optic modulator (AOM) to produce pulses with a minimum rise time and is used as an external source (coherent switching). In this work, we obtained the optical bistable loops by applying absorption coefficient (α) = 20cm-1, e sample etalon thickness (D) = 110μm, forward mirror reflectivity (Rf) = 0.6, and backward mirror reflectivity (Rb) = 0.95. The steady state characteristic of an initial detuning of the cavity (φ0) = 0.8 was studied at the conditions of no external input pulse intensity (M(t) = 0) and switching that takes place at Is(ON)= 0.57mW and Is(OFF) = 0.4mW.
Self-focusing effects in optical bistable hysteresis loops have been observed in a GaAs-GaAlAs superlattice.1 Experimentally, one sees drastic overshooting in the hysteresis loops and changes in the output profile as the imaging lens is translated along the propagation direction, thus imaging different object planes onto a fixed image plane (i.e. aperture). Nearly identical results are found by a one-transverse-dimension numerical simulation of good-cavity bistability in which the output is free-space propagated backwards in space, corresponding to the movement of the imaging lens. These effects arise from a radially-dependent phase shift caused by the excitonic nonlinear refraction and a gaussian beam profile.