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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

The Role Of Focusing For A Bistable Fabry-Perot Etalon With A Local Saturable Nonlinearity

Ulf Andersson, Olof Sahlén

Published Jan 8, 1987• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.936943

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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.
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.
Large optical nonlinearities occur in a variety of multiple quantum-well and n-i-p-i materials in which the nonlinearity saturates and there is residual absorption. The conditions for bistability when such media are placed with a Fabry-Perot etalon are discussed. It is proved analytically that the ratio of the optically induced saturated index change to the linear loss per unit length must be larger than the wavelength divided by pi . It is shown, however, that practical devices require twice this value. It is found that there is a tradeoff in cavity design between minimizing the switching intensity and minimizing the required nonlinear phase change. Finally, approximate expressions for the switching intensity versus detuning are given.>
The influence of transverse effects on optical bistability in Fabry-Perot cavity filled with saturable absorber was numerically investigated. A simple model of singlet absorption was used on numerically solving the relationships between the input and output light fields. The proposed model corresponds well to organic compounds considered as novel optical materials with third-order optical nonlinearities. The proposed optically bistable systems were demonstrated for two organic dyes of fluorescein and rhodamine 6G dispersed in transparent solid matrices. Their optically bistable behaviour was anticipated considering the homogeneous and Gaussian distribution of light energy in the radial direction. Most notable cases are discussed related to the changes of the Gaussian beam radii, positive feedback conditions in the Fabry-Perot cavity and considering linear and nonlinear absorption parameters of the organic media. The simulation results enabled us to establish numerically thresholds of Fabry-Perot mirror reflectance and Gaussian beam radius for both nonlinear organic materials, above which absorptive optical bistability can occur. The results can be helpful in design of optical switches for all-optical communication networks.