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.
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