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A theoretical analysis of the nonlinear quadratic interaction between two monochromatic plane waves at frequencies ω and 2ω in a Fabry–Perot cavity shows that all-optical control of reflectivity and transmissivity of the fundamental beam is possible under suitable conditions. We report all-optical switching of the fundamental beam for cavity lengths that vary from a few micrometers to a few millimeters. Specifically, we show that 100% all-optical switching can occur for a 6-µm cavity when the nonlinear coefficient is not greater than 20 pm/V and the input intensity does not exceed 10 GW/cm^2. Our analytical results are obtained without use of the slowly varying envelope approximation and without resort to the undepleted-pump approximation.