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For future telecommunications systems to take full advantage of the optical fiber bandwidth, it will be necessary to have components responding at picosecond speeds. The only way currently known to achieve these speeds is using all-optical switching. By using low-temperature-grown GaAs (LT-GaAs) in a compact asymmetric Fabry-Perot device, we have achieved ultrafast all-optical switching with large bandwidth, high contrast ratio, low insertion loss, and low switching energy. In this paper, we discuss the dependence of the switch performance on the mirror bandwidth and reflectivity, and the LT-GaAs layer thickness and growth conditions. We develop guidelines for the optimization of the device design to maximize the bandwidth and contrast ratio.