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We report on an all-optical interferometric optical time-division multiplexing switch that exhibits high linearity, high-switching contrast, low noise, wide bandwidth, and low crosstalk. The key element of the gain-transparent switch is a semiconductor optical amplifier (SOA), which is transparent for the data signal. However, the injection of optical control pulses in the gain wavelength region of the SOA leads to index modulations at the wavelength of the data. This variation of the refractive index can be used for interferometric switching. In the application as add/drop multiplexer, the switch has the inherent advantage of leaving the nonswitched pulses undisturbed.