An analytical theory describing all-optical wavelength converters based on cross-gain modulation (XGM) in semiconductor-optical amplifiers is derived. Our theory consists of two parts: a large-signal analysis yielding the transmission function for the signal, and a small-signal analysis in order to describe the transformation of the signal and probe intensity noise. Both the large-signal as well as the small-signal theory reveal similar performance for the co- and the counterpropagating injection scheme for bit rates up to 2.5 Gb/s. This is confirmed by computer simulations. Consequently, the counterpropagating configuration is preferable because the implementation is simpler and conversion to the same wavelength is possible. In order to increase the conversion efficiency it is better to reduce the average signal power than to increase the probe power, which additionally reduces the output power range. However, there is a tradeoff between conversion efficiency and output extinction ratio. According to the small-signal analysis, the relative-intensity noise (RIN) due to the probe and due to the amplified spontaneous emission is negligible. Moreover, the converted signal has a lower RIN than the input signal.
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