Analytical Solution for SOA-Based All-Optical Wavelength Conversion Using Transient Cross-Phase Modulation

All-optical wavelength conversion (WC) based on transient cross-phase modulation (T-XPM) of semiconductor optical amplifier (SOAs) is a promising approach to accelerate the gain recovery of SOAs. An analytical solution is deduced to explain the polarity variation of WC based on T-XPM of SOAs from the viewpoint of the impulse response functions. We conclude that both inverted and noninverted WCs can be realized when the central wavelength of the optical bandpass filter is either blue-shifted or red-shifted with respect to the wavelength of the probe signal. We are able to validate the formula against our experimental results recently published.