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Wide-band polarization free wavelength conversion based on four-wave mixing in semiconductor optical amplifiers (SOAs) subject to two pump beams has been studied in detail. With equalized forward and backward pump power, polarization independence of the converted signal was experimentally achieved when the wavelength detuning was larger than 1.24 nm. This is independent of the SOA bias current. When the wavelength detuning between the signal and one pump beam was fixed at 1.6 nm, the amplitude of the converted signal was nearly constant over a 58-nm wavelength range. A new theoretical analysis allows for signals of arbitrary polarization state to be considered. The experimental results are in good agreement with the theory developed here.