We introduce a novel model of the gain profile of multi-quantum-well semiconductor optical amplifiers (MQW-SOAs) that takes the variation of the gain spectrum with carrier density into detailed account. In this model, the gain spectrum is approximated by a cubic function and its peak gain, peak-gain wavelength, and polynomial coefficients are expressed by hyperbolic functions of carrier density. By using the proposed model, we calculated the static gain characteristics and dynamic response of cross gain modulation (XGM) of an SOA and compared them with the experimental results. Under both operation conditions, very good agreement with the experimental results was obtained.
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