Wideband Gaussian Noise Model of Nonlinear Distortions From Semiconductor Optical Amplifiers

A wideband Gaussian Noise Model of the nonlinear noise power spectral density is developed for a single semiconductor optical amplifier as described by the Agrawal model. A simple, interpretable closed-form expression is obtained for the nonlinear noise-to-signal ratio of broadband wavelength-division multiplexed signals as a function of the Agrawal model parameters, the amplifier output power and the transmission bandwidth. The accuracy of the closed-form expression and its region of validity are assessed in numerical simulations. The error is smaller than 0.1 dB when the product of bandwidth and gain recovery time $B\times\tau_c$ exceeds 100. A complete treatment of gain compression is shown to enhance nonlinear noise by a factor $1+P_\text{out}/P_\text{sat}$ compared to the first-order perturbation theory result.