Analytical modeling of a single channel nonlinear fiber optic system based on QPSK.

A first order perturbation theory is used to develop analytical expressions for the power spectral density (PSD) of the nonlinear distortions due to intra-channel four-wave mixing (IFWM). For non-Gaussian pulses, the PSD can not be calculated analytically. However, using the stationary phase approximations, we found that convolutions become simple multiplications and a simple analytical expression for the PSD of the nonlinear distortion is found. The PSD of the nonlinear distortion is combined with the amplified spontaneous emission (ASE) PSD to obtain the total variance and bit error ratio (BER). The analytically estimated BER is found to be in good agreement with numerical simulations.