Evolution of the probability density functions of Gaussian ASE noise in zero-memory nonlinear fiber

The propagation of Gaussian amplified emission noise in nonlinear optical fiber with negligible dispersion is considered. It is well known that fiber Kerr nonlinearity causes a nonlinear phase noise, also known as the Gordon–Mollenauer effect. In this paper, we examine the effect of the Kerr nonlinearity on the probability density functions of the Gaussian noise quadratures. This can lead to large deviations from the Gaussian statistics of the amplified spontaneous emission noise. Analytical statistics of the noise quadratures at the output of nonlinear fiber with negligible dispersion are derived and compared with numerical simulations. The statistics of the noise squared envelope are also presented and, based on these results, the influence of Kerr nonlinearity on the direct detection and coherent detection amplitude modulated links is discussed.