Numerical resolution of the Fokker-Planck equation for the study of phase noise filtering in coherent optical systems

Laser phase noise deteriorates the high sensitivity of heterodyne optical receivers. To reduce phase noise influence, the intermediate frequency (IF) signal resulting from the coherent detection is filtered by a narrow bandpass filter (BPF). The phase noise at the input of the BPF generates an amplitude and phase noise at the output of the BPF. The joint probability density function of these noises is evaluated in the case of a first order (RC) filter by numerical resolution of a Fokker-Planck equation. A finite difference operator splitting scheme is used. The accuracy of the numerical solution is checked comparing numerically and analytically calculated moments. In addition, a new very efficient method for the analytical calculation of moments is developed. Contour plots of the probability density for both a finite time integrator and a first order filter are compared in order to show the impact of different filter types on phase noise filtering. The marginal pdf of the amplitude and phase noise at the output of the above filters are also calculated.