A polynomial expansion method for solving the laser Fokker-Planck equation

Distribution functions of the laser amplitude and intensity can be determined by solving the laser Fokker-Planck equation. By a suitable expansion of the distribution functions in Laguerre polynomials, a system of ordinary differential equations for the coefficients of the expansion is derived and is shown to have the form of a recurrence relation with length four. Applying it to the transient solution, the averaged amplitude and the first four cumulants of the intensity distribution are obtained even for those pump parameters where the hitherto known numerical solution is not applicable.