Evolution of a statistical distribution of photons in a laser radiation field

Decoupling of equations for the diagonal and nondiagonal elements of the density matrix of laser radiation is used in an analysis of the interaction of the radiation field with an active medium. An algorithm for the calculation of the eigenvalues and eigenvectors is proposed for the diagonal elements describing the radiation field statistics. The first minimal (in respect of the magnitude) eigenvalues are calculated and nonequilibrium distribution functions are found for the dynamics of a transition from a vacuum to an equilibrium state; the results agree well with those obtained in machine (numerical) experiments. The equations for the nondiagonal elements of the density matrix are used to find the characteristic times of changes in these elements and to determine the emission line width.