Statistical properties of a many-mode laser

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Abstract
Using a generalized version of the Volterra-Wiener functional technique, we study a model for a many-mode laser action in which the coupling among modes takes place through the intensities. It is shown that the coupled Langevin equations for the field amplitudes can be solved avoiding the infinities at the mode thresholds. In particular, mean photon numbers, variances, and correlation and cross-correlation functions of the modes can be computed. In order actually to carry out the computations, it is necessary to evaluate the solution of a set of coupled deterministic first-order differential equations and to diagonalize a matrix whose dimension is given by the number of modes envisaged. As an application, the two-mode case is treated in detail and, besides a derivation of the stationary properties, in part already known, the transient photon statistics, during the buildup of the two modes, is thoroughly studied. The advantage of this approach is due to its simplicity and to the possibility of dealing with a large number of interacting modes.