Correlations in an N-mode laser

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Abstract
Analytic expressions for the correlations of the light emitted by an N‐mode laser are given. We study in particular a special case of strongest couplings and show, for example, that at steady state, the second order cross intensity correlation tends toward a negative value, −1/(N−1), for large pump parameters. We also study the time dependent solutions, and express the second order amplitude and intensity correlations of the emitted light in terms of the eigenvalues and eigenfunctions of a Schrödinger‐type differential equation which reduces to that studied by Risken for N=1 and to that studied by M‐Tehrani and Mandel for N=2. Analytic expressions which approximate the eigenvalues of this differential equation for a general N are given.