Full rate-equation description for multi-mode semiconductor lasers

A set of rate equations is presented describing the deterministic multi-mode dynamics of a semiconductor laser. Mutual interactions among the lasing modes, induced by high frequency modulations of the carrier distribution, are described by carrier-inversion moments and lead to special spectral content of each spatial mode. The Bogatov effect of asymmetric gain suppression in semiconductor lasers will be derived. We will explicitly discuss the nontrivial relationship between the modes of the nonlinear cavity and the optical spectrum of the laser output and illustrate this for a two and three-mode laser