AN EQUATION FOR THE AMPLITUDES OF THE MODES IN SEMICONDUCTOR-LASERS

A quite general equation for the time-dependent amplitudes of the modes of the electromagnetic field of a semi-conductor laser is derived in the small-signal approximation. It is shown that the modes fulfill a general orthogonality relation that follows directly from Maxwell's equations. The dependence of the dielectric function on temporally varying carrier densities is taken into account. The local changes of the carrier densities lead to a coupling of different modes. The equations for the mode amplitudes are used to derive rate equations for the photon number and the phase of a mode.