Abstract
A set of general equations describing the time-dependent behavior of a laser is derived. The derivation is based on a density matrix description of a homogeneously broadened laser transition and a semiclassical treatment of the radiation field, consisting of an arbitrary number of modes. The resulting equations resemble ordinary rate and energy conservation equations but contain additional interference terms which, in general, couple all of the modes. The strength of this coupling depends on the inhomogeneity of the population inversion as well as on the mode frequencies. The energy conservation equations imply that absorption and stimulated emission in such a system can apply, strictly speaking, only collectively to the system of modes as a whole. In addition, the threshold inversion is affected by mode coupling. Stability analysis carried out in the two-mode case indicates that a spatial inhomogeneity in the pumping rate is required for undamped oscillations. It is also concluded that coupling of off-axis modes is more likely to lead to undamped spiking than coupling of axial modes.
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