Abstract
A series of multifrequency solutions of a standing-wave laser are presented. The parameter condition under which the solutions are valid can be satisfied in dye lasers and semiconductor lasers if the cavity length is on the order of 100 \ensuremath{\mu}m and the reflectivity of the mirrors is about 99%. The physical origin of the multifrequency operations is the spatial hole burning of population inversion by standing waves. These solutions consist of (2N+1) constant mode intensities, where N=0,1,..., and may go into operation one after another as the pump parameter is increased. If the pump parameter is further increased to above a certain threshold, then another kind of instability occurs and the originally constant mode intensities begin temporal oscillation. The pump thresholds of these two kinds of instabilities are determined by linear stability analysis.
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