The semiclassical theory for gas lasers is extended from one dimension into three. Self-consistency equations of a rectangular waveguide resonator and the component equations of motion for the population matrix are derived. Laser parameters related to the waveguide structure and active medium are analyzed by solving the equations. For homogeneously broadened lasers, theoretical investigation shows that single-mode operation depends on the waveguide dimensions, the most probable speed of the active medium, and the decay constants or the saturation parameter. Under some conditions, the oscillating modes can be determined by the frequency interval and the relative excitation.
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