Theory of Multimode Laser Operation

The Lamb semiclassical laser theory is developed uniformly for multimode unidirectional ring, two-mirror, and bidirectional-ring lasers. Equations are given which determine the mode amplitudes and frequencies to third order in the electric-dipole interaction energy. A diagram technique called the perturbation tree is used to bypass most of the algebra for the complicated multimode bidirectional-ring case. Numerical results are given for a variety of multimode laser configurations in the free-run approximation. In particular it is shown that the multimode, two-mirror gas laser exhibits an asymmetric spectrum in agreement with the experimental observations of Garside. This asymmetry is found to be absent in the unidirectional-ring case and is attributed to mode competition for the same pairs of velocity ensembles (an origin related to that for the Lamb dip). The coupling role of population pulsations is discussed with numerical illustrations. Treatment of mode locking is deferred to a forthcoming companion paper.