ANALYSIS OF GAIN INTERACTION IN A MULTIMODE GAS LASER

In this paper a theory of the gain interaction among n oscillating modes is developed starting from the rate-equations viewpoint. This approach permits one to evaluate the gain interaction terms among modes due to the well-known hole burning effect in laser gain with nonhomogeneous line shape. No account was taken of phase differences among modes and the nonlinear polarization of the medium, which give rise to combination tones. By this treatment, it is also possible to find the gain and saturation terms in single frequency operation, which are similar to those derived by Lamb. Some results on the time behavior of two modes and a set of n modes are given in the subsequent sections. Finally, formal results in second-order approximation are given, as well as an evaluation of the range of validity of first-order theory for one-mode operation at the center of Doppler curve of gain. © 1969 The American Institute of Physics.