A Fox and Li analysis [Bell Syst. Tech J. 40, 453 (1961); Proc. IEEE 51, 80 (1963); IEEE J. Quantum Electron QE-4, 460 (1968)] for a laser resonator with a radially varying gain yields a picture of the mode evolution dynamics and a steady-state mode distribution which are different from the constant-gain case. When an axially maximal gain is sharply peaked, the mode-settling time is markedly reduced and the final mode distribution is more tightly focused. When the gain distribution is sharply annular, an annular or ‘‘doughnut’’-shaped mode develops. In some intermediate cases, which may be relevant to some gas lasers, a stable transverse mode never definitively evolves. Misalignments of the gain with the cavity yield distortions to the mode shape and these are also explored.

• Received 9 July 1992

DOI:https://doi.org/10.1103/PhysRevA.47.588