Beam propagation constants for a radial laser array

The beam quality of a radial laser array, quantified in terms of the M(2) propagation constant, is determined as a function of array element configuration. A lower bound on array M(2) is estimated for both phase-locked and nonphase-locked conditions. It is shown that, to achieve near-unity M(2) array, either aperture filling or spatial filtering is required in addition to phase locking. An aperture-filling method suitable for radial arrays of CO(2) slab lasers is presented.