Resonator with a back deformable mirror for the formation of a beam with a given intensity distribution

We present the results of a numerical-analytical study of formation of an output beam with a given intensity distribution for a resonator with a back deformable mirror (DM) and semitransparent spherical front mirror. Using the theory of inverse optical problems in the diffraction approximation, the basic characteristics of a laser resonator with a DM are considered as functions of the reference resonator configuration and the form of the distribution function, describing the given intensity. The laser beam formation in the reference resonator with plane-parallel and concentric configurations is compared. In the investigated resonators, the given intensity distribution is a fundamental mode; the selectivity (determined by the power losses of transverse modes) of the resonator with a DM is comparable with that of the reference resonator. It is shown that the formation of the given intensity distributions (uniform, super-Gaussian, or having several maxima) requires a DM with the amplitude of deformations of the optical surface of the order of λ and the number of control channels from 1 to nearly 10.