A new class of scalar, rotationally symmetric Gaussian-like beams is introduced. The slowly varying amplitudes of such beams are represented as analytical solutions to the paraxial wave equation, described in terms of the incomplete gamma functions and their products with quadratic exponential and power functions of different kinds. The specific functional forms of these solutions give rise to such names as gamma, gamma-Gaussian, gamma-parabolic, and gamma-anti-Gaussian beams. It is established that, within a focal volume specified by a waist size and the depth of field of about three Rayleigh lengths of the fundamental Gaussian beam of the same waist size, the parametrically optimized zero-order gamma and gamma-coupled beams possess more stabilized transverse sizes, very weak transverse irradiance sidelobes, more uniform axial irradiance distributions, and more steep controllable fall-offs of the last distributions relative to those that are inherent in the above fundamental Gaussian beam and the Bessel-Gauss beams with linear and quadratic radial dependence and the same waist size. (C) 2018 Optical Society of America.
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