The unified formalism which allows to deduce expressions for paraxial two-dimensional Gaussian-like light Kummer-Gaussian beams and Helmholtz-Gaussian beams is offered. This formalism also allows to discover correlations between them. Simple conditions of their physical realizability are formulated. New types of Kummer-Gaussian beams are discovered. Such beams are presented by the Gaussian product on the function Kummer of the complex argument and nonnegative integer index n.

Keywords: paraxial beams, Hermite-Gaussian beams, Kummer-Gaussian beams, Helmholtz-Gaussian beams, Gaussian-like beams.

S.S. Girgel – Department of Physics, F. Scorina Gomel State University, Gomel, Belarus