Family of hypergeometric laser beams.
We discuss a three-parameter family of paraxial coherent light fields that originate from a complex amplitude composed of the following four cofactors: the Gaussian beam, a logarithmic axicon, a spiral phase plate (angular harmonic), and an amplitude power function with a possible singularity at the origin of coordinates. For such types of beams, the near-field complex amplitude is proportional to the degenerate hypergeometric function, prompting the beams' name--hypergeometric (HyG) beams. When the Gaussian beam is replaced by a plane wave, the above beams change to generalized HyG modes that preserve their structure up to scale upon propagation. The intensity profile of the HyG beams is similar to that of the Bessel modes, forming a set of alternating bright and dark rings. However, the thickness of the rings of the HyG beams decreases with increasing ring number.