  A fairly general expression for a light beam is found as a solution of the
paraxial Helmholtz equation. It is achieved by exploiting appropriately chosen
complex variables which entail the separability of the equation. Next, the
expression for the beam is obtained independently by superimposing shifted
Gaussian beams, whereby the shift can be made either by a real vector (in which
case the foci of the Gaussian beams are located on a circle) or by a complex
one. The solutions found depend on several parameters, the specific choice of
which allows to obtain beams with quite different properties. For several
selected parameter values figures are drawn, demonstrating the spatial
distribution of the energy density and phase. In special cases, the effect of a
shift of the intensity peak from one branch to another and phase singularities
are observed.
