Flat-topped light beams with non-circular cross-sections

A set of flat-topped light beams with non-circular cross-sections is introduced. This set includes beams with rectangular, elliptical, pyramidal and one-dimensional Gaussian cross-sections. The one-dimensional Gaussian denotes a beam with Gaussian distribution in one direction and a long flattened distribution in the perpendicular direction. Field distributions of this set of beams can be expressed as sums of the lowest order Gaussian modes (TEM00) having different parameters. The main features of the beam are investigated throughout the space without using the orthogonal polynomials.