Free-space azimuthal paraxial wave equation: the azimuthal Bessel-Gauss beam solution.

We develop a paraxial wave equation for an azimuthally polarized field propagating in free space. The equation's beamlike solution is composed of a plane-wave propagation factor multiplied by a Bessel function of the first kind, of order one, and a Gaussian factor, which describe the transverse characteristics of the beam. We compare the propagation characteristics of the azimuthal Bessel-Gauss beam solution with a solution of the more familiar scalar paraxial wave equation, the linearly polarized Bessel-Gauss beam.