ABSTRACT
In optics, there are laser beams whose scalar complex amplitudes are described by the exact solutions of the nonparaxial Helmholtz equation. These include well-known planar and spherical waves, as well as more recently proposed Bessel modes, Mathieu beams, and parabolic laser beams. An exact analytical solution of the scalar Helmholtz equation to describe the propagation of the light beam in the positive direction of the optical axis has been derived. The complex amplitude of such a beam is proportional to the product of two linearly independent solutions of Kummer's equation. Relationships for a particular case of such beams in the form of Hankel-Bessel (HB) beams have been derived. The focusing properties of the HB beams have been studied.
