Hankel-Bessel laser beams

摘要

An analytical solution of the scalar Helmholtz equation to describe the propagation of a laser light beam in the positive direction of the optical axis is derived. The complex amplitude of such a beam is found to be in direct proportion to the product of two linearly independent solutions of Kummer's differential equation. Relationships for a particular case of such beams--namely, the Hankel-Bessel (HB) beams--are deduced. The focusing of the HB beams is studied.