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.
© 2012 Optical Society of America
Diffraction and Gratings
Original Manuscript: October 26, 2011
Manuscript Accepted: December 19, 2011
Published: April 19, 2012
Victor V. Kotlyar, Alexey A. Kovalev, and Victor A. Soifer, "Hankel–Bessel laser beams," J. Opt. Soc. Am. A 29, 741-747 (2012)