Hankel-Bessel laser beams

Victor V Kotlyar; Alexey A Kovalev; Victor A Soifer

doi:10.1364/JOSAA.29.000741

Hankel-Bessel laser beams

J Opt Soc Am A Opt Image Sci Vis. 2012 May 1;29(5):741-7. doi: 10.1364/JOSAA.29.000741.

Authors

Victor V Kotlyar¹, Alexey A Kovalev, Victor A Soifer

Affiliation

¹ Laser Measurements Laboratory, Image Processing Systems Institute of the Russian Academy of Sciences, 151 Molodogvardejskaya Street, Samara 443001, Russia.

PMID: 22561932
DOI: 10.1364/JOSAA.29.000741

Abstract

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.