Physical optics

Helmholtz–Gauss beams with quadratic radial dependence

A. B. Plachenov^a, G. N. D'yakova<sup>b

a</sup> MIREA — Russian Technological University, 119454 Moscow, Russia
^b Saint-Petersburg State University of Aerospace Instrumentation, 190000 Saint-Petersburg, Russia

Abstract: A new class of localized solutions of paraxial parabolic equation is introduced. Each solution is a product of some Gaussian-type localized axisymmetric function (different from the fundamental mode) and an amplitude factor. The latter can be expressed via an arbitrary solution of the Helmholtz equation on an auxiliary two-sheet complex surface. The class under consideration contains both well known and novel solutions, including those describing optical vortices of various orders.

Keywords: parabolic equation, quadratic beams, Gauss, Helmholtz, Bessel.

Received: 10.05.2021
Revised: 07.11.2021
Accepted: 08.11.2021

DOI: 10.21883/OS.2022.02.51993.2269-21

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