Helmholtz–Gauss Beams with Quadratic Radial Dependence

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 equa...

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Bibliographic Details
Published in:Optics and spectroscopy 2023-08, Vol.131 (8), p.728-734
Main Authors: Plachenov, A. B., Dyakova, G. N.
Format: Article
Language:English
Subjects:
Gaussian beams (optics)
Helmholtz equations
Lasers
Optical Devices
Optics
Photonics
Physics
Physics and Astronomy
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Summary: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.
ISSN:0030-400X
1562-6911
DOI:10.1134/S0030400X23060140