Open AccessПучки Гельмгольца--Гаусса с квадратичной радиальной зависимостью
Author(s) -
А.Б. Плаченов,
Г.Н. Дьякова
Publication year - 2022
Publication title -
optika i spektroskopiâ
Language(s) - English
Resource type - Journals
eISSN - 2782-6694
pISSN - 0030-4034
DOI - 10.21883/os.2022.02.51993.2269-21
Subject(s) - rotational symmetry , paraxial approximation , mathematical analysis , vortex , physics , function (biology) , class (philosophy) , amplitude , helmholtz equation , mathematics , classical mechanics , geometry , optics , mechanics , boundary value problem , beam (structure) , computer science , evolutionary biology , artificial intelligence , biology
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 well known and novel solutions, including those describing optical vortices of various orders.