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 well known and novel solutions, including those describing optical vortices of various orders. Keywords: parabolic equation, quadratic beams, Gauss, Helmholtz, Bessel.
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