Quadratic Helmholtz–Gauss beams

Abstract

We describe a new class of localized solutions of the paraxial parabolic equation, which can be represented as a product of two functions. One of them is a Gauss-type axisymmetric function different from a fundamental mode, the other one can be expressed in terms of an arbitrary solution of a certain Helmholtz equation on an auxiliary two-sheet complex surface. Some examples are considered.