Solution of paraxial wave equation for inhomogeneous media in linear and quadratic approximation

Alex Mahalov; Sergei Suslov

doi:10.1090/S0002-9939-2014-12295-7

Solution of paraxial wave equation for inhomogeneous media in linear and quadratic approximation

Research output: Contribution to journal › Article › peer-review

Abstract

We construct explicit solutions of the inhomogeneous parabolic wave equation in a linear and quadratic approximation. As examples, oscillating laser beams in a 1D parabolic waveguide, spiral light beams in 2D varying media and an effect of superfocusing of particle beams in a thin monocrystal film are briefly discussed. Transformations of nonlinear equations into the corresponding autonomous and homogeneous forms are found and a review of important applications is also given.

Original language	English (US)
Pages (from-to)	595-610
Number of pages	16
Journal	Proceedings of the American Mathematical Society
Volume	143
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-2014-12295-7
State	Published - 2015

Keywords

Airy–Gaussian–Hermite beams
Complex Ginsburg–Landau equations
Gaussian–Hermite beams
Green’s function
Nonlinear Schrödinger equations
Paraxial wave equations

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-2014-12295-7

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title = "Solution of paraxial wave equation for inhomogeneous media in linear and quadratic approximation",

abstract = "We construct explicit solutions of the inhomogeneous parabolic wave equation in a linear and quadratic approximation. As examples, oscillating laser beams in a 1D parabolic waveguide, spiral light beams in 2D varying media and an effect of superfocusing of particle beams in a thin monocrystal film are briefly discussed. Transformations of nonlinear equations into the corresponding autonomous and homogeneous forms are found and a review of important applications is also given.",

keywords = "Airy–Gaussian–Hermite beams, Complex Ginsburg–Landau equations, Gaussian–Hermite beams, Green{\textquoteright}s function, Nonlinear Schr{\"o}dinger equations, Paraxial wave equations",

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AU - Mahalov, Alex

AU - Suslov, Sergei

PY - 2015

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N2 - We construct explicit solutions of the inhomogeneous parabolic wave equation in a linear and quadratic approximation. As examples, oscillating laser beams in a 1D parabolic waveguide, spiral light beams in 2D varying media and an effect of superfocusing of particle beams in a thin monocrystal film are briefly discussed. Transformations of nonlinear equations into the corresponding autonomous and homogeneous forms are found and a review of important applications is also given.

AB - We construct explicit solutions of the inhomogeneous parabolic wave equation in a linear and quadratic approximation. As examples, oscillating laser beams in a 1D parabolic waveguide, spiral light beams in 2D varying media and an effect of superfocusing of particle beams in a thin monocrystal film are briefly discussed. Transformations of nonlinear equations into the corresponding autonomous and homogeneous forms are found and a review of important applications is also given.

KW - Airy–Gaussian–Hermite beams

KW - Complex Ginsburg–Landau equations

KW - Gaussian–Hermite beams

KW - Green’s function

KW - Nonlinear Schrödinger equations

KW - Paraxial wave equations

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UR - https://www.scopus.com/pages/publications/84948382869#tab=citedBy

U2 - 10.1090/S0002-9939-2014-12295-7

DO - 10.1090/S0002-9939-2014-12295-7

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VL - 143

SP - 595

EP - 610

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 2

ER -

Solution of paraxial wave equation for inhomogeneous media in linear and quadratic approximation

Abstract

Keywords

ASJC Scopus subject areas

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