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


Authors: Alex Mahalov and Sergei K. Suslov
Journal: Proc. Amer. Math. Soc. 143 (2015), 595-610
MSC (2010): Primary 35Q55, 35Q51; Secondary 35C05, 81Q05
DOI: https://doi.org/10.1090/S0002-9939-2014-12295-7
Published electronically: October 28, 2014
MathSciNet review: 3283647
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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.


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Additional Information

Alex Mahalov
Affiliation: School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287–1804
Email: mahalov@asu.edu

Sergei K. Suslov
Affiliation: School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287–1804
Email: sks@asu.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-12295-7
Keywords: Paraxial wave equations, Green's function, Airy--Gaussian--Hermite beams, Gaussian--Hermite beams, nonlinear Schr\"odinger equations, complex Ginsburg--Landau equations.
Received by editor(s): March 26, 2013
Published electronically: October 28, 2014
Additional Notes: This research was partially supported by AFOSR grant FA9550-11-1-0220.
Communicated by: Ken Ono
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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