Gaussian beams in inhomogeneous media: A review |
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| Authors: | Yu A Kravtsov P Berczynski |
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| Institution: | (1) Institute of Physics, Maritime University of Szczecin, Szczecin, 70-500, Poland;(2) Space Research Institute, Russian Acad. Sci., Moscow, 117 997, Russia;(3) Institute of Physics, Technical University of Szczecin, Szczecin, 70-310, Poland |
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| Abstract: | The paper outlines the most important results of the paraxial complex geometrical optics (CGO) in respect to Gaussian beams
diffraction in the smooth inhomogeneous media and discusses interrelations between CGO and other asymptotic methods, which
reduce the problem of Gaussian beam diffraction to the solution of ordinary differential equations, namely: (i) Babich’s method,
which deals with the abridged parabolic equation and describes diffraction of the Gaussian beams; (ii) complex form of the
dynamic ray tracing method, which generalizes paraxial ray approximation on Gaussian beams and (iii) paraxial WKB approximation
by Pereverzev, which gives the results, quite close to those of Babich’s method. For Gaussian beams all the methods under
consideration lead to the similar ordinary differential equations, which are complex-valued nonlinear Riccati equation and
related system of complex-valued linear equations of paraxial ray approximation. It is pointed out that Babich’s method provides
diffraction substantiation both for the paraxial CGO and for complex-valued dynamic ray tracing method. It is emphasized also
that the latter two methods are conceptually equivalent to each other, operate with the equivalent equations and in fact are
twins, though they differ by names.
The paper illustrates abilities of the paraxial CGO method by two available analytical solutions: Gaussian beam diffraction
in the homogeneous and in the lens-like media, and by the numerical example: Gaussian beam reflection from a plane-layered
medium. |
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| Keywords: | Gaussian beams Gaussian beam propagation and diffraction complex geometrical optics dynamic ray tracing method |
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