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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 6 — Jun. 1, 2006
  • pp: 1442–1451

Diffraction of a Gaussian beam in a three-dimensional smoothly inhomogeneous medium: an eikonal-based complex geometrical-optics approach

Pawel Berczynski, Konstantin Yu. Bliokh, Yuri A. Kravtsov, and Andrzej Stateczny  »View Author Affiliations


JOSA A, Vol. 23, Issue 6, pp. 1442-1451 (2006)
http://dx.doi.org/10.1364/JOSAA.23.001442


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Abstract

We present an ab initio account of the paraxial complex geometrical optics (CGO) in application to scalar Gaussian beam propagation and diffraction in a 3D smoothly inhomogeneous medium. The paraxial CGO deals with quadratic expansion of the complex eikonal and reduces the wave problem to the solution of ordinary differential equations of the Riccati type. This substantially simplifies the description of Gaussian beam diffraction as compared with full-wave or parabolic (quasi-optics) equations. For a Gaussian beam propagating in a homogeneous medium or along the symmetry axis in a lenslike medium, the CGO equations possess analytical solutions; otherwise, they can be readily solved numerically. As a nontrivial example we consider Gaussian beam propagation and diffraction along a helical ray in an axially symmetric waveguide medium. It is shown that the major axis of the beam’s elliptical cross section grows unboundedly; it is oriented predominantly in the azimuthal (binormal) direction and does not obey the parallel-transport law.

© 2006 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(080.2710) Geometric optics : Inhomogeneous optical media
(080.2720) Geometric optics : Mathematical methods (general)

History
Original Manuscript: June 20, 2005
Revised Manuscript: November 29, 2005
Manuscript Accepted: December 8, 2005

Citation
Pawel Berczynski, Konstantin Yu. Bliokh, Yuri A. Kravtsov, and Andrzej Stateczny, "Diffraction of a Gaussian beam in a three-dimensional smoothly inhomogeneous medium: an eikonal-based complex geometrical-optics approach," J. Opt. Soc. Am. A 23, 1442-1451 (2006)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-6-1442

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