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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 31, Iss. 5 — May. 1, 2014
  • pp: 914–919

Diffraction integral and propagation of Hermite–Gaussian modes in a linear refractive index medium

A. A. Kovalev, V. V. Kotlyar, and S. G. Zaskanov  »View Author Affiliations

JOSA A, Vol. 31, Issue 5, pp. 914-919 (2014)

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We derive a diffraction integral to describe the paraxial propagation of an optical beam in a graded index medium with the permittivity linearly varying with the transverse coordinate. This integral transformation is irreducible to the familiar ABCD transformation. The form of the integral transformation suggests that, unlike a straight path in a homogeneous space, any paraxial optical beam will travel on a parabola bent toward the denser medium. By way of illustration, an explicit expression for the complex amplitude of a Hermite–Gaussian beam in the linear index medium is derived.

© 2014 Optical Society of America

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(350.5500) Other areas of optics : Propagation
(260.2710) Physical optics : Inhomogeneous optical media

ToC Category:
Physical Optics

Original Manuscript: December 19, 2013
Revised Manuscript: March 4, 2014
Manuscript Accepted: March 4, 2014
Published: April 8, 2014

A. A. Kovalev, V. V. Kotlyar, and S. G. Zaskanov, "Diffraction integral and propagation of Hermite–Gaussian modes in a linear refractive index medium," J. Opt. Soc. Am. A 31, 914-919 (2014)

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