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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 22, Iss. 2 — Feb. 1, 2005
  • pp: 289–298

Helmholtz–Gauss waves

Julio C. Gutiérrez-Vega and Miguel A. Bandres  »View Author Affiliations

JOSA A, Vol. 22, Issue 2, pp. 289-298 (2005)

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A detailed study of the propagation of an arbitrary nondiffracting beam whose disturbance in the plane z=0 is modulated by a Gaussian envelope is presented. We call such a field a Helmholtz–Gauss (HzG) beam. A simple closed-form expression for the paraxial propagation of the HzG beams is written as the product of three factors: a complex amplitude depending on the z coordinate only, a Gaussian beam, and a complex scaled version of the transverse shape of the nondiffracting beam. The general expression for the angular spectrum of the HzG beams is also derived. We introduce for the first time closed-form expressions for the Mathieu–Gauss beams in elliptic coordinates and for the parabolic Gauss beams in parabolic coordinates. The properties of the considered beams are studied both analytically and numerically.

© 2005 Optical Society of America

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(140.3300) Lasers and laser optics : Laser beam shaping
(260.1960) Physical optics : Diffraction theory
(350.5500) Other areas of optics : Propagation

Original Manuscript: June 23, 2004
Revised Manuscript: August 17, 2004
Manuscript Accepted: August 18, 2004
Published: February 1, 2005

Julio C. Gutiérrez-Vega and Miguel A. Bandres, "Helmholtz–Gauss waves," J. Opt. Soc. Am. A 22, 289-298 (2005)

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