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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 20 — Oct. 2, 2006
  • pp: 8974–8988

Propagation of generalized vector Helmholtz-Gauss beams through paraxial optical systems

Raul I. Hernandez-Aranda, Julio C. Gutiérrez-Vega, Manuel Guizar-Sicairos, and Miguel A. Bandres  »View Author Affiliations


Optics Express, Vol. 14, Issue 20, pp. 8974-8988 (2006)
http://dx.doi.org/10.1364/OE.14.008974


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Abstract

We introduce the generalized vector Helmholtz-Gauss (gVHzG) beams that constitute a general family of localized beam solutions of the Maxwell equations in the paraxial domain. The propagation of the electromagnetic components through axisymmetric ABCD optical systems is expressed elegantly in a coordinate-free and closed-form expression that is fully characterized by the transformation of two independent complex beam parameters. The transverse mathematical structure of the gVHzG beams is form-invariant under paraxial transformations. Any paraxial beam with the same waist size and transverse spatial frequency can be expressed as a superposition of gVHzG beams with the appropriate weight factors. This formalism can be straightforwardly applied to propagate vector Bessel-Gauss, Mathieu-Gauss, and Parabolic-Gauss beams, among others.

© 2006 Optical Society of America

OCIS Codes
(050.1970) Diffraction and gratings : Diffractive optics
(140.3300) Lasers and laser optics : Laser beam shaping
(260.5430) Physical optics : Polarization
(350.5500) Other areas of optics : Propagation

ToC Category:
Diffraction and Gratings

History
Original Manuscript: August 2, 2006
Revised Manuscript: September 15, 2006
Manuscript Accepted: September 15, 2006
Published: October 2, 2006

Citation
Raul I. Hernandez-Aranda, Julio C. Gutiérrez-Vega, Manuel Guizar-Sicairos, and Miguel A. Bandres, "Propagation of generalized vector Helmholtz-Gauss beams through paraxial optical systems," Opt. Express 14, 8974-8988 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-20-8974


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