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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

  • Vol. 22, Iss. 9 — Sep. 1, 2005
  • pp: 1976–1980

Propagation of Hermite–Gaussian and Laguerre–Gaussian beams beyond the paraxial approximation

Kailiang Duan, Beizhan Wang, and Baida Lü  »View Author Affiliations


JOSA A, Vol. 22, Issue 9, pp. 1976-1980 (2005)
http://dx.doi.org/10.1364/JOSAA.22.001976


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Abstract

On the basis of the vectorial Rayleigh–Sommerfeld formulas and by means of the relation between Hermite and Laguerre polynomials, the analytical expressions for the propagation of the Hermite–Gaussian (HG) and Laguerre–Gaussian (LG) beams beyond the paraxial approximation are derived, with the corresponding far-field propagation expressions and that for the Gaussian beams being given as special cases of the results. Some detailed comparisons of our results with the expansion series and paraxial expressions are made, which show the advantages of our results over the expansion series. With the results obtained, some typical intensity patterns of nonparaxial HG and LG beams are shown.

© 2005 Optical Society of America

OCIS Codes
(260.1960) Physical optics : Diffraction theory
(350.5500) Other areas of optics : Propagation

History
Original Manuscript: December 23, 2004
Manuscript Accepted: March 8, 2005
Published: September 1, 2005

Citation
Kailiang Duan, Baida Lü, and Beizhan Wang, "Propagation of Hermite–Gaussian and Laguerre–Gaussian beams beyond the paraxial approximation," J. Opt. Soc. Am. A 22, 1976-1980 (2005)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-22-9-1976

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