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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

Citation
Kailiang Duan, Beizhan Wang, and Baida Lü, "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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References

  1. M. Lax, W. H. Louisell, and W. B. McKnight, "From Maxwell to paraxial wave optics," Phys. Rev. A 11, 1365-1370 (1975).
  2. T. Takenaka, M. Yokota, and O. Fukumitsu, "Propagation of light beams beyond the paraxial approximation," J. Opt. Soc. Am. A 2, 826-829 (1985).
  3. L. W. Davis, "Theory of electromagnetic beams," Phys. Rev. A 19, 1177-1179 (1979).
  4. H. Laabs, "Propagation of Hermite-Gaussian-beams beyond the paraxial approximation," Opt. Commun. 147, 1-4 (1998).
  5. H. C. Kim and Y. H. Lee, "Hermite-Gaussian and Laguerre-Gaussian beams beyond the paraxial approximation," Opt. Commun. 169, 9-16 (1999).
  6. H. Laabs and A. T. Friberg, "Nonparaxial eigenmodes of stable resonators," IEEE J. Quantum Electron. 35, 198-207 (1999).
  7. G. P. Agrawal and D. N. Pattanayak, "Gaussian beam propagation beyond the paraxial approximation," J. Opt. Soc. Am. 69, 575-578 (1979).
  8. C. G. Chen, P. T. Konkola, J. Ferrera, R. K. Heilmann, and M. L. Schattenburg, "Analyses of vector Gaussian beam propagation and the validity of paraxial and spherical approximations," J. Opt. Soc. Am. A 19, 404-412 (2002).
  9. A. Wünsche, "Transition from the paraxial approximation to exact solutions of the wave equation and application to Gaussian beams," J. Opt. Soc. Am. A 9, 765-774 (1992).
  10. Q. Cao and X. Deng, "Corrections to the paraxial approximation of an arbitrary free-propagation beam," J. Opt. Soc. Am. A 15, 1144-1148 (1998).
  11. R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, Calif., 1966).
  12. K. Duan and B. Lü, "Partially coherent vectorial nonparaxial beams," J. Opt. Soc. Am. A 21, 1924-1932 (2004).
  13. X. Zeng, C. Liang, and Y. An, "Far-field propagation of an off-axis Gaussian wave," Appl. Opt. 38, 6253-6256 (1999).
  14. I. Kimel and L. R. Elias, "Relations between Hermite and Laguerre Gaussian modes," IEEE J. Quantum Electron. 29, 2562-2567 (1993).
  15. A. E. Siegman, Lasers (University Science Books, 1986).

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