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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 18, Iss. 7 — Jul. 1, 2001
  • pp: 1618–1626

Nonparaxial Bessel–Gauss beams

Riccardo Borghi, Massimo Santarsiero, and Miguel A. Porras  »View Author Affiliations

JOSA A, Vol. 18, Issue 7, pp. 1618-1626 (2001)

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We study the nonparaxial propagation of Bessel–Gauss beams of any order. Closed-form expressions of all corrections to be added to the solution that is pertinent to the corresponding paraxial problem are found. Such corrections are expressed in terms of two families of polynomials, defined through recurrence rules, that encompass the Laguerre–Gauss polynomials for the particular case of a fundamental Gaussian beam. Numerical examples are shown.

© 2001 Optical Society of America

OCIS Codes
(030.4070) Coherence and statistical optics : Modes
(260.1960) Physical optics : Diffraction theory
(350.5500) Other areas of optics : Propagation

Original Manuscript: June 15, 2000
Revised Manuscript: December 6, 2000
Manuscript Accepted: December 6, 2000
Published: July 1, 2001

Riccardo Borghi, Massimo Santarsiero, and Miguel A. Porras, "Nonparaxial Bessel–Gauss beams," J. Opt. Soc. Am. A 18, 1618-1626 (2001)

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  1. P. Vahimaa, V. Kettunen, M. Kuittinen, J. Turunen, A. T. Friberg, “Electromagnetic analysis of nonparaxial Bessel beams generated by diffractive axicons,” J. Opt. Soc. Am. A 14, 1817–1824 (1997). [CrossRef]
  2. J. Durnin, J. J. Miceli, J. H. Eberly, “Nondiffracting beams,” Phys. Rev. Lett. 58, 1499–1501 (1987). [CrossRef] [PubMed]
  3. Z. Bouchal, M. Olivı́k, “Non-diffractive vector Bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995). [CrossRef]
  4. M. Abramowitz, I. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1972).
  5. M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975). [CrossRef]
  6. G. P. Agrawal, D. N. Pattanayak, “Gaussian beam propagation beyond the paraxial approximation,” J. Opt. Soc. Am. 69, 575–578 (1979). [CrossRef]
  7. M. Couture, P. A. Belanger, “From Gaussian beam to complex-source-point spherical wave,” Phys. Rev. A 24, 355–359 (1981). [CrossRef]
  8. G. P. Agrawal, M. Lax, “Free-space propagation beyond the paraxial approximation,” Phys. Rev. A 27, 1693–1695 (1983). [CrossRef]
  9. T. Takenaka, M. Yokota, O. Fukumitsu, “Propagation for light beams beyond the paraxial approximation,” J. Opt. Soc. Am. A 2, 826–829 (1985). [CrossRef]
  10. S. Nemoto, “Nonparaxial Gaussian beams,” Appl. Opt. 29, 1940–1946 (1990). [CrossRef] [PubMed]
  11. Q. Cao, X. Deng, “Corrections to the paraxial approximation of an arbitrary free-propagation beam,” J. Opt. Soc. Am. A 15, 1144–1148 (1998). [CrossRef]
  12. H. Laabs, “Propagation of Hermite–Gaussian beams beyond the paraxial approximation,” Opt. Commun. 147, 1–4 (1998). [CrossRef]
  13. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  14. H. Laabs, A. T. Friberg, “Nonparaxial eigenmodes of stable resonators,” IEEE J. Quantum Electron. 35, 198–207 (1999). [CrossRef]
  15. 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). [CrossRef]
  16. G. W. Forbes, “Validity of the Fresnel approximation in the diffraction of collimated beams,” J. Opt. Soc. Am. A 13, 1816–1826 (1996). [CrossRef]
  17. G. W. Forbes, D. J. Butler, R. L. Gordon, A. A. Asatryan, “Algebraic corrections for paraxial wave fields,” J. Opt. Soc. Am. A 14, 3300–3315 (1997). [CrossRef]
  18. M. A. Alonso, A. A. Asatryan, G. W. Forbes, “Beyond the Fresnel approximation for focused waves,” J. Opt. Soc. Am. A 16, 1958–1969 (1999). [CrossRef]
  19. A. T. Friberg, T. Jakkola, J. Tuovinen, “Electromagnetic Gaussian beam beyond the paraxial regime,” IEEE Trans. Antennas Propag. 40, 984–989 (1992). [CrossRef]
  20. S. Chi, Q. Guo, “Vector theory of self-focusing of an optical beam in Kerr media,” Opt. Lett. 20, 1598–1600 (1995). [CrossRef] [PubMed]
  21. A. Ciattoni, B. Crosignani, P. Di Porto, “Vectorial free-space optical propagation: a simple approach for generating all-order nonparaxial corrections,” Opt. Commun. 177, 9–13 (2000). [CrossRef]
  22. A. Ciattoni, P. Di Porto, B. Crosignani, A. Yariv, “Vectorial nonparaxial propagation equation in the presence of a tensorial refractive-index perturbation,” J. Opt. Soc. Am. B 17, 809–819 (2000). [CrossRef]
  23. C. J. R. Sheppard, S. Saghafi, “Transverse-electric and transverse-magnetic beam modes beyond the paraxial approximation,” Opt. Lett. 24, 1543–1545 (1999). [CrossRef]
  24. C. J. R. Sheppard, S. Saghafi, “Electromagnetic Gaussian beam modes beyond the paraxial approximation,” J. Opt. Soc. Am. A 16, 1381–1386 (1999). [CrossRef]
  25. D. Yerick, M. Glasner, “Forward wide-angle light propagation in semiconductor and rib waveguides,” Opt. Lett. 15, 174–176 (1990). [CrossRef]
  26. C. J. R. Sheppard, T. Wilson, “Gaussian-beam theory of lenses with annular aperture,” Microwaves Opt. Acoust. 2, 105–112 (1978). [CrossRef]
  27. F. Gori, G. Guattari, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987). [CrossRef]
  28. V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, G. Schirripa Spagnolo, “Generalized Bessel–Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).
  29. M. Santarsiero, “Propagation of generalized Bessel–Gauss beams through ABCD optical systems,” Opt. Commun. 132, 1–7 (1996). [CrossRef]
  30. R. Borghi, M. Santarsiero, “M2 factor of Bessel–Gauss beams,” Opt. Lett. 22, 262–264 (1997). [CrossRef] [PubMed]
  31. F. Gori, G. Guattari, C. Padovani, “Modal expansion for J0-correlated Schell-model sources,” Opt. Commun. 64, 311–316 (1987). [CrossRef]
  32. C. Palma, R. Borghi, G. Cincotti, “Beams originated by J0-correlated Schell-model planar sources,” Opt. Commun. 125, 113–121 (1996). [CrossRef]
  33. R. Borghi, “Superposition scheme for J0-correlated partially coherent sources,” IEEE J. Quantum Electron. 35, 849–856 (1999). [CrossRef]
  34. S. R. Seshadri, “Average characteristics of a partially coherent Bessel–Gauss optical beam,” J. Opt. Soc. Am. A 16, 2917–2927 (1999). [CrossRef]
  35. A. V. Shchegrov, E. Wolf, “Partially coherent conical beams,” Opt. Lett. 25, 141–143 (2000). [CrossRef]
  36. R. H. Jordan, D. G. Hall, “Free-space azimuthal paraxial wave equation: the azimuthal Bessel–Gauss solution,” Opt. Lett. 19, 427–429 (1994). [CrossRef] [PubMed]
  37. D. G. Hall, “Vector-beam solution of Maxwell’s wave equation,” Opt. Lett. 21, 9–12 (1996). [CrossRef] [PubMed]
  38. C. Olson, P. L. Greene, G. W. Wicks, D. G. Hall, S. Rishton, “High-order azimuthal spatial modes of concentric-circle-grating surface-emitting semiconductor lasers,” Appl. Phys. Lett. 72, 1284–1286 (1998). [CrossRef]
  39. P. L. Greene, D. G. Hall, “Properties and diffraction of vector Bessel–Gauss beams,” J. Opt. Soc. Am. A 15, 3020–3027 (1998). [CrossRef]
  40. P. Pääkkönen, J. Turunen, “Resonators with Bessel–Gauss modes,” Opt. Commun. 156, 359–366 (1998). [CrossRef]
  41. C. F. R. Caron, R. M. Potvliege, “Phase matching and harmonic generation in Bessel–Gauss beams,” J. Opt. Soc. Am. B 15, 1096–1106 (1998). [CrossRef]
  42. J. Arlt, K. Dholakia, L. Allen, M. J. Padgett, “Efficiency of second-harmonic generation with Bessel beams,” Phys. Rev. A 60, 2438–2441 (1999). [CrossRef]
  43. C. Altucci, R. Bruzzese, D. D’Antuoni, C. de Lisio, S. Solimeno, “Harmonic generation in gases by use of Bessel–Gauss laser beams,” J. Opt. Soc. Am. B 17, 34–42 (2000). [CrossRef]

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