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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. 15, Iss. 12 — Dec. 1, 1998
  • pp: 3020–3027

Properties and diffraction of vector Bessel–Gauss beams

Pamela L. Greene and Dennis G. Hall  »View Author Affiliations


JOSA A, Vol. 15, Issue 12, pp. 3020-3027 (1998)
http://dx.doi.org/10.1364/JOSAA.15.003020


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Abstract

We examine a family of Bessel–Gauss beam solutions to the vector wave equation that allow a combination of azimuthal and radial polarization in the transverse electric field. Recently reported linear and azimuthal Bessel–Gauss beams may be identified as members of this set. Several free parameters determine the form and behavior of each beam; varying these parameters can produce distinctly different intensity patterns and beam behavior. We find a general diffraction integral for circularly symmetric disturbances and investigate two special cases, a thin lens and a circular aperture.

© 1998 Optical Society of America

OCIS Codes
(140.5960) Lasers and laser optics : Semiconductor lasers
(260.1960) Physical optics : Diffraction theory
(260.5430) Physical optics : Polarization
(350.5500) Other areas of optics : Propagation

Citation
Pamela L. Greene and Dennis G. Hall, "Properties and diffraction of vector Bessel–Gauss beams," J. Opt. Soc. Am. A 15, 3020-3027 (1998)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-12-3020


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References

  1. See, for example, A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986), pp. 642–648.
  2. J. A. Arnaud, “Nonorthogonal optical waveguides and resonators,” Bell Syst. Tech. J. 49, 2311–2348 (1970).
  3. H. Zucker, “Optical resonators with variable reflectivity mirrors,” Bell Syst. Tech. J. 49, 2349–2376 (1970).
  4. L. W. Casperson, D. G. Hall, and A. A. Tovar, “Sinusoidal–Gaussian beams in complex optical systems,” J. Opt. Soc. Am. A 14, 3341–3348 (1997).
  5. L. W. Casperson and A. A. Tovar, “Hermite-sinusoidal-Gaussian beams in complex optical systems,” J. Opt. Soc. Am. A 15, 954–961 (1998).
  6. F. Gori, G. Guattari, and C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
  7. R. H. Jordan and D. G. Hall, “Free-space azimuthal paraxial wave equation: the azimuthal Bessel–Gauss beam solution,” Opt. Lett. 19, 427–429 (1994).
  8. P. L. Greene and D. G. Hall, “Diffraction characteristics of the azimuthal Bessel–Gauss beam,” J. Opt. Soc. Am. A 13, 962–966 (1996).
  9. T. Erdogan and D. G. Hall, “Circularly symmetric distributed feedback laser: coupled mode treatment of TE vector fields,” IEEE J. Quantum Electron. QE-28, 612–623 (1992).
  10. R. H. Jordan, D. G. Hall, O. King, G. Wicks, and S. Rishton, “Lasing behavior of circular grating surface-emitting semiconductor lasers,” J. Opt. Soc. Am. B 14, 449–453 (1997).
  11. C. Palma, G. Cincotti, G. Guattari, and M. Santarsiero, “Imaging of generalized Bessel–Gauss beams,” J. Mod. Opt. 43, 2269–2277 (1996).
  12. B. Lü and W. Huang, “Three-dimensional intensity distribution of focused Bessel–Gauss beams,” J. Mod. Opt. 43, 509–515 (1996).
  13. B. Lü and W. Huang, “Focal shift in unapertured Bessel–Gauss beams,” Opt. Commun. 109, 43–46 (1994).
  14. R. Borghi and M. Santarsiero, “M2 factor of Bessel–Gauss beams,” Opt. Lett. 22, 262–264 (1997).
  15. V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. S. Spagnolo, “Generalized Bessel–Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).
  16. M. Santarsiero, “Propagation of generalized Bessel–Gauss beams through ABCD optical systems,” Opt. Commun. 132, 1–7 (1996).
  17. J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
  18. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
  19. Z. Bouchal and M. Olivík, “Non-diffractive vector Bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995).
  20. D. G. Hall, “Vector-beam solutions of Maxwell’s wave equation,” Opt. Lett. 21, 9–11 (1996).
  21. T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. H. Anderson, and M. J. Rooks, “Circularly symmetric operation of a concentric-circle-grating, surface-emitting, AlGaAs/GaAs quantum-well semiconductor laser,” Appl. Phys. Lett. 60, 1921–1923 (1992).
  22. D. Pohl, “Operation of a ruby laser in the purely transverse electric mode TE01,” Appl. Phys. Lett. 20, 266–267 (1972).
  23. J. Wynne, “Generation of the rotationally symmetric TE01 and TM01 modes from a wavelength-tunable laser,” IEEE J. Quantum Electron. QE-10, 125–127 (1974).
  24. M. E. Marhic and E. Garmire, “Low-order TE0q operation of a CO2 laser for transmission through circular waveguides,” Appl. Phys. Lett. 38, 743–745 (1981).
  25. C. Olson, P. L. Greene, G. W. Wicks, D. G. Hall, and S. Rishton, “High-order azimuthal spatial modes of concentric-circle-grating surface-emitting semiconductor lasers,” Appl. Phys. Lett. 72, 1284–1286 (1998).
  26. See, for example, J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 59–60.
  27. G. Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic, San Diego, Calif., 1985), p. 585.
  28. W. Magnus, F. Oberhettinger and R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics, 3rd enlarged ed. (Springer-Verlag New York, New York, 1966), Sec. 3.8.3, p. 93.
  29. Similar results for the m=0 mode, or ABG beam, have been presented in previous work (Ref. 8) for β≈10−6 k, though they are erroneously described therein as for β≈ 10−3 k.

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