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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 8 — Aug. 1, 2006
  • pp: 1994–2001

Propagation of Helmholtz–Gauss beams in absorbing and gain media

Manuel Guizar-Sicairos and Julio C. Gutiérrez-Vega  »View Author Affiliations

JOSA A, Vol. 23, Issue 8, pp. 1994-2001 (2006)

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The propagation of Helmholtz–Gauss beams in media exhibiting loss or gain is studied. The general expressions for the field propagation, the time-averaged power on propagation, the trajectory of the beam centroid, the beam spreading, the nondiffracting distance, and the far field are derived and discussed. Explicit expressions of these parameters for Bessel–Gauss and cosine-Gauss beams are included. The general expressions can be applied straightforwardly to describe the propagation of Mathieu–Gauss and parabolic-Gauss beams in complex media as well.

© 2006 Optical Society of America

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(140.3300) Lasers and laser optics : Laser beam shaping
(260.1960) Physical optics : Diffraction theory
(350.5500) Other areas of optics : Propagation

ToC Category:
Physical Optics

Original Manuscript: October 14, 2005
Revised Manuscript: January 24, 2006
Manuscript Accepted: January 25, 2006

Manuel Guizar-Sicairos and Julio C. Gutiérrez-Vega, "Propagation of Helmholtz-Gauss beams in absorbing and gain media," J. Opt. Soc. Am. A 23, 1994-2001 (2006)

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  1. J. C. Gutiérrez-Vega and M. A. Bandres, "Helmholtz-Gauss waves," J. Opt. Soc. Am. A 22, 289-298 (2005). [CrossRef]
  2. A. P. Kiselev, "New structures in paraxial Gaussian beams," Opt. Spectrosc. 96, 479-481 (2004). [CrossRef]
  3. M. A. Bandres and J. C. Gutiérrez-Vega, "Vector Helmholtz-Gauss and vector Laplace-Gauss beams," Opt. Lett. 30, 2155-2157 (2005). [CrossRef] [PubMed]
  4. C. López-Mariscal, M. A. Bandrés, and J. C. Gutiérrez-Vega, "Characterization of Helmholtz-Gauss beams," in Laser Beam Shaping VI, F.Dickey and D.L.Shealy, eds., Proc. SPIE5876, 77-88 (2005).
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  6. J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, "Alternative formulation of nondiffracting beams: Mathieu beams," Opt. Lett. 25, 1493-1495 (2000). [CrossRef]
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  11. S. Velumani, S. K. Narayandass, D. Mangalaraj, and C. P. G. Villaban, "Laser damage studies on hot-wall-deposited cadmium selenide films," J. Mater. Sci. Lett. 16, 1974-1976 (1997). [CrossRef]
  12. J. A. Gaspar and P. Halevi, "Linear pulse propagation in an absorbing medium: effect of film thickness," Phys. Rev. B 49, 10742-10744 (1994). [CrossRef]
  13. J. C. Gutiérrez-Vega, R. M. Rodríguez-Dagnino, and S. Chávez-Cerda, "Attenuation characteristics in confocal annular elliptic waveguides and resonators," IEEE Trans. Microwave Theory Tech. 50, 1095-1100 (2002). [CrossRef]
  14. S. R. Seshadri, "Effect of absorption on the spreading of a laser beam," Opt. Lett. 29, 1179-1181 (2004). [CrossRef] [PubMed]
  15. M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, "Parabolic nondiffracting optical wave fields," Opt. Lett. 29, 44-46 (2004). [CrossRef] [PubMed]
  16. O. Svelto, Principles of Lasers, 4th ed. (Plenum, 1998).
  17. R. W. D. Nickalls, "A new approach to solving the cubic: Cardan's solution revealed," Math. Gaz. 77, 354-359 (1993). [CrossRef]

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