OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 25 — Dec. 10, 2007
  • pp: 16328–16341

Rytov theory for Helmholtz-Gauss beams in turbulent atmosphere

Rodrigo J. Noriega-Manez and Julio C. Gutiérrez-Vega  »View Author Affiliations


Optics Express, Vol. 15, Issue 25, pp. 16328-16341 (2007)
http://dx.doi.org/10.1364/OE.15.016328


View Full Text Article

Enhanced HTML    Acrobat PDF (608 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The Rytov theory for the propagation of Helmholtz-Gauss (HzG) beams in turbulent atmosphere is presented. We derive expressions for the first and second-order normalized Born approximations, the second-order moments, and the transverse intensity pattern of the HzG beams at any arbitrary propagation distance. The general formulation is applied to study the propagation of several special cases of the HzG beams, in particular, the Bessel-Gauss and Mathieu-Gauss beams and their pure nondiffracting counterparts, the Bessel and Mathieu beams. For numerical purposes, we assume the standard Kolmogorov distribution to model the power spectrum of the atmospheric fluctuations.

© 2007 Optical Society of America

OCIS Codes
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence
(010.3310) Atmospheric and oceanic optics : Laser beam transmission

ToC Category:
Atmospheric and oceanic optics

History
Original Manuscript: September 27, 2007
Revised Manuscript: November 8, 2007
Manuscript Accepted: November 20, 2007
Published: November 26, 2007

Citation
Rodrigo J. Noriega-Manez and Julio C. Gutiérrez-Vega, "Rytov theory for Helmholtz-Gauss beams in turbulent atmosphere," Opt. Express 15, 16328-16341 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-25-16328


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. L. Andrews and R. Phillips, Laser beam propagation through random media (SPIE Press, 1998).
  2. C. Y. Young, Y. V. Gilchrest, and B. R. Macon, "Turbulence-induced beam spreading of higher-order mode optical waves," Opt. Eng. 41, 1097-1103 (2002). [CrossRef]
  3. H. T. Eyyuboglu, S. Altay, and Y. Baykal, "Propagation characteristics of higher-order annular Gaussian beams in atmospheric turbulence,"Opt. Commun. 264, 25-34 (2006). [CrossRef]
  4. Y. Cai and S. He, "Average intensity and spreading of an elliptical Gaussian beam propagating in a turbulent atmosphere,"Opt. Lett. 31, 568-570 (2002). [CrossRef]
  5. Y. Cai and D. Ge, "Analytical formula for a decentered elliptical Gaussian beam propagationg in a turbulent atmosphere,"Opt. Commun. 271, 509-516 (2007). [CrossRef]
  6. H. T. Eyyuboglu and Y. Baykal, "Reciprocity of cos-Gaussian and cosh-Gaussian laser beams in turbulent atmosphere," Opt. Express 12, 4659-4674 (2004). [CrossRef] [PubMed]
  7. H. T. Eyyuboglu and Y. Baykal, "Average intensity and spreading of cosh-Gaussian beams in the turbulent atmosphere," Appl. Opt. 44, 976-983 (2005). [CrossRef] [PubMed]
  8. H. T. Eyyuboglu, "Propagation of Hermite-cosh-Gaussian laser beams in turbulent atmosphere,"Opt. Commun. 245, 37-47 (2005). [CrossRef]
  9. H. T. Eyyuboglu, "Hermite-cosine-Gaussian laser beam and its propagation characteristics in turbulent atmosphere," J. Opt. Soc. Am. A 22, 1527-1535 (2005). [CrossRef]
  10. Y. Cai and S. He, "Propagation of a partially coherent twisted anisotropic Gaussian Schell-model beam in a turbulent atmosphere," Appl. Phys. Lett. 89, 041117 (2006). [CrossRef]
  11. H. T. Eyyuboglu, "Propagation of higher order Bessel-Gaussian beams in turbulence," Appl. Phys. B,  88, 259-265 (2007). [CrossRef]
  12. Y. Cai and S. He, "Propagation of various dark hollow beams in a turbulent atmosphere," Opt. Express 14, 1353-1367 (2006). [CrossRef] [PubMed]
  13. Z. Bouchal, "Resistance of nondiffracting vortex beam against amplitude and phase perturbations," Opt. Commun. 210, 155-164 (2002). [CrossRef]
  14. Z. Bouchal, "Nondiffracting optical beams: physical properties, experiments, and applications," Czech. J. Phys. 53, 537-578 (2003). [CrossRef]
  15. J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, "Alternative formulation for invariant optical fields: Mathieu beams," Opt. Lett. 25, 1493-1495 (2000). [CrossRef]
  16. M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, "Parabolic nondiffracting optical wave fields," Opt. Lett. 29, 44-46 (2004). [CrossRef] [PubMed]
  17. Z. Bouchal, J. Wagner, and M. Chlup, "Self-reconstructionof a distorted nondiffracting beam," Opt. Commun. 151, 207-211 (1998). [CrossRef]
  18. T. Aruga, S. W. Li, S. Yoshikado, M. Takabe, and R. Li, "Nondiffracting narrow light beam with small atmospheric turbulence-induced propagation," Appl. Opt. 38, 3152-3156 (1999). [CrossRef]
  19. G. Gbur and O. Korotkova, "Angular spectrum representation for propagation of arbitrary coherent and partially coherent beams through atmospheric turbulence," J. Opt. Soc. Am. A 24, 745-752 (2007). [CrossRef]
  20. O. Korotkova and G. Gbur, "Propagation of beams with any spectral, coherence and polarization properties in turbulent atmosphere," Proc. of SPIE 6457, 64570J1-64570J12 (2007).
  21. O. Korotkova and G. Gbur, "Angular spectrum representation for propagation of random electromagnetic beams in a turbulent atmosphere," J. Opt. Soc. Am. A 24, 2728-2736 (2007). [CrossRef]
  22. R. Frehlich, "Simulation of laser propagation in a turbulent atmosphere,"Appl. Opt. 30, 393-397 (2000). [CrossRef]
  23. C. Arpali, C. Yazicioglu, H. Eyyuboglu, S. Arpali, and Y. Baykal, "Simulator for general-type beam propagation in turbulent atmosphere," Opt. Express 14, 8918-8928 (2006). [CrossRef] [PubMed]
  24. D.C. Cowan, J. Recolons, L.C. Andrews, C.Y. Young, Atmospheric Propagation III, Proc. SPIE 6215, 62150 B-1- 62150B-10 (2006).
  25. J. C. Gutiérrez-Vega and M. A. Bandres, "Helmholtz-Gauss waves," J. Opt. Soc. Am. A 22, 289-298 (2005). [CrossRef]
  26. C. López-Mariscal, M. A. Bandrés, and J. C. Gutiérrez-Vega, "Observation of the experimental propagation properties of Helmholtz-Gauss beams," Opt. Eng. 45, 068001 (2006). [CrossRef]
  27. M. Guizar-Sicairos and J. C. Gutiérrez-Vega, "Propagation of Helmholtz-Gauss beams in absorbing and gain media," J. Opt. Soc. Am. A,  23, 1994-2001 (2006). [CrossRef]
  28. M. Guizar-Sicairos and J. C. Gutiérrez-Vega, "Generalized Helmholtz-Gauss beams and its transformation by paraxial optical systems," Opt. Lett. 31, 2912-2914 (2006). [CrossRef] [PubMed]
  29. M. A. Bandres and J. C. Gutiérrez-Vega, "Vector Helmholtz-Gauss and vector Laplace-Gauss beams," Opt. Lett. 30, 2155-2157 (2005). [CrossRef] [PubMed]
  30. Raul I. Hernandez-Aranda, J. C . Gutiérrez-Vega, Manuel Guizar-Sicairos, and Miguel A. Bandres, "Propagation of generalized vector Helmholtz-Gauss beams through paraxial optical systems," Opt. Express 14, 8974-8988 (2006). [CrossRef] [PubMed]
  31. F. Gori, G. Guattari, and C. Padovani, "Bessel-Gauss beams," Opt. Commun. 64, 491-495 (1987). [CrossRef]
  32. J. C. Gutiérrez-Vega and M. A. Bandres, "On the normalization of the Mathieu-Gauss optical beams," J. Opt. Soc. Am. A,  24, 215-220 (2007). [CrossRef]
  33. M. Abramowitz, and I.A. Stegun, Handbook of Mathematical Functions (Dover, 1964).
  34. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 2000) 6th ed.
  35. A. Chafiq, Z. Hricha, A. Belafhal, "Paraxial propagation of Mathieu beams through an apertured ABCD optical system," Opt. Commun. 253,223-230 (2005). [CrossRef]
  36. Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, "Shaping soliton properties in Mathieu lattices," Opt. Lett. 31, 238-240 (2006). [CrossRef] [PubMed]
  37. S. Chávez-Cerda, M.J. Padgett, I. Allison, G.H.C. New, JulioC. Gutiérrez-Vega, A.T. O’Neil, I. MacVicar, and J. Courtial, "Holographic generation and orbital angular momentum of high-order Mathieu beams," J. Opt. B: Quantum Semiclass. Opt. 4, S52-S57, (2002). [CrossRef]
  38. C. López-Mariscal, J. C. Gutiérrez-Vega, G. Milne and K. Dholakia, "Orbital angular momentum transfer in helical Mathieu beams," Opt. Express,  14, 4182-4187 (2006). [CrossRef] [PubMed]
  39. C. A. Dartora and H. E. Hernández-Figueroa, "Properties of a localized Mathieu pulse," J. Opt. Soc. Am. A 21, 662-667 (2004). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited