Propagation of a partially coherent hollow vortex Gaussian beam through a paraxial ABCD optical system in turbulent atmosphere |
Optics Express, Vol. 20, Issue 9, pp. 9897-9910 (2012)
http://dx.doi.org/10.1364/OE.20.009897
Acrobat PDF (4176 KB)
Abstract
The propagation of a partially coherent hollow vortex Gaussian beam through a paraxial ABCD optical system in turbulent atmosphere has been investigated. The analytical expressions for the average intensity and the degree of the polarization of a partially coherent hollow vortex Gaussian beam through a paraxial ABCD optical system are derived in turbulent atmosphere, respectively. The average intensity distribution and the degree of the polarization of a partially coherent hollow vortex Gaussian beam in turbulent atmosphere are numerically demonstrated. The influences of the beam parameters, the topological charge, the transverse coherent lengths, and the structure constant of the atmospheric turbulence on the propagation of a partially coherent hollow vortex Gaussian beam in turbulent atmosphere are also examined in detail. This research is beneficial to the practical applications in free-space optical communications and the remote sensing of the dark hollow beams.
© 2012 OSA
1. Introduction
11. Y. Cai, X. Lu, and Q. Lin, “Hollow Gaussian beams and their propagation properties,” Opt. Lett. 28(13), 1084–1086 (2003). [PubMed]
12. Z. Mei and D. Zhao, “Controllable dark-hollow beams and their propagation characteristics,” J. Opt. Soc. Am. A 22(9), 1898–1902 (2005). [PubMed]
14. Z. Liu, H. Zhao, J. Liu, J. Lin, M. A. Ahmad, and S. Liu, “Generation of hollow Gaussian beams by spatial filtering,” Opt. Lett. 32(15), 2076–2078 (2007). [PubMed]
15. C. Zhao, Y. Cai, F. Wang, X. Lu, and Y. Wang, “Generation of a high-quality partially coherent dark hollow beam with a multimode fiber,” Opt. Lett. 33(12), 1389–1391 (2008). [PubMed]
16. Y. Zheng, X. Wang, F. Shen, and X. Li, “Generation of dark hollow beam via coherent combination based on adaptive optics,” Opt. Express 18(26), 26946–26958 (2010). [PubMed]
17. Y. Nie, H. Ma, X. Li, W. Hu, and J. Yang, “Generation of dark hollow femtosecond pulsed beam by phase-only liquid crystal spatial light modulator,” Appl. Opt. 50(21), 4174–4179 (2011). [PubMed]
18. D. Deng, X. Fu, C. Wei, J. Shao, and Z. Fan, “Far-field intensity distribution and M^{2} factor of hollow Gaussian beams,” Appl. Opt. 44(33), 7187–7190 (2005). [PubMed]
11. Y. Cai, X. Lu, and Q. Lin, “Hollow Gaussian beams and their propagation properties,” Opt. Lett. 28(13), 1084–1086 (2003). [PubMed]
27. H. T. Eyyuboğlu, “Hermite-cosine-Gaussian laser beam and its propagation characteristics in turbulent atmosphere,” J. Opt. Soc. Am. A 22(8), 1527–1535 (2005). [PubMed]
36. X. Liu and J. Pu, “Investigation on the scintillation reduction of elliptical vortex beams propagating in atmospheric turbulence,” Opt. Express 19(27), 26444–26450 (2011). [PubMed]
2. Propagation of a partially coherent hollow vortex Gaussian beam through a paraxial ABCD optical system in turbulent atmosphere
3. The numerical results and analyses
4. Conclusions
Acknowledgments
References and links
1. | V. I. Balykin and V. S. Letokhov, “The possibility of deep laser focusing of an atom beam into the A region,” Opt. Commun. 64, 151–156 (1987). |
2. | X. Wang and M. G. Littman, “Laser cavity for generation of variable-radius rings of light,” Opt. Lett. 18(10), 767–768 (1993). [PubMed] |
3. | H. S. Lee, B. W. Stewart, K. Choi, and H. Fenichel, “Holographic nondiverging hollow beam,” Phys. Rev. A 49(6), 4922–4927 (1994). [PubMed] |
4. | S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, “Coherent atomic waveguides from hollow optical fibers: quantized atomic motion,” Phys. Rev. A 50(3), 2680–2690 (1994). [PubMed] |
5. | C. Paterson and R. Smith, “High-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996). |
6. | J. Yin, Y. Zhu, W. Wang, Y. Wang, and W. Jhe, “Optical potential for atom guidance in a dark hollow laser beam,” J. Opt. Soc. Am. B 15, 25–33 (1998). |
7. | M. Yan, J. Yin, and Y. Zhu, “Dark-hollow-beam guiding and splitting of a low-velocity atomic beam,” J. Opt. Soc. Am. B 17, 1817–1820 (2000). |
8. | Z. Wang, Y. Dong, and Q. Lin, “Atomic trapping and guiding by quasi-dark hollow beams,” J. Opt. A, Pure Appl. Opt. 7, 147–153 (2005). |
9. | K. Zhu, H. Tang, X. Sun, X. Wang, and T. Liu, “Flattened multi-Gaussian light beams with an axial shadow generated through superposing Gaussian beams,” Opt. Commun. 207, 29–34 (2002). |
10. | V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. S. Spagnolo, “Generalized Bessel-Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996). |
11. | Y. Cai, X. Lu, and Q. Lin, “Hollow Gaussian beams and their propagation properties,” Opt. Lett. 28(13), 1084–1086 (2003). [PubMed] |
12. | Z. Mei and D. Zhao, “Controllable dark-hollow beams and their propagation characteristics,” J. Opt. Soc. Am. A 22(9), 1898–1902 (2005). [PubMed] |
13. | H. Ma, H. Cheng, W. Zhang, L. Liu, and Y. Wang, “Generation of a hollow laser beam by a multimode fiber,” Chin. Opt. Lett. 5, 460–462 (2007). |
14. | Z. Liu, H. Zhao, J. Liu, J. Lin, M. A. Ahmad, and S. Liu, “Generation of hollow Gaussian beams by spatial filtering,” Opt. Lett. 32(15), 2076–2078 (2007). [PubMed] |
15. | C. Zhao, Y. Cai, F. Wang, X. Lu, and Y. Wang, “Generation of a high-quality partially coherent dark hollow beam with a multimode fiber,” Opt. Lett. 33(12), 1389–1391 (2008). [PubMed] |
16. | Y. Zheng, X. Wang, F. Shen, and X. Li, “Generation of dark hollow beam via coherent combination based on adaptive optics,” Opt. Express 18(26), 26946–26958 (2010). [PubMed] |
17. | Y. Nie, H. Ma, X. Li, W. Hu, and J. Yang, “Generation of dark hollow femtosecond pulsed beam by phase-only liquid crystal spatial light modulator,” Appl. Opt. 50(21), 4174–4179 (2011). [PubMed] |
18. | D. Deng, X. Fu, C. Wei, J. Shao, and Z. Fan, “Far-field intensity distribution and M^{2} factor of hollow Gaussian beams,” Appl. Opt. 44(33), 7187–7190 (2005). [PubMed] |
19. | Y. Cai and S. He, “Propagation of various dark hollow beams in a turbulent atmosphere,” Opt. Express 14(4), 1353–1367 (2006). [PubMed] |
20. | H. T. Eyyuboğlu, “Propagation and coherence properties of higher order partially coherent dark hollow beams in turbulence,” Opt. Laser Technol. 40, 156–166 (2008). |
21. | G. Zhou, X. Chu, and J. Zheng, “Investigation in hollow Gaussian beam from vectorial structure,” Opt. Commun. 281, 5653–5658 (2008). |
22. | Z. Mei and D. Zhao, “Nonparaxial propagation of controllable dark-hollow beams,” J. Opt. Soc. Am. A 25(3), 537–542 (2008). [PubMed] |
23. | D. Deng and Q. Guo, “Exact nonparaxial propagation of a hollow Gaussian beam,” J. Opt. Soc. Am. B 26, 2044–2049 (2009). |
24. | Y. Yuan, Y. Cai, J. Qu, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “M^{2}-factor of coherent and partially coherent dark hollow beams propagating in turbulent atmosphere,” Opt. Express 17(20), 17344–17356 (2009). [PubMed] |
25. | H. T. Eyyuboğlu, Y. Baykal, and X. Ji, “Radius of curvature variations for annular, dark hollow and flat topped beams in turbulence,” Appl. Phys. B 99, 801–807 (2010). |
26. | L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, UK, 1995). |
27. | H. T. Eyyuboğlu, “Hermite-cosine-Gaussian laser beam and its propagation characteristics in turbulent atmosphere,” J. Opt. Soc. Am. A 22(8), 1527–1535 (2005). [PubMed] |
28. | Y. Zhu, D. Zhao, and X. Du, “Propagation of stochastic Gaussian-Schell model array beams in turbulent atmosphere,” Opt. Express 16(22), 18437–18442 (2008). [PubMed] |
29. | T. Wang, J. Pu, and Z. Chen, “Propagation of partially coherent vortex beams in a turbulent atmosphere,” Opt. Eng. 47, 036002 (2008). |
30. | G. Gbur and R. K. Tyson, “Vortex beam propagation through atmospheric turbulence and topological charge conservation,” J. Opt. Soc. Am. A 25(1), 225–230 (2008). [PubMed] |
31. | X. Du and D. Zhao, “Polarization modulation of stochastic electromagnetic beams on propagation through the turbulent atmosphere,” Opt. Express 17(6), 4257–4262 (2009). [PubMed] |
32. | X. Ji and X. Li, “Directionality of Gaussian array beams propagating in atmospheric turbulence,” J. Opt. Soc. Am. A 26(2), 236–243 (2009). [PubMed] |
33. | X. Ji, H. T. Eyyuboğlu, and Y. Baykal, “Influence of turbulence on the effective radius of curvature of radial Gaussian array beams,” Opt. Express 18(7), 6922–6928 (2010). [PubMed] |
34. | P. Zhou, X. Wang, Y. Ma, H. Ma, X. Xu, and Z. Liu, “Average intensity and spreading of Lorentz beam propagating in a turbulent atmosphere,” J. Opt. 12, 01540–01549 (2010). |
35. | C. Li and J. Pu, “Ghost imaging with partially coherent light radiation through turbulent atmosphere,” Appl. Phys. B 99, 599–604 (2010). |
36. | X. Liu and J. Pu, “Investigation on the scintillation reduction of elliptical vortex beams propagating in atmospheric turbulence,” Opt. Express 19(27), 26444–26450 (2011). [PubMed] |
37. | E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263–267 (2003). |
38. | J. Pu, O. Korotkova, and E. Wolf, “Polarization-induced spectral changes on propagation of stochastic electromagnetic beams,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5 Pt 2), 056610 (2007). [PubMed] |
39. | A. Al-Qasimi, O. Korotkova, D. James, and E. Wolf, “Definitions of the degree of polarization of a light beam,” Opt. Lett. 32(9), 1015–1016 (2007). [PubMed] |
40. | D. Zhao and E. Wolf, “Light beams whose degree of polarization does not change on propagation,” Opt. Commun. 281, 3067–3070 (2008). |
41. | M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in turbulent atmosphere,” Waves Random Media 14, 513–523 (2004). |
42. | H. T. Yura and S. G. Hanson, “Optical beam wave propagation through complex optical systems,” J. Opt. Soc. Am. A 4, 1931–1948 (1987). |
43. | I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products (Academic, San Diego, CA, 1980). |
OCIS Codes
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(030.1640) Coherence and statistical optics : Coherence
(260.5430) Physical optics : Polarization
ToC Category:
Atmospheric and Oceanic Optics
History
Original Manuscript: March 7, 2012
Revised Manuscript: April 8, 2012
Manuscript Accepted: April 9, 2012
Published: April 16, 2012
Citation
Guoquan Zhou, Yangjian Cai, and Xiuxiang Chu, "Propagation of a partially coherent hollow vortex Gaussian beam through a paraxial ABCD optical system in turbulent atmosphere," Opt. Express 20, 9897-9910 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-9-9897
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References
- V. I. Balykin and V. S. Letokhov, “The possibility of deep laser focusing of an atom beam into the A region,” Opt. Commun.64, 151–156 (1987).
- X. Wang and M. G. Littman, “Laser cavity for generation of variable-radius rings of light,” Opt. Lett.18(10), 767–768 (1993). [PubMed]
- H. S. Lee, B. W. Stewart, K. Choi, and H. Fenichel, “Holographic nondiverging hollow beam,” Phys. Rev. A49(6), 4922–4927 (1994). [PubMed]
- S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, “Coherent atomic waveguides from hollow optical fibers: quantized atomic motion,” Phys. Rev. A50(3), 2680–2690 (1994). [PubMed]
- C. Paterson and R. Smith, “High-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun.124, 121–130 (1996).
- J. Yin, Y. Zhu, W. Wang, Y. Wang, and W. Jhe, “Optical potential for atom guidance in a dark hollow laser beam,” J. Opt. Soc. Am. B15, 25–33 (1998).
- M. Yan, J. Yin, and Y. Zhu, “Dark-hollow-beam guiding and splitting of a low-velocity atomic beam,” J. Opt. Soc. Am. B17, 1817–1820 (2000).
- Z. Wang, Y. Dong, and Q. Lin, “Atomic trapping and guiding by quasi-dark hollow beams,” J. Opt. A, Pure Appl. Opt.7, 147–153 (2005).
- K. Zhu, H. Tang, X. Sun, X. Wang, and T. Liu, “Flattened multi-Gaussian light beams with an axial shadow generated through superposing Gaussian beams,” Opt. Commun.207, 29–34 (2002).
- V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. S. Spagnolo, “Generalized Bessel-Gauss beams,” J. Mod. Opt.43, 1155–1166 (1996).
- Y. Cai, X. Lu, and Q. Lin, “Hollow Gaussian beams and their propagation properties,” Opt. Lett.28(13), 1084–1086 (2003). [PubMed]
- Z. Mei and D. Zhao, “Controllable dark-hollow beams and their propagation characteristics,” J. Opt. Soc. Am. A22(9), 1898–1902 (2005). [PubMed]
- H. Ma, H. Cheng, W. Zhang, L. Liu, and Y. Wang, “Generation of a hollow laser beam by a multimode fiber,” Chin. Opt. Lett.5, 460–462 (2007).
- Z. Liu, H. Zhao, J. Liu, J. Lin, M. A. Ahmad, and S. Liu, “Generation of hollow Gaussian beams by spatial filtering,” Opt. Lett.32(15), 2076–2078 (2007). [PubMed]
- C. Zhao, Y. Cai, F. Wang, X. Lu, and Y. Wang, “Generation of a high-quality partially coherent dark hollow beam with a multimode fiber,” Opt. Lett.33(12), 1389–1391 (2008). [PubMed]
- Y. Zheng, X. Wang, F. Shen, and X. Li, “Generation of dark hollow beam via coherent combination based on adaptive optics,” Opt. Express18(26), 26946–26958 (2010). [PubMed]
- Y. Nie, H. Ma, X. Li, W. Hu, and J. Yang, “Generation of dark hollow femtosecond pulsed beam by phase-only liquid crystal spatial light modulator,” Appl. Opt.50(21), 4174–4179 (2011). [PubMed]
- D. Deng, X. Fu, C. Wei, J. Shao, and Z. Fan, “Far-field intensity distribution and M2 factor of hollow Gaussian beams,” Appl. Opt.44(33), 7187–7190 (2005). [PubMed]
- Y. Cai and S. He, “Propagation of various dark hollow beams in a turbulent atmosphere,” Opt. Express14(4), 1353–1367 (2006). [PubMed]
- H. T. Eyyuboğlu, “Propagation and coherence properties of higher order partially coherent dark hollow beams in turbulence,” Opt. Laser Technol.40, 156–166 (2008).
- G. Zhou, X. Chu, and J. Zheng, “Investigation in hollow Gaussian beam from vectorial structure,” Opt. Commun.281, 5653–5658 (2008).
- Z. Mei and D. Zhao, “Nonparaxial propagation of controllable dark-hollow beams,” J. Opt. Soc. Am. A25(3), 537–542 (2008). [PubMed]
- D. Deng and Q. Guo, “Exact nonparaxial propagation of a hollow Gaussian beam,” J. Opt. Soc. Am. B26, 2044–2049 (2009).
- Y. Yuan, Y. Cai, J. Qu, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “M2-factor of coherent and partially coherent dark hollow beams propagating in turbulent atmosphere,” Opt. Express17(20), 17344–17356 (2009). [PubMed]
- H. T. Eyyuboğlu, Y. Baykal, and X. Ji, “Radius of curvature variations for annular, dark hollow and flat topped beams in turbulence,” Appl. Phys. B99, 801–807 (2010).
- L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, UK, 1995).
- H. T. Eyyuboğlu, “Hermite-cosine-Gaussian laser beam and its propagation characteristics in turbulent atmosphere,” J. Opt. Soc. Am. A22(8), 1527–1535 (2005). [PubMed]
- Y. Zhu, D. Zhao, and X. Du, “Propagation of stochastic Gaussian-Schell model array beams in turbulent atmosphere,” Opt. Express16(22), 18437–18442 (2008). [PubMed]
- T. Wang, J. Pu, and Z. Chen, “Propagation of partially coherent vortex beams in a turbulent atmosphere,” Opt. Eng.47, 036002 (2008).
- G. Gbur and R. K. Tyson, “Vortex beam propagation through atmospheric turbulence and topological charge conservation,” J. Opt. Soc. Am. A25(1), 225–230 (2008). [PubMed]
- X. Du and D. Zhao, “Polarization modulation of stochastic electromagnetic beams on propagation through the turbulent atmosphere,” Opt. Express17(6), 4257–4262 (2009). [PubMed]
- X. Ji and X. Li, “Directionality of Gaussian array beams propagating in atmospheric turbulence,” J. Opt. Soc. Am. A26(2), 236–243 (2009). [PubMed]
- X. Ji, H. T. Eyyuboğlu, and Y. Baykal, “Influence of turbulence on the effective radius of curvature of radial Gaussian array beams,” Opt. Express18(7), 6922–6928 (2010). [PubMed]
- P. Zhou, X. Wang, Y. Ma, H. Ma, X. Xu, and Z. Liu, “Average intensity and spreading of Lorentz beam propagating in a turbulent atmosphere,” J. Opt.12, 01540–01549 (2010).
- C. Li and J. Pu, “Ghost imaging with partially coherent light radiation through turbulent atmosphere,” Appl. Phys. B99, 599–604 (2010).
- X. Liu and J. Pu, “Investigation on the scintillation reduction of elliptical vortex beams propagating in atmospheric turbulence,” Opt. Express19(27), 26444–26450 (2011). [PubMed]
- E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A312, 263–267 (2003).
- J. Pu, O. Korotkova, and E. Wolf, “Polarization-induced spectral changes on propagation of stochastic electromagnetic beams,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.75(5 Pt 2), 056610 (2007). [PubMed]
- A. Al-Qasimi, O. Korotkova, D. James, and E. Wolf, “Definitions of the degree of polarization of a light beam,” Opt. Lett.32(9), 1015–1016 (2007). [PubMed]
- D. Zhao and E. Wolf, “Light beams whose degree of polarization does not change on propagation,” Opt. Commun.281, 3067–3070 (2008).
- M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in turbulent atmosphere,” Waves Random Media14, 513–523 (2004).
- H. T. Yura and S. G. Hanson, “Optical beam wave propagation through complex optical systems,” J. Opt. Soc. Am. A4, 1931–1948 (1987).
- I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products (Academic, San Diego, CA, 1980).
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