## Light sources generating self-splitting beams and their propagation in non-Kolmogorov turbulence |

Optics Express, Vol. 22, Issue 11, pp. 13029-13040 (2014)

http://dx.doi.org/10.1364/OE.22.013029

Acrobat PDF (11668 KB)

### Abstract

A class of random sources producing far fields self-splitting intensity profiles with variable spacing between the *x* and *y* directions is introduced. The beam conditions for ensuring the sources to generate a beam are derived. Based on the derived analytical expression, the evolution behavior of the beams produced by these families of sources in free space and turbulence atmospheric are explored and comparatively analyzed. By changing the modulation parameters *n* and *m*, the degree of coherence of Gaussian Schell-model source in the *x* and *y* directions are modulated respectively, and then the number of splitting beams and the spacing between splitting beams can be adjusted. It is illustrated that the self-splitting intensity profile is stable when beams propagate in free space, but they eventually transformed into a Gaussian profiles when it passes at sufficiently large distances from its source through the turbulent atmosphere.

© 2014 Optical Society of America

## 1. Introduction

## 2. Light source model and beam conditions

33. F. Gori and M. Santarsiero, “Devising genuine spatial correlation functions,” Opt. Lett. **32**(24), 3531–3533 (2007). [CrossRef] [PubMed]

21. C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. **39**(4), 769–772 (2014). [CrossRef] [PubMed]

6. A. Suryanto and E. Van Groesen, “Self-splitting of multisoliton bound states in planar Kerr waveguides,” Opt. Commun. **258**(2), 264–274 (2006). [CrossRef]

*z*-axis. On substituting from Eq. (8) into Eq. (10) and then into (9) we finally obtain the following expression for the CSD function in the far zone generated by an OCGSM source

**r**(

*z*axis [10]. Since the value of hyperbolic cosine function is always greater than 1, this is so ifHence, the beam conditions for the OCGSM sources are

## 3. Propagation laws in non-Kolmogorov turbulence and free space

## 4. Numerical results

*n*= 5 and

*m*= 5 at several distances

*z*from the source plane on propagation free space. One clearly sees that the transverse distribution of the beam’s spectral density from a Gaussian distribution of source plane gradually split into four beams with the increase of transmission distance. So we can term this light beam generated by the novel family of source with Gaussian spectral density and orthogonal cosine-Gaussian Schell-model correlation as

*self-splitting beams*. The reason for this feature is that the Gaussian Schell correlation model is modified by the cosine function in

*x*and

*y*directions, respectively. The experimental realization of a random light source with the orthogonal cosine-Gaussian Schell-model correlation can be made with the help of the spatial light modulator (SLM) [21

21. C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. **39**(4), 769–772 (2014). [CrossRef] [PubMed]

*x*or

*y*one direction. Figures 3(d) and 3(e) show the spacing between the

*x*and

*y*directions are not equal due to the modulation factor in two directions are not equal. Therefore, the modulation factors

*n*and

*m*to the degree of coherence of source determine the spacing between the split beams. When

## 5. Concluding remarks

*n*and

*m*in

*x*and

*y*directions. The parameters

*n*and

*m*play key role to the formation of splitting beam and provides a convenient tool for adjusting the number of splitting beams and the spacing between splitting beams. The beam conditions for such source a beamlike are derived and discussed. The analytical formula for the cross-spectral density function of beams on propagation in free and in turbulent atmosphere is derived and used to explore and comparatively analyzed the evolution behavior of the spectral density. We have found that the novel source can produce a self-splitting intensity distribution in the far field in free place as well as at short distance in the turbulence atmosphere, depending on the values of the refractive-index structure parameter

## Acknowledgment

## References and links

1. | D. Cassettari, B. Hessmo, R. Folman, T. Maier, and J. Schmiedmayer, “Beam splitter for guided atoms,” Phys. Rev. Lett. |

2. | A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. |

3. | Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, and K. Hamamoto, “High-power (>110mW) superluminescent diodes by using active multimode interferometer,” IEEE Photon. Technol. Lett. |

4. | Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, and K. Hamamoto, “Thermal resistance reduction in high power superluminescent diodes by using active multi-mode interferometer,” Appl. Phys. Lett. |

5. | J. P. Torres and L. Torner, “Self-splitting of beams into spatial solitons in planar waveguides made of quadratic nonlinear media,” Opt. Quantum Electron. |

6. | A. Suryanto and E. Van Groesen, “Self-splitting of multisoliton bound states in planar Kerr waveguides,” Opt. Commun. |

7. | A. W. Snyder, A. V. Buryak, and D. J. Mitchell, “Beam splitting on weak illumination,” Opt. Lett. |

8. | V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. |

9. | P. Halevi, “Beam splitting by a plane-parallel absorptive slab,” Opt. Lett. |

10. | L. Mandel and E. Wolf, |

11. | S. Sahin and O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett. |

12. | Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt. |

13. | H. Lajunen and T. Saastamoinen, “Propagation characteristics of partially coherent beams with spatially varying correlations,” Opt. Lett. |

14. | Z. Tong and O. Korotkova, “Nonuniformly correlated light beams in uniformly correlated media,” Opt. Lett. |

15. | Z. Tong and O. Korotkova, “Electromagnetic nonuniformly correlated beams,” J. Opt. Soc. Am. A |

16. | Z. Mei, Z. Tong, and O. Korotkova, “Electromagnetic non-uniformly correlated beams in turbulent atmosphere,” Opt. Express |

17. | Z. Mei and O. Korotkova, “Random sources generating ring-shaped beams,” Opt. Lett. |

18. | Z. Mei and O. Korotkova, “Cosine-Gaussian Schell-model sources,” Opt. Lett. |

19. | Z. Mei, “Light sources generating self-focusing beams of variable focal length,” Opt. Lett. |

20. | O. Korotkova, “Random sources for rectangular far fields,” Opt. Lett. |

21. | C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. |

22. | J. Pu and O. Korotkova, “Propagation of the degree of cross-polarization of a stochastic electromagnetic beam through the turbulent atmosphere,” Opt. Commun. |

23. | X. Du, D. Zhao, and O. Korotkova, “Changes in the statistical properties of stochastic anisotropic electromagnetic beams on propagation in the turbulent atmosphere,” Opt. Express |

24. | I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. |

25. | G. Zhou and X. Chu, “Propagation of a partially coherent cosine-Gaussian beam through an ABCD optical system in turbulent atmosphere,” Opt. Express |

26. | E. Shchepakina and O. Korotkova, “Second-order statistics of stochastic electromagnetic beams propagating through non-Kolmogorov turbulence,” Opt. Express |

27. | F. Wang and Y. Cai, “Second-order statistics of a twisted Gaussian Schell-model beam in turbulent atmosphere,” Opt. Express |

28. | A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence,” Opt. Commun. |

29. | O. Korotkova and E. Shchepakina, “Color changes in stochastic light fields propagating in non-Kolmogorov turbulence,” Opt. Lett. |

30. | X. Ji and X. Li, “M |

31. | Z. Mei, E. Shchepakina, and O. Korotkova, “Propagation of cosine-Gaussian-correlated Schell-model beams in atmospheric turbulence,” Opt. Express |

32. | Z. Mei and O. Korotkova, “Electromagnetic cosine-Gaussian Schell-model beams in free space and atmospheric turbulence,” Opt. Express |

33. | F. Gori and M. Santarsiero, “Devising genuine spatial correlation functions,” Opt. Lett. |

**OCIS Codes**

(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence

(030.1640) Coherence and statistical optics : Coherence

(030.6600) Coherence and statistical optics : Statistical optics

**ToC Category:**

Coherence and Statistical Optics

**History**

Original Manuscript: April 18, 2014

Revised Manuscript: May 12, 2014

Manuscript Accepted: May 14, 2014

Published: May 21, 2014

**Citation**

Zhangrong Mei, "Light sources generating self-splitting beams and their propagation in non-Kolmogorov turbulence," Opt. Express **22**, 13029-13040 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-11-13029

Sort: Year | Journal | Reset

### References

- D. Cassettari, B. Hessmo, R. Folman, T. Maier, J. Schmiedmayer, “Beam splitter for guided atoms,” Phys. Rev. Lett. 85(26), 5483–5487 (2000). [CrossRef] [PubMed]
- A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11(5), 288–290 (1986). [CrossRef] [PubMed]
- Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, K. Hamamoto, “High-power (>110mW) superluminescent diodes by using active multimode interferometer,” IEEE Photon. Technol. Lett. 22(10), 721–723 (2010). [CrossRef]
- Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, K. Hamamoto, “Thermal resistance reduction in high power superluminescent diodes by using active multi-mode interferometer,” Appl. Phys. Lett. 100(3), 031108 (2012). [CrossRef]
- J. P. Torres, L. Torner, “Self-splitting of beams into spatial solitons in planar waveguides made of quadratic nonlinear media,” Opt. Quantum Electron. 29(7), 757–776 (1997). [CrossRef]
- A. Suryanto, E. Van Groesen, “Self-splitting of multisoliton bound states in planar Kerr waveguides,” Opt. Commun. 258(2), 264–274 (2006). [CrossRef]
- A. W. Snyder, A. V. Buryak, D. J. Mitchell, “Beam splitting on weak illumination,” Opt. Lett. 23(1), 4–6 (1998). [CrossRef] [PubMed]
- V. Tikhonenko, J. Christou, B. Luther-Davies, “Three dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76(15), 2698–2701 (1996). [CrossRef] [PubMed]
- P. Halevi, “Beam splitting by a plane-parallel absorptive slab,” Opt. Lett. 7(10), 469–470 (1982). [CrossRef] [PubMed]
- L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
- S. Sahin, O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett. 37(14), 2970–2972 (2012). [CrossRef] [PubMed]
- Z. Mei, O. Korotkova, E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt. 15(2), 025705 (2013). [CrossRef]
- H. Lajunen, T. Saastamoinen, “Propagation characteristics of partially coherent beams with spatially varying correlations,” Opt. Lett. 36(20), 4104–4106 (2011). [CrossRef] [PubMed]
- Z. Tong, O. Korotkova, “Nonuniformly correlated light beams in uniformly correlated media,” Opt. Lett. 37(15), 3240–3242 (2012). [CrossRef] [PubMed]
- Z. Tong, O. Korotkova, “Electromagnetic nonuniformly correlated beams,” J. Opt. Soc. Am. A 29(10), 2154–2158 (2012). [CrossRef] [PubMed]
- Z. Mei, Z. Tong, O. Korotkova, “Electromagnetic non-uniformly correlated beams in turbulent atmosphere,” Opt. Express 20(24), 26458–26463 (2012). [CrossRef] [PubMed]
- Z. Mei, O. Korotkova, “Random sources generating ring-shaped beams,” Opt. Lett. 38(2), 91–93 (2013). [CrossRef] [PubMed]
- Z. Mei, O. Korotkova, “Cosine-Gaussian Schell-model sources,” Opt. Lett. 38(14), 2578–2580 (2013). [CrossRef] [PubMed]
- Z. Mei, “Light sources generating self-focusing beams of variable focal length,” Opt. Lett. 39(2), 347–350 (2014). [CrossRef] [PubMed]
- O. Korotkova, “Random sources for rectangular far fields,” Opt. Lett. 39(1), 64–67 (2014). [CrossRef] [PubMed]
- C. Liang, F. Wang, X. Liu, Y. Cai, O. Korotkova, “Experimental generation of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39(4), 769–772 (2014). [CrossRef] [PubMed]
- J. Pu, O. Korotkova, “Propagation of the degree of cross-polarization of a stochastic electromagnetic beam through the turbulent atmosphere,” Opt. Commun. 282(9), 1691–1698 (2009). [CrossRef]
- X. Du, D. Zhao, O. Korotkova, “Changes in the statistical properties of stochastic anisotropic electromagnetic beams on propagation in the turbulent atmosphere,” Opt. Express 15(25), 16909–16915 (2007). [CrossRef] [PubMed]
- I. Toselli, L. C. Andrews, R. L. Phillips, V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47(2), 026003 (2008). [CrossRef]
- G. Zhou, X. Chu, “Propagation of a partially coherent cosine-Gaussian beam through an ABCD optical system in turbulent atmosphere,” Opt. Express 17(13), 10529–10534 (2009). [CrossRef] [PubMed]
- E. Shchepakina, O. Korotkova, “Second-order statistics of stochastic electromagnetic beams propagating through non-Kolmogorov turbulence,” Opt. Express 18(10), 10650–10658 (2010). [CrossRef] [PubMed]
- F. Wang, Y. Cai, “Second-order statistics of a twisted Gaussian Schell-model beam in turbulent atmosphere,” Opt. Express 18(24), 24661–24672 (2010). [CrossRef] [PubMed]
- A. Zilberman, E. Golbraikh, N. S. Kopeika, “Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence,” Opt. Commun. 283(7), 1229–1235 (2010). [CrossRef]
- O. Korotkova, E. Shchepakina, “Color changes in stochastic light fields propagating in non-Kolmogorov turbulence,” Opt. Lett. 35(22), 3772–3774 (2010). [CrossRef] [PubMed]
- X. Ji, X. Li, “M2-factor of truncated partially coherent beams propagating through atmospheric turbulence,” J. Opt. Soc. Am. A 28(6), 970–975 (2011). [CrossRef] [PubMed]
- Z. Mei, E. Shchepakina, O. Korotkova, “Propagation of cosine-Gaussian-correlated Schell-model beams in atmospheric turbulence,” Opt. Express 21(15), 17512–17519 (2013). [CrossRef] [PubMed]
- Z. Mei, O. Korotkova, “Electromagnetic cosine-Gaussian Schell-model beams in free space and atmospheric turbulence,” Opt. Express 21(22), 27246–27259 (2013). [CrossRef] [PubMed]
- F. Gori, M. Santarsiero, “Devising genuine spatial correlation functions,” Opt. Lett. 32(24), 3531–3533 (2007). [CrossRef] [PubMed]

## 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.