## Scattering of multi-Gaussian Schell-model beams on a random medium |

Optics Express, Vol. 21, Issue 21, pp. 24781-24792 (2013)

http://dx.doi.org/10.1364/OE.21.024781

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### Abstract

Using the angular spectrum representation of plane waves, we investigate the scattering of multi-Gaussian Schell-model (MGSM) beams from a random medium within the accuracy of the first-order Born approximation. The far-zone properties, including the normalized spectral density and the spectral degree of coherence, are discussed. It is shown that the normalized spectral density and the spectral degree of coherence are influenced by the boundary of the beam profile (i.e.,

© 2013 Optical Society of America

## 1. Introduction

8. Y. Xin, Y. He, Y. Chen, and J. Li, “Correlation between intensity fluctuations of light scattered from a quasi-homogeneous random media,” Opt. Lett. **35**(23), 4000–4002 (2010). [CrossRef] [PubMed]

9. J. Jannson, T. Jannson, and E. Wolf, “Spatial coherence discrimination in scattering,” Opt. Lett. **13**(12), 1060–1062 (1988). [CrossRef] [PubMed]

10. P. S. Carney and E. Wolf, “An energy theorem for scattering of partially coherent beams,” Opt. Commun. **155**(1–3), 1–6 (1998). [CrossRef]

11. T. D. Visser, D. G. Fischer, and E. Wolf, “Scattering of light from quasi-homogeneous sources by quasi-homogeneous media,” J. Opt. Soc. Am. A **23**(7), 1631–1638 (2006). [CrossRef] [PubMed]

12. T. van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, “Effects of spatial coherence on the angular distribution of radiant intensity generated by scattering on a sphere,” Phys. Rev. Lett. **104**(17), 173902 (2010). [CrossRef] [PubMed]

13. Y. Zhang and D. Zhao, “Scattering of Hermite-Gaussian beams on Gaussian Schell-model random media,” Opt. Commun. **300**, 38–44 (2013). [CrossRef]

14. S. Sahin and O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett. **37**(14), 2970–2972 (2012). [CrossRef] [PubMed]

15. O. Korotkova, S. Sahin, and E. Shchepakina, “Multi-Gaussian Schell-model beams,” J. Opt. Soc. Am. A **29**(10), 2159–2164 (2012). [CrossRef] [PubMed]

16. Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboglu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. **305**, 57–65 (2013). [CrossRef]

17. Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt. **15**(2), 025705 (2013). [CrossRef]

## 2. Scattering of a partially coherent stochastic beam on a random medium

*D*. Such a field may be of an arbitrary form and can be represented as an angular spectrum of plane waves propagating into the

12. T. van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, “Effects of spatial coherence on the angular distribution of radiant intensity generated by scattering on a sphere,” Phys. Rev. Lett. **104**(17), 173902 (2010). [CrossRef] [PubMed]

## 3. Scattering of multi-Gaussian Schell-model beams on a Gaussian Schell-model random medium

14. S. Sahin and O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett. **37**(14), 2970–2972 (2012). [CrossRef] [PubMed]

## 4. Numerical simulations and discussions

## 5. Conclusion

## Acknowledgments

## References and links

1. | E. Wolf, |

2. | D. Zhao and T. Wang, “Direct and inverse problem in the theory of light scattering,” Prog. Opt. |

3. | D. Zhao, O. Korotkova, and E. Wolf, “Application of correlation-induced spectral changes to inverse scattering,” Opt. Lett. |

4. | T. Wang and D. Zhao, “Determination of pair-structure factor of scattering potential of a collection of particles,” Opt. Lett. |

5. | X. Du and D. Zhao, “Scattering of light by Gaussian-correlated quasi-homogeneous anisotropic media,” Opt. Lett. |

6. | Z. Tong and O. Korotkova, “Theory of weak scattering of stochastic electromagnetic fields from deterministic and random media,” Phys. Rev. A |

7. | C. Ding, Y. Cai, O. Korotkova, Y. Zhang, and L. Pan, “Scattering-induced changes in the temporal coherence length and the pulse duration of a partially coherent plane-wave pulse,” Opt. Lett. |

8. | Y. Xin, Y. He, Y. Chen, and J. Li, “Correlation between intensity fluctuations of light scattered from a quasi-homogeneous random media,” Opt. Lett. |

9. | J. Jannson, T. Jannson, and E. Wolf, “Spatial coherence discrimination in scattering,” Opt. Lett. |

10. | P. S. Carney and E. Wolf, “An energy theorem for scattering of partially coherent beams,” Opt. Commun. |

11. | T. D. Visser, D. G. Fischer, and E. Wolf, “Scattering of light from quasi-homogeneous sources by quasi-homogeneous media,” J. Opt. Soc. Am. A |

12. | T. van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, “Effects of spatial coherence on the angular distribution of radiant intensity generated by scattering on a sphere,” Phys. Rev. Lett. |

13. | Y. Zhang and D. Zhao, “Scattering of Hermite-Gaussian beams on Gaussian Schell-model random media,” Opt. Commun. |

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

15. | O. Korotkova, S. Sahin, and E. Shchepakina, “Multi-Gaussian Schell-model beams,” J. Opt. Soc. Am. A |

16. | Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboglu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. |

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

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

19. | M. Born and E. Wolf, |

**OCIS Codes**

(290.0290) Scattering : Scattering

(140.3295) Lasers and laser optics : Laser beam characterization

(290.5825) Scattering : Scattering theory

**ToC Category:**

Scattering

**History**

Original Manuscript: August 2, 2013

Manuscript Accepted: September 26, 2013

Published: October 9, 2013

**Citation**

Yuanyuan Zhang and Daomu Zhao, "Scattering of multi-Gaussian Schell-model beams on a random medium," Opt. Express **21**, 24781-24792 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-21-24781

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### References

- E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University Press, 2007).
- D. Zhao and T. Wang, “Direct and inverse problem in the theory of light scattering,” Prog. Opt.57, 262–308 (2012).
- D. Zhao, O. Korotkova, and E. Wolf, “Application of correlation-induced spectral changes to inverse scattering,” Opt. Lett.32(24), 3483–3485 (2007). [CrossRef] [PubMed]
- T. Wang and D. Zhao, “Determination of pair-structure factor of scattering potential of a collection of particles,” Opt. Lett.35(3), 318–320 (2010). [CrossRef] [PubMed]
- X. Du and D. Zhao, “Scattering of light by Gaussian-correlated quasi-homogeneous anisotropic media,” Opt. Lett.35(3), 384–386 (2010). [CrossRef] [PubMed]
- Z. Tong and O. Korotkova, “Theory of weak scattering of stochastic electromagnetic fields from deterministic and random media,” Phys. Rev. A82(3), 033836 (2010). [CrossRef]
- C. Ding, Y. Cai, O. Korotkova, Y. Zhang, and L. Pan, “Scattering-induced changes in the temporal coherence length and the pulse duration of a partially coherent plane-wave pulse,” Opt. Lett.36(4), 517–519 (2011). [CrossRef] [PubMed]
- Y. Xin, Y. He, Y. Chen, and J. Li, “Correlation between intensity fluctuations of light scattered from a quasi-homogeneous random media,” Opt. Lett.35(23), 4000–4002 (2010). [CrossRef] [PubMed]
- J. Jannson, T. Jannson, and E. Wolf, “Spatial coherence discrimination in scattering,” Opt. Lett.13(12), 1060–1062 (1988). [CrossRef] [PubMed]
- P. S. Carney and E. Wolf, “An energy theorem for scattering of partially coherent beams,” Opt. Commun.155(1–3), 1–6 (1998). [CrossRef]
- T. D. Visser, D. G. Fischer, and E. Wolf, “Scattering of light from quasi-homogeneous sources by quasi-homogeneous media,” J. Opt. Soc. Am. A23(7), 1631–1638 (2006). [CrossRef] [PubMed]
- T. van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, “Effects of spatial coherence on the angular distribution of radiant intensity generated by scattering on a sphere,” Phys. Rev. Lett.104(17), 173902 (2010). [CrossRef] [PubMed]
- Y. Zhang and D. Zhao, “Scattering of Hermite-Gaussian beams on Gaussian Schell-model random media,” Opt. Commun.300, 38–44 (2013). [CrossRef]
- S. Sahin and O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett.37(14), 2970–2972 (2012). [CrossRef] [PubMed]
- O. Korotkova, S. Sahin, and E. Shchepakina, “Multi-Gaussian Schell-model beams,” J. Opt. Soc. Am. A29(10), 2159–2164 (2012). [CrossRef] [PubMed]
- Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboglu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun.305, 57–65 (2013). [CrossRef]
- Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt.15(2), 025705 (2013). [CrossRef]
- L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).
- M. Born and E. Wolf, Principles of Optics, 7th ed (Cambridge University Press, 1999).

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