## Simulator for general-type beam propagation in turbulent atmosphere

Optics Express, Vol. 14, Issue 20, pp. 8918-8928 (2006)

http://dx.doi.org/10.1364/OE.14.008918

Acrobat PDF (1095 KB)

### Abstract

A simulator is designed in MATLAB code which gives the propagation characteristics of a general-type beam in turbulent atmosphere. When the required source and medium parameters are entered, the simulator yields the average intensity profile along the propagation axis in a video format. In our simulator, the user can choose the option of a “user defined beam” in which the source and medium parameters are selected as requested by the user by entering numerical values in the relevant menu boxes. Alternatively, the user can proceed with the option of “pre-defined beam” in which the average intensity profiles of beams such as annular, cos-Gaussian, sine-Gaussian, cosh-Gaussian, sinh-Gaussian, their higher-order counterparts and flat-topped can be observed as they propagate in a turbulent atmosphere. Some samples of the simulator output are presented.

© 2006 Optical Society of America

## 1. Introduction

## 2. Formulation

12. Y. Baykal, “Formulation of correlations for general-type beams in atmospheric turbulence,” J. Opt. Soc. Am. A **23**, 889–893 (2006). [CrossRef]

*k*=2

*π*/

*λ*is the wave number with

*λ*being the wavelength and

*j*=(-1)

^{0.5}.

*I*(

**p**,

*L*)〉, of a general beam on a receiver plane located at

*L*distance away from the source can be found from extended Huygens-Fresnel integral in the following way [13]

2. S. C. H. Wang and M. A. Plonus, “Optical beam propagation for a partially coherent source in the turbulent atmosphere,” J. Opt. Soc. Am. **69**, 1297–1304 (1979). [CrossRef]

*ψ*being the fluctuations of the complex amplitude,

*p*

_{x}and

*p*

_{y}are the

*x*and

*y*components of the receiver plane vector

**p**, such that

**p**=(

*p*

_{x},

*p*

_{y}),

*ρ*

_{0}=(0.545

*k*

^{2}

*L*)

^{-3/5}is the coherence length of a spherical wave propagating in the turbulent medium and

*u*(

**s**

_{1}), when multiplied by its conjugate

*u*

^{*}(

**s**

_{2}), indicated by the sign *, will be

*E*

_{y}is attained by changing all

*x*subscripts to

*y*in

*E*

_{x},

*S*

_{y}is constructed by changing all

*x*subscripts to

*y*in

*S*

_{x}given by Eq. (8),

*T*

_{ℓx}

_{1}=1×3×....(2

*ℓ*

_{xi}-1) for

*ℓ*

_{x}

_{1}≠0 where

*i*=1,2, all appearances in the form of

## 3. Results and discussion

*N*,

*A*

_{ℓ},

*θ*

_{ℓ},

*α*

_{sxℓ},

*α*

_{syℓ},

*F*

_{xℓ},

*F*

_{yℓ},

*n*

_{ℓ},

*m*

_{ℓ},

*V*

_{xℓ},

*V*

_{yℓ},

*λ*,

*L*are supplied to Eq. (6). Presently, the remaining parameters are internally set as

*α*

_{xℓ}=1/

*α*

_{sxℓ},

*a*

_{yℓ}=1/

*α*

_{syℓ},

*b*

_{xℓ}=

*b*

_{yℓ}=0.

*x*-

*y*symmetry. In this context,

*n*,

*m*are positive integers,

*α*

_{s},

*F*and

*V*are positive numeric values conforming to the following equalities for cos-Gaussian, cosh-Gaussian, sine-Gaussian, sinh-Gaussian, Hermite-cosh-Gaussian, Hermite-sine-Gaussian, Hermite-sinh-Gaussian, Hermite-cos-Gaussian beams,

*n*=

*n*

_{1}=

*n*

_{2},

*m*=

*m*

_{1}=

*m*

_{2},

*α*

_{s}=

*α*

_{sx}

_{1}=

*α*

_{sx}

_{2}=

*α*

_{sy}

_{1}=

*α*

_{sy}

_{2},

*F*=

*F*

_{x}

_{1}=

*F*

_{x}

_{2}=

*F*

_{y}

_{1}=

*F*

_{y}

_{2},

*V*=

*V*

_{x}

_{1}=

*V*

_{x}

_{2}=

*V*

_{y}

_{1}=

*V*

_{y}

_{2}. For higherorder annular beam

*α*

_{s}

_{1}>

*α*

_{s}

_{2}.

*L*=1 km with the settings given in the Fig. Here the upper left picture is the intensity plot of the beam viewed perpendicular to the propagation axis, where more brightness means higher intensity spots. The second picture to the right in the upper row refers to the contour plot of the beam. Finally the right one of the second row is the 3D picture of the beam. Figure 3 displays the same for a pre-defined Hermite-cosh-Gaussian beam at

*L*=2 km, where all the settings are again given in the Fig. In Figs. 2 and 3, 〈

*I*

_{r}

*N*〉 means that for the receiver intensity, the following normalization is applied

7. H. T. Eyyuboğlu and Y. Baykal, “Hermite-sine-Gaussian and Hermite-sinh-Gaussian laser beams in turbulent atmosphere,” J. Opt. Soc. Am. A **22**, 2709–2718 (2005). [CrossRef]

## 4. Conclusion

## References and links

1. | Z. I. Feizulin and Y. Kravtsov, “Broadening of a laser beam in a turbulent medium,” Radiophys. Quantum Electron |

2. | S. C. H. Wang and M. A. Plonus, “Optical beam propagation for a partially coherent source in the turbulent atmosphere,” J. Opt. Soc. Am. |

3. | R. L. Phillips and L. C. Andrews, “Spot size and divergence for Laguerre Gaussian beams of any order,” Appl. Opt. |

4. | C. Y. Young, Y. V. Gilchrest, and B. R. Macon, “Turbulence induced beam spreading of higher order mode optical waves,” Opt. Eng. |

5. | H. T. Eyyuboğlu and Y. Baykal, “Average intensity and spreading of cosh-Gaussian laser beams in the turbulent atmosphere,” Appl. Opt. |

6. | H. T. Eyyuboğlu and Y. Baykal, “Analysis of reciprocity of cos-Gaussian and cosh-Gaussian laser beams in turbulent atmosphere,” Opt. Express |

7. | H. T. Eyyuboğlu and Y. Baykal, “Hermite-sine-Gaussian and Hermite-sinh-Gaussian laser beams in turbulent atmosphere,” J. Opt. Soc. Am. A |

8. | Y. Cai and S. He, “Average intensity and spreading of an elliptical Gaussian beam in a turbulent atmosphere,” Opt. Lett. |

9. | Y. Cai and S. He, “Propagation of various dark hollow beams in a turbulent atmosphere,” Opt. Express |

10. | H. T. Eyyuboğlu, Ç. Arpali, and Y. Baykal, “Flat topped beams and their characteristics in turbulent media,” Opt. Express |

11. | H. T. Eyyuboğlu, S. Altay, and Y. Baykal, “Propagation characteristics of higher-order annular Gaussian beams in atmospheric turbulence,” Opt. Commun. |

12. | Y. Baykal, “Formulation of correlations for general-type beams in atmospheric turbulence,” J. Opt. Soc. Am. A |

13. | L. C. Andrews and R. L. Phillips, |

14. | I. S. Gradshteyn and I. M. Ryzhik, |

**OCIS Codes**

(010.1290) Atmospheric and oceanic optics : Atmospheric optics

(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: August 8, 2006

Revised Manuscript: September 12, 2006

Manuscript Accepted: September 19, 2006

Published: October 2, 2006

**Citation**

Çaglar Arpali, Canan Yazicioglu, Halil T. Eyyuboglu, Serap A. Arpali, and Yahya Baykal, "Simulator for general-type beam propagation in turbulent atmosphere," Opt. Express **14**, 8918-8928 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-20-8918

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### References

- Z. I. Feizulin and Y. Kravtsov, "Broadening of a laser beam in a turbulent medium," Radiophys. Quantum Electron 10, 33-35 (1967). [CrossRef]
- S. C. H. Wang and M. A. Plonus, "Optical beam propagation for a partially coherent source in the turbulent atmosphere," J. Opt. Soc. Am. 69, 1297-1304 (1979). [CrossRef]
- R. L. Phillips and L. C. Andrews, "Spot size and divergence for Laguerre Gaussian beams of any order," Appl. Opt. 22, 643-644 (1983). [CrossRef] [PubMed]
- 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]
- H. T. Eyyuboğlu and Y. Baykal, "Average intensity and spreading of cosh-Gaussian laser beams in the turbulent atmosphere," Appl. Opt. 44, 976-983 (2005). [CrossRef] [PubMed]
- H. T. Eyyuboğlu and Y. Baykal, "Analysis of reciprocity of cos-Gaussian and cosh-Gaussian laser beams in turbulent atmosphere," Opt. Express 12, 4659-4674 (2004). [CrossRef] [PubMed]
- H. T. Eyyuboğlu and Y. Baykal, "Hermite-sine-Gaussian and Hermite-sinh-Gaussian laser beams in turbulent atmosphere," J. Opt. Soc. Am. A 22, 2709-2718 (2005). [CrossRef]
- Y. Cai and S. He, "Average intensity and spreading of an elliptical Gaussian beam in a turbulent atmosphere," Opt. Lett. 31, 568-570 (2006). [CrossRef] [PubMed]
- Y. Cai and S. He, "Propagation of various dark hollow beams in a turbulent atmosphere," Opt. Express 14, 1353-1367 (2006). [CrossRef] [PubMed]
- H. T. Eyyuboğlu, Ç. Arpali, and Y. Baykal, "Flat topped beams and their characteristics in turbulent media," Opt. Express 14, 4196-4207 (2006). [CrossRef] [PubMed]
- H. T. Eyyuboğlu, S. Altay, and Y. Baykal, "Propagation characteristics of higher-order annular Gaussian beams in atmospheric turbulence," Opt. Commun. 26425-34 (2006). [CrossRef]
- Y. Baykal, "Formulation of correlations for general-type beams in atmospheric turbulence," J. Opt. Soc. Am. A 23, 889-893 (2006). [CrossRef]
- L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, (SPIE, Bellingham, Washington, 2005).
- I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic Press, New York, 2000).

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