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

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References

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  1. Z. I. Feizulin and Y. Kravtsov, "Broadening of a laser beam in a turbulent medium," Radiophys. Quantum Electron 10, 33-35 (1967).
    [CrossRef]
  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]
  3. 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]
  4. 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]
  5. 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]
  6. 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]
  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]
  8. 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]
  9. Y. Cai and S. He, "Propagation of various dark hollow beams in a turbulent atmosphere," Opt. Express 14, 1353-1367 (2006).
    [CrossRef] [PubMed]
  10. 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]
  11. 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]
  12. Y. Baykal, "Formulation of correlations for general-type beams in atmospheric turbulence," J. Opt. Soc. Am. A 23, 889-893 (2006).
    [CrossRef]
  13. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, (SPIE, Bellingham, Washington, 2005).
  14. I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic Press, New York, 2000).

2006

2005

2004

2002

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]

1983

1979

1967

Z. I. Feizulin and Y. Kravtsov, "Broadening of a laser beam in a turbulent medium," Radiophys. Quantum Electron 10, 33-35 (1967).
[CrossRef]

Altay, S.

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]

Andrews, L. C.

Arpali, Ç.

Baykal, Y.

Cai, Y.

Eyyuboglu, H. T.

Feizulin, Z. I.

Z. I. Feizulin and Y. Kravtsov, "Broadening of a laser beam in a turbulent medium," Radiophys. Quantum Electron 10, 33-35 (1967).
[CrossRef]

Gilchrest, Y. V.

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]

He, S.

Kravtsov, Y.

Z. I. Feizulin and Y. Kravtsov, "Broadening of a laser beam in a turbulent medium," Radiophys. Quantum Electron 10, 33-35 (1967).
[CrossRef]

Macon, B. R.

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]

Phillips, R. L.

Plonus, M. A.

Wang, S. C. H.

Young, C. Y.

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]

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

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]

Opt. Eng.

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]

Opt. Express

Opt. Lett.

Radiophys. Quantum Electron

Z. I. Feizulin and Y. Kravtsov, "Broadening of a laser beam in a turbulent medium," Radiophys. Quantum Electron 10, 33-35 (1967).
[CrossRef]

Other

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).

Supplementary Material (4)

» Media 1: AVI (2006 KB)     
» Media 2: AVI (1812 KB)     
» Media 3: AVI (1823 KB)     
» Media 4: AVI (1276 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

User interface for (a) user defined beam and (b) pre-defined beam (annular case).

Fig. 2.
Fig. 2.

Different views of a general beam with given parameters along the propagation axis at L=1 km.

Fig. 3.
Fig. 3.

Different views of an Hermite-cosh-Gaussian beam along the propagation axis at L=2 km.

Fig. 4.
Fig. 4.

(2.0 MB) Progress of a general beam belonging to Fig. 2 along the propagation axis at (a) L=0 km, (b) 1 km, (c) 3 km and (d) 5 km.

Fig. 5.
Fig. 5.

(1.81 MB) Progress of an Hermite-sine-Gaussian beam along the propagation axis at (a) L=0 km, (b) 1 km, (c) 3 km and (d) 5 km.

Fig. 6.
Fig. 6.

(1.82 MB) Progress of a higher-order annular beam along the propagation axis at (a) L=0 km, (b) 1 km, (c) 3 km and (d) 5 km.

Fig. 7.
Fig. 7.

(1.27 MB) Progress of a flat-topped beam along the propagation axis at (a) L=0 km, (b) 1 km, (c) 6 km and (d) 10 km.

Tables (1)

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Table 1. Parameter Usage for Pre-Defined Beam Types

Equations (20)

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u ( s ) = = 1 N A exp ( j θ ) H n ( a x s x + b x t ) exp [ ( 0.5 k α x s x 2 + j V x s x ) ]
× H m ( a y s y + b x ) exp [ ( 0.5 k α y s y 2 + j V y t s y ) ] ,
α x = 1 ( k α s x 2 ) + j F x , α y = 1 ( k α s y 2 ) + j F y ,
I ( p , L ) = ( k 2 π L ) 2 d s 1 2 d s 2 2 u ( s 1 ) u * ( s 2 )
× exp { j k [ ( p s 1 ) 2 ( p s 2 ) 2 ] 2 L } exp [ ψ ( s 1 , p ) + ψ * ( s 2 , p ) ] ,
exp [ ψ ( s 1 , p ) + ψ * ( s 2 , p ) ] exp [ ρ 0 2 ( s 1 s 2 ) 2 ] ,
u ( s 1 ) u * ( s 2 ) = 1 = 1 N 2 = 1 N A 1 A 2 * exp [ j ( θ 1 θ 2 ) ]
× H n 1 ( a x 1 s 1 x + b x 1 ) exp [ ( 0.5 k α x 1 s 1 x 2 + j V x 1 s 1 x ) ]
× H m 1 ( a y 1 s 1 y + b y 1 ) exp [ ( 0.5 k α y 1 s 1 y 2 + j V y 1 s 1 y ) ]
× H n 2 * ( a x 2 s 2 x + b x 2 ) exp [ ( 0.5 k α x 2 * s 2 x 2 j V x 2 * s 2 x ) ]
× H m 2 * ( a y 2 s 2 y + b y 2 ) exp [ ( 0.5 k α y 2 * s 2 y 2 j V y 2 * s 2 y ) ] ,
I ( p , L ) = b 2 ρ 0 4 [ ρ 0 4 ( a s x 1 j b ) ( a s x 2 * + j b ) 1 ] 1/2 E x E y S x S y [ ρ 0 4 ( a s y 1 j b ) ( a s y 2 * + j b ) 1 ] 1/2 ,
E x = exp ( { ( V x 1 + 2 b p x ) 2 4 ( a s x 1 j b ) + [ ρ 0 2 ( V x 2 * + 2 b p x ) ( a s x 1 j b ) V x 1 2 b p x ] 2 4 ( a s x 1 j b ) [ ρ 0 4 ( a s x 1 j b ) ( a s x 2 * + j b ) 1 ] } ) ,
S x = 1 = 1 N 2 = 1 N x 1 = 0 [ n 1 2 ] n x 1 = 0 n 1 2 x 1 k x 1 = 0 [ n x 1 2 ] n x 11 = 0 n x 1 2 k x 1 x 2 = 0 [ n 2 2 ] n x 2 = 0 n 2 2 x 2 k x 2 = 0 [ ( n x 11 + n x 2 ) 2 ] T x 1 T x 2 A 1 A 2 * exp [ j ( θ 1 θ 2 ) ]
× ( j ) n x 1 + n x 2 2 k x 1 2 k x 2 ( 1 ) x 1 + x 2 2 n 1 + n 2 x 1 x 2 n x 1 n x 2
× ( n 1 2 x 1 ) ( n 2 2 x 2 ) ( n 1 2 x 1 n x 1 ) ( n x 1 2 k x 1 n x 11 ) ( n 2 2 x 2 n x 2 ) ( n x 1 ) ! ( n x 1 2 k x 1 ) ! ( k x 1 ) !
× ( n x 11 + n x 2 ) ! ( n x 11 + n x 2 2 k x 2 ) ! ( k x 2 ) ! ( a x 1 ) n x 1 ( a x 2 * ) n x 2 ( b x 1 ) n 1 2 x 1 n x 1 ( b x 2 * ) n 2 2 z 2 n x 2 ( ρ 0 2 ) n x 2
× [ ρ 0 4 ( a s x 1 j b ) ( a s x 2 * + j b ) 1 ] n x 11 n x 2 + x 2 ( a s x 1 j b ) n x 1 + x 1 + x 2 ( V x 1 + 2 b p x ) n x 1 2 k x n x 11
× [ ρ 0 2 ( V x 2 * + 2 b p x ) ( a s x 1 j b ) + V x 1 + 2 b p x ] n x 11 + n x 2 2 k x 2 ,
I r N = I ( p , L ) Max [ u ( s ) u * ( s ) ] ,

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