Abstract

A detailed experimental study of spatial characteristics for laser beams propagating through the turbulent aerojet has been performed. The obtained results for radiation wavelengths of 0.53, 1.06, and 10.6μm were used for the development of the numerical mathematical model for beam propagation through an extreme turbulent medium. The combination of parameters and algorithms for the numerical model was determined, which made it possible to obtain computational laser beam spatial characteristics that agreed quite well with the experimental data. Good agreement between the results points to the possibility, in principle, to regard the central jet area as a medium locally homogeneous in the statistical sense and anisotropic on the turbulent outer scales.

© 2008 Optical Society of America

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References

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  1. C. B. Hogge and W. L. Visinsky, “Laser beam probing of jet exhaust turbulence,” Appl. Opt. 10, 889-892 (1971).
    [CrossRef] [PubMed]
  2. O. M. Belotserkovskii and A. M. Oparin, Numerical Experiment on the Turbulence: From Order to Chaos (Nauka, 2000).
  3. G. N. Abramovich, T. A. Girshovich, S. Yu. Krasheninnikov, A. N. Sekundov, and I. P. Smirnov, Theory of the Turbulent Jet (Nauka, 1984).
  4. D. L. Knepp, “Multiple phase-screen calculation of the temporal behavior of stochastic waves,” Proc. IEEE 71, 722-737 (1983).
    [CrossRef]
  5. V. P. Kandidov, “Monte-carlo method in nonlinear statistical optics,” Usp. Fiz. Nauk 166, 1309-1338 (1996).
    [CrossRef]
  6. D. I. Dmitriev, Yu. N. Yevchenko, I. V. Ivanova, and V. S. Sirazetdinov, “Multiframe recording of laser radiation disturbed by turbulent jet from an aircraft,” J. Opt. Technol. 68, 378-380 (2001).
    [CrossRef]
  7. V. S. Sirazetdinov, I. V. Ivanova, A. D. Starikov, D. H. Titterton, T. A. Sheremetyeva, G. N. Filippov, and Yu. N.Yevchenko, “Experimental study of the structure of laser beams disturbed by turbulent stream of aircraft engine,” Proc. SPIE 3927, 397-405 (2000).
    [CrossRef]
  8. V. S. Sirazetdinov, A. D. Starikov, and D. G. Titterton, “Study of laser beam propagation through a jet aircraft engine's exhaust,” Proc. SPIE 4167, 120-129 (2000).
    [CrossRef]
  9. V. S. Sirazetdinov, D. I. Dmitriev, I. V. Ivanova, and D. H. Titterton, “Effect of turbojet engine on laser radiation. Part 1. Angular spectrum for disturbed beams,” Atmos. Oceanic Opt. 14, 906-910 (2001).
  10. V. S. Sirazetdinov, D. I. Dmitriev, I. V. Ivanova, and D. H. Titterton, “Effect of turbojet engine on laser radiation. Part 2. Random wandering of disturbed beams,” Atmos. Oceanic Opt. 14, 900-905 (2001).
  11. V. S. Sirazetdinov, D. I. Dmitriev, I. V. Ivanova, and D. H. Titterton, “Statistics of the structural state fluctuations for laser beams disturbed by a jet of aero-engine,” Atmos. Oceanic Opt. 17, 47-53 (2004).
  12. V. P. Lukin and B. V. Fortes, Adaptive Formation of Beams and Images in the Atmosphere (Publishing House SB RAN, 1999).
  13. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).
  14. V. I. Tatarski, Wave Propagation in the Turbulent Atmosphere (Nauka, 1967).
  15. A. S. Gurvich, A. I. Kon, V. L. Mironov, and S. S. Khmelevtsov, Laser Radiation in the Turbulent Atmosphere (Nauka, 1976).
  16. V. S. Sirazetdinov and I. V. Ivanova, “Simulation of laser beams propagation through turbulent medium by means of Fresnel transformation,” Proc. SPIE 5743, 81-93 (2004).
    [CrossRef]
  17. J. M. Martin and S. M. Flatté, “Intensity images and statistics from numerical simulation of wave propagation in 3-D random media,” Appl. Opt. 27, 2111-2126 (1988).
    [CrossRef] [PubMed]
  18. M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, and V. V. Pokasov,“Similarity relations and their experimental testing under strong intensity fluctuations of laser radiation,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Mir, 1981), pp. 130-168.

2004

V. S. Sirazetdinov, D. I. Dmitriev, I. V. Ivanova, and D. H. Titterton, “Statistics of the structural state fluctuations for laser beams disturbed by a jet of aero-engine,” Atmos. Oceanic Opt. 17, 47-53 (2004).

V. S. Sirazetdinov and I. V. Ivanova, “Simulation of laser beams propagation through turbulent medium by means of Fresnel transformation,” Proc. SPIE 5743, 81-93 (2004).
[CrossRef]

2001

V. S. Sirazetdinov, D. I. Dmitriev, I. V. Ivanova, and D. H. Titterton, “Effect of turbojet engine on laser radiation. Part 1. Angular spectrum for disturbed beams,” Atmos. Oceanic Opt. 14, 906-910 (2001).

V. S. Sirazetdinov, D. I. Dmitriev, I. V. Ivanova, and D. H. Titterton, “Effect of turbojet engine on laser radiation. Part 2. Random wandering of disturbed beams,” Atmos. Oceanic Opt. 14, 900-905 (2001).

D. I. Dmitriev, Yu. N. Yevchenko, I. V. Ivanova, and V. S. Sirazetdinov, “Multiframe recording of laser radiation disturbed by turbulent jet from an aircraft,” J. Opt. Technol. 68, 378-380 (2001).
[CrossRef]

2000

V. S. Sirazetdinov, I. V. Ivanova, A. D. Starikov, D. H. Titterton, T. A. Sheremetyeva, G. N. Filippov, and Yu. N.Yevchenko, “Experimental study of the structure of laser beams disturbed by turbulent stream of aircraft engine,” Proc. SPIE 3927, 397-405 (2000).
[CrossRef]

V. S. Sirazetdinov, A. D. Starikov, and D. G. Titterton, “Study of laser beam propagation through a jet aircraft engine's exhaust,” Proc. SPIE 4167, 120-129 (2000).
[CrossRef]

1996

V. P. Kandidov, “Monte-carlo method in nonlinear statistical optics,” Usp. Fiz. Nauk 166, 1309-1338 (1996).
[CrossRef]

1988

1971

Appl. Opt.

Atmos. Oceanic Opt.

V. S. Sirazetdinov, D. I. Dmitriev, I. V. Ivanova, and D. H. Titterton, “Effect of turbojet engine on laser radiation. Part 1. Angular spectrum for disturbed beams,” Atmos. Oceanic Opt. 14, 906-910 (2001).

V. S. Sirazetdinov, D. I. Dmitriev, I. V. Ivanova, and D. H. Titterton, “Effect of turbojet engine on laser radiation. Part 2. Random wandering of disturbed beams,” Atmos. Oceanic Opt. 14, 900-905 (2001).

V. S. Sirazetdinov, D. I. Dmitriev, I. V. Ivanova, and D. H. Titterton, “Statistics of the structural state fluctuations for laser beams disturbed by a jet of aero-engine,” Atmos. Oceanic Opt. 17, 47-53 (2004).

J. Opt. Technol.

Proc. SPIE

V. S. Sirazetdinov, I. V. Ivanova, A. D. Starikov, D. H. Titterton, T. A. Sheremetyeva, G. N. Filippov, and Yu. N.Yevchenko, “Experimental study of the structure of laser beams disturbed by turbulent stream of aircraft engine,” Proc. SPIE 3927, 397-405 (2000).
[CrossRef]

V. S. Sirazetdinov, A. D. Starikov, and D. G. Titterton, “Study of laser beam propagation through a jet aircraft engine's exhaust,” Proc. SPIE 4167, 120-129 (2000).
[CrossRef]

V. S. Sirazetdinov and I. V. Ivanova, “Simulation of laser beams propagation through turbulent medium by means of Fresnel transformation,” Proc. SPIE 5743, 81-93 (2004).
[CrossRef]

Usp. Fiz. Nauk

V. P. Kandidov, “Monte-carlo method in nonlinear statistical optics,” Usp. Fiz. Nauk 166, 1309-1338 (1996).
[CrossRef]

Other

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, and V. V. Pokasov,“Similarity relations and their experimental testing under strong intensity fluctuations of laser radiation,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Mir, 1981), pp. 130-168.

O. M. Belotserkovskii and A. M. Oparin, Numerical Experiment on the Turbulence: From Order to Chaos (Nauka, 2000).

G. N. Abramovich, T. A. Girshovich, S. Yu. Krasheninnikov, A. N. Sekundov, and I. P. Smirnov, Theory of the Turbulent Jet (Nauka, 1984).

D. L. Knepp, “Multiple phase-screen calculation of the temporal behavior of stochastic waves,” Proc. IEEE 71, 722-737 (1983).
[CrossRef]

V. P. Lukin and B. V. Fortes, Adaptive Formation of Beams and Images in the Atmosphere (Publishing House SB RAN, 1999).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

V. I. Tatarski, Wave Propagation in the Turbulent Atmosphere (Nauka, 1967).

A. S. Gurvich, A. I. Kon, V. L. Mironov, and S. S. Khmelevtsov, Laser Radiation in the Turbulent Atmosphere (Nauka, 1976).

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Figures (6)

Fig. 1
Fig. 1

Diagram of the setup for the first series of experiments: D, aperture diaphragm; O1–O4, lenses; CCD, photoreceiver (CCD camera); PC, computer video recorder; W, optical wedge (a beam splitter).

Fig. 2
Fig. 2

Diagram of the setup for the second series of experiments: 1, laser; 2, telescopic system; 3, aeroengine; 4 and 5, CCD cameras; 6, computer video recorder; 7, attenuators; D, aperture diaphragm; O1 and O2, lenses; M1 and M2, mirrors; W1 and W2, wedges.

Fig. 3
Fig. 3

Comparison of experiments and simulations for a beam angular half-width θ at the 1 / e level in the horizontal ( θ x , along the jet) and vertical ( θ y ) directions: (a) for the 10 mm beams and (b) for the 30 mm beams. The line shows exact agreement. λ = 1.06 μm and φ = 90 ° : (○)  θ x , (•)  θ y . λ = 0.53 μm and φ = 90 ° : (□)  θ x , (▪)  θ y . λ = 1.06 μm and φ = 45 ° : (△)  θ x , (▴)  θ y . λ = 0.53 μm and φ = 45 ° : (▿)  θ x , (▾)  θ y . λ = 1.06 μm and φ = 10 ° : (⋄)  θ x , (♦)  θ y . λ = 0.53 μm and φ = 10 ° : (☆)  θ x , (★)  θ y . λ = 10.6 μm and φ = 60 ° : (+ θ x , y ( θ x , y θ y ). λ = 1.06 μm and φ = 60 ° : (× θ x .

Fig. 4
Fig. 4

Comparison of experiments and simulations for the dispersion of beams centroid wandering in the horizontal ( σ x along the jet) and vertical ( σ y ) directions: (a) for the 10 mm beams and (b) for the 30 mm beams. The line shows exact agreement. λ = 1.06 μm and φ = 90 ° : (○)  σ x , (•)  σ y . λ = 0.53 μm and φ = 90 ° : (□)  σ x , (▪)  σ y . λ = 1.06 μm and φ = 45 ° : (△)  σ x , (▴)  σ y . λ = 0.53 μm and φ = 45 ° : (▿)  σ x , (▾)  σ y . λ = 1.06 μm and φ = 10 ° : (⋄)  σ x , (♦)  σ y . λ = 0.53 μm and φ = 10 ° : (☆)  σ x , (★)  σ y . λ = 10.6 μm and φ = 60 ° : (+ σ x , y ( σ x σ y ). λ = 1.06 μm and φ = 60 ° : (× σ x .

Fig. 5
Fig. 5

Comparison of numerical and experimental results for the dispersion of intensity fluctuations β 2 = [ ( I I ) 2 ] / ( I ) 2 on an axis of disturbed beams: (a) for the 10 mm beams and (b) for the 30 mm beams. The line shows exact agreement. (•)  λ = 1.06    μm and (○)  λ = 0.53 μm in the case of beam-jet intersection angle φ = 90 ° . (▴)  λ = 1.06    μm and (▵)  λ = 0.53 μm in the case of beam-jet intersection angle φ = 45 ° . (☆)  λ = 1.06    μm and (⋄)  λ = 0.53 μm in the case of beam-jet intersection angle φ = 10 ° . (+ λ = 10.6    μm and (× λ = 1.06 μm in the case of beam-jet intersection angle φ = 60 ° .

Fig. 6
Fig. 6

Examples of typical instantaneous images for disturbed laser beams in the far field, obtained experimentally (the left column) and by calculations.

Tables (3)

Tables Icon

Table 1 Angular Half-Width of the Beam at 1 / e Level θ 1 / e and Dispersion of the Beam Centroid Wandering in the Horizontal (Along the Jet) σ x and Vertical (Across the Jet) σ y Directions Averaged on an Ensemble of Single Realizations (1000 Frames for λ = 1.06 μm and 100 Frames for λ = 10.6 μm )

Tables Icon

Table 2 Angular Half-Width of the Beam at 1 / e Level θ 1 / e and Dispersion of the Beam Centroid Wandering in the Horizontal (Along the Jet) σ x and Vertical (Across the Jet) σ y Directions Averaged on an Ensemble of Single Realizations (1500 Frames) a

Tables Icon

Table 3 Angular Half-Width of the Beam at 1 / e Level θ 1 / e and Dispersion of the Beam Centroid Wandering in the Horizontal (Along the Jet) σ x and Vertical (Across the Jet) σ y Directions Averaged on an Ensemble of Single Realizations (1500 Frames) a

Equations (17)

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I ( θ ) = 0 2 a e D ( r ) / 2 J o ( K r θ ) γ ( r ) r d r 0 2 a e D ( r ) / 2 γ ( r ) r d r ,
D ( r ) = 2.77 K 2 C n 2 L t [ π L 0 5 / 3 Γ ( 1 / 6 ) ( r L 0 / 2 ) 5 / 6 K 5 / 6 ( r / L 0 ) ] ,
Φ ( p ) = 0.033 C n 2 [ ( 1 L 0 ) 2 + p 2 ] 11 / 6 .
σ x , y = 1 π K 2 a 2 0 2 a [ D ( ρ ) + D ( ρ ) ρ ] [ arccos ( ρ 2 a ) ( ρ 2 a ) 1 ρ 2 4 a 2 ] ρ d ρ .
Φ 1 ( p ) = 0.033 C n 2 { [ ( 1 L 0 ) 2 + p 2 ] 11 / 6 + Q [ ( 2 π L s ) 2 + p 2 ] 11 / 6 } .
Φ a ( p ) = 0.033 C n 2 { ( L 0 x L 0 y ) 11 / 6 [ 1 + ( p x L 0 x ) 2 + ( p y L 0 y ) 2 ] 11 / 6 } ,
D ( r ) = π K 2 L t + [ 1 cos ( p · r ) ] Φ ( p x , p y ) d 2 p ,
D ( x , y ) = 2.92 K 2 L t C n 2 [ ( x 2 + y 2 ) 5 / 6 0.2 [ 3 [ ( L 0 x L 0 y ) 2 x 2 + ( L 0 y L 0 x ) 2 y 2 ] + x 2 + y 2 ( L 0 x L 0 y ) 1 / 6 ] ] .
S ( x , y ) = Re { n = N / 2 N / 2 m = N / 2 N / 2 ( a n , m + i b n , m ) Δ p K 2 π L t Φ n ( p n , p m ) exp [ i 2 π L ( n x + m y ) ] } ,
a n , m = b n , m = 0 , a n , m 2 = b n , m 2 = 1.
Δ p = 2 π / L , p n = n Δ p , p m = m Δ p .
Φ n ( p ) = 0.033 C n 2 { ( L 0 x L 0 y ) 11 / 6 [ 1 + ( p x L 0 x ) 2 + ( p y L 0 y ) 2 ] 11 / 6 + Q [ ( 2 π L s ) 2 + p 2 ] 11 / 6 } ,
U ( x , y , z ) = exp [ i K ( z - z ) + i K ( x 2 + y 2 ) 2 ( z - z ) ] i λ ( z - z ) × D { U ( x , y , z ) exp [ i K ( x 2 + y 2 ) 2 ( z - z ) ] } exp [ - i ( q x x + q y y ) ] d x d y ,
U ( k h , j h , Z ) = exp { i [ K Z + π h 2 λ Z ( k 2 + j 2 ) ] } i N × h h n = - N / 2 N / 2 m = - N / 2 m = N / 2 U ( n h , m h ) exp [ i h 2 λ Z ( n 2 + m 2 ) ] exp [ - i 2 π ( n k + m j ) N ] ,
Ψ ( x + h , y c ) Ψ ( x , y c ) < π ,
Ψ ( x c , y + h ) Ψ ( x c , y ) < π .
Δ Z < ( 2 π λ ) - 7 / 5 ( 1.45 0 Δ Z C n 2 ( Z ) d Z ) - 6 / 5 .

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