Abstract

In this paper, the effect of thermal blooming of an Airy beam propagating through the atmosphere is examined, and the effect of atmospheric turbulence is not considered. The changes of the intensity distribution, the centroid position and the mean-squared beam width of an Airy beam propagating through the atmosphere are studied by using the four-dimensional (4D) computer code of the time-dependent propagation of Airy beams through the atmosphere. It is shown that an Airy beam can’t retain its shape and the structure when the Airy beam propagates through the atmosphere due to thermal blooming except for the short propagation distance, or the short time, or the low beam power. The thermal blooming results in a central dip of the center lobe, and causes the center lobe to spread and decrease. In contrast with the center lobe, the side lobes are less affected by thermal blooming, such that the intensity maximum of the side lobe may be larger than that of the center lobe. However, the cross wind can reduce the effect of thermal blooming. When there exists the cross wind velocity vx in x direction, the dependence of centroid position in x direction on vx is not monotonic, and there exists a minimum, but the centroid position in y direction is nearly independent of vx.

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  1. M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys.47(3), 264–267 (1979).
    [CrossRef]
  2. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett.32(8), 979–981 (2007).
    [CrossRef] [PubMed]
  3. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett.99(21), 213901 (2007).
    [CrossRef] [PubMed]
  4. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett.33(3), 207–209 (2008).
    [CrossRef] [PubMed]
  5. I. M. Besieris and A. M. Shaarawi, “A note on an accelerating finite energy Airy beam,” Opt. Lett.32(16), 2447–2449 (2007).
    [CrossRef] [PubMed]
  6. J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express16(17), 12880–12891 (2008).
    [CrossRef] [PubMed]
  7. Y. Gu and G. Gbur, “Scintillation of Airy beam arrays in atmospheric turbulence,” Opt. Lett.35(20), 3456–3458 (2010).
    [CrossRef] [PubMed]
  8. H. T. Eyyuboğlu, “Scintillation behavior of Airy beam,” Opt. Laser Technol.47, 232–236 (2013).
    [CrossRef]
  9. M. A. Bandres and J. C. Gutiérrez-Vega, “Airy-Gauss beams and their transformation by paraxial optical systems,” Opt. Express15(25), 16719–16728 (2007).
    [CrossRef] [PubMed]
  10. X. Chu, “Evolution of an Airy beam in turbulence,” Opt. Lett.36(14), 2701–2703 (2011).
    [CrossRef] [PubMed]
  11. D. C. Smith, “High-power laser propagation: Thermal blooming,” Proc. IEEE65(12), 1679–1714 (1977).
    [CrossRef]
  12. J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-Dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. (Berl.)10(2), 129–160 (1976).
    [CrossRef]
  13. J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-Dependent propagation of high energy laser beams through the atmosphere: II,” Appl. Phys. (Berl.)14(1), 99–115 (1977).
    [CrossRef]
  14. B. V. Fortes and V. P. Lukin, “Estimation of turbulent and thermal blooming degradation and required characterization of adaptive system,” Proc. SPIE3706, 361–367 (1999).
    [CrossRef]
  15. F. G. Gebhardt, “Twenty-five years of thermal blooming: an overview,” Proc. SPIE1221, 2–25 (1990).
    [CrossRef]
  16. H. Weber, “Propagation of higher-order intensity moments in quadratic-index media,” Opt. Quantum Electron.24(9), S1027–S1049 (1992).
    [CrossRef]

2013 (1)

H. T. Eyyuboğlu, “Scintillation behavior of Airy beam,” Opt. Laser Technol.47, 232–236 (2013).
[CrossRef]

2011 (1)

2010 (1)

2008 (2)

2007 (4)

1999 (1)

B. V. Fortes and V. P. Lukin, “Estimation of turbulent and thermal blooming degradation and required characterization of adaptive system,” Proc. SPIE3706, 361–367 (1999).
[CrossRef]

1992 (1)

H. Weber, “Propagation of higher-order intensity moments in quadratic-index media,” Opt. Quantum Electron.24(9), S1027–S1049 (1992).
[CrossRef]

1990 (1)

F. G. Gebhardt, “Twenty-five years of thermal blooming: an overview,” Proc. SPIE1221, 2–25 (1990).
[CrossRef]

1979 (1)

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys.47(3), 264–267 (1979).
[CrossRef]

1977 (2)

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-Dependent propagation of high energy laser beams through the atmosphere: II,” Appl. Phys. (Berl.)14(1), 99–115 (1977).
[CrossRef]

D. C. Smith, “High-power laser propagation: Thermal blooming,” Proc. IEEE65(12), 1679–1714 (1977).
[CrossRef]

1976 (1)

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-Dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. (Berl.)10(2), 129–160 (1976).
[CrossRef]

Balazs, N. L.

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys.47(3), 264–267 (1979).
[CrossRef]

Bandres, M. A.

Berry, M. V.

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys.47(3), 264–267 (1979).
[CrossRef]

Besieris, I. M.

Broky, J.

Christodoulides, D. N.

Chu, X.

Dogariu, A.

Eyyuboglu, H. T.

H. T. Eyyuboğlu, “Scintillation behavior of Airy beam,” Opt. Laser Technol.47, 232–236 (2013).
[CrossRef]

Feit, M. D.

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-Dependent propagation of high energy laser beams through the atmosphere: II,” Appl. Phys. (Berl.)14(1), 99–115 (1977).
[CrossRef]

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-Dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. (Berl.)10(2), 129–160 (1976).
[CrossRef]

Fleck, J. A.

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-Dependent propagation of high energy laser beams through the atmosphere: II,” Appl. Phys. (Berl.)14(1), 99–115 (1977).
[CrossRef]

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-Dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. (Berl.)10(2), 129–160 (1976).
[CrossRef]

Fortes, B. V.

B. V. Fortes and V. P. Lukin, “Estimation of turbulent and thermal blooming degradation and required characterization of adaptive system,” Proc. SPIE3706, 361–367 (1999).
[CrossRef]

Gbur, G.

Gebhardt, F. G.

F. G. Gebhardt, “Twenty-five years of thermal blooming: an overview,” Proc. SPIE1221, 2–25 (1990).
[CrossRef]

Gu, Y.

Gutiérrez-Vega, J. C.

Lukin, V. P.

B. V. Fortes and V. P. Lukin, “Estimation of turbulent and thermal blooming degradation and required characterization of adaptive system,” Proc. SPIE3706, 361–367 (1999).
[CrossRef]

Morris, J. R.

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-Dependent propagation of high energy laser beams through the atmosphere: II,” Appl. Phys. (Berl.)14(1), 99–115 (1977).
[CrossRef]

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-Dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. (Berl.)10(2), 129–160 (1976).
[CrossRef]

Shaarawi, A. M.

Siviloglou, G. A.

Smith, D. C.

D. C. Smith, “High-power laser propagation: Thermal blooming,” Proc. IEEE65(12), 1679–1714 (1977).
[CrossRef]

Weber, H.

H. Weber, “Propagation of higher-order intensity moments in quadratic-index media,” Opt. Quantum Electron.24(9), S1027–S1049 (1992).
[CrossRef]

Am. J. Phys. (1)

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys.47(3), 264–267 (1979).
[CrossRef]

Appl. Phys. (Berl.) (2)

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-Dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. (Berl.)10(2), 129–160 (1976).
[CrossRef]

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-Dependent propagation of high energy laser beams through the atmosphere: II,” Appl. Phys. (Berl.)14(1), 99–115 (1977).
[CrossRef]

Opt. Express (2)

Opt. Laser Technol. (1)

H. T. Eyyuboğlu, “Scintillation behavior of Airy beam,” Opt. Laser Technol.47, 232–236 (2013).
[CrossRef]

Opt. Lett. (5)

Opt. Quantum Electron. (1)

H. Weber, “Propagation of higher-order intensity moments in quadratic-index media,” Opt. Quantum Electron.24(9), S1027–S1049 (1992).
[CrossRef]

Phys. Rev. Lett. (1)

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett.99(21), 213901 (2007).
[CrossRef] [PubMed]

Proc. IEEE (1)

D. C. Smith, “High-power laser propagation: Thermal blooming,” Proc. IEEE65(12), 1679–1714 (1977).
[CrossRef]

Proc. SPIE (2)

B. V. Fortes and V. P. Lukin, “Estimation of turbulent and thermal blooming degradation and required characterization of adaptive system,” Proc. SPIE3706, 361–367 (1999).
[CrossRef]

F. G. Gebhardt, “Twenty-five years of thermal blooming: an overview,” Proc. SPIE1221, 2–25 (1990).
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

3D intensity distribution I(x, y, z) for different values of the propagation distance z when P = 5 × 105W, t = 0.6s and v = 0. (a) z = 0, (b) z = 0.1km, (c) z = 0.4km, (d) z = 0.6km, (e) z = 0.8km, (f) z = 1.2km.

Fig. 2
Fig. 2

Counter lines of I(x, y, z) for different values of the propagation distance z when P = 5 × 105W, t = 0.6s and v = 0. (a) z = 0, (b) z = 0.1km, (c) z = 1.2km.

Fig. 3
Fig. 3

3D intensity distribution I(x, y, z) for different values of the time t when P = 6 × 105W, z = 1km and v = 0. (a) in vacuum, (b) t = 0.024s, (c) t = 0.12s, (d) t = 0.256s, (e) t = 0.4s, (f) t = 0.616s.

Fig. 4
Fig. 4

Counter lines of I(x, y, z) for different values of the time t when P = 6 × 105W, z = 1km and v = 0. (a) in vacuum, (b) t = 0.024s, (c) t = 0.616s

Fig. 5
Fig. 5

3D intensity distribution I(x, y, z) for different values of the power P when t = 0.8s, z = 1km and v = 0. (a) in vacuum, (b) P = 104W, (c) P = 105W, (d) P = 2 × 105W, (e) P = 3 × 105W, (f) P = 6 × 105W.

Fig. 6
Fig. 6

Counter lines of I(x, y, z) for different values of the power P when t = 0.8s, z = 1km and v = 0. (a) in vacuum, (b) P = 104W, (c) P = 6 × 105W.

Fig. 7
Fig. 7

3D intensity distribution I(x, y, z) for different values of the cross wind velocity vx when t = 0.64s, z = 1km and P = 6 × 105W. (a) vx = 0, (b) vx = 0.15m/s, (c) vx = 0.4m/s, (d) vx = 0.6m/s, (e) vx = 0.8m/s, (f) vx = 1m/s.

Fig. 8
Fig. 8

Counter lines of I(x, y, z) for different values of the cross wind velocity vx when t = 0.64s, z = 1km and P = 6 × 105W. (a) vx = 0, (b) vx = 0.15m/s, (c) vx = 1m/s.

Fig. 9
Fig. 9

Mean-squared beam width w (wx = wy = w) versus the propagation distance z when P = 3 × 105W, t = 0.6s and v = 0.

Fig. 10
Fig. 10

Mean-squared beam width w (wx = wy = w) versus the time t when P = 6 × 105W, z = 1km and v = 0.

Fig. 11
Fig. 11

Mean-squared beam width w (wx = wy = w) versus the power P when t = 0.8s, z = 1km and v = 0.

Fig. 12
Fig. 12

Centroid position x ¯ , y ¯ versus the cross wind velocity vx when t = 0.64s, z = 1km and P = 6 × 105W.

Fig. 13
Fig. 13

Mean-squared beam width wx, wy versus the cross wind velocity vx when t = 0.64s, z = 1km and P = 6 × 105W.

Equations (7)

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2ik U z = 2 U+ k 2 δεU,
I= | U | 2 exp(αz),
U n+1 =exp( i 4k Δz 2 )exp( ik 2 z n z n +Δz δεdz )exp( i 4k Δz 2 ) U n .
ρ t +vρ= ( γ1 )α c s 2 I,
U(x,y,z=0)=Ai( x w 0 )exp( a x w 0 )Ai( y w 0 )exp( a y w 0 ),
x ¯ = xI(x,y,z)dxdy I(x,y,z)dxdy , y ¯ = yI(x,y,z)dxdy I(x,y,z)dxdy ,
w x 2 = 4 (x x ¯ ) 2 I(x,y,z)dxdy I(x,y,z)dxdy , w y 2 = 4 (y y ¯ ) 2 I(x,y,z)dxdy I(x,y,z)dxdy ,

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