Abstract

A laser beam propagation model that accounts for the joint effect of atmospheric turbulence and refractivity is introduced and evaluated through numerical simulations. In the numerical analysis of laser beam propagation, refractive index inhomogeneities along the atmospheric propagation path were represented by a combination of the turbulence-induced random fluctuations described in the framework of classical Kolmogorov turbulence theory and large-scale refractive index variations caused by the presence of an inverse temperature layer. The results demonstrate that an inverse temperature layer located in the vicinity of a laser beam’s propagation path may strongly impact the laser beam statistical characteristics including the beam wander and long-exposure beam footprint, and be a reason for refractivity-induced spatial anisotropy of these characteristics.

© 2017 Optical Society of America

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References

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  1. J. C. Wyngaard, Turbulence in the Atmosphere (Cambridge University Press, 2010).
  2. C. G. Nunalee, P. He, S. Basu, J. Minet, and M. A. Vorontsov, “Mapping optical ray trajectories through island wake vortices,” Meteorol. Atmos. Phys. 127(3), 355–368 (2015).
  3. P. He, C. G. Nunalee, S. Basu, J. Minet, M. A. Vorontsov, and S. T. Fiorino, “Influence of heterogeneous refractivity on optical wave propagation in coastal environments,” Meteorol. Atmos. Phys. 127(6), 685–699 (2015).
  4. M. Vorontsov, J. Riker, G. Carhart, V. S. Gudimetla, L. Beresnev, T. Weyrauch, and L. C. Roberts., “Deep turbulence effects compensation experiments with a cascaded adaptive optics system using a 3.63 m telescope,” Appl. Opt. 48(1), A47–A57 (2009).
    [PubMed]
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  7. S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics. 4. Wave Propagation Through Random Media (Springer, 1989).
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    [PubMed]
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  19. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

2017 (1)

2015 (2)

C. G. Nunalee, P. He, S. Basu, J. Minet, and M. A. Vorontsov, “Mapping optical ray trajectories through island wake vortices,” Meteorol. Atmos. Phys. 127(3), 355–368 (2015).

P. He, C. G. Nunalee, S. Basu, J. Minet, M. A. Vorontsov, and S. T. Fiorino, “Influence of heterogeneous refractivity on optical wave propagation in coastal environments,” Meteorol. Atmos. Phys. 127(6), 685–699 (2015).

2009 (1)

2003 (2)

1988 (1)

1982 (1)

1980 (1)

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, 129–160 (1976).

1941 (1)

A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers,” Dokl. Akad. Nauk SSSR 30, 299–303 (1941).

Basu, S.

C. G. Nunalee, P. He, S. Basu, J. Minet, and M. A. Vorontsov, “Mapping optical ray trajectories through island wake vortices,” Meteorol. Atmos. Phys. 127(3), 355–368 (2015).

P. He, C. G. Nunalee, S. Basu, J. Minet, M. A. Vorontsov, and S. T. Fiorino, “Influence of heterogeneous refractivity on optical wave propagation in coastal environments,” Meteorol. Atmos. Phys. 127(6), 685–699 (2015).

Beresnev, L.

Carhart, G.

Feit, M. D.

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, 129–160 (1976).

Fiorino, S. T.

P. He, C. G. Nunalee, S. Basu, J. Minet, M. A. Vorontsov, and S. T. Fiorino, “Influence of heterogeneous refractivity on optical wave propagation in coastal environments,” Meteorol. Atmos. Phys. 127(6), 685–699 (2015).

Flatté, S. M.

Fleck, J. A.

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, 129–160 (1976).

Frappa, E.

Gudimetla, V. S.

He, P.

P. He, C. G. Nunalee, S. Basu, J. Minet, M. A. Vorontsov, and S. T. Fiorino, “Influence of heterogeneous refractivity on optical wave propagation in coastal environments,” Meteorol. Atmos. Phys. 127(6), 685–699 (2015).

C. G. Nunalee, P. He, S. Basu, J. Minet, and M. A. Vorontsov, “Mapping optical ray trajectories through island wake vortices,” Meteorol. Atmos. Phys. 127(3), 355–368 (2015).

Kolmogorov, A. N.

A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers,” Dokl. Akad. Nauk SSSR 30, 299–303 (1941).

Können, G. P.

Lehn, W. H.

Martin, J. M.

Minet, J.

C. G. Nunalee, P. He, S. Basu, J. Minet, and M. A. Vorontsov, “Mapping optical ray trajectories through island wake vortices,” Meteorol. Atmos. Phys. 127(3), 355–368 (2015).

P. He, C. G. Nunalee, S. Basu, J. Minet, M. A. Vorontsov, and S. T. Fiorino, “Influence of heterogeneous refractivity on optical wave propagation in coastal environments,” Meteorol. Atmos. Phys. 127(6), 685–699 (2015).

Morris, J. R.

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, 129–160 (1976).

Nunalee, C. G.

P. He, C. G. Nunalee, S. Basu, J. Minet, M. A. Vorontsov, and S. T. Fiorino, “Influence of heterogeneous refractivity on optical wave propagation in coastal environments,” Meteorol. Atmos. Phys. 127(6), 685–699 (2015).

C. G. Nunalee, P. He, S. Basu, J. Minet, and M. A. Vorontsov, “Mapping optical ray trajectories through island wake vortices,” Meteorol. Atmos. Phys. 127(3), 355–368 (2015).

Riker, J.

Roberts, L. C.

Southwell, W. H.

Valley, G. C.

van der Werf, S. Y.

Vorontsov, M.

Vorontsov, M. A.

C. G. Nunalee, P. He, S. Basu, J. Minet, and M. A. Vorontsov, “Mapping optical ray trajectories through island wake vortices,” Meteorol. Atmos. Phys. 127(3), 355–368 (2015).

P. He, C. G. Nunalee, S. Basu, J. Minet, M. A. Vorontsov, and S. T. Fiorino, “Influence of heterogeneous refractivity on optical wave propagation in coastal environments,” Meteorol. Atmos. Phys. 127(6), 685–699 (2015).

Weyrauch, T.

Young, A. T.

Appl. Opt. (6)

Appl. Phys. (Berl.) (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, 129–160 (1976).

Dokl. Akad. Nauk SSSR (1)

A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers,” Dokl. Akad. Nauk SSSR 30, 299–303 (1941).

J. Opt. Soc. Am. (1)

Meteorol. Atmos. Phys. (2)

C. G. Nunalee, P. He, S. Basu, J. Minet, and M. A. Vorontsov, “Mapping optical ray trajectories through island wake vortices,” Meteorol. Atmos. Phys. 127(3), 355–368 (2015).

P. He, C. G. Nunalee, S. Basu, J. Minet, M. A. Vorontsov, and S. T. Fiorino, “Influence of heterogeneous refractivity on optical wave propagation in coastal environments,” Meteorol. Atmos. Phys. 127(6), 685–699 (2015).

Other (8)

A. D. Wheelon, Electromagnetic Scintillation vol. 1: Geometrical Optics (Cambridge University, 2001).

V. I. Tatarskii, Wave Propagation in Turbulent Medium (McGraw-Hill, 1961).

S. F. Clifford, “The classical theory of wave propagation in a turbulent medium,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer Berlin Heidelberg, 1978).

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics. 4. Wave Propagation Through Random Media (Springer, 1989).

J. C. Wyngaard, Turbulence in the Atmosphere (Cambridge University Press, 2010).

J. D. Schmidt, Numerical Simulations of Optical Wave Propagation with Examples in MATLAB, (Bellingham, 2010).

M. C. Roggemann, B. M. Welsh, and B. R. Hunt, Imaging through Turbulence (CRC New York, 1996).

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

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Figures (5)

Fig. 1
Fig. 1 Schematic illustration of a laser beam centroid trajectory L (white solid line) that crosses a horizontally oriented refractive layer represented by background color density modulation. The turbulence eddies are shown by randomly located shapes of various sizes.
Fig. 2
Fig. 2 Short-exposure intensity distributions of a Gaussian beam along the propagation path in turbulent atmosphere in the presence of standard (MUSA76-type) refractivity at the distance z = 0 (left column), z = 5 km (middle column) and z = 10 km (right column). The top row images show intensity distributions inside the entire (~3.6 × 3.6 m2) computational area, the bottom row images present the same intensity distributions displayed inside 0.2 × 0.2 m2 squares centered relative to the corresponding beam centroids.
Fig. 3
Fig. 3 Dependences of: (a) long-exposure vertical displacements of beam centroid trajectory Δ C and Δ T , and (b) their standard deviations σ c and σ T on propagation distance z. The results are obtained using conventional wave optics [Eq. (2)] and WORTEX [Eqs. (4)-(7)] beam propagation models.
Fig. 4
Fig. 4 Impact of ocean-type ITL on the Gaussian laser beam characteristics at distance z along optical axis for the transmission angles α = 1.0 mrad and α = 3.0 mrad: (a) long-exposure beam centroid vertical displacement Δ T (h) (z) h T (z) turb ; (b) and (c) are examples of instantaneous beam centroid trajectory deviations δ T (h) (z) h T (z) Δ T (h) (z) in vertical direction from the turbulence-averaged trajectory Δ T (h) (z) for α = 1.0 mrad (b), and α = 3.0 mrad (c); and (d) standard deviations of beam centroid fluctuations along vertical σ T (h) (z) and horizontal σ T (x) (z) directions. The ITL height is indicated in (a) by dashed line. The standard deviations σ T (x) (z) for the transmission angles α = 1.0 mrad and α = 3.0 mrad are coincide and shown in (d) by a single dotted line.
Fig. 5
Fig. 5 Impact of desert-type ITL on the Gaussian laser beam characteristics at distance z along the optical axis for the transmission angles α = 1.0 mrad and α = 3.0 mrad: (a) long-exposure beam centroid vertical displacement Δ T (h) (z) h T (z) turb ; (b) and (c) are examples of instantaneous beam centroid trajectory deviations δ T (h) (z) h T (z) Δ T (h) (z) in vertical direction from the turbulence-averaged trajectory Δ T (h) (z) for α = 1.0 mrad (b), and α = 3.0 mrad (c); and (d) standard deviations of beam centroid fluctuations along vertical σ T (h) (z) and horizontal σ T (x) (z) directions. The ITL height is indicated in (a) by dashed line. The standard deviations σ T (x) (z) for the transmission angles α = 1.0 mrad and α = 3.0 mrad are coincide and shown in (d) by a single dotted line.

Equations (13)

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n( r ¯ ,t)= n 0 + n refr ( r ¯ ,t)+ n turb ( r ¯ ,t),
2ik A(r,z) z = 2 A(r,z)+ k 2 [ n 2 (r,z) n 0 2 1 ]A(r,z).
n refr ( r ¯ ) d r ¯ T dl =θ, dθ dl = n refr ( r ¯ ),
2ik A(r,l) l = 2 A(r,l)+2 k 2 n turb (r,l)A(r,l).
[ n 0 + n refr ( r ¯ ) ] d( r ¯ T + δ turb ) dl =θ, d( θ+ θ turb ) dl = n refr ( r ¯ ).
δ turb (l)= W 1 r | A( r,l ) | 2 d 2 r ,
θ turb ( l )= W 1 κ| A( κ,l ) | 2 d 2 κ ,
n refr ( r ¯ )= n refr ( h )= A D P 0 T( h ) exp[ B 0 h g( h ) g(0) d h T( h ) ],
T( h )= T MUSA76 ( h )+ T ITL ( h ),
T ITL ( h )=ΔT{ 1 1+exp[ ( h h ITL )/ w ITL ] 1 },
φ (m) ( r )=k z m Δz/2 z m + Δz/2 [ n turb ( r,z )+ n refr ( r,z ) ]dz , .
r c (z) turb = W 1 r | A( r,z ) | 2 d 2 r turb ,
σ c (z)= [ y c (z) Δ c (z) ] 2 turb 1/2 / Δ c (z).

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