Abstract
Evolution of branch points in the distorted optical field is studied when a laser beam propagates through turbulent atmosphere along an uplink path. Two categories of propagation events are mainly explored for the same propagation height: fixed wavelength with change of the turbulence strength and fixed turbulence strength with change of the wavelength. It is shown that, when the beam propagates to a certain height, the density of the branchpoints reaches its maximum and such a height changes with the turbulence strength but nearly remains constant with different wavelengths. The relationship between the density of branchpoints and the Rytov number is also given. A fitted formula describing the relationship between the density of branchpoints and propagation height with different turbulence strength and wavelength is found out. Interestingly, this formula is very similar to the formula used for describing the Blackbody radiation in physics. The results obtained may be helpful for atmospheric optics, astronomy and optical communication.
© 2014 Optical Society of America
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References
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 Article Order
 
 Year
 
 Author
 
 Publication
 J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A Math. Phys. Sci. 336(1605), 165–190 (1974).
[Crossref]  J. F. Nye, “The motion and structure of dislocation in wavefronts,” Proc. R. Soc. London A Math. Phys. Sci. 378(1773), 219–239 (1981).
[Crossref]  N. B. Baranova, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, and B. Y. Zel’dovich, “Wavefront dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A 73(5), 525–528 (1983).
[Crossref]  V. A. Tartakovski and N. N. Mayer, “Phase dislocation and minimal phase representation of the wave function,” Atmos. Oceanic Opt. 8, 231–235 (1995).
 B. V. Fortes and V. Lukin, “The effects of wavefront dislocations on the atmospheric adaptive optical systems performance,” Proc. SPIE 2778, 1002–1003 (1996).
 I. Freund and N. Shvartsman, “Wavefield phase singularities: The sign principle,” Phys. Rev. A 50(6), 5164–5172 (1994).
[Crossref] [PubMed] 
R. Rao, “Statistics of the fractal structure and phase singularity of a plane light wave propagation in atmospheric turbulence,” Appl. Opt. 47(2), 269–276 (2008).
[Crossref] [PubMed] 
D. L. Fried and J. L. Vaughn, “Branch cuts in the phase function,” Appl. Opt. 31(15), 2865–2882 (1992).
[Crossref] [PubMed] 
D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A 15(10), 2759–2768 (1998).
[Crossref]  C. Fan, Y. Wang, and Z. Gong, “Effect of branch points on adaptive optics,” High Power Laser Particle Beams 15, 435–438 (2003).

C. Fan, Y. Wang, and Z. Gong, “Effects of different beacon wavelengths on atmospheric compensation in strong scintillation,” Appl. Opt. 43(22), 4334–4338 (2004).
[Crossref] [PubMed]  Y. Li, “Branch point effect on adaptive correction,” Proc. SPIE 5490, 1064–1070 (2004).
[Crossref] 
C. A. Primmerman, T. R. Price, R. A. Humphreys, B. G. Zollars, H. T. Barclay, and J. H. Herrmann, “Atmosphericcompensation experiments in strongscintillation conditions,” Appl. Opt. 34(12), 2081–2088 (1995).
[Crossref] [PubMed]  D. C. Ghiglia and M. D. Pritt, Two Dimensional Phase Unwrapping: Theory, Algorithms, and Software (John Wiley, 1998).
 E.O. Le Bigot, W. J. Wild, and E. J. Kibblewhite, “Branch point reconstructors for discontinuous light phase functions,” Proc. SPIE 3381, 76–87 (1998).
[Crossref]  B. Wang, A. C. Koivunen, and M. C. Roggemann, “Comparison of branch point and least squares reconstructors for laser beam transmission through the atmosphere,” Proc. SPIE 3763, 41–49 (1999).
[Crossref]  D. L. Fried, “Adaptive optics wave function reconstruction and phase unwrapping when branch points are present,” Opt. Commun. 200(1–6), 43–72 (2001).
[Crossref] 
V. V. Voitsekhovich, D. Kouznetsov, and D. K. Morozov, “Density of turbulenceinduced phase dislocations,” Appl. Opt. 37(21), 4525–4535 (1998).
[Crossref] [PubMed] 
M. Chen and F. S. Roux, “Accelerating the annihilation of an optical vortex dipole in a Gaussian beam,” J. Opt. Soc. Am. A 25(6), 1279–1286 (2008).
[Crossref] [PubMed] 
F. S. Roux, “Anomalous transient behavior from an inhomogeneous initial optical vortex density,” J. Opt. Soc. Am. A 28(4), 621–626 (2011).
[Crossref] [PubMed] 
F. S. Roux, “How to distinguish between the annihilation and the creation of optical vortices,” Opt. Lett. 38(19), 3895–3898 (2013).
[Crossref] [PubMed]  D. J. Sanchez and D. W. Oesch, “The aggregate behavior of branch points  the creation and evolution of branch points,” Proc. SPIE 7466, 746605 (2009).
[Crossref]  D. W. Oesch, D. J. Sanchez, C. M. TewksburyChristle, and P. R. Kelly, “The aggregate behavior of branch points  branch point density as a characteristic of an atmospheric turbulence simulator,” Proc. SPIE 7466, 746606 (2009).
[Crossref]  D. W. Oesch, D. J. Sanchez, C. M. TewksburyChristle, and P. R. Kelly, “The aggregate behavior of branch points  altitude and strength of atmospheric turbulence layers,” Proc. SPIE 7816, 781605 (2010).
[Crossref] 
D. W. Oesch, D. J. Sanchez, and C. L. Matson, “The aggregate behavior of branch pointsmeasuring the number and velocity of atmospheric turbulence layers,” Opt. Express 18(21), 22377–22392 (2010).
[Crossref] [PubMed]  D. J. Sanchez, D. W. Oesch, and P. R. Kelly, “The aggregate behavior of branch points  theoretical calculation of branch point velocity,” Proc. SPIE 8380, 83800P (2012).
[Crossref] 
D. W. Oesch, D. J. Sanchez, and C. M. TewksburyChristle, “Aggregate behavior of branch pointspersistent pairs,” Opt. Express 20(2), 1046–1059 (2012).
[Crossref] [PubMed]  D. W. Oesch, D. J. Sanchez, and P. R. Kelly, “Optical vortex density in Rytov saturated atmospheric turbulence,” in FiO (2012), FW3A. 3.

D. J. Sanchez and D. W. Oesch, “Localization of angular momentum in optical waves propagating through turbulence,” Opt. Express 19(25), 25388–25396 (2011).
[Crossref] [PubMed] 
D. J. Sanchez and D. W. Oesch, “Orbital angular momentum in optical waves propagating through distributed turbulence,” Opt. Express 19(24), 24596–24608 (2011).
[Crossref] [PubMed]  X. Qian, W. Zhu, and R. Rao, “Phase screen distribution for simulating laser propagation along an inhomogeneous atmospheric path,” Acta Phys. Sin. 58, 6633–6638 (2009).
 D. L. Fried, “Scaling laws for propagation through turbulence,” Atmos. Oceanic Opt. 11, 982–990 (1998).
 R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence: Evaluation and Application of Mellin Transforms, 2nd ed. (SPIE, 2007).
2013 (1)
F. S. Roux, “How to distinguish between the annihilation and the creation of optical vortices,” Opt. Lett. 38(19), 3895–3898 (2013).
[Crossref]
[PubMed]
2012 (2)
D. W. Oesch, D. J. Sanchez, and C. M. TewksburyChristle, “Aggregate behavior of branch pointspersistent pairs,” Opt. Express 20(2), 1046–1059 (2012).
[Crossref]
[PubMed]
D. J. Sanchez, D. W. Oesch, and P. R. Kelly, “The aggregate behavior of branch points  theoretical calculation of branch point velocity,” Proc. SPIE 8380, 83800P (2012).
[Crossref]
2011 (3)
F. S. Roux, “Anomalous transient behavior from an inhomogeneous initial optical vortex density,” J. Opt. Soc. Am. A 28(4), 621–626 (2011).
[Crossref]
[PubMed]
D. J. Sanchez and D. W. Oesch, “Orbital angular momentum in optical waves propagating through distributed turbulence,” Opt. Express 19(24), 24596–24608 (2011).
[Crossref]
[PubMed]
D. J. Sanchez and D. W. Oesch, “Localization of angular momentum in optical waves propagating through turbulence,” Opt. Express 19(25), 25388–25396 (2011).
[Crossref]
[PubMed]
2010 (2)
D. W. Oesch, D. J. Sanchez, C. M. TewksburyChristle, and P. R. Kelly, “The aggregate behavior of branch points  altitude and strength of atmospheric turbulence layers,” Proc. SPIE 7816, 781605 (2010).
[Crossref]
D. W. Oesch, D. J. Sanchez, and C. L. Matson, “The aggregate behavior of branch pointsmeasuring the number and velocity of atmospheric turbulence layers,” Opt. Express 18(21), 22377–22392 (2010).
[Crossref]
[PubMed]
2009 (3)
X. Qian, W. Zhu, and R. Rao, “Phase screen distribution for simulating laser propagation along an inhomogeneous atmospheric path,” Acta Phys. Sin. 58, 6633–6638 (2009).
D. J. Sanchez and D. W. Oesch, “The aggregate behavior of branch points  the creation and evolution of branch points,” Proc. SPIE 7466, 746605 (2009).
[Crossref]
D. W. Oesch, D. J. Sanchez, C. M. TewksburyChristle, and P. R. Kelly, “The aggregate behavior of branch points  branch point density as a characteristic of an atmospheric turbulence simulator,” Proc. SPIE 7466, 746606 (2009).
[Crossref]
2008 (2)
R. Rao, “Statistics of the fractal structure and phase singularity of a plane light wave propagation in atmospheric turbulence,” Appl. Opt. 47(2), 269–276 (2008).
[Crossref]
[PubMed]
M. Chen and F. S. Roux, “Accelerating the annihilation of an optical vortex dipole in a Gaussian beam,” J. Opt. Soc. Am. A 25(6), 1279–1286 (2008).
[Crossref]
[PubMed]
2004 (2)
C. Fan, Y. Wang, and Z. Gong, “Effects of different beacon wavelengths on atmospheric compensation in strong scintillation,” Appl. Opt. 43(22), 4334–4338 (2004).
[Crossref]
[PubMed]
Y. Li, “Branch point effect on adaptive correction,” Proc. SPIE 5490, 1064–1070 (2004).
[Crossref]
2003 (1)
C. Fan, Y. Wang, and Z. Gong, “Effect of branch points on adaptive optics,” High Power Laser Particle Beams 15, 435–438 (2003).
2001 (1)
D. L. Fried, “Adaptive optics wave function reconstruction and phase unwrapping when branch points are present,” Opt. Commun. 200(1–6), 43–72 (2001).
[Crossref]
1999 (1)
B. Wang, A. C. Koivunen, and M. C. Roggemann, “Comparison of branch point and least squares reconstructors for laser beam transmission through the atmosphere,” Proc. SPIE 3763, 41–49 (1999).
[Crossref]
1998 (4)
D. L. Fried, “Scaling laws for propagation through turbulence,” Atmos. Oceanic Opt. 11, 982–990 (1998).
D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A 15(10), 2759–2768 (1998).
[Crossref]
E.O. Le Bigot, W. J. Wild, and E. J. Kibblewhite, “Branch point reconstructors for discontinuous light phase functions,” Proc. SPIE 3381, 76–87 (1998).
[Crossref]
V. V. Voitsekhovich, D. Kouznetsov, and D. K. Morozov, “Density of turbulenceinduced phase dislocations,” Appl. Opt. 37(21), 4525–4535 (1998).
[Crossref]
[PubMed]
1996 (1)
B. V. Fortes and V. Lukin, “The effects of wavefront dislocations on the atmospheric adaptive optical systems performance,” Proc. SPIE 2778, 1002–1003 (1996).
1995 (2)
V. A. Tartakovski and N. N. Mayer, “Phase dislocation and minimal phase representation of the wave function,” Atmos. Oceanic Opt. 8, 231–235 (1995).
C. A. Primmerman, T. R. Price, R. A. Humphreys, B. G. Zollars, H. T. Barclay, and J. H. Herrmann, “Atmosphericcompensation experiments in strongscintillation conditions,” Appl. Opt. 34(12), 2081–2088 (1995).
[Crossref]
[PubMed]
1994 (1)
I. Freund and N. Shvartsman, “Wavefield phase singularities: The sign principle,” Phys. Rev. A 50(6), 5164–5172 (1994).
[Crossref]
[PubMed]
1992 (1)
D. L. Fried and J. L. Vaughn, “Branch cuts in the phase function,” Appl. Opt. 31(15), 2865–2882 (1992).
[Crossref]
[PubMed]
1983 (1)
N. B. Baranova, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, and B. Y. Zel’dovich, “Wavefront dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A 73(5), 525–528 (1983).
[Crossref]
1981 (1)
J. F. Nye, “The motion and structure of dislocation in wavefronts,” Proc. R. Soc. London A Math. Phys. Sci. 378(1773), 219–239 (1981).
[Crossref]
1974 (1)
J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A Math. Phys. Sci. 336(1605), 165–190 (1974).
[Crossref]
Baranova, N. B.
N. B. Baranova, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, and B. Y. Zel’dovich, “Wavefront dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A 73(5), 525–528 (1983).
[Crossref]
Barclay, H. T.
C. A. Primmerman, T. R. Price, R. A. Humphreys, B. G. Zollars, H. T. Barclay, and J. H. Herrmann, “Atmosphericcompensation experiments in strongscintillation conditions,” Appl. Opt. 34(12), 2081–2088 (1995).
[Crossref]
[PubMed]
Berry, M. V.
J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A Math. Phys. Sci. 336(1605), 165–190 (1974).
[Crossref]
Chen, M.
M. Chen and F. S. Roux, “Accelerating the annihilation of an optical vortex dipole in a Gaussian beam,” J. Opt. Soc. Am. A 25(6), 1279–1286 (2008).
[Crossref]
[PubMed]
Fan, C.
C. Fan, Y. Wang, and Z. Gong, “Effects of different beacon wavelengths on atmospheric compensation in strong scintillation,” Appl. Opt. 43(22), 4334–4338 (2004).
[Crossref]
[PubMed]
C. Fan, Y. Wang, and Z. Gong, “Effect of branch points on adaptive optics,” High Power Laser Particle Beams 15, 435–438 (2003).
Fortes, B. V.
B. V. Fortes and V. Lukin, “The effects of wavefront dislocations on the atmospheric adaptive optical systems performance,” Proc. SPIE 2778, 1002–1003 (1996).
Freund, I.
I. Freund and N. Shvartsman, “Wavefield phase singularities: The sign principle,” Phys. Rev. A 50(6), 5164–5172 (1994).
[Crossref]
[PubMed]
Fried, D. L.
D. L. Fried, “Adaptive optics wave function reconstruction and phase unwrapping when branch points are present,” Opt. Commun. 200(1–6), 43–72 (2001).
[Crossref]
D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A 15(10), 2759–2768 (1998).
[Crossref]
D. L. Fried, “Scaling laws for propagation through turbulence,” Atmos. Oceanic Opt. 11, 982–990 (1998).
D. L. Fried and J. L. Vaughn, “Branch cuts in the phase function,” Appl. Opt. 31(15), 2865–2882 (1992).
[Crossref]
[PubMed]
Gong, Z.
C. Fan, Y. Wang, and Z. Gong, “Effects of different beacon wavelengths on atmospheric compensation in strong scintillation,” Appl. Opt. 43(22), 4334–4338 (2004).
[Crossref]
[PubMed]
C. Fan, Y. Wang, and Z. Gong, “Effect of branch points on adaptive optics,” High Power Laser Particle Beams 15, 435–438 (2003).
Herrmann, J. H.
C. A. Primmerman, T. R. Price, R. A. Humphreys, B. G. Zollars, H. T. Barclay, and J. H. Herrmann, “Atmosphericcompensation experiments in strongscintillation conditions,” Appl. Opt. 34(12), 2081–2088 (1995).
[Crossref]
[PubMed]
Humphreys, R. A.
C. A. Primmerman, T. R. Price, R. A. Humphreys, B. G. Zollars, H. T. Barclay, and J. H. Herrmann, “Atmosphericcompensation experiments in strongscintillation conditions,” Appl. Opt. 34(12), 2081–2088 (1995).
[Crossref]
[PubMed]
Kelly, P. R.
D. J. Sanchez, D. W. Oesch, and P. R. Kelly, “The aggregate behavior of branch points  theoretical calculation of branch point velocity,” Proc. SPIE 8380, 83800P (2012).
[Crossref]
D. W. Oesch, D. J. Sanchez, C. M. TewksburyChristle, and P. R. Kelly, “The aggregate behavior of branch points  altitude and strength of atmospheric turbulence layers,” Proc. SPIE 7816, 781605 (2010).
[Crossref]
D. W. Oesch, D. J. Sanchez, C. M. TewksburyChristle, and P. R. Kelly, “The aggregate behavior of branch points  branch point density as a characteristic of an atmospheric turbulence simulator,” Proc. SPIE 7466, 746606 (2009).
[Crossref]
Kibblewhite, E. J.
E.O. Le Bigot, W. J. Wild, and E. J. Kibblewhite, “Branch point reconstructors for discontinuous light phase functions,” Proc. SPIE 3381, 76–87 (1998).
[Crossref]
Koivunen, A. C.
B. Wang, A. C. Koivunen, and M. C. Roggemann, “Comparison of branch point and least squares reconstructors for laser beam transmission through the atmosphere,” Proc. SPIE 3763, 41–49 (1999).
[Crossref]
Kouznetsov, D.
V. V. Voitsekhovich, D. Kouznetsov, and D. K. Morozov, “Density of turbulenceinduced phase dislocations,” Appl. Opt. 37(21), 4525–4535 (1998).
[Crossref]
[PubMed]
Le Bigot, E.O.
E.O. Le Bigot, W. J. Wild, and E. J. Kibblewhite, “Branch point reconstructors for discontinuous light phase functions,” Proc. SPIE 3381, 76–87 (1998).
[Crossref]
Li, Y.
Y. Li, “Branch point effect on adaptive correction,” Proc. SPIE 5490, 1064–1070 (2004).
[Crossref]
Lukin, V.
B. V. Fortes and V. Lukin, “The effects of wavefront dislocations on the atmospheric adaptive optical systems performance,” Proc. SPIE 2778, 1002–1003 (1996).
Mamaev, A. V.
N. B. Baranova, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, and B. Y. Zel’dovich, “Wavefront dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A 73(5), 525–528 (1983).
[Crossref]
Matson, C. L.
D. W. Oesch, D. J. Sanchez, and C. L. Matson, “The aggregate behavior of branch pointsmeasuring the number and velocity of atmospheric turbulence layers,” Opt. Express 18(21), 22377–22392 (2010).
[Crossref]
[PubMed]
Mayer, N. N.
V. A. Tartakovski and N. N. Mayer, “Phase dislocation and minimal phase representation of the wave function,” Atmos. Oceanic Opt. 8, 231–235 (1995).
Morozov, D. K.
V. V. Voitsekhovich, D. Kouznetsov, and D. K. Morozov, “Density of turbulenceinduced phase dislocations,” Appl. Opt. 37(21), 4525–4535 (1998).
[Crossref]
[PubMed]
Nye, J. F.
J. F. Nye, “The motion and structure of dislocation in wavefronts,” Proc. R. Soc. London A Math. Phys. Sci. 378(1773), 219–239 (1981).
[Crossref]
J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A Math. Phys. Sci. 336(1605), 165–190 (1974).
[Crossref]
Oesch, D. W.
D. W. Oesch, D. J. Sanchez, and C. M. TewksburyChristle, “Aggregate behavior of branch pointspersistent pairs,” Opt. Express 20(2), 1046–1059 (2012).
[Crossref]
[PubMed]
D. J. Sanchez, D. W. Oesch, and P. R. Kelly, “The aggregate behavior of branch points  theoretical calculation of branch point velocity,” Proc. SPIE 8380, 83800P (2012).
[Crossref]
D. J. Sanchez and D. W. Oesch, “Localization of angular momentum in optical waves propagating through turbulence,” Opt. Express 19(25), 25388–25396 (2011).
[Crossref]
[PubMed]
D. J. Sanchez and D. W. Oesch, “Orbital angular momentum in optical waves propagating through distributed turbulence,” Opt. Express 19(24), 24596–24608 (2011).
[Crossref]
[PubMed]
D. W. Oesch, D. J. Sanchez, and C. L. Matson, “The aggregate behavior of branch pointsmeasuring the number and velocity of atmospheric turbulence layers,” Opt. Express 18(21), 22377–22392 (2010).
[Crossref]
[PubMed]
D. W. Oesch, D. J. Sanchez, C. M. TewksburyChristle, and P. R. Kelly, “The aggregate behavior of branch points  altitude and strength of atmospheric turbulence layers,” Proc. SPIE 7816, 781605 (2010).
[Crossref]
D. J. Sanchez and D. W. Oesch, “The aggregate behavior of branch points  the creation and evolution of branch points,” Proc. SPIE 7466, 746605 (2009).
[Crossref]
D. W. Oesch, D. J. Sanchez, C. M. TewksburyChristle, and P. R. Kelly, “The aggregate behavior of branch points  branch point density as a characteristic of an atmospheric turbulence simulator,” Proc. SPIE 7466, 746606 (2009).
[Crossref]
Pilipetsky, N. F.
N. B. Baranova, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, and B. Y. Zel’dovich, “Wavefront dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A 73(5), 525–528 (1983).
[Crossref]
Price, T. R.
C. A. Primmerman, T. R. Price, R. A. Humphreys, B. G. Zollars, H. T. Barclay, and J. H. Herrmann, “Atmosphericcompensation experiments in strongscintillation conditions,” Appl. Opt. 34(12), 2081–2088 (1995).
[Crossref]
[PubMed]
Primmerman, C. A.
C. A. Primmerman, T. R. Price, R. A. Humphreys, B. G. Zollars, H. T. Barclay, and J. H. Herrmann, “Atmosphericcompensation experiments in strongscintillation conditions,” Appl. Opt. 34(12), 2081–2088 (1995).
[Crossref]
[PubMed]
Qian, X.
X. Qian, W. Zhu, and R. Rao, “Phase screen distribution for simulating laser propagation along an inhomogeneous atmospheric path,” Acta Phys. Sin. 58, 6633–6638 (2009).
Rao, R.
X. Qian, W. Zhu, and R. Rao, “Phase screen distribution for simulating laser propagation along an inhomogeneous atmospheric path,” Acta Phys. Sin. 58, 6633–6638 (2009).
R. Rao, “Statistics of the fractal structure and phase singularity of a plane light wave propagation in atmospheric turbulence,” Appl. Opt. 47(2), 269–276 (2008).
[Crossref]
[PubMed]
Roggemann, M. C.
B. Wang, A. C. Koivunen, and M. C. Roggemann, “Comparison of branch point and least squares reconstructors for laser beam transmission through the atmosphere,” Proc. SPIE 3763, 41–49 (1999).
[Crossref]
Roux, F. S.
F. S. Roux, “How to distinguish between the annihilation and the creation of optical vortices,” Opt. Lett. 38(19), 3895–3898 (2013).
[Crossref]
[PubMed]
F. S. Roux, “Anomalous transient behavior from an inhomogeneous initial optical vortex density,” J. Opt. Soc. Am. A 28(4), 621–626 (2011).
[Crossref]
[PubMed]
M. Chen and F. S. Roux, “Accelerating the annihilation of an optical vortex dipole in a Gaussian beam,” J. Opt. Soc. Am. A 25(6), 1279–1286 (2008).
[Crossref]
[PubMed]
Sanchez, D. J.
D. J. Sanchez, D. W. Oesch, and P. R. Kelly, “The aggregate behavior of branch points  theoretical calculation of branch point velocity,” Proc. SPIE 8380, 83800P (2012).
[Crossref]
D. W. Oesch, D. J. Sanchez, and C. M. TewksburyChristle, “Aggregate behavior of branch pointspersistent pairs,” Opt. Express 20(2), 1046–1059 (2012).
[Crossref]
[PubMed]
D. J. Sanchez and D. W. Oesch, “Orbital angular momentum in optical waves propagating through distributed turbulence,” Opt. Express 19(24), 24596–24608 (2011).
[Crossref]
[PubMed]
D. J. Sanchez and D. W. Oesch, “Localization of angular momentum in optical waves propagating through turbulence,” Opt. Express 19(25), 25388–25396 (2011).
[Crossref]
[PubMed]
D. W. Oesch, D. J. Sanchez, and C. L. Matson, “The aggregate behavior of branch pointsmeasuring the number and velocity of atmospheric turbulence layers,” Opt. Express 18(21), 22377–22392 (2010).
[Crossref]
[PubMed]
D. W. Oesch, D. J. Sanchez, C. M. TewksburyChristle, and P. R. Kelly, “The aggregate behavior of branch points  altitude and strength of atmospheric turbulence layers,” Proc. SPIE 7816, 781605 (2010).
[Crossref]
D. J. Sanchez and D. W. Oesch, “The aggregate behavior of branch points  the creation and evolution of branch points,” Proc. SPIE 7466, 746605 (2009).
[Crossref]
D. W. Oesch, D. J. Sanchez, C. M. TewksburyChristle, and P. R. Kelly, “The aggregate behavior of branch points  branch point density as a characteristic of an atmospheric turbulence simulator,” Proc. SPIE 7466, 746606 (2009).
[Crossref]
Shkunov, V. V.
N. B. Baranova, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, and B. Y. Zel’dovich, “Wavefront dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A 73(5), 525–528 (1983).
[Crossref]
Shvartsman, N.
I. Freund and N. Shvartsman, “Wavefield phase singularities: The sign principle,” Phys. Rev. A 50(6), 5164–5172 (1994).
[Crossref]
[PubMed]
Tartakovski, V. A.
V. A. Tartakovski and N. N. Mayer, “Phase dislocation and minimal phase representation of the wave function,” Atmos. Oceanic Opt. 8, 231–235 (1995).
TewksburyChristle, C. M.
D. W. Oesch, D. J. Sanchez, and C. M. TewksburyChristle, “Aggregate behavior of branch pointspersistent pairs,” Opt. Express 20(2), 1046–1059 (2012).
[Crossref]
[PubMed]
D. W. Oesch, D. J. Sanchez, C. M. TewksburyChristle, and P. R. Kelly, “The aggregate behavior of branch points  altitude and strength of atmospheric turbulence layers,” Proc. SPIE 7816, 781605 (2010).
[Crossref]
D. W. Oesch, D. J. Sanchez, C. M. TewksburyChristle, and P. R. Kelly, “The aggregate behavior of branch points  branch point density as a characteristic of an atmospheric turbulence simulator,” Proc. SPIE 7466, 746606 (2009).
[Crossref]
Vaughn, J. L.
D. L. Fried and J. L. Vaughn, “Branch cuts in the phase function,” Appl. Opt. 31(15), 2865–2882 (1992).
[Crossref]
[PubMed]
Voitsekhovich, V. V.
V. V. Voitsekhovich, D. Kouznetsov, and D. K. Morozov, “Density of turbulenceinduced phase dislocations,” Appl. Opt. 37(21), 4525–4535 (1998).
[Crossref]
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Figures (3)
The vertical profile of turbulence strength with HV model
The density of branchpoints versus (a) propagation height and (b) Rytov number with different turbulence strength (λ = 1.06μm).
The density of branchpoints versus (a) propagation height and (b) Rytov number with different wavelength (C_{n}^{2}(0) = 4.104 × 10^{−14}m^{2/3}).
Tables (2)
Table 1 The values of fitting parameters for different turbulence strength with the fixed wavelength λ = 1.06μm
Table 2 The values of fitting parameters for different wavelength with the fixed surface level value of turbulence strength C_{n}^{2}(0) = 4.104 × 10^{−14}m^{2/3}
Equations (9)
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