Abstract

Transformation of vortex Bessel beams during propagation in turbulent atmosphere is theoretically analyzed. Deforming influence of the random inhomogeneity of the turbulent medium on propagation of diffraction-free beams leads to disappearance of their invariant properties. In the given research, features of evolution of the spatial structure of distribution of mean intensity of vortex Bessel beams in turbulent atmosphere are analyzed. A quantitative criterion of possibility of carrying over of a dark central domain by vortex Bessel beams in a turbulent atmosphere is derived. The analysis of the behavior of several physical parameters of mean-level optical radiation shows that the shape stability of a vortex Bessel beam increases with the topological charge of this beam during its propagation in a turbulent atmosphere.

© 2014 Optical Society of America

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References

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  12. C. F. R. Caron and R. M. Potvliege, “Bessel-modulated Gaussian beams with quadratic radial dependence,” Opt. Commun. 164, 83–93 (1999).
    [CrossRef]
  13. S. R. Seshadri, “Average characteristics of a partially coherent Bessel-Gauss optical beam,” J. Opt. Soc. Am. A 16, 2917–2927 (1999).
    [CrossRef]
  14. A. V. Shchegrov and E. Wolf, “Partially coherent conical beams,” Opt. Lett. 25, 141–143 (2000).
    [CrossRef]
  15. S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155–165 (2002).
    [CrossRef]
  16. H. T. Eyyuboğlu, “Propagation of higher order Bessel-Gaussian beams in turbulence,” Appl. Phys. B 88, 259–265 (2007).
    [CrossRef]
  17. B. Chen, Z. Chen, and J. Pu, “Propagation of partially coherent Bessel-Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 40, 820–827 (2008).
    [CrossRef]
  18. K. Zhu, G. Zhou, X. Li, X. Zheng, and H. Tang, “Propagation of Bessel-Gaussian beams with optical vortices in turbulent atmosphere,” Opt. Express 16, 21315–21320 (2008).
    [CrossRef]
  19. H. T. Eyyuboğlu, E. Sermutlu, Y. Baykal, Y. Cai, and O. Korotkova, “Intensity fluctuations in J-Bessel-Gaussian beams of all orders propagating in turbulent atmosphere,” Appl. Phys. B 93, 605–611 (2008).
    [CrossRef]
  20. H. T. Eyyuboğlu and F. Hardalac, “Propagation of modified Bessel-Gaussian beams in turbulence,” Opt. Laser Technol. 40, 343–351 (2008).
    [CrossRef]
  21. Y. Zhang and T. Zhu, “Propagation of Helmholtz-Gauss beams in weak turbulent atmosphere,” Chin. Opt. Lett. 6, 79–82 (2008).
    [CrossRef]
  22. B. Chen and J. Pu, “Propagation of Gauss-Bessel beams in turbulent atmosphere,” Chin. Phys. B 18, 1033–1039 (2009).
    [CrossRef]
  23. Ch. Ding, L. Pan, and B. Lu, “Phase singularities and spectral changes of spectrally partially coherent higher-order Bessel-Gauss pulsed beams,” J. Opt. Soc. Am. A 26, 2654–2661 (2009).
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    [CrossRef]
  25. I. P. Lukin, “Coherence of the higher modes of Bessel beams in turbulent atmosphere,” Proc. SPIE 8696, 86960A (2012).
    [CrossRef]
  26. I. P. Lukin, “Formation of a ring dislocation of a coherence of a vortex optical beam in turbulent atmosphere,” Proc. SPIE 9066, 90660Q (2013).
    [CrossRef]
  27. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).
  28. I. P. Lukin, “Coherence of a Bessel beam in a turbulent atmosphere,” Atmos. Oceanic Opt. 25, 328–337 (2012) {Optika atmosfery i okeana 25, 393–402 (2012) [in Russian]}.
    [CrossRef]

2013 (1)

I. P. Lukin, “Formation of a ring dislocation of a coherence of a vortex optical beam in turbulent atmosphere,” Proc. SPIE 9066, 90660Q (2013).
[CrossRef]

2012 (2)

I. P. Lukin, “Coherence of a Bessel beam in a turbulent atmosphere,” Atmos. Oceanic Opt. 25, 328–337 (2012) {Optika atmosfery i okeana 25, 393–402 (2012) [in Russian]}.
[CrossRef]

I. P. Lukin, “Coherence of the higher modes of Bessel beams in turbulent atmosphere,” Proc. SPIE 8696, 86960A (2012).
[CrossRef]

2010 (1)

2009 (2)

2008 (5)

B. Chen, Z. Chen, and J. Pu, “Propagation of partially coherent Bessel-Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 40, 820–827 (2008).
[CrossRef]

H. T. Eyyuboğlu, E. Sermutlu, Y. Baykal, Y. Cai, and O. Korotkova, “Intensity fluctuations in J-Bessel-Gaussian beams of all orders propagating in turbulent atmosphere,” Appl. Phys. B 93, 605–611 (2008).
[CrossRef]

H. T. Eyyuboğlu and F. Hardalac, “Propagation of modified Bessel-Gaussian beams in turbulence,” Opt. Laser Technol. 40, 343–351 (2008).
[CrossRef]

Y. Zhang and T. Zhu, “Propagation of Helmholtz-Gauss beams in weak turbulent atmosphere,” Chin. Opt. Lett. 6, 79–82 (2008).
[CrossRef]

K. Zhu, G. Zhou, X. Li, X. Zheng, and H. Tang, “Propagation of Bessel-Gaussian beams with optical vortices in turbulent atmosphere,” Opt. Express 16, 21315–21320 (2008).
[CrossRef]

2007 (1)

H. T. Eyyuboğlu, “Propagation of higher order Bessel-Gaussian beams in turbulence,” Appl. Phys. B 88, 259–265 (2007).
[CrossRef]

2002 (1)

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155–165 (2002).
[CrossRef]

2000 (2)

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[CrossRef]

A. V. Shchegrov and E. Wolf, “Partially coherent conical beams,” Opt. Lett. 25, 141–143 (2000).
[CrossRef]

1999 (3)

1998 (1)

1997 (2)

1996 (1)

V. P. Koronkevich, A. A. Kharisov, M. T. Gail, and Ch. Schutz, “Multiorder diffractive lenses for the formation of Bessel beams,” Avtometriya 5, 38–43 (1996) [in Russian].

1989 (1)

1987 (2)

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[CrossRef]

1986 (1)

Agura, T.

Andrews, D. L.

D. L. Andrews, Structured Light and Its Applications: An Introduction To Phase-Structured Beams and Nanoscale Optical Forces (Academic, 2008).

Andrews, L. C.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).

Arlt, J.

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[CrossRef]

Baykal, Y.

H. T. Eyyuboğlu, E. Sermutlu, Y. Baykal, Y. Cai, and O. Korotkova, “Intensity fluctuations in J-Bessel-Gaussian beams of all orders propagating in turbulent atmosphere,” Appl. Phys. B 93, 605–611 (2008).
[CrossRef]

Bernal, J.

Borghi, R.

Cai, Y.

H. T. Eyyuboğlu, E. Sermutlu, Y. Baykal, Y. Cai, and O. Korotkova, “Intensity fluctuations in J-Bessel-Gaussian beams of all orders propagating in turbulent atmosphere,” Appl. Phys. B 93, 605–611 (2008).
[CrossRef]

Carbajal-Domingues, A.

Caron, C. F. R.

C. F. R. Caron and R. M. Potvliege, “Bessel-modulated Gaussian beams with quadratic radial dependence,” Opt. Commun. 164, 83–93 (1999).
[CrossRef]

Chen, B.

B. Chen and J. Pu, “Propagation of Gauss-Bessel beams in turbulent atmosphere,” Chin. Phys. B 18, 1033–1039 (2009).
[CrossRef]

B. Chen, Z. Chen, and J. Pu, “Propagation of partially coherent Bessel-Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 40, 820–827 (2008).
[CrossRef]

Chen, Z.

B. Chen, Z. Chen, and J. Pu, “Propagation of partially coherent Bessel-Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 40, 820–827 (2008).
[CrossRef]

Dholakia, K.

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[CrossRef]

Ding, Ch.

Durnin, J.

Eberly, J. H.

Eyyuboglu, H. T.

H. T. Eyyuboğlu, E. Sermutlu, Y. Baykal, Y. Cai, and O. Korotkova, “Intensity fluctuations in J-Bessel-Gaussian beams of all orders propagating in turbulent atmosphere,” Appl. Phys. B 93, 605–611 (2008).
[CrossRef]

H. T. Eyyuboğlu and F. Hardalac, “Propagation of modified Bessel-Gaussian beams in turbulence,” Opt. Laser Technol. 40, 343–351 (2008).
[CrossRef]

H. T. Eyyuboğlu, “Propagation of higher order Bessel-Gaussian beams in turbulence,” Appl. Phys. B 88, 259–265 (2007).
[CrossRef]

Friberg, A. T.

Gail, M. T.

V. P. Koronkevich, A. A. Kharisov, M. T. Gail, and Ch. Schutz, “Multiorder diffractive lenses for the formation of Bessel beams,” Avtometriya 5, 38–43 (1996) [in Russian].

Gori, F.

R. Borghi, M. Santarsiero, and F. Gori, “Axial intensity of apertured Bessel beams,” J. Opt. Soc. Am. A 14, 23–26 (1997).
[CrossRef]

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Hardalac, F.

H. T. Eyyuboğlu and F. Hardalac, “Propagation of modified Bessel-Gaussian beams in turbulence,” Opt. Laser Technol. 40, 343–351 (2008).
[CrossRef]

Herman, R. M.

Kharisov, A. A.

V. P. Koronkevich, A. A. Kharisov, M. T. Gail, and Ch. Schutz, “Multiorder diffractive lenses for the formation of Bessel beams,” Avtometriya 5, 38–43 (1996) [in Russian].

Koronkevich, V. P.

V. P. Koronkevich, A. A. Kharisov, M. T. Gail, and Ch. Schutz, “Multiorder diffractive lenses for the formation of Bessel beams,” Avtometriya 5, 38–43 (1996) [in Russian].

Korotkova, O.

H. T. Eyyuboğlu, E. Sermutlu, Y. Baykal, Y. Cai, and O. Korotkova, “Intensity fluctuations in J-Bessel-Gaussian beams of all orders propagating in turbulent atmosphere,” Appl. Phys. B 93, 605–611 (2008).
[CrossRef]

Li, R.

Li, Sh. W.

Li, X.

Lu, B.

Lukin, I. P.

I. P. Lukin, “Formation of a ring dislocation of a coherence of a vortex optical beam in turbulent atmosphere,” Proc. SPIE 9066, 90660Q (2013).
[CrossRef]

I. P. Lukin, “Coherence of a Bessel beam in a turbulent atmosphere,” Atmos. Oceanic Opt. 25, 328–337 (2012) {Optika atmosfery i okeana 25, 393–402 (2012) [in Russian]}.
[CrossRef]

I. P. Lukin, “Coherence of the higher modes of Bessel beams in turbulent atmosphere,” Proc. SPIE 8696, 86960A (2012).
[CrossRef]

Martin-Ruiz, A.

Miceli, J. J.

Niconoff, G. M.

Orlov, S.

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155–165 (2002).
[CrossRef]

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Pan, L.

Phillips, R. L.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).

Potvliege, R. M.

C. F. R. Caron and R. M. Potvliege, “Bessel-modulated Gaussian beams with quadratic radial dependence,” Opt. Commun. 164, 83–93 (1999).
[CrossRef]

Pu, J.

B. Chen and J. Pu, “Propagation of Gauss-Bessel beams in turbulent atmosphere,” Chin. Phys. B 18, 1033–1039 (2009).
[CrossRef]

B. Chen, Z. Chen, and J. Pu, “Propagation of partially coherent Bessel-Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 40, 820–827 (2008).
[CrossRef]

Regelskis, K.

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155–165 (2002).
[CrossRef]

Santarsiero, M.

Schutz, Ch.

V. P. Koronkevich, A. A. Kharisov, M. T. Gail, and Ch. Schutz, “Multiorder diffractive lenses for the formation of Bessel beams,” Avtometriya 5, 38–43 (1996) [in Russian].

Sermutlu, E.

H. T. Eyyuboğlu, E. Sermutlu, Y. Baykal, Y. Cai, and O. Korotkova, “Intensity fluctuations in J-Bessel-Gaussian beams of all orders propagating in turbulent atmosphere,” Appl. Phys. B 93, 605–611 (2008).
[CrossRef]

Seshadri, S. R.

Shchegrov, A. V.

Smilgevicius, V.

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155–165 (2002).
[CrossRef]

Stabinis, A.

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155–165 (2002).
[CrossRef]

Takabe, M.

Tang, H.

Turunen, J.

Vasara, A.

Wiggins, T. A.

Wolf, E.

Yoshikado, Sh.

Zhang, Y.

Zheng, X.

Zhou, G.

Zhu, K.

Zhu, T.

Appl. Opt. (3)

Appl. Phys. B (2)

H. T. Eyyuboğlu, “Propagation of higher order Bessel-Gaussian beams in turbulence,” Appl. Phys. B 88, 259–265 (2007).
[CrossRef]

H. T. Eyyuboğlu, E. Sermutlu, Y. Baykal, Y. Cai, and O. Korotkova, “Intensity fluctuations in J-Bessel-Gaussian beams of all orders propagating in turbulent atmosphere,” Appl. Phys. B 93, 605–611 (2008).
[CrossRef]

Atmos. Oceanic Opt. (1)

I. P. Lukin, “Coherence of a Bessel beam in a turbulent atmosphere,” Atmos. Oceanic Opt. 25, 328–337 (2012) {Optika atmosfery i okeana 25, 393–402 (2012) [in Russian]}.
[CrossRef]

Avtometriya (1)

V. P. Koronkevich, A. A. Kharisov, M. T. Gail, and Ch. Schutz, “Multiorder diffractive lenses for the formation of Bessel beams,” Avtometriya 5, 38–43 (1996) [in Russian].

Chin. Opt. Lett. (1)

Chin. Phys. B (1)

B. Chen and J. Pu, “Propagation of Gauss-Bessel beams in turbulent atmosphere,” Chin. Phys. B 18, 1033–1039 (2009).
[CrossRef]

J. Opt. Soc. Am. A (6)

Opt. Commun. (4)

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

C. F. R. Caron and R. M. Potvliege, “Bessel-modulated Gaussian beams with quadratic radial dependence,” Opt. Commun. 164, 83–93 (1999).
[CrossRef]

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155–165 (2002).
[CrossRef]

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[CrossRef]

Opt. Express (2)

Opt. Laser Technol. (2)

B. Chen, Z. Chen, and J. Pu, “Propagation of partially coherent Bessel-Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 40, 820–827 (2008).
[CrossRef]

H. T. Eyyuboğlu and F. Hardalac, “Propagation of modified Bessel-Gaussian beams in turbulence,” Opt. Laser Technol. 40, 343–351 (2008).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (2)

I. P. Lukin, “Coherence of the higher modes of Bessel beams in turbulent atmosphere,” Proc. SPIE 8696, 86960A (2012).
[CrossRef]

I. P. Lukin, “Formation of a ring dislocation of a coherence of a vortex optical beam in turbulent atmosphere,” Proc. SPIE 9066, 90660Q (2013).
[CrossRef]

Other (2)

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).

D. L. Andrews, Structured Light and Its Applications: An Introduction To Phase-Structured Beams and Nanoscale Optical Forces (Academic, 2008).

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Figures (7)

Fig. 1.
Fig. 1.

Mean intensity of a vortex Bessel beam at its optical axis in a turbulent atmosphere at different values of the beam topological charge.

Fig. 2.
Fig. 2.

Parameters of mean intensity distribution of a vortex Bessel beam during its propagation in a turbulent atmosphere versus the beam topological charge.

Fig. 3.
Fig. 3.

Coordinate of the first maximum of a vortex Bessel beam in a turbulent atmosphere as a function of the beam topological charge.

Fig. 4.
Fig. 4.

Intensity at the first maximum of a vortex Bessel beam in a turbulent atmosphere as a function of the beam topological charge.

Fig. 5.
Fig. 5.

Internal radius of the first light ring of a vortex Bessel beam during propagation in a turbulent atmosphere.

Fig. 6.
Fig. 6.

External radius of the first light ring of a vortex Bessel beam during propagation in a turbulent atmosphere.

Fig. 7.
Fig. 7.

Cross sections of vortex Bessel beams in a turbulent atmosphere.

Tables (1)

Tables Icon

Table 1. Limiting Values of the Parameter qmax as a Function of the Topological Charge m

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

E0(ρ)=E0(ρ,φ)=E0Jm(βρ)exp(imφ),
I(x,R)=E(x,R)E*(x,R)=k24π2x2dρ1dρ2Γ2(0)(ρ1,ρ2)×exp{ikxR(ρ1ρ2)+ik2x(ρ12ρ22)πk2x01dξH[ξ(ρ1ρ2)]},
Γ2(0)(ρ1,ρ2)=E0(ρ1)E0*(ρ2);H(μ)=2dκΦn(κ)[1cos(κμ)];
πk2x01dξH[ξ(ρ1ρ2)]ρ05/301dξ|ξ(ρ1ρ2)|5/313ρ02(ρ1ρ2)2,
ρ0=(1.4572Cn2k2x)3/5,
I(x,R)I(x,R,φR)E02k2πix(12i3q)exp[ixβ22k(12i3q)+ikR22x(12i3q)]×0dρ02πdφρJm(βρ)exp[im(φRφ)]{R2i3qρexp[i(φRφ)]}m[R249q2ρ24i3qRρcos(φRφ)]m/2×Jm[β(12i3q)R249q2ρ24i3qRρcos(φRφ)]×exp[ik2x(12i3q)ρ2ikx(12i3q)Rρcos(φRφ)],
I(x,R)=E02Jm2(βR).
I(x,0)E02exp(23x2β2k2ρ02)Im(23x2β2k2ρ02),
ρ0h(m)βkx,
h(m)1ζmax(m)form1,
ζmax(m)130.30exp(8.79×103m)129.97.

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