Abstract

We present some results obtained by numerical modeling of the propagation of vortex beams LG0l through a randomly inhomogeneous medium. The vortex beams are the lower order Laguerre–Gaussian modes. Such beams, if propagated under conditions of weak turbulence, also experience distortions, like a Gaussian beam. However, the statistically averaged vortex beams (LG0l) conserve the central intensity dip with a nonzero intensity on the beam axis. The beam broadening of vortex beams is analyzed. The average vortex beams are found to be broadened less than the Gaussian beam while propagated through a randomly inhomogeneous medium. The higher the topological charge l is, the smaller the beam broadening is.

© 2012 Optical Society of America

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  1. Y. Baykal, “Log-amplitude and phase fluctuations of higher-order annular laser beams in a turbulent medium,” J. Opt. Soc. Am. A 22, 672–679 (2005).
    [CrossRef]
  2. H. T. Eyyuboğlu, Y. E. Yenice, and Y. Baykal, “Higher order annular Gaussian laser beam propagation in free space,” Opt. Eng. 45, 038002 (2006).
    [CrossRef]
  3. H. T. Eyyuboğlu, S. Altay, and Y. Baykal, “Propagation characteristics of higher order annular Gaussian beams in atmospheric turbulence,” Opt. Commun. 264, 25–34 (2006).
    [CrossRef]
  4. Y. J. Cai and S. L. He, “Propagation of various dark hollow beams in a turbulent atmosphere,” Opt. Express 14, 1353–1367 (2006).
    [CrossRef]
  5. F. E. S. Vetelino and L. C. Andrews, “Annular Gaussian beams in turbulent media,” Proc. SPIE 5160, 86–97 (2004).
    [CrossRef]
  6. E. G. Abramochkin and V. G. Volostnikov, “Spiral light beams,” Phys. Usp. 47, 1177–1203 (2004).
  7. M. Vasnetsov and K. Staliunas, eds., Optical Vortices, Vol. 228, Horizons in World Physics (Nova Science, 1999).
  8. M. S. Soskin and M. V. Vasnetsov, “Singular optics,” in Progress in Optics, E. Wolf, ed. (North-Holland, 2001), pp. 219–287.
  9. S. Ramee and R. Simon, “Effect of holes and vortices on beam quality,” J. Opt. Soc. Am. A 17, 84–94 (2000).
    [CrossRef]
  10. S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. Abraham, “Creation of Laguerre–Gaussian laser modes using diffractive optics,” Phys. Rev. A 66, 043801 (2002).
    [CrossRef]
  11. J. Courtial and M. J. Padgett, “Performance of a cylindrical lens mode converter for producing Laguerre–Gaussian laser modes,” Opt. Commun. 159, 13–18 (1999).
    [CrossRef]
  12. C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94, 153901 (2005).
    [CrossRef]
  13. P. A. Konyaev, V. P. Lukin, and V. A. Sennikov, “Effect of phase fluctuations on propagation of the vortex beams,” Atmos. Oceanic Opt. 19, 924–927 (2006).
  14. A. E. Siegman, Lasers (Oxford University, 1986), Chap. 19.
  15. V. E. Zuev, P. A. Konyaev, and V. P. Lukin, “Minimization of atmospheric distortions of optical waves by methods of adaptive optics,” translated from Izv. Vyssh. Uchebn. Zaved. Fizika 28, 6–29 (1985).
  16. V. P. Lukin, F. Yu. Kanev, P. A. Konyaev, and B. V. Fortes, “Numerical model of atmospheric adaptive optical system,” Atmos. Oceanic Opt. 8, 210–222 (1995).

2006

H. T. Eyyuboğlu, Y. E. Yenice, and Y. Baykal, “Higher order annular Gaussian laser beam propagation in free space,” Opt. Eng. 45, 038002 (2006).
[CrossRef]

H. T. Eyyuboğlu, S. Altay, and Y. Baykal, “Propagation characteristics of higher order annular Gaussian beams in atmospheric turbulence,” Opt. Commun. 264, 25–34 (2006).
[CrossRef]

P. A. Konyaev, V. P. Lukin, and V. A. Sennikov, “Effect of phase fluctuations on propagation of the vortex beams,” Atmos. Oceanic Opt. 19, 924–927 (2006).

Y. J. Cai and S. L. He, “Propagation of various dark hollow beams in a turbulent atmosphere,” Opt. Express 14, 1353–1367 (2006).
[CrossRef]

2005

Y. Baykal, “Log-amplitude and phase fluctuations of higher-order annular laser beams in a turbulent medium,” J. Opt. Soc. Am. A 22, 672–679 (2005).
[CrossRef]

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94, 153901 (2005).
[CrossRef]

2004

F. E. S. Vetelino and L. C. Andrews, “Annular Gaussian beams in turbulent media,” Proc. SPIE 5160, 86–97 (2004).
[CrossRef]

E. G. Abramochkin and V. G. Volostnikov, “Spiral light beams,” Phys. Usp. 47, 1177–1203 (2004).

2002

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. Abraham, “Creation of Laguerre–Gaussian laser modes using diffractive optics,” Phys. Rev. A 66, 043801 (2002).
[CrossRef]

2000

1999

J. Courtial and M. J. Padgett, “Performance of a cylindrical lens mode converter for producing Laguerre–Gaussian laser modes,” Opt. Commun. 159, 13–18 (1999).
[CrossRef]

1995

V. P. Lukin, F. Yu. Kanev, P. A. Konyaev, and B. V. Fortes, “Numerical model of atmospheric adaptive optical system,” Atmos. Oceanic Opt. 8, 210–222 (1995).

1985

V. E. Zuev, P. A. Konyaev, and V. P. Lukin, “Minimization of atmospheric distortions of optical waves by methods of adaptive optics,” translated from Izv. Vyssh. Uchebn. Zaved. Fizika 28, 6–29 (1985).

Abraham, E. R.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. Abraham, “Creation of Laguerre–Gaussian laser modes using diffractive optics,” Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Abramochkin, E. G.

E. G. Abramochkin and V. G. Volostnikov, “Spiral light beams,” Phys. Usp. 47, 1177–1203 (2004).

Altay, S.

H. T. Eyyuboğlu, S. Altay, and Y. Baykal, “Propagation characteristics of higher order annular Gaussian beams in atmospheric turbulence,” Opt. Commun. 264, 25–34 (2006).
[CrossRef]

Andrews, L. C.

F. E. S. Vetelino and L. C. Andrews, “Annular Gaussian beams in turbulent media,” Proc. SPIE 5160, 86–97 (2004).
[CrossRef]

Baykal, Y.

H. T. Eyyuboğlu, S. Altay, and Y. Baykal, “Propagation characteristics of higher order annular Gaussian beams in atmospheric turbulence,” Opt. Commun. 264, 25–34 (2006).
[CrossRef]

H. T. Eyyuboğlu, Y. E. Yenice, and Y. Baykal, “Higher order annular Gaussian laser beam propagation in free space,” Opt. Eng. 45, 038002 (2006).
[CrossRef]

Y. Baykal, “Log-amplitude and phase fluctuations of higher-order annular laser beams in a turbulent medium,” J. Opt. Soc. Am. A 22, 672–679 (2005).
[CrossRef]

Cai, Y. J.

Courtial, J.

J. Courtial and M. J. Padgett, “Performance of a cylindrical lens mode converter for producing Laguerre–Gaussian laser modes,” Opt. Commun. 159, 13–18 (1999).
[CrossRef]

Eyyuboglu, H. T.

H. T. Eyyuboğlu, Y. E. Yenice, and Y. Baykal, “Higher order annular Gaussian laser beam propagation in free space,” Opt. Eng. 45, 038002 (2006).
[CrossRef]

H. T. Eyyuboğlu, S. Altay, and Y. Baykal, “Propagation characteristics of higher order annular Gaussian beams in atmospheric turbulence,” Opt. Commun. 264, 25–34 (2006).
[CrossRef]

Fortes, B. V.

V. P. Lukin, F. Yu. Kanev, P. A. Konyaev, and B. V. Fortes, “Numerical model of atmospheric adaptive optical system,” Atmos. Oceanic Opt. 8, 210–222 (1995).

He, S. L.

Kanev, F. Yu.

V. P. Lukin, F. Yu. Kanev, P. A. Konyaev, and B. V. Fortes, “Numerical model of atmospheric adaptive optical system,” Atmos. Oceanic Opt. 8, 210–222 (1995).

Kennedy, S. A.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. Abraham, “Creation of Laguerre–Gaussian laser modes using diffractive optics,” Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Konyaev, P. A.

P. A. Konyaev, V. P. Lukin, and V. A. Sennikov, “Effect of phase fluctuations on propagation of the vortex beams,” Atmos. Oceanic Opt. 19, 924–927 (2006).

V. P. Lukin, F. Yu. Kanev, P. A. Konyaev, and B. V. Fortes, “Numerical model of atmospheric adaptive optical system,” Atmos. Oceanic Opt. 8, 210–222 (1995).

V. E. Zuev, P. A. Konyaev, and V. P. Lukin, “Minimization of atmospheric distortions of optical waves by methods of adaptive optics,” translated from Izv. Vyssh. Uchebn. Zaved. Fizika 28, 6–29 (1985).

Lukin, V. P.

P. A. Konyaev, V. P. Lukin, and V. A. Sennikov, “Effect of phase fluctuations on propagation of the vortex beams,” Atmos. Oceanic Opt. 19, 924–927 (2006).

V. P. Lukin, F. Yu. Kanev, P. A. Konyaev, and B. V. Fortes, “Numerical model of atmospheric adaptive optical system,” Atmos. Oceanic Opt. 8, 210–222 (1995).

V. E. Zuev, P. A. Konyaev, and V. P. Lukin, “Minimization of atmospheric distortions of optical waves by methods of adaptive optics,” translated from Izv. Vyssh. Uchebn. Zaved. Fizika 28, 6–29 (1985).

Padgett, M. J.

J. Courtial and M. J. Padgett, “Performance of a cylindrical lens mode converter for producing Laguerre–Gaussian laser modes,” Opt. Commun. 159, 13–18 (1999).
[CrossRef]

Paterson, C.

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94, 153901 (2005).
[CrossRef]

Porterfield, J. Z.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. Abraham, “Creation of Laguerre–Gaussian laser modes using diffractive optics,” Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Ramee, S.

Sennikov, V. A.

P. A. Konyaev, V. P. Lukin, and V. A. Sennikov, “Effect of phase fluctuations on propagation of the vortex beams,” Atmos. Oceanic Opt. 19, 924–927 (2006).

Siegman, A. E.

A. E. Siegman, Lasers (Oxford University, 1986), Chap. 19.

Simon, R.

Soskin, M. S.

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” in Progress in Optics, E. Wolf, ed. (North-Holland, 2001), pp. 219–287.

Szabo, M. J.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. Abraham, “Creation of Laguerre–Gaussian laser modes using diffractive optics,” Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Teslow, H.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. Abraham, “Creation of Laguerre–Gaussian laser modes using diffractive optics,” Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Vasnetsov, M. V.

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” in Progress in Optics, E. Wolf, ed. (North-Holland, 2001), pp. 219–287.

Vetelino, F. E. S.

F. E. S. Vetelino and L. C. Andrews, “Annular Gaussian beams in turbulent media,” Proc. SPIE 5160, 86–97 (2004).
[CrossRef]

Volostnikov, V. G.

E. G. Abramochkin and V. G. Volostnikov, “Spiral light beams,” Phys. Usp. 47, 1177–1203 (2004).

Yenice, Y. E.

H. T. Eyyuboğlu, Y. E. Yenice, and Y. Baykal, “Higher order annular Gaussian laser beam propagation in free space,” Opt. Eng. 45, 038002 (2006).
[CrossRef]

Zuev, V. E.

V. E. Zuev, P. A. Konyaev, and V. P. Lukin, “Minimization of atmospheric distortions of optical waves by methods of adaptive optics,” translated from Izv. Vyssh. Uchebn. Zaved. Fizika 28, 6–29 (1985).

Atmos. Oceanic Opt.

P. A. Konyaev, V. P. Lukin, and V. A. Sennikov, “Effect of phase fluctuations on propagation of the vortex beams,” Atmos. Oceanic Opt. 19, 924–927 (2006).

V. P. Lukin, F. Yu. Kanev, P. A. Konyaev, and B. V. Fortes, “Numerical model of atmospheric adaptive optical system,” Atmos. Oceanic Opt. 8, 210–222 (1995).

Izv. Vyssh. Uchebn. Zaved. Fizika

V. E. Zuev, P. A. Konyaev, and V. P. Lukin, “Minimization of atmospheric distortions of optical waves by methods of adaptive optics,” translated from Izv. Vyssh. Uchebn. Zaved. Fizika 28, 6–29 (1985).

J. Opt. Soc. Am. A

Opt. Commun.

H. T. Eyyuboğlu, S. Altay, and Y. Baykal, “Propagation characteristics of higher order annular Gaussian beams in atmospheric turbulence,” Opt. Commun. 264, 25–34 (2006).
[CrossRef]

J. Courtial and M. J. Padgett, “Performance of a cylindrical lens mode converter for producing Laguerre–Gaussian laser modes,” Opt. Commun. 159, 13–18 (1999).
[CrossRef]

Opt. Eng.

H. T. Eyyuboğlu, Y. E. Yenice, and Y. Baykal, “Higher order annular Gaussian laser beam propagation in free space,” Opt. Eng. 45, 038002 (2006).
[CrossRef]

Opt. Express

Phys. Rev. A

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. Abraham, “Creation of Laguerre–Gaussian laser modes using diffractive optics,” Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Phys. Rev. Lett.

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94, 153901 (2005).
[CrossRef]

Phys. Usp.

E. G. Abramochkin and V. G. Volostnikov, “Spiral light beams,” Phys. Usp. 47, 1177–1203 (2004).

Proc. SPIE

F. E. S. Vetelino and L. C. Andrews, “Annular Gaussian beams in turbulent media,” Proc. SPIE 5160, 86–97 (2004).
[CrossRef]

Other

M. Vasnetsov and K. Staliunas, eds., Optical Vortices, Vol. 228, Horizons in World Physics (Nova Science, 1999).

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” in Progress in Optics, E. Wolf, ed. (North-Holland, 2001), pp. 219–287.

A. E. Siegman, Lasers (Oxford University, 1986), Chap. 19.

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Figures (3)

Fig. 1.
Fig. 1.

(а) Intensity and (b) phase of the initial collimated vortex beam with l=1; profiles of the beam intensity calculated for some propagation distances (c)–(f) z=0.0, 0.2, 0.4, 0.6 using the values of the dimensionless parameter C2=0.1.4/CO

Fig. 2.
Fig. 2.

Dependences of Reff (z) for averaged vortex beams (LG01) (l=0, 1, 2, 3) at C2=0.1.

Fig. 3.
Fig. 3.

Dependence of the scintillation index σI2 on the dimensionless turbulence parameter C2, obtained in the experiment for Gaussian beam LG00 propagating in turbulence for z0 values equal to 0.2 and 0.4, respectively.

Equations (12)

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Ul(r,θ,z)=Aw(z)(r2w(z))lexp[r2w2(z)]×exp[ikr22R(z)]exp(ilθ)exp[iϕ(z)],
Il(r,z)=|Ul(r,z,θ)|2=A2w2(z)(r2w(z))2lexp[2r2w2(z)].
U0(r,z)=Aw(z)exp[r2w2(z)]exp[ikr22R(z)]exp[iϕ(z)].
reff(z)=2r2I(r)dSI(r)dS=w(z)l+12,rd(z)=w(z)l2.
Ul(r,θ)=1πl!rlexp[r22]exp[ilθ].
Il(r)=1πl!r2ler2.
U0(r)=(1/π)er2/2,
Ul(r,θ)=1πl!rler2/2eilθ(x+iy)ler2/2,l=1,2,3
Uz=i2k(2x2+2y2+2k2δn)U,
δn(r,z)=m=1M[δ(zzm)zm1zmδn(r,zt)dzt]=k1m=1M[δ(zzm)ϕm(r)],
F(κx,κy)=C2(κ02+κx2+κy2)11/6exp[(κx2+κy2)/κm2],κ0=2π/L0,κm=2π/l0.
R˜eff(z)=reff(z)/reff(z=0).

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