Abstract

We study numerically the mutual propagation of two fractional topological charge Laguerre–Gaussian (LG) light beams in the moving atmosphere with the thermal nonlinearity. The fractional charge beam is constructed as a weighted superposition of a finite number of the standard LG modes with integer charges. Numerical simulations demonstrate an enhanced stability of the cross-section intensity distribution of the fractional charge LG beams against the thermal blooming, as compared with the case of integer charge beams. The dominant mechanism of such a stability results from the multimodal structure of the fractional charge beams.

© 2010 Optical Society of America

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References

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  1. M. S. Soskin and M. V. Vasnetsov, in Progress in Optics, E.Wolf, ed. (North-Holland, 2001), Vol. 42, p. 219.
    [CrossRef]
  2. A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, in Progress in Optics, E.Wolf, ed. (North-Holland, 2005), Vol. 47, pp. 291-350.
    [CrossRef]
  3. G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas'ko, S. M. Barnett, and S. Franke-Arnold, Opt. Express 12, 5448 (2004).
    [CrossRef] [PubMed]
  4. K. T. Gahagan and G. A. Swartzlander, Jr., Opt. Lett. 21, 827 (1996).
    [CrossRef] [PubMed]
  5. G. Foo, D. M. Palacios, and G. A. Swartzlander, Jr., Opt. Lett. 30, 3308 (2005).
    [CrossRef]
  6. J. W. Armstrong, C. Yeh, and K. E. Wilson, Opt. Lett. 23, 1087 (1998).
    [CrossRef]
  7. B. Sprenger, J. Zhang, Z. H. Lu, and L. J. Wang, Opt. Lett. 34, 965 (2009).
    [CrossRef] [PubMed]
  8. V. V. Vorob'ev, Prog. Quantum Electron. 15, 1 (1991).
    [CrossRef]
  9. V. V. Dudorov and V. V. Kolosov, Proc. SPIE 5160, 78 (2004).
    [CrossRef]
  10. M. V. Berry, J. Opt. A 6, 259 (2004).
    [CrossRef]
  11. I. V. Basistiy, V. A. Pas'ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, J. Opt. A 6, S166 (2004).
    [CrossRef]
  12. J. B. Götte, K. O'Holleran, D. Preece, F. Flossmann, S. Franke-Arnold, S. M. Barnett, and M. Padgett, Opt. Express 16, 993 (2008).
    [CrossRef] [PubMed]
  13. M. A. Molchan, E. V. Doktorov, and R. A. Vlasov, J. Opt. A 11, 015706 (2009).
    [CrossRef]
  14. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).

2009 (2)

M. A. Molchan, E. V. Doktorov, and R. A. Vlasov, J. Opt. A 11, 015706 (2009).
[CrossRef]

B. Sprenger, J. Zhang, Z. H. Lu, and L. J. Wang, Opt. Lett. 34, 965 (2009).
[CrossRef] [PubMed]

2008 (1)

2005 (1)

2004 (4)

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas'ko, S. M. Barnett, and S. Franke-Arnold, Opt. Express 12, 5448 (2004).
[CrossRef] [PubMed]

V. V. Dudorov and V. V. Kolosov, Proc. SPIE 5160, 78 (2004).
[CrossRef]

M. V. Berry, J. Opt. A 6, 259 (2004).
[CrossRef]

I. V. Basistiy, V. A. Pas'ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, J. Opt. A 6, S166 (2004).
[CrossRef]

1998 (1)

1996 (1)

1991 (1)

V. V. Vorob'ev, Prog. Quantum Electron. 15, 1 (1991).
[CrossRef]

Agrawal, G. P.

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).

Armstrong, J. W.

Barnett, S. M.

Basistiy, I. V.

I. V. Basistiy, V. A. Pas'ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, J. Opt. A 6, S166 (2004).
[CrossRef]

Berry, M. V.

M. V. Berry, J. Opt. A 6, 259 (2004).
[CrossRef]

Courtial, J.

Desyatnikov, A. S.

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, in Progress in Optics, E.Wolf, ed. (North-Holland, 2005), Vol. 47, pp. 291-350.
[CrossRef]

Doktorov, E. V.

M. A. Molchan, E. V. Doktorov, and R. A. Vlasov, J. Opt. A 11, 015706 (2009).
[CrossRef]

Dudorov, V. V.

V. V. Dudorov and V. V. Kolosov, Proc. SPIE 5160, 78 (2004).
[CrossRef]

Flossmann, F.

Foo, G.

Franke-Arnold, S.

Gahagan, K. T.

Gibson, G.

Götte, J. B.

Kivshar, Yu. S.

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, in Progress in Optics, E.Wolf, ed. (North-Holland, 2005), Vol. 47, pp. 291-350.
[CrossRef]

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).

Kolosov, V. V.

V. V. Dudorov and V. V. Kolosov, Proc. SPIE 5160, 78 (2004).
[CrossRef]

Lu, Z. H.

Molchan, M. A.

M. A. Molchan, E. V. Doktorov, and R. A. Vlasov, J. Opt. A 11, 015706 (2009).
[CrossRef]

O'Holleran, K.

Padgett, M.

Padgett, M. J.

Palacios, D. M.

Pas'ko, V.

Pas'ko, V. A.

I. V. Basistiy, V. A. Pas'ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, J. Opt. A 6, S166 (2004).
[CrossRef]

Preece, D.

Slyusar, V. V.

I. V. Basistiy, V. A. Pas'ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, J. Opt. A 6, S166 (2004).
[CrossRef]

Soskin, M. S.

I. V. Basistiy, V. A. Pas'ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, J. Opt. A 6, S166 (2004).
[CrossRef]

M. S. Soskin and M. V. Vasnetsov, in Progress in Optics, E.Wolf, ed. (North-Holland, 2001), Vol. 42, p. 219.
[CrossRef]

Sprenger, B.

Swartzlander, G. A.

Torner, L.

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, in Progress in Optics, E.Wolf, ed. (North-Holland, 2005), Vol. 47, pp. 291-350.
[CrossRef]

Vasnetsov, M.

Vasnetsov, M. V.

I. V. Basistiy, V. A. Pas'ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, J. Opt. A 6, S166 (2004).
[CrossRef]

M. S. Soskin and M. V. Vasnetsov, in Progress in Optics, E.Wolf, ed. (North-Holland, 2001), Vol. 42, p. 219.
[CrossRef]

Vlasov, R. A.

M. A. Molchan, E. V. Doktorov, and R. A. Vlasov, J. Opt. A 11, 015706 (2009).
[CrossRef]

Vorob'ev, V. V.

V. V. Vorob'ev, Prog. Quantum Electron. 15, 1 (1991).
[CrossRef]

Wang, L. J.

Wilson, K. E.

Yeh, C.

Zhang, J.

J. Opt. A (3)

M. V. Berry, J. Opt. A 6, 259 (2004).
[CrossRef]

I. V. Basistiy, V. A. Pas'ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, J. Opt. A 6, S166 (2004).
[CrossRef]

M. A. Molchan, E. V. Doktorov, and R. A. Vlasov, J. Opt. A 11, 015706 (2009).
[CrossRef]

Opt. Express (2)

Opt. Lett. (4)

Proc. SPIE (1)

V. V. Dudorov and V. V. Kolosov, Proc. SPIE 5160, 78 (2004).
[CrossRef]

Prog. Quantum Electron. (1)

V. V. Vorob'ev, Prog. Quantum Electron. 15, 1 (1991).
[CrossRef]

Other (3)

M. S. Soskin and M. V. Vasnetsov, in Progress in Optics, E.Wolf, ed. (North-Holland, 2001), Vol. 42, p. 219.
[CrossRef]

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, in Progress in Optics, E.Wolf, ed. (North-Holland, 2005), Vol. 47, pp. 291-350.
[CrossRef]

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).

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Figures (5)

Fig. 1
Fig. 1

FCB with M = 1.5 , q = 0.3 , and n modes = 20 : (a) intensity distribution, (b) phase, (c) distribution of the index p, (d) values of the weight coefficients | c m | 2 .

Fig. 2
Fig. 2

Evolution of the total intensity | Ψ | 2 of the vector beam consisting of ordinary LG modes A ρ e ρ 2 / 2 + i M ϕ , with q = 0.3 and charges of M = 1 ( A = 0.71 ) and M = 2 ( A = 0.71 ) .

Fig. 3
Fig. 3

Intensity evolution of the vector LG beam with the fractional charges of (a) M u = 1.5 ( A = 1.3 ) and (b) M v = 3.5 ( A = 1.3 ) , and (c) total intensity | Ψ | 2 = | u | 2 + | v | 2 . Here q = 0.3 .

Fig. 4
Fig. 4

Evolution of the total intensity | Ψ | 2 of the vector beam with the fractional charge components M u = 1.5 and M v = 3.5 constructed from (a) two modes in Eq. (4), (b) six modes, and (c) 20 modes. On all plots, q = 0.3 .

Fig. 5
Fig. 5

Intensity cross-section configuration at z = 1.5 for (a) scalar beam with the charge of M = 1.5 and (b) fractional charge of M u = 1.5 component of the vector beam (another component M v = 3.5 ). For both plots, q = 0.07 .

Equations (4)

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2 i k E Z + Δ E + k 2 ( i α k + T ϵ 0 ϵ T ) E = 0.
v T X = α I ρ 0 c p ,
2 i Ψ z + q ( 2 x 2 + 2 y 2 ) Ψ 2 q Ψ x | Ψ | 2 d x = 0.
u M ( ρ , ϕ , z = 0 ) = A m = m min m max c m l p m ( ρ , ϕ , z = 0 ) ,

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