Abstract

We consider theoretically and experimentally an array of singular beams whose axes lie on the surface of a hyperboloid of revolution. We show that such a singular array can carry a very high orbital angular momentum. Experimental results demonstrate a way of generating such singular arrays.

© 2006 Optical Society of America

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References

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  1. V. Vasnetsov and K. Staliunas, eds., Optical Vortices, Vol. 228 of Horizons of World Physics (Nova Science, 1999).
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    [CrossRef]
  3. J. Courtial, K. Dholakia, L. Allen, and M. Padgett, Opt. Commun. 144, 210 (1997).
    [CrossRef]
  4. M. Vasnetsov, V. Pas'ko, and M. Soskin, New J. Phys. 7, 2 (2005).
    [CrossRef]
  5. I. Maleev and G. Swartzlander, J. Opt. Soc. Am. B 20, 1169 (2003).
    [CrossRef]
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  7. M. Berry, in Proc. SPIE 3487, 6 (1998).
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    [CrossRef] [PubMed]
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2006

J. Gore, Z. Bryant, M. D. Stone, M. Nöllmann, N. R. Cozzarelli, and C. Bustamante, Nature 439, 100 (2006).
[CrossRef] [PubMed]

2005

2003

2002

A. Desyatnikov and Yu. Kivshar, J. Opt. A, Pure Appl. Opt. 4, S58 (2002).

1997

J. Courtial, K. Dholakia, L. Allen, and M. Padgett, Opt. Commun. 144, 210 (1997).
[CrossRef]

Allen, L.

J. Courtial, K. Dholakia, L. Allen, and M. Padgett, Opt. Commun. 144, 210 (1997).
[CrossRef]

L. Allen, M. Paddget, and B. Babiker, in Progress in Optics, E.Wolf, ed. (Elsevier, 1999), Vol. 39, pp. 291-372.
[CrossRef]

Babiker, B.

L. Allen, M. Paddget, and B. Babiker, in Progress in Optics, E.Wolf, ed. (Elsevier, 1999), Vol. 39, pp. 291-372.
[CrossRef]

Berry, M.

M. Berry, in Proc. SPIE 3487, 6 (1998).

Bryant, Z.

J. Gore, Z. Bryant, M. D. Stone, M. Nöllmann, N. R. Cozzarelli, and C. Bustamante, Nature 439, 100 (2006).
[CrossRef] [PubMed]

Bustamante, C.

J. Gore, Z. Bryant, M. D. Stone, M. Nöllmann, N. R. Cozzarelli, and C. Bustamante, Nature 439, 100 (2006).
[CrossRef] [PubMed]

Courtial, J.

J. Courtial, K. Dholakia, L. Allen, and M. Padgett, Opt. Commun. 144, 210 (1997).
[CrossRef]

Cozzarelli, N. R.

J. Gore, Z. Bryant, M. D. Stone, M. Nöllmann, N. R. Cozzarelli, and C. Bustamante, Nature 439, 100 (2006).
[CrossRef] [PubMed]

Desyatnikov, A.

A. Desyatnikov and Yu. Kivshar, J. Opt. A, Pure Appl. Opt. 4, S58 (2002).

Dholakia, K.

J. Courtial, K. Dholakia, L. Allen, and M. Padgett, Opt. Commun. 144, 210 (1997).
[CrossRef]

Gore, J.

J. Gore, Z. Bryant, M. D. Stone, M. Nöllmann, N. R. Cozzarelli, and C. Bustamante, Nature 439, 100 (2006).
[CrossRef] [PubMed]

Izdebskaya, Ya.

Kivshar, Yu.

A. Desyatnikov and Yu. Kivshar, J. Opt. A, Pure Appl. Opt. 4, S58 (2002).

Maleev, I.

Nöllmann, M.

J. Gore, Z. Bryant, M. D. Stone, M. Nöllmann, N. R. Cozzarelli, and C. Bustamante, Nature 439, 100 (2006).
[CrossRef] [PubMed]

Paddget, M.

L. Allen, M. Paddget, and B. Babiker, in Progress in Optics, E.Wolf, ed. (Elsevier, 1999), Vol. 39, pp. 291-372.
[CrossRef]

Padgett, M.

J. Courtial, K. Dholakia, L. Allen, and M. Padgett, Opt. Commun. 144, 210 (1997).
[CrossRef]

Pas'ko, V.

M. Vasnetsov, V. Pas'ko, and M. Soskin, New J. Phys. 7, 2 (2005).
[CrossRef]

Roux, F.

F. Roux, Opt. Commun. 22, 31 (2003).
[CrossRef]

Shvedov, V.

Soskin, M.

M. Vasnetsov, V. Pas'ko, and M. Soskin, New J. Phys. 7, 2 (2005).
[CrossRef]

Staliunas, K.

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

Stone, M. D.

J. Gore, Z. Bryant, M. D. Stone, M. Nöllmann, N. R. Cozzarelli, and C. Bustamante, Nature 439, 100 (2006).
[CrossRef] [PubMed]

Swartzlander, G.

Vasnetsov, M.

M. Vasnetsov, V. Pas'ko, and M. Soskin, New J. Phys. 7, 2 (2005).
[CrossRef]

Vasnetsov, V.

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

Volyar, A.

J. Opt. A, Pure Appl. Opt.

A. Desyatnikov and Yu. Kivshar, J. Opt. A, Pure Appl. Opt. 4, S58 (2002).

J. Opt. Soc. Am. B

Nature

J. Gore, Z. Bryant, M. D. Stone, M. Nöllmann, N. R. Cozzarelli, and C. Bustamante, Nature 439, 100 (2006).
[CrossRef] [PubMed]

New J. Phys.

M. Vasnetsov, V. Pas'ko, and M. Soskin, New J. Phys. 7, 2 (2005).
[CrossRef]

Opt. Commun.

J. Courtial, K. Dholakia, L. Allen, and M. Padgett, Opt. Commun. 144, 210 (1997).
[CrossRef]

F. Roux, Opt. Commun. 22, 31 (2003).
[CrossRef]

Opt. Lett.

Other

M. Berry, in Proc. SPIE 3487, 6 (1998).

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

L. Allen, M. Paddget, and B. Babiker, in Progress in Optics, E.Wolf, ed. (Elsevier, 1999), Vol. 39, pp. 291-372.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Sketch of the array with three beams lodged on the surface of a hyperboloid of revolution in space (a) and (b) their projection on the plane z = 0 .

Fig. 2
Fig. 2

Intensity distribution in different states { N , l , M } of the array: I, z = 0 ; II, III, z = 2 m ; I, III, theory; II, experiment.

Fig. 3
Fig. 3

Distinguishing curves: (a), (b) η ( R ) ; (c), (d) η ( α ¯ ) .

Equations (11)

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x n = r cos ( φ φ n ) r 0 , y n = r sin ( φ φ n ) α z ,
z n = α r sin ( φ φ n ) + z .
r n 2 = x n 2 + y n 2 = r 2 + r 0 2 2 r r 0 cos ϑ n 2 α r z sin ϑ n ,
Ψ n = 1 Z n [ r n exp ( i σ ϑ n ) C Z n ] M exp ( i k r n 2 2 Z n ) exp ( i k z n ) ,
Ψ = n = 1 N Ψ n exp ( i Δ n ) .
Ψ = N Ψ 0 m = exp [ i ( m N l ) φ ] s = 0 M ( M s ) C M s r s [ m N ( l + σ s ) ] 2 I m N ( l + σ s ) ( ξ r ) ,
L z = A 1 s = 0 ν = 0 M ( M s ) ( M ν ) R 2 M ( s + ν ) m = 2 N m ( 2 l + σ s + σ ν ) 2 ( m N l ) J ( m , s , ν , ξ 2 ) ,
L z = π N 2 exp ( r 0 2 ρ 2 + ξ 2 2 ) ρ 2 m = ( m N l ) m N 1 I m N 1 ( ξ 2 2 ) .
η = L z Ψ Ψ = 1 K j = 1 K [ l N m j ( s j , ν j ) ] ,
M ( s j + ν j ) + 2 m j N l σ s j + 2 m j N l σ ν t = min
η = σ M + 2 α ¯ R = σ M + k r 0 α .

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