Abstract

We propose a design for a phase mask for generating an optical vortex with suppressed sidelobes in the focal plane where the radius of the intensity ring is variable. A radial modulation added to conventional phase mask exp(ilθ) projects the light diffracted from different annular zones into a single intensity ring in the focal plane.

© 2006 Optical Society of America

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References

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  1. L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [Crossref] [PubMed]
  2. G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas'ko, S. Barnett, and S. Franke-Arnold, Opt. Express 12, 5448 (2004).
    [Crossref] [PubMed]
  3. Z. Bouchal and R. Celechovsky, New J. Phys. 6, 131 (2004).
    [Crossref]
  4. H. He, M. Friese, N. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
    [Crossref] [PubMed]
  5. J. Curtis and D. Grier, Phys. Rev. Lett. 90, 133901 (2003).
    [Crossref] [PubMed]
  6. J. Lin, X. Yuan, S. Tao, X. Peng, and H. Niu, Opt. Express 13, 3862 (2005).
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  8. K. Gahagan and G. Swartzlander, J. Opt. Soc. Am. B 16, 533 (1999).
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]

2005 (3)

2004 (3)

2003 (1)

J. Curtis and D. Grier, Phys. Rev. Lett. 90, 133901 (2003).
[Crossref] [PubMed]

2000 (1)

J. Courtial and M. Padgett, Opt. Commun. 173, 269 (2000).
[Crossref]

1999 (1)

1998 (1)

1996 (1)

1995 (1)

H. He, M. Friese, N. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[Crossref] [PubMed]

1993 (1)

Z. Jaroszewicz and A. Kolodziejczyk, Opt. Commun. 102, 391 (1993).
[Crossref]

1992 (1)

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[Crossref] [PubMed]

Allen, L.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[Crossref] [PubMed]

Barnett, S.

Beijersbergen, M.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[Crossref] [PubMed]

Bouchal, Z.

Z. Bouchal and R. Celechovsky, New J. Phys. 6, 131 (2004).
[Crossref]

Celechovsky, R.

Z. Bouchal and R. Celechovsky, New J. Phys. 6, 131 (2004).
[Crossref]

Courtial, J.

Curtis, J.

J. Curtis and D. Grier, Phys. Rev. Lett. 90, 133901 (2003).
[Crossref] [PubMed]

Franke-Arnold, S.

Friese, M.

H. He, M. Friese, N. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[Crossref] [PubMed]

Gahagan, K.

Gaskill, J. D.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, 1978).

Gibson, G.

Grier, D.

Gruzberg, I.

Guo, C.

He, H.

H. He, M. Friese, N. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[Crossref] [PubMed]

He, J.

Heckenberg, N.

H. He, M. Friese, N. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[Crossref] [PubMed]

Jaroszewicz, Z.

Z. Jaroszewicz and A. Kolodziejczyk, Opt. Commun. 102, 391 (1993).
[Crossref]

Kolodziejczyk, A.

Z. Jaroszewicz and A. Kolodziejczyk, Opt. Commun. 102, 391 (1993).
[Crossref]

Lin, J.

Liu, X.

Niu, H.

Padgett, M.

Pas'ko, V.

Peng, X.

Ren, X.

Rozas, D.

Rubinsztein-Dunlop, H.

H. He, M. Friese, N. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[Crossref] [PubMed]

Sacks, Z.

Spreeuw, R.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[Crossref] [PubMed]

Sundbeck, S.

Swartzlander, G.

Tao, S.

Vasnetsov, M.

Wang, H.

Woerdman, J.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[Crossref] [PubMed]

Yuan, X.

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (2)

New J. Phys. (1)

Z. Bouchal and R. Celechovsky, New J. Phys. 6, 131 (2004).
[Crossref]

Opt. Commun. (2)

Z. Jaroszewicz and A. Kolodziejczyk, Opt. Commun. 102, 391 (1993).
[Crossref]

J. Courtial and M. Padgett, Opt. Commun. 173, 269 (2000).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. A (1)

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

H. He, M. Friese, N. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[Crossref] [PubMed]

J. Curtis and D. Grier, Phys. Rev. Lett. 90, 133901 (2003).
[Crossref] [PubMed]

Other (1)

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, 1978).

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Figures (4)

Fig. 1
Fig. 1

The 40th Bessel function of the first kind (dashed curve) and amplitude profile (solid curve) created by focusing a helical beam of l = 40 . The horizontal axis denotes a dimensionless variable k R ρ f . The vertical dotted lines indicate the positions of the first two odd roots of the Bessel function.

Fig. 2
Fig. 2

Focal plane intensity distribution of a helical beam of l = 40 with a circular aperture of radius R (dashed curve) and the intensity distribution contributed by an annular zone with inner radius ( x 1 x 3 ) R and outer radius R (solid curve).

Fig. 3
Fig. 3

Intensity distributions in the focal plane: (a) produced by phase mask exp ( i l θ ) , (b) five primary peaks of I 1 I 5 generated by five annular zones and the remaining intensity generated by the central region of phase mask exp ( i l θ ) , (c) produced by phase mask g ( r ) exp ( i l θ ) uniformly illuminated, (d) produced by phase mask g ( r ) exp ( i l θ ) illuminated by a Gaussian beam.

Fig. 4
Fig. 4

Intensity patterns in the focal plane: (a) conventional optical vortex, (b) modified optical vortex.

Equations (7)

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E ( r , θ ) = A ( r ) exp ( i l θ ) ,
E f ( ρ , ϕ ) = k f exp ( i k 2 f ρ 2 ) exp ( i l ϕ ) 0 R J l ( k r ρ f ) r d r ,
A f ( ρ ) = f k ρ 2 0 k ρ R f J l ( u ) u d u .
A f ( ρ ) = f k ρ 2 [ 0 k ρ R 2 f J l ( u ) u d u 0 k ρ R 1 f J l ( u ) u d u ] ,
R 2 = ( x 1 x 3 ) R 1 ,
R i = ( x 1 x 3 ) i R , i = 1 , 2 , .
g ( r ) = { exp ( i 40.9 w r ) q R < r R exp ( i 38.9 w r ) q 2 R < r q R exp ( i 36 w r ) q 3 R < r q 2 R exp ( i 32.3 w r ) q 4 R < r q 3 R exp ( i 23.8 w r ) q 5 R < r q 4 R 1 0 r q 5 R } ,

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