Abstract

We report a new effect in which the diffraction from a partially blocked angular phase pattern occupying half of the input plane produces a partial vortex output pattern that is rotated by 90° compared with the input. The energy is sent into a different quadrant of the output plane from the input plane. The rotation direction depends on whether the angular phase pattern is clockwise or counterclockwise. When we combine clockwise and counterclockwise angular phase patterns on separate horizontal halves of the input plane, we create an interference effect in one half of the output plane, while the other half remains dark.

© 2005 Optical Society of America

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References

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  1. M. Mansuripur and E. M. Wright, Opt. Photon. News 10(2), 40 (1999).
    [CrossRef]
  2. J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
    [CrossRef]
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    [CrossRef] [PubMed]
  4. H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Mod. Opt. 42, 217 (1995).
    [CrossRef]
  5. J. A. Davis, L. L. Haavig, and D. M. Cottrell, Appl. Opt. 36, 2376 (1997).
    [CrossRef] [PubMed]
  6. J. A. Davis, D. E. McNamara, and D. M. Cottrell, Opt. Lett. 25, 99 (2000).
    [CrossRef]
  7. J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, Opt. Eng. 38, 1051 (1999).
    [CrossRef]
  8. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, 1978), Chap. 7.
  9. J. A. Davis, E. Carcole, and D. M. CottrellAppl. Opt. 35, 599 (1996).
    [CrossRef] [PubMed]

2004 (1)

2000 (1)

1999 (2)

M. Mansuripur and E. M. Wright, Opt. Photon. News 10(2), 40 (1999).
[CrossRef]

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, Opt. Eng. 38, 1051 (1999).
[CrossRef]

1997 (1)

1996 (1)

1995 (1)

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Mod. Opt. 42, 217 (1995).
[CrossRef]

1974 (1)

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Amako, J.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, Opt. Eng. 38, 1051 (1999).
[CrossRef]

Berry, M. V.

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Carcole, E.

Cottrell, D. M.

Crabtree, K.

Davis, J. A.

Gaskill, J. D.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, 1978), Chap. 7.

Haavig, L. L.

He, H.

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Mod. Opt. 42, 217 (1995).
[CrossRef]

Heckenberg, N. R.

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Mod. Opt. 42, 217 (1995).
[CrossRef]

Mansuripur, M.

M. Mansuripur and E. M. Wright, Opt. Photon. News 10(2), 40 (1999).
[CrossRef]

McNamara, D. E.

Moreno, I.

Nye, J. F.

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Rubinsztein-Dunlop, H.

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Mod. Opt. 42, 217 (1995).
[CrossRef]

Sonehara, T.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, Opt. Eng. 38, 1051 (1999).
[CrossRef]

Tsai, P.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, Opt. Eng. 38, 1051 (1999).
[CrossRef]

Wright, E. M.

M. Mansuripur and E. M. Wright, Opt. Photon. News 10(2), 40 (1999).
[CrossRef]

Appl. Opt. (3)

J. Mod. Opt. (1)

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Mod. Opt. 42, 217 (1995).
[CrossRef]

Opt. Eng. (1)

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, Opt. Eng. 38, 1051 (1999).
[CrossRef]

Opt. Lett. (1)

Opt. Photon. News (1)

M. Mansuripur and E. M. Wright, Opt. Photon. News 10(2), 40 (1999).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Other (1)

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, 1978), Chap. 7.

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Figures (3)

Fig. 1
Fig. 1

(a) Vortex-producing lens with counterclockwise angular phase m = 12 , (b) output intensity; (c) lens with counterclockwise angular phase m = 12 in right half, (d) output intensity; (e) lens with clockwise angular phase m = 12 in left half, (f) output intensity; (g) lens with clockwise angular phase m = 12 in right half, (h) output intensity.

Fig. 2
Fig. 2

Computer simulations showing (a) real and (b) imaginary output electric fields for the first convolution term and (c) real and (d) imaginary output electric fields for the second convolution term in Eq. (4).

Fig. 3
Fig. 3

(a) Vortex-producing lens with counterclockwise angular phase in the right half and clockwise angular phase in the left half, where m = 12 ; (b) experimental output intensity; (c) lens with counterclockwise angular phase in the right half subtracted from clockwise angular phase in the left half, where m = 12 ; (d) experimental output intensity.

Equations (4)

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V m ( ρ , ϕ ) = exp ( i m ϕ ) .
Z m ( ρ , ϕ , f ) = exp ( i m ϕ ) exp ( i π ρ 2 λ f ) .
f ( x ) = step ( x ) exp ( i m ϕ ) = [ 1 2 + 1 2 sgn ( x ) ] [ exp ( i m ϕ ) ] .
F ( u ) = 1 2 I [ exp ( i m ϕ ) ] + 1 i 2 π u I [ exp ( i m ϕ ) ] .

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