Abstract

A generalized model of a double-wedge phase element containing two side-by-side parallel phase ramps with arbitrary slope angles is proposed. We study the diffracted optical field of a double-wedge element in terms of orbital angular momentum states. Analytical calculations reveal how the radius and position of the illuminating laser beam affect the composition of orbital angular momentum generated by the phase wedges.

© 2007 Optical Society of America

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2005 (3)

2004 (1)

2003 (1)

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

2002 (3)

V. G. Shvedov, Ya. V. Izdebskaya, A. N. Alekseev, and A. V. Volyar, Tech. Phys. Lett. 28, 256 (2002).
[Crossref]

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2002).
[Crossref] [PubMed]

V. N. Gorshkov, A. N. Khoroshun, and M. S. Soskin, Proc. SPIE 4705, 65 (2002).
[Crossref]

2001 (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[Crossref] [PubMed]

1997 (2)

1996 (1)

1995 (1)

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

1994 (1)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[Crossref]

1992 (1)

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

1989 (1)

P. Coullet, L. Gil, and F. Rocca, Opt. Commun. 73, 403 (1989).
[Crossref]

1979 (1)

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 1979).

1974 (1)

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

Alekseev, A. N.

V. G. Shvedov, Ya. V. Izdebskaya, A. N. Alekseev, and A. V. Volyar, Tech. Phys. Lett. 28, 256 (2002).
[Crossref]

Allen, L.

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Lett. 22, 52 (1997).
[Crossref] [PubMed]

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

Barnett, S. M.

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[Crossref]

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

Berry, M. V.

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

Chang, J.-S.

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[Crossref]

Coullet, P.

P. Coullet, L. Gil, and F. Rocca, Opt. Commun. 73, 403 (1989).
[Crossref]

Courtial, J.

Curtis, J. E.

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

Dholakia, K.

Franke-Arnold, S.

Friese, M. E. J.

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

Gahagan, K. T.

Gibson, G.

Gil, L.

P. Coullet, L. Gil, and F. Rocca, Opt. Commun. 73, 403 (1989).
[Crossref]

Gorshkov, V. N.

V. N. Gorshkov, A. N. Khoroshun, and M. S. Soskin, Proc. SPIE 4705, 65 (2002).
[Crossref]

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 1979).

Grier, D. G.

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

He, H.

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

Heckenberg, N. R.

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

Izdebskaya, Y.

Izdebskaya, Ya. V.

V. G. Shvedov, Ya. V. Izdebskaya, A. N. Alekseev, and A. V. Volyar, Tech. Phys. Lett. 28, 256 (2002).
[Crossref]

Jeon, J.-H.

Khoroshun, A. N.

V. N. Gorshkov, A. N. Khoroshun, and M. S. Soskin, Proc. SPIE 4705, 65 (2002).
[Crossref]

Kim, G.-H.

Ko, K.-H.

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[Crossref]

Lee, J.-H.

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[Crossref] [PubMed]

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2002).
[Crossref] [PubMed]

Moon, H.-J.

Nye, J. F.

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

Padgett, M. J.

Pas'ko, V.

Pas'ko, V. A.

M. V. Vasnetsov, V. A. Pas'ko, and M. S. Soskin, New J. Phys. 7, 46 (2005).
[Crossref]

Rocca, F.

P. Coullet, L. Gil, and F. Rocca, Opt. Commun. 73, 403 (1989).
[Crossref]

Rubinsztein-Dunlop, H.

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

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 1979).

Shvedov, V.

Shvedov, V. G.

V. G. Shvedov, Ya. V. Izdebskaya, A. N. Alekseev, and A. V. Volyar, Tech. Phys. Lett. 28, 256 (2002).
[Crossref]

Simpson, N. B.

Soskin, M. S.

M. V. Vasnetsov, V. A. Pas'ko, and M. S. Soskin, New J. Phys. 7, 46 (2005).
[Crossref]

V. N. Gorshkov, A. N. Khoroshun, and M. S. Soskin, Proc. SPIE 4705, 65 (2002).
[Crossref]

Spreeuw, R. J. C.

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

Swartzlander, G. A.

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2002).
[Crossref] [PubMed]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2002).
[Crossref] [PubMed]

Vasnetsov, M.

Vasnetsov, M. V.

M. V. Vasnetsov, V. A. Pas'ko, and M. S. Soskin, New J. Phys. 7, 46 (2005).
[Crossref]

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[Crossref] [PubMed]

Volyar, A.

Volyar, A. V.

V. G. Shvedov, Ya. V. Izdebskaya, A. N. Alekseev, and A. V. Volyar, Tech. Phys. Lett. 28, 256 (2002).
[Crossref]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[Crossref] [PubMed]

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[Crossref]

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

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[Crossref] [PubMed]

Appl. Opt. (1)

Nature (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[Crossref] [PubMed]

New J. Phys. (1)

M. V. Vasnetsov, V. A. Pas'ko, and M. S. Soskin, New J. Phys. 7, 46 (2005).
[Crossref]

Opt. Commun. (2)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[Crossref]

P. Coullet, L. Gil, and F. Rocca, Opt. Commun. 73, 403 (1989).
[Crossref]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. A (1)

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

Phys. Rev. Lett. (3)

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

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

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2002).
[Crossref] [PubMed]

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

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

Proc. SPIE (1)

V. N. Gorshkov, A. N. Khoroshun, and M. S. Soskin, Proc. SPIE 4705, 65 (2002).
[Crossref]

Tech. Phys. Lett. (1)

V. G. Shvedov, Ya. V. Izdebskaya, A. N. Alekseev, and A. V. Volyar, Tech. Phys. Lett. 28, 256 (2002).
[Crossref]

Other (1)

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 1979).

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Figures (3)

Fig. 1
Fig. 1

Weight of the OAM state l as a function of the dimensionless beam radius a. (a) l = 1 when d = ( 2 n + 1 ) π , (b) l = 2 when d = 2 n π .

Fig. 2
Fig. 2

Weight distributions over OAM states ranging from l = 5 to l = 5 . (a) a = 1.68 and d = ( 2 n + 1 ) π , (b) a = 3.27 and d = 2 n π .

Fig. 3
Fig. 3

Far-field intensity distributions produced by phase wedges. The incident laser beam propagation direction is marked by a cross. (a) Single wedge with a = π 2 , (b) double wedge with a = 1.68 , (c) 3D plot of the pattern in (a), (d) 3D plot of the pattern in (b).

Equations (10)

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t ( x , y ) = { exp [ i ( k 1 x + d 1 ) ] , y 0 exp [ i ( k 2 x + d 2 ) ] , y < 0 } ,
t 0 ( x , y ) = exp { i [ 0.5 ( k 1 + k 2 ) x + d 1 ] } .
T ( r , θ ) = { exp ( i k x ) = exp ( i k r cos θ ) , 0 θ < π exp [ i ( k x + d ) ] = exp ( i d ) exp ( i k r cos θ ) , π θ < 2 π } ,
u 0 ( r ) = { 1 , 0 r R 0 , r > R } .
u ( r , θ ) = u 0 ( r ) T ( r , θ ) = l = a l ( r ) exp ( i l θ ) ,
P l = 1 2 π 2 R 2 0 R 0 2 π T ( r , θ ) exp ( i l θ ) d θ 2 r d r .
P l ( a , d ) = { 1 exp ( i d ) 2 2 π 2 a 2 0 a I o 2 ( sgn ( l ) z ; l ) z d z , l odd 1 + exp ( i d ) 2 4 [ J 0 ( a ) 2 + J 1 ( a ) 2 ] , l = 0 1 + exp ( i d ) 2 2 π 2 a 2 0 a I e 2 ( sgn ( l ) z ; l ) z d z , l 0 , l even } ,
I o ( x ; n ) = ( 1 ) n 1 2 π J n ( x ) + 1 x m = 1 n + 1 2 ( 1 ) m 1 ( n m ) ! ( m 1 ) ! 2 n 2 m + 2 [ sin x k = 0 n 2 m + 1 2 ( 1 ) k 1 ( n 2 m 2 k + 1 ) ! 1 x 2 k + cos x k = 0 n 2 m 1 2 ( 1 ) k 1 ( n 2 m 2 k ) ! 1 x 2 k + 1 ] ,
I e ( x ; n ) = ( 1 ) n 2 π J n ( x ) 1 x 2 m = 1 n 2 ( 1 ) m 1 ( n m ) ! ( m 1 ) ! 2 n 2 m + 2 [ sin x k = 0 n 2 m 2 ( 1 ) k 1 ( n 2 m 2 k ) ! 1 x 2 k + cos x k = 0 n 2 m 2 ( 1 ) k + 1 1 ( n 2 m 2 k + 1 ) ! 1 x 2 k 1 ] .
P 1 ( a , π ) = [ J 1 2 ( a ) J 0 ( a ) J 2 ( a ) ] + 4 a 3 π F 3 2 ( 5 4 , 7 4 ; 2 , 5 2 , 5 2 ; a 2 ) + 4 π 2 a 2 [ ln ( 2 a ) c i ( 2 a ) + γ ] ,

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