Abstract

We make optical vortices of different topological charge and diffract them through a quadratic phase mask using the same spatial light modulator. This phase mask shows the diffraction in which the positive diffracted order has different dynamics than the negative diffracted order. The diffraction pattern and its orientation depend on the charge of the vortex as well as its sign. The experimental results are verified with exact analytical results.

© 2012 Optical Society of America

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References

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2011 (6)

2010 (2)

J. Hickmann, E. Fonseca, W. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

G. Berkhout, M. Lavery, J. Courtial, M. Beijersbergen, and M. Padgett, Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

2009 (1)

2008 (2)

G. Berkhout and M. Beijersbergen, Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef]

L. Janicijevic and S. Topuzoski, J. Opt. Soc. Am. A 25, 2659 (2008).
[CrossRef]

2007 (1)

G. Molina-Terriza, J. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

2004 (2)

1999 (1)

1993 (1)

M. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

Allen, L.

M. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

L. Allen, M. J. Padgett, and M. Babiker, in Progress in Optics, Vol. 39 (Elsevier, 1999), p. 291.

Anderson, Ma.

Babiker, M.

L. Allen, M. J. Padgett, and M. Babiker, in Progress in Optics, Vol. 39 (Elsevier, 1999), p. 291.

Banerji, J.

Barnett, S.

Baumgartl, J.

Beijersbergen, M.

G. Berkhout, M. Lavery, M. Padgett, and M. Beijersbergen, Opt. Lett. 36, 1863 (2011).
[CrossRef]

G. Berkhout, M. Lavery, J. Courtial, M. Beijersbergen, and M. Padgett, Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

G. Berkhout and M. Beijersbergen, Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef]

M. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

Bekshaev, A.

A. Bekshaev, M. Soskin, and M. Vasnetsov, Opt. Commun. 241, 237 (2004).
[CrossRef]

Berkhout, G.

G. Berkhout, M. Lavery, M. Padgett, and M. Beijersbergen, Opt. Lett. 36, 1863 (2011).
[CrossRef]

G. Berkhout, M. Lavery, J. Courtial, M. Beijersbergen, and M. Padgett, Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

G. Berkhout and M. Beijersbergen, Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef]

Blanchard, P. M.

Chávez-Cerda, S.

J. Hickmann, E. Fonseca, W. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

Courtial, J.

G. Berkhout, M. Lavery, J. Courtial, M. Beijersbergen, and M. Padgett, Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

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

de Araujo, L.

Dholakia, K.

Fonseca, E.

J. Hickmann, E. Fonseca, W. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

Franke-Arnold, S.

Gibson, G.

Goodman, J.

J. Goodman, Introduction to Fourier Optics (Roberts & Company, 2004).

Greenaway, A. H.

Guo, C.

Han, Y.

Hickmann, J.

J. Hickmann, E. Fonseca, W. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

Janicijevic, L.

Kumar, A.

Lavery, M.

G. Berkhout, M. Lavery, M. Padgett, and M. Beijersbergen, Opt. Lett. 36, 1863 (2011).
[CrossRef]

G. Berkhout, M. Lavery, J. Courtial, M. Beijersbergen, and M. Padgett, Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

Lu, L.

Molina-Terriza, G.

G. Molina-Terriza, J. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Mourka, A.

Padgett, M.

Padgett, M. J.

L. Allen, M. J. Padgett, and M. Babiker, in Progress in Optics, Vol. 39 (Elsevier, 1999), p. 291.

Pas’ko, V.

Prabhakar, S.

Shanor, C.

Singh, R. P.

Soares, W.

J. Hickmann, E. Fonseca, W. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

Soskin, M.

A. Bekshaev, M. Soskin, and M. Vasnetsov, Opt. Commun. 241, 237 (2004).
[CrossRef]

Topuzoski, S.

Torner, L.

G. Molina-Terriza, J. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Torres, J.

G. Molina-Terriza, J. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Vaity, P.

van der Veen, H. E. L. O.

M. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

Vasnetsov, M.

Wang, H.

Woerdman, J. P.

M. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

Wright, E.

Zhao, G.

Appl. Opt. (1)

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

Nat. Phys. (1)

G. Molina-Terriza, J. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Opt. Commun. (2)

A. Bekshaev, M. Soskin, and M. Vasnetsov, Opt. Commun. 241, 237 (2004).
[CrossRef]

M. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

Opt. Express (2)

Opt. Lett. (6)

Phys. Rev. Lett. (3)

G. Berkhout and M. Beijersbergen, Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef]

G. Berkhout, M. Lavery, J. Courtial, M. Beijersbergen, and M. Padgett, Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

J. Hickmann, E. Fonseca, W. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

Other (2)

L. Allen, M. J. Padgett, and M. Babiker, in Progress in Optics, Vol. 39 (Elsevier, 1999), p. 291.

J. Goodman, Introduction to Fourier Optics (Roberts & Company, 2004).

Supplementary Material (4)

» Media 1: MOV (26247 KB)     
» Media 2: MOV (47054 KB)     
» Media 3: MOV (12644 KB)     
» Media 4: MOV (23116 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

Experimental setup: BS, beamsplitter; SLM, spatial light modulator; M1, M2, mirrors; CCD, camera; QPM, quadratic phase mask; FG, fork grating.

Fig. 2.
Fig. 2.

Experimental intensity profiles of negative (first row) (Media 1) and positive (second row) (Media 2) diffraction order at different distance z.

Fig. 3.
Fig. 3.

Theoretical intensity profiles of negative (first row) (Media 3) and positive (second row) (Media 4) diffraction order at different distances of z.

Fig. 4.
Fig. 4.

Experimental intensity profiles of positively (first row) and negatively (second row) charged vortices at distance z=110cm.

Fig. 5.
Fig. 5.

Theoretical intensity profiles corresponding to experimental intensity profiles in Fig. 5.

Equations (6)

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E(x1,y1)=(x1+sgniy1wo)mexp[(x12+y12)wo2],
t(y1)=exp[iM2cos[4π3wf2(y1yo)2]],
Et(x1,y1)=t(y1)E(x1,y1).
E(x2,y2)=ki2πLexp[ik2L(2L2+x22+y22)]Et(x1,y1)exp[ik2L((x12+y12)2(x1x2+y1y2))]dx1dy1,
E(x2,y2)=k2L(2wo)mq=iqJq(M/2)exp[i4πqyo23wf2]exp[ik2(2L+x22Rx+y22L(y2+byo)2Ry)]exp[(x22wx2+(y2+byo)2wy2)]n=0mm!sgnn(i)mn+1n!(mn)!dxmn+1dyn+1Hmn[kdxx22L]Hn[kdy(y2+byo)2L],
Rx=L+zr2L,Ry=L(1+b)[(1+b)2+(Lzr)2],wx=wo1+(Lzr)2,wy=wo(1+b)2+(Lzr)2,dx=wo1izrL,dy=wo1i(1+b)zrL,zr=kwo22,b=8πLq3kwf2.

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