Abstract

We study square and triangular optical lattice formation using a diffraction technique with light-possessing orbital angular momentum (OAM). We demonstrate that it is possible to use Fraunhofer diffraction of light by a square aperture to unveil OAM about two times bigger than would be possible with a triangular aperture. We notice that the pattern remains truncated until a topological charge (TC) equal to 20 with good precision. Even though a square pattern cannot be used to determine the TC sign, it is possible to measure high order of the modulus and sign of the TC up to 20, combining patterns of the triangular and square apertures.

© 2014 Optical Society of America

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    [CrossRef]
  2. J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2013 (3)

L. Veissier, A. Nicolas, L. Giner, D. Maxein, A. S. Sheremet, E. Giacobino, and J. Laurat, Opt. Lett. 38, 712 (2013).
[CrossRef]

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, Science 340, 1545 (2013).
[CrossRef]

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, Nat. Commun. 4, 2432 (2013).
[CrossRef]

2011 (3)

2010 (2)

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

A. Kumar, P. Vaity, and R. P. Singh, Opt. Commun. 283, 4141 (2010).
[CrossRef]

2009 (1)

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, Opt. Laser Eng. 47, 123 (2009).

2008 (1)

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

2007 (1)

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

2006 (1)

2003 (1)

D. G. Grier, Nature 424, 810 (2003).
[CrossRef]

2002 (1)

D. P. Caetano, M. P. Almeida, P. H. S. Ribeiro, J. A. O. Huguenin, B. C. dos Santos, and A. Z. Khoury, Phys. Rev. A 66, 041801(R) (2002).
[CrossRef]

2001 (1)

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

1999 (1)

J. W. R. Tabosa and D. V. Petrov, Phys. Rev. Lett. 83, 4967 (1999).
[CrossRef]

1997 (1)

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997).
[CrossRef]

1992 (1)

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

1987 (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

1986 (1)

1985 (1)

1971 (1)

Alfano, R. R.

Allen, L.

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997).
[CrossRef]

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

Almeida, M. P.

D. P. Caetano, M. P. Almeida, P. H. S. Ribeiro, J. A. O. Huguenin, B. C. dos Santos, and A. Z. Khoury, Phys. Rev. A 66, 041801(R) (2002).
[CrossRef]

Aolita, L.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, Nat. Commun. 4, 2432 (2013).
[CrossRef]

Beijersbergen, M. W.

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

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

Berkhout, G. C. G.

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

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, Science 340, 1545 (2013).
[CrossRef]

Caetano, D. P.

D. P. Caetano, M. P. Almeida, P. H. S. Ribeiro, J. A. O. Huguenin, B. C. dos Santos, and A. Z. Khoury, Phys. Rev. A 66, 041801(R) (2002).
[CrossRef]

Chavez-Cerda, S.

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

Condell, W. J.

Courtial, J.

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997).
[CrossRef]

D’Ambrosio, V.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, Nat. Commun. 4, 2432 (2013).
[CrossRef]

Del Re, L.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, Nat. Commun. 4, 2432 (2013).
[CrossRef]

Dholakia, K.

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997).
[CrossRef]

dos Santos, B. C.

D. P. Caetano, M. P. Almeida, P. H. S. Ribeiro, J. A. O. Huguenin, B. C. dos Santos, and A. Z. Khoury, Phys. Rev. A 66, 041801(R) (2002).
[CrossRef]

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Ferreira, Q. S.

Fonseca, E. J. S.

Q. S. Ferreira, A. J. Jesus-Silva, E. J. S. Fonseca, and J. M. Hickmann, Opt. Lett. 36, 3106 (2011).
[CrossRef]

P. H. F. Mesquita, A. J. Jesus-Silva, E. J. S. Fonseca, and J. M. Hickmann, Opt. Express 19, 20616 (2011).
[CrossRef]

J. M. Hickmann, E. J. S. Fonseca, and A. J. Jesus-Silva, Europhys. Lett. 96, 64006 (2011).
[CrossRef]

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

Ghai, D. P.

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, Opt. Laser Eng. 47, 123 (2009).

Giacobino, E.

Giner, L.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Grier, D. G.

D. G. Grier, Nature 424, 810 (2003).
[CrossRef]

Hickmann, J. M.

Q. S. Ferreira, A. J. Jesus-Silva, E. J. S. Fonseca, and J. M. Hickmann, Opt. Lett. 36, 3106 (2011).
[CrossRef]

J. M. Hickmann, E. J. S. Fonseca, and A. J. Jesus-Silva, Europhys. Lett. 96, 64006 (2011).
[CrossRef]

P. H. F. Mesquita, A. J. Jesus-Silva, E. J. S. Fonseca, and J. M. Hickmann, Opt. Express 19, 20616 (2011).
[CrossRef]

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

Huang, H.

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, Science 340, 1545 (2013).
[CrossRef]

Huguenin, J. A. O.

D. P. Caetano, M. P. Almeida, P. H. S. Ribeiro, J. A. O. Huguenin, B. C. dos Santos, and A. Z. Khoury, Phys. Rev. A 66, 041801(R) (2002).
[CrossRef]

Jesus-Silva, A. J.

Jones, A. L.

Khoury, A. Z.

D. P. Caetano, M. P. Almeida, P. H. S. Ribeiro, J. A. O. Huguenin, B. C. dos Santos, and A. Z. Khoury, Phys. Rev. A 66, 041801(R) (2002).
[CrossRef]

Kirk, J. P.

Kristensen, P.

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, Science 340, 1545 (2013).
[CrossRef]

Kumar, A.

A. Kumar, P. Vaity, and R. P. Singh, Opt. Commun. 283, 4141 (2010).
[CrossRef]

Kwek, L. C.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, Nat. Commun. 4, 2432 (2013).
[CrossRef]

Laurat, J.

Li, Y.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, Nat. Commun. 4, 2432 (2013).
[CrossRef]

Mair, A.

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

Marrucci, L.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, Nat. Commun. 4, 2432 (2013).
[CrossRef]

Maxein, D.

Mesquita, P. H. F.

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Molina-Terriza, G.

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

Nicolas, A.

Padgett, M. J.

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997).
[CrossRef]

Petrov, D. V.

J. W. R. Tabosa and D. V. Petrov, Phys. Rev. Lett. 83, 4967 (1999).
[CrossRef]

Ramachandran, S.

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, Science 340, 1545 (2013).
[CrossRef]

Ren, Y. X.

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, Science 340, 1545 (2013).
[CrossRef]

Ribeiro, P. H. S.

D. P. Caetano, M. P. Almeida, P. H. S. Ribeiro, J. A. O. Huguenin, B. C. dos Santos, and A. Z. Khoury, Phys. Rev. A 66, 041801(R) (2002).
[CrossRef]

Sciarrino, F.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, Nat. Commun. 4, 2432 (2013).
[CrossRef]

Senthilkumaran, P.

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, Opt. Laser Eng. 47, 123 (2009).

Sheremet, A. S.

Singh, R. P.

A. Kumar, P. Vaity, and R. P. Singh, Opt. Commun. 283, 4141 (2010).
[CrossRef]

Sirohi, R. S.

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, Opt. Laser Eng. 47, 123 (2009).

Slussarenko, S.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, Nat. Commun. 4, 2432 (2013).
[CrossRef]

Soares, W. C.

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

Spagnolo, N.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, Nat. Commun. 4, 2432 (2013).
[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]

Sztul, H. I.

Tabosa, J. W. R.

J. W. R. Tabosa and D. V. Petrov, Phys. Rev. Lett. 83, 4967 (1999).
[CrossRef]

Torner, L.

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

Torres, J. P.

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

Tur, M.

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, Science 340, 1545 (2013).
[CrossRef]

Vaity, P.

A. Kumar, P. Vaity, and R. P. Singh, Opt. Commun. 283, 4141 (2010).
[CrossRef]

Vaziri, A.

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

Veissier, L.

Walborn, S. P.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, Nat. Commun. 4, 2432 (2013).
[CrossRef]

Weihs, G.

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

Willner, A. E.

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, Science 340, 1545 (2013).
[CrossRef]

Woerdman, J. P.

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

Yue, Y.

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, Science 340, 1545 (2013).
[CrossRef]

Zauderer, E.

Zeilinger, A.

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

Europhys. Lett. (1)

J. M. Hickmann, E. J. S. Fonseca, and A. J. Jesus-Silva, Europhys. Lett. 96, 64006 (2011).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Nat. Commun. (1)

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, Nat. Commun. 4, 2432 (2013).
[CrossRef]

Nat. Phys. (1)

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

Nature (2)

D. G. Grier, Nature 424, 810 (2003).
[CrossRef]

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

Opt. Commun. (1)

A. Kumar, P. Vaity, and R. P. Singh, Opt. Commun. 283, 4141 (2010).
[CrossRef]

Opt. Express (1)

Opt. Laser Eng. (1)

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, Opt. Laser Eng. 47, 123 (2009).

Opt. Lett. (3)

Phys. Rev. A (3)

D. P. Caetano, M. P. Almeida, P. H. S. Ribeiro, J. A. O. Huguenin, B. C. dos Santos, and A. Z. Khoury, Phys. Rev. A 66, 041801(R) (2002).
[CrossRef]

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

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997).
[CrossRef]

Phys. Rev. Lett. (4)

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

J. W. R. Tabosa and D. V. Petrov, Phys. Rev. Lett. 83, 4967 (1999).
[CrossRef]

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

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

Science (1)

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, Science 340, 1545 (2013).
[CrossRef]

Other (1)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

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Figures (5)

Fig. 1.
Fig. 1.

Experimental setup: A is an aperture (triangular or square), li are lenses, and SLM is the spatial light modulator.

Fig. 2.
Fig. 2.

Diffraction patterns corresponding to the numerical results of Eq. (2) for square and triangular apertures for m=18, 19, and 20.

Fig. 3.
Fig. 3.

Diffraction patterns contour plots for a square aperture (left column) and a triangular aperture (right column) shown in white. We also present colorful contour plots for single edges diffraction patterns superimposed in the same figure. The TC for (c) to (d) is m=0 and for (e) to (f) is m=4.

Fig. 4.
Fig. 4.

Diffraction patterns contour plots for (a) square aperture and (b) triangular aperture shown in white. We also present colorful contour plots for single edges diffraction patterns superimposed in the same figure. The TC is m=20 for both cases.

Fig. 5.
Fig. 5.

Experimental results to the Fraunhofer diffraction pattern by a square (top) and triangular apertures (bottom).

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

Em(ρ,ϕ)=Aρmexp(imϕ),
Ef(k⃗)=+τ(r⃗)Ei(r⃗)eik⃗r⃗dr⃗.
E±|m|(kx,ky)=Aa2+a2a2+a2(x±iy)|m|exp[i(kxx+kyy)]dxdy,
Em(kx,ky)=A(ikxky)ma2+a2a2+a2exp[i(kxx+kyy)]dxdy=A(ikxky)m2sin(akx/2)kx2sin(aky/2)ky,

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