Abstract

We study the Fraunhofer diffraction problem while taking into account the orbital angular momentum of light. In this case, the phase singularity of the light beam is incident on the slit in two different cases: in one, it is incident slightly above the slit, and in the other it is centered on the slit. We observed that the symmetry and the fringe formation in the interference pattern strongly depend on the amount of orbital angular momentum and the slit position in relation to the beam.

© 2011 Optical Society of America

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    [CrossRef]
  2. J. P. Torres, Y. Deyanova, L. Torner, and G. Molina-Terriza, Phys. Rev. A 67, 052313 (2003).
    [CrossRef]
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    [CrossRef] [PubMed]
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  8. M. Granata, C. Buy, R. Ward, and M. Barsuglia, Phys. Rev. Lett. 105, 231102 (2010).
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    [CrossRef]
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    [CrossRef] [PubMed]
  11. N. Matsumoto, T. Ando, T. Inoue, Y. Ohtake, N. Fukuchi, and T. Hara, J. Opt. Soc. Am. A 25, 1642 (2008).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  17. D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, Opt. Lasers Eng. 47, 123 (2009).
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  18. H. I. Sztul and R. R. Alfano, Opt. Lett. 31, 999 (2006).
    [CrossRef] [PubMed]
  19. A. Kumar, P. Vaity, and R. P. Singh, Opt. Commun. 283, 4141 (2010).
    [CrossRef]
  20. B. Jack, M. J. Padgett, and S. Franke-Arnold, New J. Phys. 10, 103013 (2008).
    [CrossRef]
  21. V. Arrizon, U. Ruiz, R. Carrada, and L. A. Gonzalez, J. Opt. Soc. Am. A 24, 3500 (2007).
    [CrossRef]
  22. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley Interscience, 2007).

2010

S. Straupe and S. Kulik, Nat. Photonics 4, 585 (2010).
[CrossRef]

M. Granata, C. Buy, R. Ward, and M. Barsuglia, Phys. Rev. Lett. 105, 231102 (2010).
[CrossRef]

P. Fulda, K. Kokeyama, S. Chelkowski, and A. Freise, Phys. Rev. D 82, 012002 (2010).
[CrossRef]

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

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

2009

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, Opt. Lasers Eng. 47, 123 (2009).
[CrossRef]

G. C. G. Berkhout and M. W. Beijersbergen, J. Opt. A 11, 094021 (2009).
[CrossRef]

V. Arrizon, D. Sanchez-de-la-Llave, U. Ruiz, and G. Mendez, Opt. Lett. 34, 1456 (2009).
[CrossRef] [PubMed]

C. S. Guo, S. J. Yue, and G. X. Wei, Appl. Phys. Lett. 94, 231104 (2009).
[CrossRef]

2008

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

N. Matsumoto, T. Ando, T. Inoue, Y. Ohtake, N. Fukuchi, and T. Hara, J. Opt. Soc. Am. A 25, 1642 (2008).
[CrossRef]

B. Jack, M. J. Padgett, and S. Franke-Arnold, New J. Phys. 10, 103013 (2008).
[CrossRef]

2007

V. Arrizon, U. Ruiz, R. Carrada, and L. A. Gonzalez, J. Opt. Soc. Am. A 24, 3500 (2007).
[CrossRef]

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley Interscience, 2007).

2006

2005

2004

2003

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

J. P. Torres, Y. Deyanova, L. Torner, and G. Molina-Terriza, Phys. Rev. A 67, 052313 (2003).
[CrossRef]

2001

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2001).
[CrossRef]

1992

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

Alfano, R. R.

Allen, L.

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

Ando, T.

Arrizon, V.

Barnett, S. M.

Barsuglia, M.

M. Granata, C. Buy, R. Ward, and M. Barsuglia, Phys. Rev. Lett. 105, 231102 (2010).
[CrossRef]

Beijersbergen, M. W.

G. C. G. Berkhout and M. W. Beijersbergen, J. Opt. A 11, 094021 (2009).
[CrossRef]

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

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

Berkhout, G. C. G.

G. C. G. Berkhout and M. W. Beijersbergen, J. Opt. A 11, 094021 (2009).
[CrossRef]

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

Buy, C.

M. Granata, C. Buy, R. Ward, and M. Barsuglia, Phys. Rev. Lett. 105, 231102 (2010).
[CrossRef]

Carrada, R.

Chavez-Cerda, S.

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

Chelkowski, S.

P. Fulda, K. Kokeyama, S. Chelkowski, and A. Freise, Phys. Rev. D 82, 012002 (2010).
[CrossRef]

Courtial, J.

Deyanova, Y.

J. P. Torres, Y. Deyanova, L. Torner, and G. Molina-Terriza, Phys. Rev. A 67, 052313 (2003).
[CrossRef]

Fonseca, E. J. S.

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

Foo, G.

Franke-Arnold, S.

Freise, A.

P. Fulda, K. Kokeyama, S. Chelkowski, and A. Freise, Phys. Rev. D 82, 012002 (2010).
[CrossRef]

Fukuchi, N.

Fulda, P.

P. Fulda, K. Kokeyama, S. Chelkowski, and A. Freise, Phys. Rev. D 82, 012002 (2010).
[CrossRef]

Ghai, D. P.

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, Opt. Lasers Eng. 47, 123 (2009).
[CrossRef]

Gibson, G.

Gonzalez, L. A.

Granata, M.

M. Granata, C. Buy, R. Ward, and M. Barsuglia, Phys. Rev. Lett. 105, 231102 (2010).
[CrossRef]

Grier, D. G.

Guo, C. S.

C. S. Guo, S. J. Yue, and G. X. Wei, Appl. Phys. Lett. 94, 231104 (2009).
[CrossRef]

Hara, T.

Hickmann, J. M.

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

Inoue, T.

Jack, B.

B. Jack, M. J. Padgett, and S. Franke-Arnold, New J. Phys. 10, 103013 (2008).
[CrossRef]

Kokeyama, K.

P. Fulda, K. Kokeyama, S. Chelkowski, and A. Freise, Phys. Rev. D 82, 012002 (2010).
[CrossRef]

Kulik, S.

S. Straupe and S. Kulik, Nat. Photonics 4, 585 (2010).
[CrossRef]

Kumar, A.

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

Ladavac, K.

Matsumoto, N.

Mendez, G.

Molina-Terriza, G.

J. P. Torres, Y. Deyanova, L. Torner, and G. Molina-Terriza, Phys. Rev. A 67, 052313 (2003).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2001).
[CrossRef]

Ohtake, Y.

Padgett, M. J.

Palacios, D. M.

Pas’ko, V.

Ruiz, U.

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley Interscience, 2007).

Sanchez-de-la-Llave, D.

Senthilkumaran, P.

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, Opt. Lasers Eng. 47, 123 (2009).
[CrossRef]

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. Lasers Eng. 47, 123 (2009).
[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] [PubMed]

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]

Straupe, S.

S. Straupe and S. Kulik, Nat. Photonics 4, 585 (2010).
[CrossRef]

Swartzlander, G. A.

Sztul, H. I.

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley Interscience, 2007).

Torner, L.

J. P. Torres, Y. Deyanova, L. Torner, and G. Molina-Terriza, Phys. Rev. A 67, 052313 (2003).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2001).
[CrossRef]

Torres, J. P.

J. P. Torres, Y. Deyanova, L. Torner, and G. Molina-Terriza, Phys. Rev. A 67, 052313 (2003).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2001).
[CrossRef]

Vaity, P.

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

Vasnetsov, M.

Ward, R.

M. Granata, C. Buy, R. Ward, and M. Barsuglia, Phys. Rev. Lett. 105, 231102 (2010).
[CrossRef]

Wei, G. X.

C. S. Guo, S. J. Yue, and G. X. Wei, Appl. Phys. Lett. 94, 231104 (2009).
[CrossRef]

Woerdman, J. P.

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

Yue, S. J.

C. S. Guo, S. J. Yue, and G. X. Wei, Appl. Phys. Lett. 94, 231104 (2009).
[CrossRef]

Appl. Phys. Lett.

C. S. Guo, S. J. Yue, and G. X. Wei, Appl. Phys. Lett. 94, 231104 (2009).
[CrossRef]

J. Opt. A

G. C. G. Berkhout and M. W. Beijersbergen, J. Opt. A 11, 094021 (2009).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Photonics

S. Straupe and S. Kulik, Nat. Photonics 4, 585 (2010).
[CrossRef]

Nature

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

New J. Phys.

B. Jack, M. J. Padgett, and S. Franke-Arnold, New J. Phys. 10, 103013 (2008).
[CrossRef]

Opt. Commun.

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

Opt. Express

Opt. Lasers Eng.

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, Opt. Lasers Eng. 47, 123 (2009).
[CrossRef]

Opt. Lett.

Phys. Rev. A

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

J. P. Torres, Y. Deyanova, L. Torner, and G. Molina-Terriza, Phys. Rev. A 67, 052313 (2003).
[CrossRef]

Phys. Rev. D

P. Fulda, K. Kokeyama, S. Chelkowski, and A. Freise, Phys. Rev. D 82, 012002 (2010).
[CrossRef]

Phys. Rev. Lett.

M. Granata, C. Buy, R. Ward, and M. Barsuglia, Phys. Rev. Lett. 105, 231102 (2010).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2001).
[CrossRef]

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

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

Other

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley Interscience, 2007).

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Figures (5)

Fig. 1
Fig. 1

(a) Experimental setup. (b) Arrangement of the slit and higher-order LG beams generated by the SLM; where 2 a is the length of the slit and d is the distance from the center of the beam to the center of the slit. (c) Numerical simulation of intensity distribution over the slit for m = 0 , m = 2 , and m = 5 for d = 0 .

Fig. 2
Fig. 2

Diffraction patterns and phase diagrams for m = 0 , 1, 2, 4, and 5 (from left to right) for d = 0 . (top) Numerical simulation. (middle) Experimental results corresponding to top row. (bottom) Phase diagrams along the slit.

Fig. 3
Fig. 3

Diffraction patterns and phase diagrams for m = 0 , 1, 2, 4, and 5 (from left to right) and d = 0.2 R . (top) Simulated diffraction patterns. (middle) Experimental results corresponding to top row. (bottom) Phase diagrams inside the slit.

Fig. 4
Fig. 4

Phase profiles along the slit center. The topological charge is (a)  m = 1 and (b)  m = 5 for d = 0 and d = 0.2 R .

Fig. 5
Fig. 5

Interference pattern for the two Gaussian intensity profiles with a linear phase along the beam.

Equations (4)

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E LG ( ρ , ϕ , z ) = A m , p [ W 0 W ( z ) ] ( ρ W ( z ) ) m L p m ( 2 ρ 2 W 2 ( z ) ) × exp ( ρ 2 W 2 ( z ) ) exp [ i k z i k ρ 2 2 R ( z ) i m ϕ + i ( m + 2 p + 1 ) ζ ( z ) ] ,
E ( x , y , z ) A E ( x , y , 0 ) e i k z ( x x + y y ) d x d y ,
E ( x ) = exp ( i ϕ 1 ) exp ( ( x + x 0 ) 2 w 0 2 ) + exp ( i ϕ 2 ) exp ( ( x x 0 ) 2 w 0 2 ) ,
E ( v x ) exp ( i β x 0 ) exp [ ( i β w 0 2 + x 0 w 0 + i π v x w 0 ) 2 ] + exp ( i β x 0 ) exp [ ( i β w 0 2 x 0 w 0 + i π v x w 0 ) 2 ] .

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