Abstract

This Letter reports an experimental and theoretical study of the response of a quadrant detector (QD) to an incident vortex beam, specifically a Laguerre–Gaussian (LG) beam. We have found that the LG beam response depends on the vorticity index . We compare LG beams with hard-ringed beams and find that at higher values, the QD response to LG beams can be approximated by its response to hard-ringed beams. Our findings are important in view of the increasing interest in optical vortex beams.

© 2011 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]

2010

A. Picón, A. Benseny, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, New J. Phys. 12, 083053 (2010).
[CrossRef]

S. Cui and Y. C. Soh, Appl. Phys. Lett. 96, 081102(2010).
[CrossRef]

E. J. Lee, Y. Park, C. S. Kim, and T. Kouh, Curr. Appl. Phys. 10, 834 (2010).
[CrossRef]

Y. Panduputra, T. W. Ng, A. Neild, and M. Robinson, Appl. Opt. 49, 3669 (2010).
[CrossRef] [PubMed]

M. Merano, N. Hermosa, A. Aiello, and J. P. Woerdman, Phys. Rev. A 82, 023817 (2010).
[CrossRef]

J. Hamazaki, R. Morita, K. Chujo, Y. Kobayashi, S. Tanda, and T. Omatsu, Opt. Express 18, 2144 (2010).
[CrossRef] [PubMed]

J.-Y. Vinet, Phys. Rev. D 82, 042003 (2010).
[CrossRef]

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

2007

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

2005

2003

2002

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

2001

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

1997

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

1993

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

1992

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

1975

H. J. Woltring, IEEE Trans. Electron. Devices 22, 581 (1975).
[CrossRef]

Aiello, A.

M. Merano, N. Hermosa, A. Aiello, and J. P. Woerdman, Phys. Rev. A 82, 023817 (2010).
[CrossRef]

Allen, L.

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

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

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

Almeida, M. P.

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

Barsuglia, M.

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

Beijersbergen, M. W.

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

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

Benseny, A.

A. Picón, A. Benseny, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, New J. Phys. 12, 083053 (2010).
[CrossRef]

Buy, C.

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

Caetano, D. P.

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

Calvo, G. F.

A. Picón, A. Benseny, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, New J. Phys. 12, 083053 (2010).
[CrossRef]

Chujo, K.

Courtial, J.

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

Cui, S.

S. Cui and Y. C. Soh, Appl. Phys. Lett. 96, 081102(2010).
[CrossRef]

de Aldana, J. R. Vázquez

A. Picón, A. Benseny, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, New J. Phys. 12, 083053 (2010).
[CrossRef]

Dholakia, K.

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

dos Santos, B. Coutinho

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

Fujii, M.

Granata, M.

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

Grier, D.

Gruzberg, I.

Hamazaki, J.

Hermosa, N.

M. Merano, N. Hermosa, A. Aiello, and J. P. Woerdman, Phys. Rev. A 82, 023817 (2010).
[CrossRef]

Huguenin, J. A. O.

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

Iketaki, Y.

Khoury, A. Z.

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

Kim, C. S.

E. J. Lee, Y. Park, C. S. Kim, and T. Kouh, Curr. Appl. Phys. 10, 834 (2010).
[CrossRef]

Kobayashi, Y.

Kouh, T.

E. J. Lee, Y. Park, C. S. Kim, and T. Kouh, Curr. Appl. Phys. 10, 834 (2010).
[CrossRef]

Lee, E. J.

E. J. Lee, Y. Park, C. S. Kim, and T. Kouh, Curr. Appl. Phys. 10, 834 (2010).
[CrossRef]

Mair, A.

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

Merano, M.

M. Merano, N. Hermosa, A. Aiello, and J. P. Woerdman, Phys. Rev. A 82, 023817 (2010).
[CrossRef]

Molina-Terriza, G.

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

Mompart, J.

A. Picón, A. Benseny, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, New J. Phys. 12, 083053 (2010).
[CrossRef]

Morita, R.

Neild, A.

Ng, T. W.

Omatsu, T.

Padgett, M. J.

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

Panduputra, Y.

Park, Y.

E. J. Lee, Y. Park, C. S. Kim, and T. Kouh, Curr. Appl. Phys. 10, 834 (2010).
[CrossRef]

Picón, A.

A. Picón, A. Benseny, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, New J. Phys. 12, 083053 (2010).
[CrossRef]

Plaja, L.

A. Picón, A. Benseny, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, New J. Phys. 12, 083053 (2010).
[CrossRef]

Ribeiro, P. H. Souto

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

Robinson, M.

Roso, L.

A. Picón, A. Benseny, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, New J. Phys. 12, 083053 (2010).
[CrossRef]

Sakai, M.

Soh, Y. C.

S. Cui and Y. C. Soh, Appl. Phys. Lett. 96, 081102(2010).
[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]

Sundbeck, S.

Tanda, S.

Torner, L.

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

Torres, J. P.

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

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

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

Vaziri, A.

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

Vinet, J.-Y.

J.-Y. Vinet, Phys. Rev. D 82, 042003 (2010).
[CrossRef]

Ward, R.

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

Watanabe, T.

Weihs, G.

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

Woerdman, J. P.

M. Merano, N. Hermosa, A. Aiello, and J. P. Woerdman, Phys. Rev. A 82, 023817 (2010).
[CrossRef]

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

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

Woltring, H. J.

H. J. Woltring, IEEE Trans. Electron. Devices 22, 581 (1975).
[CrossRef]

Yamamoto, K.

Zeilinger, A.

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

Appl. Opt.

Appl. Phys. Lett.

S. Cui and Y. C. Soh, Appl. Phys. Lett. 96, 081102(2010).
[CrossRef]

Curr. Appl. Phys.

E. J. Lee, Y. Park, C. S. Kim, and T. Kouh, Curr. Appl. Phys. 10, 834 (2010).
[CrossRef]

IEEE Trans. Electron. Devices

H. J. Woltring, IEEE Trans. Electron. Devices 22, 581 (1975).
[CrossRef]

Nature

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

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

Nature Phys.

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

New J. Phys.

A. Picón, A. Benseny, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, New J. Phys. 12, 083053 (2010).
[CrossRef]

Opt. Commun.

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

Opt. Express

Opt. Lett.

Phys. Rev. A

M. Merano, N. Hermosa, A. Aiello, and J. P. Woerdman, Phys. Rev. A 82, 023817 (2010).
[CrossRef]

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

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

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

Phys. Rev. D

J.-Y. Vinet, Phys. Rev. D 82, 042003 (2010).
[CrossRef]

Phys. Rev. Lett.

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

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Figures (3)

Fig. 1
Fig. 1

LG beam incident on a quadrant detector. The difference in the photocurrents from the four panels is related to the displacement of the beam from the center.

Fig. 2
Fig. 2

Calibration constant K LG varies for different values of . Larger values give smaller calibration constants. The drawn curve is the theoretical prediction, while the points marked by open squares are experimentally obtained, both for LG beams. The error bars are mainly attributed to the imperfect purity of the LG mode. The dashed curve shows the theoretical prediction when the LG soft-ring beam is approximated as a hard ring (see text). The hard-ring beam at = 0 is a top-hat beam. The inset is the percent difference between the solid curve and the dashed curve.

Fig. 3
Fig. 3

Calibration constant K of a hard-ring beam as a function of ( R 2 / R 2 ) . Solid curve, the theoretical prediction while the points marked by open squares are experimentally obtained. We ascribed the error bars to the noise implied by the low intensity of the hard-ring beams.

Tables (1)

Tables Icon

Table 1 Calibration Constants K for the Dimensionless Response ( I x I = K Δ x ) of the Quadrant Detector with Different Beam Profiles at Displacement Δ x Much Smaller Than the Diameter of the Beam

Equations (4)

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

I x I = I A + I C ( I B + I D ) I A + I B + I C + I D , I y I = I A + I B ( I C + I D ) I A + I B + I C + I D ,
I ( x , y ) = 2 π ω z 2 1 | | ! [ 2 ω z 2 ( x 2 + y 2 ) ] | | e 2 ω z 2 ( x 2 + y 2 ) ,
I x I = 0 x 0 I ( x , y ) d y d x 0 0 I ( x , y ) d y d x
I x I = 2 3 / 2 Γ ( 1 2 + | | ) x ω z π | | !

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