Abstract

An efficient method for exploring the orbital angular momentum of an optical vortex beam is provided. The method, based on a triangular multipoint plate, can easily determine both the sign and the magnitude of the topological charge of the optical vortices. We demonstrate its feasibility by measuring the orbital angular momentum of Laguerre–Gaussian laser beams.

© 2011 Optical Society of America

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References

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  1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
    [CrossRef] [PubMed]
  2. J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104, 103601 (2010).
    [CrossRef] [PubMed]
  3. J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
    [CrossRef]
  4. H. I. Sztul and R. R. Alfano, “Double-slit interference with Laguerre–Gaussian beams,” Opt. Lett. 31, 999–1001 (2006).
    [CrossRef] [PubMed]
  5. G. C. G. Berkhout and M. W. Beijersbergen, “Method for probing the orbital angular momentum of optical vortices in electromagnetic waves from astronomical objects,” Phys. Rev. Lett. 101, 100801 (2008).
    [CrossRef] [PubMed]
  6. Y. Li, H. Liu, Z. Chen, J. Pu, and B. Yao, “Measuring the topological charge of integer and fraction vortices by using multipoint plates,” Opt. Rev. 18, 7–12 (2011).
    [CrossRef]
  7. I. Moreno, J. A. Davis, B. M. L. Pascoguin, M. J. Mitry, and D. M. Cottrell, “Vortex sensing diffraction gratings,” Opt. Lett. 34, 2927–2929 (2009).
    [CrossRef] [PubMed]
  8. C. S. Guo, L. L. Lu, and H. T. Wang, “Characterizing topological charge of optical vortices by using an annular aperture,” Opt. Lett. 34, 3686–3688 (2009).
    [CrossRef] [PubMed]
  9. J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chavez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).
    [CrossRef] [PubMed]
  10. L. E. E. de Araujo1 and M. E. Anderson, “Measuring vortex charge with a triangular aperture,” Opt. Lett. 36, 787–789(2011).
    [CrossRef]
  11. Y. Liu, H. Tao, J. Pu, and B. Lü, “Detecting the topological charge of vortex beams by using an annular triangle aperture,” Opt. Laser Technol. 43, 1233–1236 (2011).
    [CrossRef]

2011

Y. Li, H. Liu, Z. Chen, J. Pu, and B. Yao, “Measuring the topological charge of integer and fraction vortices by using multipoint plates,” Opt. Rev. 18, 7–12 (2011).
[CrossRef]

L. E. E. de Araujo1 and M. E. Anderson, “Measuring vortex charge with a triangular aperture,” Opt. Lett. 36, 787–789(2011).
[CrossRef]

Y. Liu, H. Tao, J. Pu, and B. Lü, “Detecting the topological charge of vortex beams by using an annular triangle aperture,” Opt. Laser Technol. 43, 1233–1236 (2011).
[CrossRef]

2010

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chavez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef] [PubMed]

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104, 103601 (2010).
[CrossRef] [PubMed]

2009

2008

G. C. G. Berkhout and M. W. Beijersbergen, “Method for probing the orbital angular momentum of optical vortices in electromagnetic waves from astronomical objects,” Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef] [PubMed]

2006

2002

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[CrossRef]

1992

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Alfano, R. R.

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Anderson, M. E.

Beijersbergen, M. W.

G. C. G. Berkhout and M. W. Beijersbergen, “Method for probing the orbital angular momentum of optical vortices in electromagnetic waves from astronomical objects,” Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef] [PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Berkhout, G. C. G.

G. C. G. Berkhout and M. W. Beijersbergen, “Method for probing the orbital angular momentum of optical vortices in electromagnetic waves from astronomical objects,” Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef] [PubMed]

Chan, C. T.

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104, 103601 (2010).
[CrossRef] [PubMed]

Chavez-Cerda, S.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chavez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef] [PubMed]

Chen, Z.

Y. Li, H. Liu, Z. Chen, J. Pu, and B. Yao, “Measuring the topological charge of integer and fraction vortices by using multipoint plates,” Opt. Rev. 18, 7–12 (2011).
[CrossRef]

Cottrell, D. M.

Curtis, J. E.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[CrossRef]

Davis, J. A.

de Araujo1, L. E. E.

Fonseca, E. J. S.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chavez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef] [PubMed]

Grier, D. G.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[CrossRef]

Guo, C. S.

Hickmann, J. M.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chavez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef] [PubMed]

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[CrossRef]

Li, Y.

Y. Li, H. Liu, Z. Chen, J. Pu, and B. Yao, “Measuring the topological charge of integer and fraction vortices by using multipoint plates,” Opt. Rev. 18, 7–12 (2011).
[CrossRef]

Lin, Z.

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104, 103601 (2010).
[CrossRef] [PubMed]

Liu, H.

Y. Li, H. Liu, Z. Chen, J. Pu, and B. Yao, “Measuring the topological charge of integer and fraction vortices by using multipoint plates,” Opt. Rev. 18, 7–12 (2011).
[CrossRef]

Liu, Y.

Y. Liu, H. Tao, J. Pu, and B. Lü, “Detecting the topological charge of vortex beams by using an annular triangle aperture,” Opt. Laser Technol. 43, 1233–1236 (2011).
[CrossRef]

Lu, L. L.

Lü, B.

Y. Liu, H. Tao, J. Pu, and B. Lü, “Detecting the topological charge of vortex beams by using an annular triangle aperture,” Opt. Laser Technol. 43, 1233–1236 (2011).
[CrossRef]

Mitry, M. J.

Moreno, I.

Ng, J.

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104, 103601 (2010).
[CrossRef] [PubMed]

Pascoguin, B. M. L.

Pu, J.

Y. Liu, H. Tao, J. Pu, and B. Lü, “Detecting the topological charge of vortex beams by using an annular triangle aperture,” Opt. Laser Technol. 43, 1233–1236 (2011).
[CrossRef]

Y. Li, H. Liu, Z. Chen, J. Pu, and B. Yao, “Measuring the topological charge of integer and fraction vortices by using multipoint plates,” Opt. Rev. 18, 7–12 (2011).
[CrossRef]

Soares, W. C.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chavez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” 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, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Sztul, H. I.

Tao, H.

Y. Liu, H. Tao, J. Pu, and B. Lü, “Detecting the topological charge of vortex beams by using an annular triangle aperture,” Opt. Laser Technol. 43, 1233–1236 (2011).
[CrossRef]

Wang, H. T.

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Yao, B.

Y. Li, H. Liu, Z. Chen, J. Pu, and B. Yao, “Measuring the topological charge of integer and fraction vortices by using multipoint plates,” Opt. Rev. 18, 7–12 (2011).
[CrossRef]

Opt. Commun.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[CrossRef]

Opt. Laser Technol.

Y. Liu, H. Tao, J. Pu, and B. Lü, “Detecting the topological charge of vortex beams by using an annular triangle aperture,” Opt. Laser Technol. 43, 1233–1236 (2011).
[CrossRef]

Opt. Lett.

Opt. Rev.

Y. Li, H. Liu, Z. Chen, J. Pu, and B. Yao, “Measuring the topological charge of integer and fraction vortices by using multipoint plates,” Opt. Rev. 18, 7–12 (2011).
[CrossRef]

Phys. Rev. A

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett.

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104, 103601 (2010).
[CrossRef] [PubMed]

G. C. G. Berkhout and M. W. Beijersbergen, “Method for probing the orbital angular momentum of optical vortices in electromagnetic waves from astronomical objects,” Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef] [PubMed]

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chavez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Geometry and notation of a TMP with N points on each side ( N = 4 ). The points are indicated by white dots.

Fig. 2
Fig. 2

Simulated far-field intensity patterns for LG beams with different topological charges l diffracted by the TMPs with different N points calculated from Eq. (7). (a)  N = 2 , (b)  N = 4 , (c)  N = 6 , (d)  N = 8 , (e)  N = 20 .

Fig. 3
Fig. 3

Simulated far-field intensity patterns for LG beams with different topological charges l diffracted by the TMP with N = 6 calculated from Eq. (7).

Fig. 4
Fig. 4

Setup to measure the far-field intensity patterns of LG beams diffracted by a TMP.

Fig. 5
Fig. 5

Measured far-field intensity patterns for LG beams with different positive topological charges l diffracted by a TMP with N = 6 .

Fig. 6
Fig. 6

Measured far-field intensity patterns for LG beams with different negative topological charges l diffracted by a TMP with N = 6 .

Equations (7)

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E p l ( r , ϕ , z ) r | l | L p l ( 2 r 2 w 2 ) exp ( r 2 w 2 ) exp ( i l ϕ ) ,
τ ( x , y ) = n = 1 N 1 δ ( x x 0 , y y 01 ) + n = 1 N 2 δ ( x x 0 , y y 02 ) + n = 0 N 1 δ ( x + 3 6 a , y y 03 ) ,
x 0 = 3 6 a + n N 1 3 2 a ,
y 01 = 3 3 x 0 + a 3 ,
y 02 = 3 3 x 0 a 3 ,
y 03 = a 2 + n N 1 a .
I l ( x , y , z ) | i λ z exp ( i k ( z + x 2 + y 2 2 z ) ) × [ n = 1 N 1 ( x 0 2 + y 01 2 ) | l | exp ( x 0 2 + y 01 2 w 2 ) exp ( i l arctan ( x 0 , y 01 ) ) exp ( i k z ( x 0 x + y 01 y ) ) + n = 1 N 2 ( x 0 2 + y 02 2 ) | l | exp ( x 0 2 + y 02 2 w 2 ) exp ( i l arctan ( x 0 , y 02 ) ) exp ( i k z ( x 0 x + y 02 y ) ) + n = 0 N 1 ( a 2 12 + y 03 2 ) | l | exp ( a 2 / 12 + y 03 2 w 2 ) exp ( i l arctan ( 3 6 a , y 03 ) ) exp ( i k z ( 3 6 a x + y 03 y ) ) ] | 2 ,

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