Abstract

Vortex beams with fractional topological charge (FTC) have many special characteristics and novel applications. However, one of the obstacles for their application is the difficulty of precisely determining the FTC of fractional vortex beams. We find that when a vortex beam with an FTC illuminates a dynamic angular double slit (ADS), the far-field interference patterns that include the information of the FTC of the beam at the angular bisector direction of the ADS vary periodically. Based on this property, a simple dynamic ADS device and data fitting method can be used to precisely measure the FTC of a vortex light beam with an error of less than 5%.

© 2016 Chinese Laser Press

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References

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    [Crossref]

2016 (2)

J. Zhou, W. Zhang, and L. Chen, “Experimental detection of high-order or fractional orbital angular momentum of light based on a robust mode converter,” Appl. Phys. Lett. 108, 111108 (2016).
[Crossref]

P. Li, B. Wang, X. Song, and X. Zhang, “Non-destructive identification of twisted light,” Opt. Lett. 41, 1574–1577 (2016).
[Crossref]

2015 (2)

D. Fu, D. Chen, R. Liu, Y. Wang, H. Gao, F. Li, and P. Zhang, “Probing the topological charge of a vortex beam with dynamic angular double slits,” Opt. Lett. 40, 788–791 (2015).
[Crossref]

X. Li, Y. Tai, Z. Nie, H. Wang, H. Li, J. Wang, J. Tang, and Y. Wang, “Fraunhofer diffraction of Laguerre-Gaussian beam caused by a dynamic superposed dual-triangular aperture,” Opt. Eng. 54, 123113 (2015).
[Crossref]

2014 (2)

H. Zhou, L. Shi, X. Zhang, and J. Dong, “Dynamic interferometry measurement of orbital angular momentum of light,” Opt. Lett. 39, 6058–6061 (2014).
[Crossref]

O. Emile, J. Emile, and C. Brousseau, “Determination of the topological charge of a twisted beam with a Fresnel bi-prism,” J. Opt. 16, 125703 (2014).
[Crossref]

2013 (3)

R. Liu, J. Long, F. Wang, Y. Wang, P. Zhang, H. Hao, and F. Li, “Characterizing the phase profile of a vortex beam with angular-double-slit interference,” J. Opt. 15, 125712 (2013).
[Crossref]

M. Liu, “Probing the vortex beams with fractional and integral topological charges using weak random scattering screen,” Eur. Phys. J. D 67, 244 (2013).
[Crossref]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref]

2012 (2)

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

H.-C. Huang, Y.-T. Lin, and M.-F. Shih, “Measuring the fractional orbital angular momentum of a vortex light beam by cascaded Mach-Zehnder interferometers,” Opt. Commun. 285, 383–388 (2012).
[Crossref]

2011 (3)

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
[Crossref]

M. J. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5, 343–348 (2011).
[Crossref]

A. Mourka, J. Baumgartl, C. Shanor, K. Dholakia, and E. M. Wright, “Visualization of the birth of an optical vortex using diffraction from a triangular aperture,” Opt. Express 19, 5760–5771 (2011).
[Crossref]

2010 (4)

G. Situ, M. Warber, G. Pedrini, and W. Osten, “Phase contrast enhancement in microscopy using spiral phase filtering,” Opt. Commun. 283, 1273–1277 (2010).
[Crossref]

N. Zhang, “Analysis of fractional vortex beams using a vortex grating spectrum analyzer,” Appl. Opt. 49, 2456–2462 (2010).
[Crossref]

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–665 (2010).
[Crossref]

C.-S. Guo, Y.-N. Yu, and Z. Hong, “Optical sorting using an array of optical vortices with fractional topological charge,” Opt. Commun. 283, 1889–1893 (2010).
[Crossref]

2009 (2)

G. Situ, G. Pedrini, and W. Osten, “Spiral phase filtering and orientation-selective edge detection/enhancement,” J. Opt. Soc. Am. A 26, 1788–1797 (2009).
[Crossref]

B. Jack, J. Leach, J. Romero, S. Franke-Arnold, M. Ritsch-Marte, S. M. Barnett, and M. J. Padgett, “Holographic ghost imaging and the violation of a bell inequality,” Phys. Rev. Lett. 103, 083602 (2009).
[Crossref]

2008 (2)

2007 (1)

G. F. Calvo, A. Picón, and A. Bramon, “Measuring two-photon orbital angular momentum entanglement,” Phys. Rev. A 75, 012319 (2007).
[Crossref]

2006 (1)

S. S. R. Oemrawsingh, J. A. de Jong, X. Ma, A. Aiello, E. R. Eliel, G. W. ’t Hooft, and J. P. Woerdman, “High-dimensional mode analyzers for spatial quantum entanglement,” Phys. Rev. A 73, 032339 (2006).
[Crossref]

2005 (3)

2004 (5)

W. M. Lee, X.-C. Yuan, and K. Dholakia, “Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step,” Opt. Commun. 239, 129–135 (2004).
[Crossref]

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A 6, 259–268 (2004).
[Crossref]

J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71 (2004).
[Crossref]

S. S. R. Oemrawsingh, A. Aiello, E. R. Eliel, G. Nienhaus, and J. P. Woerdman, “How to observe high-dimensional two-photon entanglement with only two detectors,” Phys. Rev. Lett. 92, 217901 (2004).
[Crossref]

G. Gibson, J. Courtial, and M. J. Padgett, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
[Crossref]

2003 (2)

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[Crossref]

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90, 133901 (2003).
[Crossref]

2001 (2)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (2001).
[Crossref]

1997 (1)

1995 (1)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref]

1992 (2)

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]

S. J. van Enk and G. Nienhuis, “Eigenfunction description of laser beams and orbital angular momentum of light,” Opt. Commun. 94, 147–158 (1992).
[Crossref]

’t Hooft, G. W.

S. S. R. Oemrawsingh, J. A. de Jong, X. Ma, A. Aiello, E. R. Eliel, G. W. ’t Hooft, and J. P. Woerdman, “High-dimensional mode analyzers for spatial quantum entanglement,” Phys. Rev. A 73, 032339 (2006).
[Crossref]

Ahmed, N.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Aiello, A.

S. S. R. Oemrawsingh, J. A. de Jong, X. Ma, A. Aiello, E. R. Eliel, G. W. ’t Hooft, and J. P. Woerdman, “High-dimensional mode analyzers for spatial quantum entanglement,” Phys. Rev. A 73, 032339 (2006).
[Crossref]

A. Aiello, S. S. R. Oemrawsingh, E. R. Eliel, and J. P. Woerdman, “Nonlocality of high-dimensional two-photon orbital angular momentum states,” Phys. Rev. A 72, 052114 (2005).
[Crossref]

S. S. R. Oemrawsingh, A. Aiello, E. R. Eliel, G. Nienhaus, and J. P. Woerdman, “How to observe high-dimensional two-photon entanglement with only two detectors,” Phys. Rev. Lett. 92, 217901 (2004).
[Crossref]

Allen, L.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–313 (2008).
[Crossref]

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, “Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner,” Opt. Lett. 22, 52–54 (1997).
[Crossref]

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]

Barnett, S. M.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–665 (2010).
[Crossref]

B. Jack, J. Leach, J. Romero, S. Franke-Arnold, M. Ritsch-Marte, S. M. Barnett, and M. J. Padgett, “Holographic ghost imaging and the violation of a bell inequality,” Phys. Rev. Lett. 103, 083602 (2009).
[Crossref]

J. B. Götte, K. O’Holleran, D. Preece, F. Flossmann, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Light beams with fractional orbital angular momentum and their vortex structure,” Opt. Express 16, 993–1006 (2008).
[Crossref]

Baumgartl, J.

Beijersbergen, M. W.

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]

Bernet, S.

Berry, M. V.

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A 6, 259–268 (2004).
[Crossref]

Bowman, R.

M. J. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5, 343–348 (2011).
[Crossref]

Boyd, R. W.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–665 (2010).
[Crossref]

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref]

Bramon, A.

G. F. Calvo, A. Picón, and A. Bramon, “Measuring two-photon orbital angular momentum entanglement,” Phys. Rev. A 75, 012319 (2007).
[Crossref]

Brousseau, C.

O. Emile, J. Emile, and C. Brousseau, “Determination of the topological charge of a twisted beam with a Fresnel bi-prism,” J. Opt. 16, 125703 (2014).
[Crossref]

Calvo, G. F.

G. F. Calvo, A. Picón, and A. Bramon, “Measuring two-photon orbital angular momentum entanglement,” Phys. Rev. A 75, 012319 (2007).
[Crossref]

Chen, D.

Chen, L.

J. Zhou, W. Zhang, and L. Chen, “Experimental detection of high-order or fractional orbital angular momentum of light based on a robust mode converter,” Appl. Phys. Lett. 108, 111108 (2016).
[Crossref]

Cižmár, T.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
[Crossref]

Courtial, J.

Curtis, J. E.

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90, 133901 (2003).
[Crossref]

de Jong, J. A.

S. S. R. Oemrawsingh, J. A. de Jong, X. Ma, A. Aiello, E. R. Eliel, G. W. ’t Hooft, and J. P. Woerdman, “High-dimensional mode analyzers for spatial quantum entanglement,” Phys. Rev. A 73, 032339 (2006).
[Crossref]

Dholakia, K.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
[Crossref]

A. Mourka, J. Baumgartl, C. Shanor, K. Dholakia, and E. M. Wright, “Visualization of the birth of an optical vortex using diffraction from a triangular aperture,” Opt. Express 19, 5760–5771 (2011).
[Crossref]

W. M. Lee, X.-C. Yuan, and K. Dholakia, “Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step,” Opt. Commun. 239, 129–135 (2004).
[Crossref]

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, “Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner,” Opt. Lett. 22, 52–54 (1997).
[Crossref]

Dolinar, S.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Dong, J.

Eliel, E. R.

S. S. R. Oemrawsingh, J. A. de Jong, X. Ma, A. Aiello, E. R. Eliel, G. W. ’t Hooft, and J. P. Woerdman, “High-dimensional mode analyzers for spatial quantum entanglement,” Phys. Rev. A 73, 032339 (2006).
[Crossref]

A. Aiello, S. S. R. Oemrawsingh, E. R. Eliel, and J. P. Woerdman, “Nonlocality of high-dimensional two-photon orbital angular momentum states,” Phys. Rev. A 72, 052114 (2005).
[Crossref]

S. S. R. Oemrawsingh, A. Aiello, E. R. Eliel, G. Nienhaus, and J. P. Woerdman, “How to observe high-dimensional two-photon entanglement with only two detectors,” Phys. Rev. Lett. 92, 217901 (2004).
[Crossref]

Emile, J.

O. Emile, J. Emile, and C. Brousseau, “Determination of the topological charge of a twisted beam with a Fresnel bi-prism,” J. Opt. 16, 125703 (2014).
[Crossref]

Emile, O.

O. Emile, J. Emile, and C. Brousseau, “Determination of the topological charge of a twisted beam with a Fresnel bi-prism,” J. Opt. 16, 125703 (2014).
[Crossref]

Fazal, I. M.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Flossmann, F.

Franke-Arnold, S.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–665 (2010).
[Crossref]

B. Jack, J. Leach, J. Romero, S. Franke-Arnold, M. Ritsch-Marte, S. M. Barnett, and M. J. Padgett, “Holographic ghost imaging and the violation of a bell inequality,” Phys. Rev. Lett. 103, 083602 (2009).
[Crossref]

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–313 (2008).
[Crossref]

J. B. Götte, K. O’Holleran, D. Preece, F. Flossmann, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Light beams with fractional orbital angular momentum and their vortex structure,” Opt. Express 16, 993–1006 (2008).
[Crossref]

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref]

Fu, D.

Fürhapter, S.

Gao, H.

Gibson, G.

Götte, J. B.

Grier, D. G.

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N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
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J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–665 (2010).
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J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71 (2004).
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C.-S. Guo, Y.-N. Yu, and Z. Hong, “Optical sorting using an array of optical vortices with fractional topological charge,” Opt. Commun. 283, 1889–1893 (2010).
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W. M. Lee, X.-C. Yuan, and K. Dholakia, “Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step,” Opt. Commun. 239, 129–135 (2004).
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N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
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J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
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A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
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Zhang, P.

D. Fu, D. Chen, R. Liu, Y. Wang, H. Gao, F. Li, and P. Zhang, “Probing the topological charge of a vortex beam with dynamic angular double slits,” Opt. Lett. 40, 788–791 (2015).
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J. Zhou, W. Zhang, and L. Chen, “Experimental detection of high-order or fractional orbital angular momentum of light based on a robust mode converter,” Appl. Phys. Lett. 108, 111108 (2016).
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Zhou, H.

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Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. Zhou, W. Zhang, and L. Chen, “Experimental detection of high-order or fractional orbital angular momentum of light based on a robust mode converter,” Appl. Phys. Lett. 108, 111108 (2016).
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M. Liu, “Probing the vortex beams with fractional and integral topological charges using weak random scattering screen,” Eur. Phys. J. D 67, 244 (2013).
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J. Opt. Soc. Am. A (1)

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Nature (2)

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Figures (4)

Fig. 1.
Fig. 1. Schematic of ADS interference. α is the width of an angular single slit, and ϕ is the angle between dynamic two single slits. q 1 , q 2 , and q 3 are three points on the mask and o q 3 is the angular bisector of q 1 o q 2 . P is a point on the far field (with q 1 P = q 2 P ), which is chosen to observe interferential intensity. θ represents an additional phase on one single slit.
Fig. 2.
Fig. 2. Sketch of the experimental setup. The inset shows the mask pattern loaded on the SLM.
Fig. 3.
Fig. 3. I ϕ curves in polar coordinates when the additional phase θ is zero. The black dots are the experimental data and the green solid curves are fits of the data. M is the theoretical FTC and | M f | is the modulus of the FTC, which is obtained by fitting the experimental data to the fitting function.
Fig. 4.
Fig. 4. Contrasted I ϕ curves between θ = 0 (the blue curve) and θ = π / 2 (the purple curve) with M = 4.3 .

Equations (2)

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I 1 + cos [ M ( ϕ + θ / M ) ] .
I 0 = a 0 + a 1 sin ( M t ϕ ) + b 1 cos ( M t ϕ ) ) .

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