Abstract

Higher-order optical vortices are inherently unstable in the sense that they tend to split up in a series of vortices with unity charge. We demonstrate this vortex-splitting phenomenon in beams produced with holograms and spatial light modulators and discuss its generic and practically unavoidable nature. To analyze the splitting phenomena in detail, we use a multi-pinhole interferometer to map the combined amplitude and phase profile of the optical field. This technique, which is based on the analysis of the far-field interference pattern observed behind an opaque screen perforated with multiple pinholes, turns out to be very robust and can among others be used to study very ’dark’ regions of electromagnetic fields. Furthermore, the vortex splitting provides an ultra-sensitive measurement method of unwanted scattering from holograms and other phase-changing optical elements.

© 2012 OSA

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    [CrossRef]
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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]

W. Löffler, A. Aiello, and J. P. Woerdman, “Observation of OAM sidebands due to optical reflection,” pre-print (2012), arXiv:1204.4003 (PRL, in print).

2011 (1)

2010 (3)

T. Ando, N. Matsumoto, Y. Ohtake, Y. Takiguchi, and T. Inoue, “Structure of optical singularities in coaxial superpositions of Laguerre-Gaussian modes,” J. Opt. Soc. Am. A 27, 2602–2612 (2010).
[CrossRef]

E. Serabyn, D. Mawet, and R. Burruss, “An image of an exoplanet separated by two diffraction beamwidths from a star,” Nature 464, 1018–1020 (2010).
[CrossRef] [PubMed]

H. Di Lorenzo Pires, H. C. B. Florijn, and M. P. van Exter, “Measurement of the spiral spectrum of entangled two-photon states,” Phys. Rev. Lett. 104, 020505 (2010).
[CrossRef] [PubMed]

2009 (2)

G. C. G. Berkhout and M. W. Beijersbergen, “Using a multipoint interferometer to measure the orbital angular momentum of light in astronomy,” J. Opt. A 11, 094021 (2009).
[CrossRef]

C.-S. Guo, S.-J. Yue, and G.-X. Wei, “Measuring the orbital angular momentum of optical vortices using a multipinhole plate,” Appl. Phys. Lett. 94, 231104 (2009).
[CrossRef]

2008 (3)

L. Janicijevic and S. Topuzoski, “Fresnel and Fraunhofer diffraction of a Gaussian laser beam by fork-shaped gratings,” J. Opt. Soc. Am. A 25, 2659–2669 (2008).
[CrossRef]

V. G. Denisenko, A. Minovich, A. S. Desyatnikov, W. Krolikowski, M. S. Soskin, and Y. S. Kivshar, “Mapping phases of singular scaler light fields,” Opt. Lett. 35, 89–91 (2008).
[CrossRef]

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]

2007 (1)

2006 (2)

K. O’Holleran, M. J. Padgett, and M. R. Dennis, “Topology of optical vortex lines formed by the interference of three, four, and five plane waves,” Opt. Expr. 14, 3039–3044 (2006).
[CrossRef]

M. R. Dennis, “Rows of optical vortices from elliptically perturbing a high-order beam,” Opt. Lett. 31, 1325–1327 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (1)

S. S. R. Oemrawsingh, J. A. W. van Houwelingen, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, and G. W. ’t Hooft, “Half-integral spiral phase plates for optical wavelengths,” J. Opt. A 6, S228–S290 (2004).
[CrossRef]

2001 (2)

M. V. Berry and M. R. Dennis, “Knotted and linked phase singularities in monochromatic waves,” Proc. R. Soc. Lond. A 457, 2251–2263 (2001).
[CrossRef]

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

1997 (1)

M. S. Soskin, V. N. Gorshkow, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

1993 (2)

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[CrossRef]

E. G. Churin, J. Hossfeld, and T. Tschudi, “Polarization configurations with singular point former by computer generated holograms,” Opt. Commun. 99, 13–17 (1993).
[CrossRef]

1992 (3)

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, 8185–81891992.
[CrossRef] [PubMed]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
[CrossRef] [PubMed]

V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

1978 (1)

M. R. Sharpe and D. Irish, “Stray light in diffraction grating monochromators,” Opt. Acta 25, 861–893 (1978).
[CrossRef]

1974 (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A 336, 165–190 (1974).
[CrossRef]

’t Hooft, G. W.

S. S. R. Oemrawsingh, J. A. W. van Houwelingen, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, and G. W. ’t Hooft, “Half-integral spiral phase plates for optical wavelengths,” J. Opt. A 6, S228–S290 (2004).
[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.

W. Löffler, A. Aiello, and J. P. Woerdman, “Observation of OAM sidebands due to optical reflection,” pre-print (2012), arXiv:1204.4003 (PRL, in print).

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, 8185–81891992.
[CrossRef] [PubMed]

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (Taylor & Francis, 2003).
[CrossRef]

Ando, T.

Barnett, S. M.

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (Taylor & Francis, 2003).
[CrossRef]

Basistiy, I. V.

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[CrossRef]

Bazhenov, V. Y.

V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

Bazhenov, V. Yu.

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[CrossRef]

Beijersbergen, M. W.

G. C. G. Berkhout and M. W. Beijersbergen, “Using a multipoint interferometer to measure the orbital angular momentum of light in astronomy,” J. Opt. A 11, 094021 (2009).
[CrossRef]

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, 8185–81891992.
[CrossRef] [PubMed]

Berkhout, G. C. G.

G. C. G. Berkhout and M. W. Beijersbergen, “Using a multipoint interferometer to measure the orbital angular momentum of light in astronomy,” J. Opt. A 11, 094021 (2009).
[CrossRef]

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]

Berry, M. V.

M. V. Berry and M. R. Dennis, “Knotted and linked phase singularities in monochromatic waves,” Proc. R. Soc. Lond. A 457, 2251–2263 (2001).
[CrossRef]

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A 336, 165–190 (1974).
[CrossRef]

Burruss, R.

E. Serabyn, D. Mawet, and R. Burruss, “An image of an exoplanet separated by two diffraction beamwidths from a star,” Nature 464, 1018–1020 (2010).
[CrossRef] [PubMed]

Churin, E. G.

E. G. Churin, J. Hossfeld, and T. Tschudi, “Polarization configurations with singular point former by computer generated holograms,” Opt. Commun. 99, 13–17 (1993).
[CrossRef]

Denisenko, V. G.

V. G. Denisenko, A. Minovich, A. S. Desyatnikov, W. Krolikowski, M. S. Soskin, and Y. S. Kivshar, “Mapping phases of singular scaler light fields,” Opt. Lett. 35, 89–91 (2008).
[CrossRef]

Dennis, M. R.

M. R. Dennis, “Rows of optical vortices from elliptically perturbing a high-order beam,” Opt. Lett. 31, 1325–1327 (2006).
[CrossRef] [PubMed]

K. O’Holleran, M. J. Padgett, and M. R. Dennis, “Topology of optical vortex lines formed by the interference of three, four, and five plane waves,” Opt. Expr. 14, 3039–3044 (2006).
[CrossRef]

M. V. Berry and M. R. Dennis, “Knotted and linked phase singularities in monochromatic waves,” Proc. R. Soc. Lond. A 457, 2251–2263 (2001).
[CrossRef]

M. R. Dennis and J. B. Götte, “Topological aberration of optical vortex beams and singularimetry of dielectric interfaces,” pre-print (2012), arXiv:1205.6457.

Desyatnikov, A. S.

V. G. Denisenko, A. Minovich, A. S. Desyatnikov, W. Krolikowski, M. S. Soskin, and Y. S. Kivshar, “Mapping phases of singular scaler light fields,” Opt. Lett. 35, 89–91 (2008).
[CrossRef]

Di Lorenzo Pires, H.

H. Di Lorenzo Pires, H. C. B. Florijn, and M. P. van Exter, “Measurement of the spiral spectrum of entangled two-photon states,” Phys. Rev. Lett. 104, 020505 (2010).
[CrossRef] [PubMed]

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]

Eliel, E. R.

S. S. R. Oemrawsingh, J. A. W. van Houwelingen, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, and G. W. ’t Hooft, “Half-integral spiral phase plates for optical wavelengths,” J. Opt. A 6, S228–S290 (2004).
[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]

Florijn, H. C. B.

H. Di Lorenzo Pires, H. C. B. Florijn, and M. P. van Exter, “Measurement of the spiral spectrum of entangled two-photon states,” Phys. Rev. Lett. 104, 020505 (2010).
[CrossRef] [PubMed]

Foo, G.

Gorshkow, V. N.

M. S. Soskin, V. N. Gorshkow, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

Götte, J. B.

M. R. Dennis and J. B. Götte, “Topological aberration of optical vortex beams and singularimetry of dielectric interfaces,” pre-print (2012), arXiv:1205.6457.

Guo, C.-S.

C.-S. Guo, S.-J. Yue, and G.-X. Wei, “Measuring the orbital angular momentum of optical vortices using a multipinhole plate,” Appl. Phys. Lett. 94, 231104 (2009).
[CrossRef]

Heckenberg, N. R.

M. S. Soskin, V. N. Gorshkow, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
[CrossRef] [PubMed]

Hell, S.W.

Hossfeld, J.

E. G. Churin, J. Hossfeld, and T. Tschudi, “Polarization configurations with singular point former by computer generated holograms,” Opt. Commun. 99, 13–17 (1993).
[CrossRef]

Huang, H.

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]

Inoue, T.

Irish, D.

M. R. Sharpe and D. Irish, “Stray light in diffraction grating monochromators,” Opt. Acta 25, 861–893 (1978).
[CrossRef]

Janicijevic, L.

Keller, J.

Kivshar, Y. S.

V. G. Denisenko, A. Minovich, A. S. Desyatnikov, W. Krolikowski, M. S. Soskin, and Y. S. Kivshar, “Mapping phases of singular scaler light fields,” Opt. Lett. 35, 89–91 (2008).
[CrossRef]

Kloosterboer, J. G.

S. S. R. Oemrawsingh, J. A. W. van Houwelingen, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, and G. W. ’t Hooft, “Half-integral spiral phase plates for optical wavelengths,” J. Opt. A 6, S228–S290 (2004).
[CrossRef]

Krolikowski, W.

V. G. Denisenko, A. Minovich, A. S. Desyatnikov, W. Krolikowski, M. S. Soskin, and Y. S. Kivshar, “Mapping phases of singular scaler light fields,” Opt. Lett. 35, 89–91 (2008).
[CrossRef]

Kumar, A.

Löffler, W.

W. Löffler, A. Aiello, and J. P. Woerdman, “Observation of OAM sidebands due to optical reflection,” pre-print (2012), arXiv:1204.4003 (PRL, in print).

Mair, A.

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

Malos, J. T.

M. S. Soskin, V. N. Gorshkow, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

Matsumoto, N.

Mawet, D.

E. Serabyn, D. Mawet, and R. Burruss, “An image of an exoplanet separated by two diffraction beamwidths from a star,” Nature 464, 1018–1020 (2010).
[CrossRef] [PubMed]

McDuff, R.

Minovich, A.

V. G. Denisenko, A. Minovich, A. S. Desyatnikov, W. Krolikowski, M. S. Soskin, and Y. S. Kivshar, “Mapping phases of singular scaler light fields,” Opt. Lett. 35, 89–91 (2008).
[CrossRef]

Nye, J. F.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A 336, 165–190 (1974).
[CrossRef]

O’Holleran, K.

K. O’Holleran, M. J. Padgett, and M. R. Dennis, “Topology of optical vortex lines formed by the interference of three, four, and five plane waves,” Opt. Expr. 14, 3039–3044 (2006).
[CrossRef]

Oemrawsingh, S. S. R.

S. S. R. Oemrawsingh, J. A. W. van Houwelingen, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, and G. W. ’t Hooft, “Half-integral spiral phase plates for optical wavelengths,” J. Opt. A 6, S228–S290 (2004).
[CrossRef]

Ohtake, Y.

Padgett, M. J.

K. O’Holleran, M. J. Padgett, and M. R. Dennis, “Topology of optical vortex lines formed by the interference of three, four, and five plane waves,” Opt. Expr. 14, 3039–3044 (2006).
[CrossRef]

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (Taylor & Francis, 2003).
[CrossRef]

Palacios, D. M.

Ren, Y.

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]

Schönle, A.

Serabyn, E.

E. Serabyn, D. Mawet, and R. Burruss, “An image of an exoplanet separated by two diffraction beamwidths from a star,” Nature 464, 1018–1020 (2010).
[CrossRef] [PubMed]

Sharpe, M. R.

M. R. Sharpe and D. Irish, “Stray light in diffraction grating monochromators,” Opt. Acta 25, 861–893 (1978).
[CrossRef]

Singh, R. P.

Smith, C. P.

Soskin, M. S.

V. G. Denisenko, A. Minovich, A. S. Desyatnikov, W. Krolikowski, M. S. Soskin, and Y. S. Kivshar, “Mapping phases of singular scaler light fields,” Opt. Lett. 35, 89–91 (2008).
[CrossRef]

M. S. Soskin, V. N. Gorshkow, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[CrossRef]

V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

Spreeuw, R. J. C.

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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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Vaity, P.

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H. Di Lorenzo Pires, H. C. B. Florijn, and M. P. van Exter, “Measurement of the spiral spectrum of entangled two-photon states,” Phys. Rev. Lett. 104, 020505 (2010).
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S. S. R. Oemrawsingh, J. A. W. van Houwelingen, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, and G. W. ’t Hooft, “Half-integral spiral phase plates for optical wavelengths,” J. Opt. A 6, S228–S290 (2004).
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M. S. Soskin, V. N. Gorshkow, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
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V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
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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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S. S. R. Oemrawsingh, J. A. W. van Houwelingen, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, and G. W. ’t Hooft, “Half-integral spiral phase plates for optical wavelengths,” J. Opt. A 6, S228–S290 (2004).
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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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C.-S. Guo, S.-J. Yue, and G.-X. Wei, “Measuring the orbital angular momentum of optical vortices using a multipinhole plate,” Appl. Phys. Lett. 94, 231104 (2009).
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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).
[CrossRef] [PubMed]

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Willner, A. E.

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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W. Löffler, A. Aiello, and J. P. Woerdman, “Observation of OAM sidebands due to optical reflection,” pre-print (2012), arXiv:1204.4003 (PRL, in print).

S. S. R. Oemrawsingh, J. A. W. van Houwelingen, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, and G. W. ’t Hooft, “Half-integral spiral phase plates for optical wavelengths,” J. Opt. A 6, S228–S290 (2004).
[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, 8185–81891992.
[CrossRef] [PubMed]

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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).
[CrossRef]

Yang, J.-Y.

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]

Yue, S.-J.

C.-S. Guo, S.-J. Yue, and G.-X. Wei, “Measuring the orbital angular momentum of optical vortices using a multipinhole plate,” Appl. Phys. Lett. 94, 231104 (2009).
[CrossRef]

Yue, Y.

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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Appl. Phys. Lett. (1)

C.-S. Guo, S.-J. Yue, and G.-X. Wei, “Measuring the orbital angular momentum of optical vortices using a multipinhole plate,” Appl. Phys. Lett. 94, 231104 (2009).
[CrossRef]

J. Mod. Opt. (1)

V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

J. Opt. A (2)

S. S. R. Oemrawsingh, J. A. W. van Houwelingen, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, and G. W. ’t Hooft, “Half-integral spiral phase plates for optical wavelengths,” J. Opt. A 6, S228–S290 (2004).
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G. C. G. Berkhout and M. W. Beijersbergen, “Using a multipoint interferometer to measure the orbital angular momentum of light in astronomy,” J. Opt. A 11, 094021 (2009).
[CrossRef]

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Nat. Photonics (1)

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]

Nature (2)

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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Opt. Commun. (2)

E. G. Churin, J. Hossfeld, and T. Tschudi, “Polarization configurations with singular point former by computer generated holograms,” Opt. Commun. 99, 13–17 (1993).
[CrossRef]

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[CrossRef]

Opt. Expr. (1)

K. O’Holleran, M. J. Padgett, and M. R. Dennis, “Topology of optical vortex lines formed by the interference of three, four, and five plane waves,” Opt. Expr. 14, 3039–3044 (2006).
[CrossRef]

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Opt. Lett. (4)

Phys. Rev. A (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, 8185–81891992.
[CrossRef] [PubMed]

M. S. Soskin, V. N. Gorshkow, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

Phys. Rev. Lett. (2)

H. Di Lorenzo Pires, H. C. B. Florijn, and M. P. van Exter, “Measurement of the spiral spectrum of entangled two-photon states,” Phys. Rev. Lett. 104, 020505 (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).
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L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (Taylor & Francis, 2003).
[CrossRef]

J. P. Torres and L. Torner, Twisted Photons (John Wiley, 2011).
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M. R. Dennis and J. B. Götte, “Topological aberration of optical vortex beams and singularimetry of dielectric interfaces,” pre-print (2012), arXiv:1205.6457.

W. Löffler, A. Aiello, and J. P. Woerdman, “Observation of OAM sidebands due to optical reflection,” pre-print (2012), arXiv:1204.4003 (PRL, in print).

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Figures (9)

Fig. 1
Fig. 1

Schematic overview of the set-up used to generate and analyze the optical vortices. The beam produced by the Helium-Neon laser is attenuated with a filter wheel (FW), collimated by a lens (L1), and sent to a fork hologram (FH). A diaphragm (D) allows selecting the desired diffraction order, corresponding to the desired topological charge of the vortex. Lens (L2) in an f-f configuration creates a far field image at the plane where the imaging process takes place. Two different detection systems (A and B) were mounted alternatively on a motorized translation stage. System A makes a direct image of the intensity profile at the pinhole (P) by using a lens (L4) in a 2f-2f configuration. System B uses a lens (L3) to image the far-field diffraction pattern of the multi-pinhole interferometer (MPI) onto the CCD camera.

Fig. 2
Fig. 2

Intensity profiles of three different diffraction orders ( = 1,3,5) created in our set-up by using lens L1(f1 = 750 mm) to illuminate the dislocation hologram with a Gaussian beam with a flat wavefront. Circles represents the experimental data averaged over the azimuthal angle, solid curves are intensity functions derived from Eq. (2), also called Kummer beams, while the dashed blue curves are Laguerre-Gauss intensity profiles with the same waist parameter.

Fig. 3
Fig. 3

Images of the dark region inside the = +3 and = −3 diffracted beams. Images (a) and (c) are direct intensity images taken with detection system A in Fig. 1; the sharp circular edge shows the pinhole used to block the light from the brighter outer regions (grid lines spaced by 100 μm). In Images (b) and (d) a reference beam was introduced to generate interference fringes and observe the single-charged vortices as ”fork-shaped” fringes; the white-dashed curves are meant to guide the eye.

Fig. 4
Fig. 4

Sketch of the aperture plane of a multi-pinhole interferometer (MPI), comprising N = 7 pinholes arranged along a circumference. The MPI allows one to sample the impinging field at each of the pinholes and retrieve the set of N complex amplitudes {E1,..., EN}, apart from an overall phase factor. If the pinholes are small enough - the picture shows the case b/a = 0.2 - amplitude and phase can be considered to be constant over each of the sampled areas.

Fig. 5
Fig. 5

Sketch of the working principle of a multi-pinhole interferometer. (a) shows the measured far-field diffraction pattern of an = +1 vortex impinging on an MPI with N = 7 pinholes of diameter b = 20 μm arranged on a circle of radius a = 100 μm. (b) shows the (inverse) Fourier transformed image of this diffraction pattern. The white heptagon and the set of interference terms { E i E j * } give an idea of how the single complex amplitudes {Em} are retrieved in the analysis process.

Fig. 6
Fig. 6

Scan of (a) an = +3 and (b) an = −3 diffracted beam with the multi-pinhole interferometer technique. Each one of the seven plots corresponds to a single -component in the decomposition of the vortex into the basis of radially independent optical vortex modes. The results clearly shows the presence of three single charged vortices, and no trace of the originals = ±3 vortices. Note also the agreement in the relative position of the vortices, with respect to Fig. 3. The red-dashed line in the bottom-left figure denotes the cross section used for Fig. 8.

Fig. 7
Fig. 7

Scan of (a) an = +5 diffracted beam with the multi-pinhole interferometer technique. In this case the only = 0,±1 plots are shown, because the = ±2,±3 contributions are negligible. Note the prominent splitting and the almost symmetric placement of the unity-charge vortices on a circle.

Fig. 8
Fig. 8

Expected and measured resolution of a multi-pinhole interferometer. Dashed lines represent the Lorentzian shaped resolution curve given by Eq. (8); P0 in red; P1 in blue. Crosses are experimental results obtained by scanning the MPI over a pure = 1 vortex and averaging these results over the azimuthal angle. The circles show cross sections of a single split vortex in the third-order diffracted beam (indicated by the red-dashed line in Fig. 6.

Fig. 9
Fig. 9

Images of the dark region inside some optical vortices of different topological charge ( = 1,...,5) generated with a spatial light modulator(SLM). Sizes of the pinholes are 400 μm for = 1,2,3, 700 μm for = 4, and 800 μm for = 5; all frames are 900 μm × 900 μm. The pictures show that higher-order optical vortices exhibit similar splitting behavior, independently of the optical system used to produce them. See text for details.

Equations (13)

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u , p = 0 L G ( r , ϕ ) ( r w ) | l | exp ( r 2 w 2 ) exp ( i ϕ ) ,
u ˜ ( r , ϕ ) exp ( r 2 2 w 2 ) r w [ I ( 1 ) / 2 ( r 2 2 w 2 ) I ( + 1 ) / 2 ( r 2 2 w 2 ) ] exp ( i ϕ )
λ 1 N m = 1 N E m exp ( i 2 π m / N ) .
P 1 P = 1 1 + ( r / a ) 2
E ( x , y ) = D ( x + i y ) 2 + E o = D [ x + i ( y + d ) ] [ x + i ( y d ) ] ,
P 1 P = 1 1 + [ ( y 0 2 d 2 ) 2 + a 4 ] / ( 2 a y 0 ) 2 .
( r 0 w ) 2 | l | = | | ! 2 | | I b I ,
I ( μ , ν ) = I 0 | m = 1 N E m [ circ ( x x m , y y m ) ] | 2 ,
g ( x , y ) = 1 [ I ( μ , ν ) ] = n , m = 1 N P m n ( x , y ) E m E n * .
S m = n = 1 n m N a m n , P m = n = 1 n m N a m n φ m n ,
S m = n = 1 n m N a m n = A m ( n = 1 N A n A m )
A m = S m / ( n = 1 N A n A m ) .
( ϕ 1 , , ϕ n ) = [ M eff ] 1 ( P 2 , , P N ) .

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