Abstract

We present a design to generate structurally propagation invariant light beams carrying non-integer orbital angular momentum (OAM) using Hermite-Laguerre-Gaussian (HLG) modes. Different from previous techniques, the symmetry axes of our beams are fixed when varying the OAM; this simplifies the calibration technique for beam positional measurement using a quadrant detector. We have also demonstrated analytically and experimentally that both the OAM value and the HLG mode orientation play an important role in the quadrant detector response. The assumption that a quadrant detector is most sensitive at the beam center does not always hold for anisotropic beam profiles, such as HLG beams.

© 2012 OSA

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  1. E. Abramochkin and V. Volostnikov, “Beam transformation and nontransformed beams,” Opt. Commun.83, 123–125 (1991).
    [CrossRef]
  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. A45, 8185–8189 (1992).
    [CrossRef] [PubMed]
  3. H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt.42, 217–223 (1995).
    [CrossRef]
  4. M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics5, 343–348 (2011).
    [CrossRef]
  5. S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. ’tHooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett.95, 240501 (2005).
    [CrossRef] [PubMed]
  6. B. J. Pors, F. Miatto, G. W. ’t Hooft, E. R. Eliel, and J. P. Woerdman, “High-dimensional entanglement with orbital-angular-momentum states of light,” J. Opt.13, 064008 (2011).
    [CrossRef]
  7. J. Sato, M. Endo, S. Yamaguchi, K. Nanri, and T. Fujioka, “Simple annular-beam generator with a laser-diode-pumped axially off-set power build-up cavity,” Opt. Commun.277, 342–348 (2007).
    [CrossRef]
  8. G. C. G. Berkhout and M. Beijersbergen, “Measuring optical vortices in a speckle pattern using a multi-pinhole interferometer,” Opt. Express18, 13836–13841 (2010).
    [CrossRef] [PubMed]
  9. F. Tamburini, B. Thidé, G. Molina-Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys.7, 195–197 (2011).
    [CrossRef]
  10. M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A82, 023817 (2010).
    [CrossRef]
  11. S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Spiral phase contrast imaging in microscopy,” Opt. Express13, 689–694 (2005).
    [CrossRef] [PubMed]
  12. M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun.96, 123–132 (1993).
    [CrossRef]
  13. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun.112, 321–327 (1994).
    [CrossRef]
  14. G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun.127, 183–188 (1996).
    [CrossRef]
  15. J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre-Gaussian modes by computer-generated holograms,” J. Mod. Opt.45, 1231–1237 (1998).
    [CrossRef]
  16. L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett.96, 163905 (2006).
    [CrossRef] [PubMed]
  17. G. Machavariani, N. Davidson, E. Hasman, S. Bilt, A. Ishaaya, and A. A. Friesem, “Efficient conversion of a Gaussian beam to a high purity helical beam,” Opt. Commun209, 265–271 (2002).
    [CrossRef]
  18. S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, “Creation of Laguerre-Gaussian laser modes using diffractive optics,” Phys. Rev. A66, 043801 (2002).
    [CrossRef]
  19. S.-C. Chu and K. Otsuka, “Doughnut-like beam generation of Laguerre-Gaussian mode with extremely high mode purity,” Opt. Commun.281, 1647–1653 (2008).
    [CrossRef]
  20. N. Matsumoto, T. Ando, T. Inoue, Y. Ohtake, N. Fukuchi, and T. Hara, “Generation of high-quality higher-order Laguerre-Gaussian beams using liquid-crystal-on-silicon spatial light modulators,” J. Opt. Soc. Am. A25, 1642–1651 (2008).
    [CrossRef]
  21. T. Ando, Y. Ohtake, N. Matsumoto, T. Inoue, and N. Fukuchi, “Mode purities of Laguerre–Gaussian beams generated via complex-amplitude modulation using phase-only spatial light modulators,” Opt. Lett34, 34–36 (2009).
    [CrossRef]
  22. M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A: Pure Appl. Opt.6, 259–268 (2004).
    [CrossRef]
  23. J. B. Götte, K. O’Holleran, D. Preece, F. Flossman, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Light beams with fractional orbital angular momentum and their vortex structure,” Opt. Express16, 993–1006 (2008).
    [CrossRef] [PubMed]
  24. D. P. O’Dwyer, C. F. Phelan, Y. P. Rakovich, P. R. Eastham, J. G. Lunney, and J. F. Donegan, “Generation of continuously tunable fractional optical orbital angular momentum using internal conical diffraction,” Opt. Express18, 16480–16485 (2010).
    [CrossRef]
  25. A. T. O’Neil and J. Courtial, “Mode transformations in terms of the constituent Hermite-Gaussian or LaguerreGaussian modes and the variable-phase mode converter,” Opt. Commun.181, 35–45 (2000).
    [CrossRef]
  26. E. G. Abramochkin and V. G. Volostnikov, “Generalized Gaussian beams,” J. Opt. A: Pure Appl. Opt.6, S157–S161 (2004).
    [CrossRef]
  27. J. Visser and G. Nienhuis, “Orbital angular momentum of general astigmatic modes,” Phys. Rev. A70, 013809 (2004).
    [CrossRef]
  28. E. G. Abramochkin, E. Razueva, and V. G. Volostnikov, “General astigmatic transform of Hermite-Laguerre-Gaussian beams,” J. Opt. Soc. Am. A27, 2506–2513 (2010).
    [CrossRef]
  29. E. J. Lee, Y. Park, C. S. Kim, and T. Kouh, “Detection sensitivity of the optical beam deflection method characterized with the optical spot size on the detector,” Curr. Appl. Phys.10, 834–837 (2010).
    [CrossRef]
  30. Y. Panduputra, T. W. Ng, A. Neild, and M. Robinson, “Intensity influence on Gaussian beam laser based measurements using quadrant photodiodes,” Appl. Opt.49, 3669–3675 (2010).
    [CrossRef] [PubMed]
  31. N. Hermosa, A. Aiello, and J. P. Woerdman, “Quadrant detector calibration for vortex beams,” Opt. Lett.36, 409–411 (2011).
    [CrossRef] [PubMed]
  32. S. J. M. Habraken, “Cylindrical lens mode converters and OAM,” Personal Communication (2010).

2011

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics5, 343–348 (2011).
[CrossRef]

B. J. Pors, F. Miatto, G. W. ’t Hooft, E. R. Eliel, and J. P. Woerdman, “High-dimensional entanglement with orbital-angular-momentum states of light,” J. Opt.13, 064008 (2011).
[CrossRef]

F. Tamburini, B. Thidé, G. Molina-Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys.7, 195–197 (2011).
[CrossRef]

N. Hermosa, A. Aiello, and J. P. Woerdman, “Quadrant detector calibration for vortex beams,” Opt. Lett.36, 409–411 (2011).
[CrossRef] [PubMed]

2010

2009

T. Ando, Y. Ohtake, N. Matsumoto, T. Inoue, and N. Fukuchi, “Mode purities of Laguerre–Gaussian beams generated via complex-amplitude modulation using phase-only spatial light modulators,” Opt. Lett34, 34–36 (2009).
[CrossRef]

2008

2007

J. Sato, M. Endo, S. Yamaguchi, K. Nanri, and T. Fujioka, “Simple annular-beam generator with a laser-diode-pumped axially off-set power build-up cavity,” Opt. Commun.277, 342–348 (2007).
[CrossRef]

2006

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett.96, 163905 (2006).
[CrossRef] [PubMed]

2005

S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Spiral phase contrast imaging in microscopy,” Opt. Express13, 689–694 (2005).
[CrossRef] [PubMed]

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. ’tHooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett.95, 240501 (2005).
[CrossRef] [PubMed]

2004

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

E. G. Abramochkin and V. G. Volostnikov, “Generalized Gaussian beams,” J. Opt. A: Pure Appl. Opt.6, S157–S161 (2004).
[CrossRef]

J. Visser and G. Nienhuis, “Orbital angular momentum of general astigmatic modes,” Phys. Rev. A70, 013809 (2004).
[CrossRef]

2002

G. Machavariani, N. Davidson, E. Hasman, S. Bilt, A. Ishaaya, and A. A. Friesem, “Efficient conversion of a Gaussian beam to a high purity helical beam,” Opt. Commun209, 265–271 (2002).
[CrossRef]

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, “Creation of Laguerre-Gaussian laser modes using diffractive optics,” Phys. Rev. A66, 043801 (2002).
[CrossRef]

2000

A. T. O’Neil and J. Courtial, “Mode transformations in terms of the constituent Hermite-Gaussian or LaguerreGaussian modes and the variable-phase mode converter,” Opt. Commun.181, 35–45 (2000).
[CrossRef]

1998

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre-Gaussian modes by computer-generated holograms,” J. Mod. Opt.45, 1231–1237 (1998).
[CrossRef]

1996

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun.127, 183–188 (1996).
[CrossRef]

1995

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt.42, 217–223 (1995).
[CrossRef]

1994

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun.112, 321–327 (1994).
[CrossRef]

1993

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun.96, 123–132 (1993).
[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. A45, 8185–8189 (1992).
[CrossRef] [PubMed]

1991

E. Abramochkin and V. Volostnikov, “Beam transformation and nontransformed beams,” Opt. Commun.83, 123–125 (1991).
[CrossRef]

’t Hooft, G. W.

B. J. Pors, F. Miatto, G. W. ’t Hooft, E. R. Eliel, and J. P. Woerdman, “High-dimensional entanglement with orbital-angular-momentum states of light,” J. Opt.13, 064008 (2011).
[CrossRef]

’tHooft, G. W.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. ’tHooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett.95, 240501 (2005).
[CrossRef] [PubMed]

Abraham, E. R. I.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, “Creation of Laguerre-Gaussian laser modes using diffractive optics,” Phys. Rev. A66, 043801 (2002).
[CrossRef]

Abramochkin, E.

E. Abramochkin and V. Volostnikov, “Beam transformation and nontransformed beams,” Opt. Commun.83, 123–125 (1991).
[CrossRef]

Abramochkin, E. G.

E. G. Abramochkin, E. Razueva, and V. G. Volostnikov, “General astigmatic transform of Hermite-Laguerre-Gaussian beams,” J. Opt. Soc. Am. A27, 2506–2513 (2010).
[CrossRef]

E. G. Abramochkin and V. G. Volostnikov, “Generalized Gaussian beams,” J. Opt. A: Pure Appl. Opt.6, S157–S161 (2004).
[CrossRef]

Aiello, A.

N. Hermosa, A. Aiello, and J. P. Woerdman, “Quadrant detector calibration for vortex beams,” Opt. Lett.36, 409–411 (2011).
[CrossRef] [PubMed]

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A82, 023817 (2010).
[CrossRef]

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. ’tHooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett.95, 240501 (2005).
[CrossRef] [PubMed]

Allen, L.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre-Gaussian modes by computer-generated holograms,” J. Mod. Opt.45, 1231–1237 (1998).
[CrossRef]

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun.127, 183–188 (1996).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun.96, 123–132 (1993).
[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. A45, 8185–8189 (1992).
[CrossRef] [PubMed]

Ando, T.

T. Ando, Y. Ohtake, N. Matsumoto, T. Inoue, and N. Fukuchi, “Mode purities of Laguerre–Gaussian beams generated via complex-amplitude modulation using phase-only spatial light modulators,” Opt. Lett34, 34–36 (2009).
[CrossRef]

N. Matsumoto, T. Ando, T. Inoue, Y. Ohtake, N. Fukuchi, and T. Hara, “Generation of high-quality higher-order Laguerre-Gaussian beams using liquid-crystal-on-silicon spatial light modulators,” J. Opt. Soc. Am. A25, 1642–1651 (2008).
[CrossRef]

Anzolin, G.

F. Tamburini, B. Thidé, G. Molina-Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys.7, 195–197 (2011).
[CrossRef]

Arlt, J.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre-Gaussian modes by computer-generated holograms,” J. Mod. Opt.45, 1231–1237 (1998).
[CrossRef]

Barnett, S. M.

Beijersbergen, M.

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun.112, 321–327 (1994).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun.96, 123–132 (1993).
[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. A45, 8185–8189 (1992).
[CrossRef] [PubMed]

Berkhout, G. C. G.

Bernet, S.

Berry, M. V.

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

Bilt, S.

G. Machavariani, N. Davidson, E. Hasman, S. Bilt, A. Ishaaya, and A. A. Friesem, “Efficient conversion of a Gaussian beam to a high purity helical beam,” Opt. Commun209, 265–271 (2002).
[CrossRef]

Bowman, R.

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics5, 343–348 (2011).
[CrossRef]

Chu, S.-C.

S.-C. Chu and K. Otsuka, “Doughnut-like beam generation of Laguerre-Gaussian mode with extremely high mode purity,” Opt. Commun.281, 1647–1653 (2008).
[CrossRef]

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun.112, 321–327 (1994).
[CrossRef]

Courtial, J.

A. T. O’Neil and J. Courtial, “Mode transformations in terms of the constituent Hermite-Gaussian or LaguerreGaussian modes and the variable-phase mode converter,” Opt. Commun.181, 35–45 (2000).
[CrossRef]

Davidson, N.

G. Machavariani, N. Davidson, E. Hasman, S. Bilt, A. Ishaaya, and A. A. Friesem, “Efficient conversion of a Gaussian beam to a high purity helical beam,” Opt. Commun209, 265–271 (2002).
[CrossRef]

Dholakia, K.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre-Gaussian modes by computer-generated holograms,” J. Mod. Opt.45, 1231–1237 (1998).
[CrossRef]

Donegan, J. F.

Eastham, P. R.

Eliel, E. R.

B. J. Pors, F. Miatto, G. W. ’t Hooft, E. R. Eliel, and J. P. Woerdman, “High-dimensional entanglement with orbital-angular-momentum states of light,” J. Opt.13, 064008 (2011).
[CrossRef]

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. ’tHooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett.95, 240501 (2005).
[CrossRef] [PubMed]

Endo, M.

J. Sato, M. Endo, S. Yamaguchi, K. Nanri, and T. Fujioka, “Simple annular-beam generator with a laser-diode-pumped axially off-set power build-up cavity,” Opt. Commun.277, 342–348 (2007).
[CrossRef]

Flossman, F.

Franke-Arnold, S.

Friesem, A. A.

G. Machavariani, N. Davidson, E. Hasman, S. Bilt, A. Ishaaya, and A. A. Friesem, “Efficient conversion of a Gaussian beam to a high purity helical beam,” Opt. Commun209, 265–271 (2002).
[CrossRef]

Fujioka, T.

J. Sato, M. Endo, S. Yamaguchi, K. Nanri, and T. Fujioka, “Simple annular-beam generator with a laser-diode-pumped axially off-set power build-up cavity,” Opt. Commun.277, 342–348 (2007).
[CrossRef]

Fukuchi, N.

T. Ando, Y. Ohtake, N. Matsumoto, T. Inoue, and N. Fukuchi, “Mode purities of Laguerre–Gaussian beams generated via complex-amplitude modulation using phase-only spatial light modulators,” Opt. Lett34, 34–36 (2009).
[CrossRef]

N. Matsumoto, T. Ando, T. Inoue, Y. Ohtake, N. Fukuchi, and T. Hara, “Generation of high-quality higher-order Laguerre-Gaussian beams using liquid-crystal-on-silicon spatial light modulators,” J. Opt. Soc. Am. A25, 1642–1651 (2008).
[CrossRef]

Fürhapter, S.

Götte, J. B.

Habraken, S. J. M.

S. J. M. Habraken, “Cylindrical lens mode converters and OAM,” Personal Communication (2010).

Hara, T.

Hasman, E.

G. Machavariani, N. Davidson, E. Hasman, S. Bilt, A. Ishaaya, and A. A. Friesem, “Efficient conversion of a Gaussian beam to a high purity helical beam,” Opt. Commun209, 265–271 (2002).
[CrossRef]

He, H.

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt.42, 217–223 (1995).
[CrossRef]

Heckenberg, N. R.

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt.42, 217–223 (1995).
[CrossRef]

Hermosa, N.

N. Hermosa, A. Aiello, and J. P. Woerdman, “Quadrant detector calibration for vortex beams,” Opt. Lett.36, 409–411 (2011).
[CrossRef] [PubMed]

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A82, 023817 (2010).
[CrossRef]

Inoue, T.

T. Ando, Y. Ohtake, N. Matsumoto, T. Inoue, and N. Fukuchi, “Mode purities of Laguerre–Gaussian beams generated via complex-amplitude modulation using phase-only spatial light modulators,” Opt. Lett34, 34–36 (2009).
[CrossRef]

N. Matsumoto, T. Ando, T. Inoue, Y. Ohtake, N. Fukuchi, and T. Hara, “Generation of high-quality higher-order Laguerre-Gaussian beams using liquid-crystal-on-silicon spatial light modulators,” J. Opt. Soc. Am. A25, 1642–1651 (2008).
[CrossRef]

Ishaaya, A.

G. Machavariani, N. Davidson, E. Hasman, S. Bilt, A. Ishaaya, and A. A. Friesem, “Efficient conversion of a Gaussian beam to a high purity helical beam,” Opt. Commun209, 265–271 (2002).
[CrossRef]

Jesacher, A.

Kennedy, S. A.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, “Creation of Laguerre-Gaussian laser modes using diffractive optics,” Phys. Rev. A66, 043801 (2002).
[CrossRef]

Kim, C. S.

E. J. Lee, Y. Park, C. S. Kim, and T. Kouh, “Detection sensitivity of the optical beam deflection method characterized with the optical spot size on the detector,” Curr. Appl. Phys.10, 834–837 (2010).
[CrossRef]

Kouh, T.

E. J. Lee, Y. Park, C. S. Kim, and T. Kouh, “Detection sensitivity of the optical beam deflection method characterized with the optical spot size on the detector,” Curr. Appl. Phys.10, 834–837 (2010).
[CrossRef]

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun.112, 321–327 (1994).
[CrossRef]

Lee, E. J.

E. J. Lee, Y. Park, C. S. Kim, and T. Kouh, “Detection sensitivity of the optical beam deflection method characterized with the optical spot size on the detector,” Curr. Appl. Phys.10, 834–837 (2010).
[CrossRef]

Lunney, J. G.

Ma, X.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. ’tHooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett.95, 240501 (2005).
[CrossRef] [PubMed]

Machavariani, G.

G. Machavariani, N. Davidson, E. Hasman, S. Bilt, A. Ishaaya, and A. A. Friesem, “Efficient conversion of a Gaussian beam to a high purity helical beam,” Opt. Commun209, 265–271 (2002).
[CrossRef]

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett.96, 163905 (2006).
[CrossRef] [PubMed]

Marrucci, L.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett.96, 163905 (2006).
[CrossRef] [PubMed]

Matsumoto, N.

T. Ando, Y. Ohtake, N. Matsumoto, T. Inoue, and N. Fukuchi, “Mode purities of Laguerre–Gaussian beams generated via complex-amplitude modulation using phase-only spatial light modulators,” Opt. Lett34, 34–36 (2009).
[CrossRef]

N. Matsumoto, T. Ando, T. Inoue, Y. Ohtake, N. Fukuchi, and T. Hara, “Generation of high-quality higher-order Laguerre-Gaussian beams using liquid-crystal-on-silicon spatial light modulators,” J. Opt. Soc. Am. A25, 1642–1651 (2008).
[CrossRef]

Merano, M.

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A82, 023817 (2010).
[CrossRef]

Miatto, F.

B. J. Pors, F. Miatto, G. W. ’t Hooft, E. R. Eliel, and J. P. Woerdman, “High-dimensional entanglement with orbital-angular-momentum states of light,” J. Opt.13, 064008 (2011).
[CrossRef]

Molina-Terriza, G.

F. Tamburini, B. Thidé, G. Molina-Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys.7, 195–197 (2011).
[CrossRef]

Nanri, K.

J. Sato, M. Endo, S. Yamaguchi, K. Nanri, and T. Fujioka, “Simple annular-beam generator with a laser-diode-pumped axially off-set power build-up cavity,” Opt. Commun.277, 342–348 (2007).
[CrossRef]

Neild, A.

Ng, T. W.

Nienhuis, G.

J. Visser and G. Nienhuis, “Orbital angular momentum of general astigmatic modes,” Phys. Rev. A70, 013809 (2004).
[CrossRef]

O’Dwyer, D. P.

O’Holleran, K.

O’Neil, A. T.

A. T. O’Neil and J. Courtial, “Mode transformations in terms of the constituent Hermite-Gaussian or LaguerreGaussian modes and the variable-phase mode converter,” Opt. Commun.181, 35–45 (2000).
[CrossRef]

Oemrawsingh, S. S. R.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. ’tHooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett.95, 240501 (2005).
[CrossRef] [PubMed]

Ohtake, Y.

T. Ando, Y. Ohtake, N. Matsumoto, T. Inoue, and N. Fukuchi, “Mode purities of Laguerre–Gaussian beams generated via complex-amplitude modulation using phase-only spatial light modulators,” Opt. Lett34, 34–36 (2009).
[CrossRef]

N. Matsumoto, T. Ando, T. Inoue, Y. Ohtake, N. Fukuchi, and T. Hara, “Generation of high-quality higher-order Laguerre-Gaussian beams using liquid-crystal-on-silicon spatial light modulators,” J. Opt. Soc. Am. A25, 1642–1651 (2008).
[CrossRef]

Otsuka, K.

S.-C. Chu and K. Otsuka, “Doughnut-like beam generation of Laguerre-Gaussian mode with extremely high mode purity,” Opt. Commun.281, 1647–1653 (2008).
[CrossRef]

Padgett, M.

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics5, 343–348 (2011).
[CrossRef]

Padgett, M. J.

J. B. Götte, K. O’Holleran, D. Preece, F. Flossman, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Light beams with fractional orbital angular momentum and their vortex structure,” Opt. Express16, 993–1006 (2008).
[CrossRef] [PubMed]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre-Gaussian modes by computer-generated holograms,” J. Mod. Opt.45, 1231–1237 (1998).
[CrossRef]

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun.127, 183–188 (1996).
[CrossRef]

Panduputra, Y.

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett.96, 163905 (2006).
[CrossRef] [PubMed]

Park, Y.

E. J. Lee, Y. Park, C. S. Kim, and T. Kouh, “Detection sensitivity of the optical beam deflection method characterized with the optical spot size on the detector,” Curr. Appl. Phys.10, 834–837 (2010).
[CrossRef]

Phelan, C. F.

Pors, B. J.

B. J. Pors, F. Miatto, G. W. ’t Hooft, E. R. Eliel, and J. P. Woerdman, “High-dimensional entanglement with orbital-angular-momentum states of light,” J. Opt.13, 064008 (2011).
[CrossRef]

Porterfield, J. Z.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, “Creation of Laguerre-Gaussian laser modes using diffractive optics,” Phys. Rev. A66, 043801 (2002).
[CrossRef]

Preece, D.

Rakovich, Y. P.

Razueva, E.

Ritsch-Marte, M.

Robertson, D. A.

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun.127, 183–188 (1996).
[CrossRef]

Robinson, M.

Rubinsztein-Dunlop, H.

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt.42, 217–223 (1995).
[CrossRef]

Sato, J.

J. Sato, M. Endo, S. Yamaguchi, K. Nanri, and T. Fujioka, “Simple annular-beam generator with a laser-diode-pumped axially off-set power build-up cavity,” Opt. Commun.277, 342–348 (2007).
[CrossRef]

Smith, G. M.

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun.127, 183–188 (1996).
[CrossRef]

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. A45, 8185–8189 (1992).
[CrossRef] [PubMed]

Szabo, M. J.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, “Creation of Laguerre-Gaussian laser modes using diffractive optics,” Phys. Rev. A66, 043801 (2002).
[CrossRef]

Tamburini, F.

F. Tamburini, B. Thidé, G. Molina-Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys.7, 195–197 (2011).
[CrossRef]

Teslow, H.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, “Creation of Laguerre-Gaussian laser modes using diffractive optics,” Phys. Rev. A66, 043801 (2002).
[CrossRef]

Thidé, B.

F. Tamburini, B. Thidé, G. Molina-Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys.7, 195–197 (2011).
[CrossRef]

Turnbull, G. A.

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun.127, 183–188 (1996).
[CrossRef]

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

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun.96, 123–132 (1993).
[CrossRef]

Visser, J.

J. Visser and G. Nienhuis, “Orbital angular momentum of general astigmatic modes,” Phys. Rev. A70, 013809 (2004).
[CrossRef]

Voigt, D.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. ’tHooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett.95, 240501 (2005).
[CrossRef] [PubMed]

Volostnikov, V.

E. Abramochkin and V. Volostnikov, “Beam transformation and nontransformed beams,” Opt. Commun.83, 123–125 (1991).
[CrossRef]

Volostnikov, V. G.

E. G. Abramochkin, E. Razueva, and V. G. Volostnikov, “General astigmatic transform of Hermite-Laguerre-Gaussian beams,” J. Opt. Soc. Am. A27, 2506–2513 (2010).
[CrossRef]

E. G. Abramochkin and V. G. Volostnikov, “Generalized Gaussian beams,” J. Opt. A: Pure Appl. Opt.6, S157–S161 (2004).
[CrossRef]

Woerdman, J. P.

N. Hermosa, A. Aiello, and J. P. Woerdman, “Quadrant detector calibration for vortex beams,” Opt. Lett.36, 409–411 (2011).
[CrossRef] [PubMed]

B. J. Pors, F. Miatto, G. W. ’t Hooft, E. R. Eliel, and J. P. Woerdman, “High-dimensional entanglement with orbital-angular-momentum states of light,” J. Opt.13, 064008 (2011).
[CrossRef]

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A82, 023817 (2010).
[CrossRef]

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. ’tHooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett.95, 240501 (2005).
[CrossRef] [PubMed]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun.112, 321–327 (1994).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun.96, 123–132 (1993).
[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. A45, 8185–8189 (1992).
[CrossRef] [PubMed]

Yamaguchi, S.

J. Sato, M. Endo, S. Yamaguchi, K. Nanri, and T. Fujioka, “Simple annular-beam generator with a laser-diode-pumped axially off-set power build-up cavity,” Opt. Commun.277, 342–348 (2007).
[CrossRef]

Appl. Opt.

Curr. Appl. Phys.

E. J. Lee, Y. Park, C. S. Kim, and T. Kouh, “Detection sensitivity of the optical beam deflection method characterized with the optical spot size on the detector,” Curr. Appl. Phys.10, 834–837 (2010).
[CrossRef]

J. Mod. Opt.

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt.42, 217–223 (1995).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre-Gaussian modes by computer-generated holograms,” J. Mod. Opt.45, 1231–1237 (1998).
[CrossRef]

J. Opt.

B. J. Pors, F. Miatto, G. W. ’t Hooft, E. R. Eliel, and J. P. Woerdman, “High-dimensional entanglement with orbital-angular-momentum states of light,” J. Opt.13, 064008 (2011).
[CrossRef]

J. Opt. A: Pure Appl. Opt.

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

E. G. Abramochkin and V. G. Volostnikov, “Generalized Gaussian beams,” J. Opt. A: Pure Appl. Opt.6, S157–S161 (2004).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Photonics

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics5, 343–348 (2011).
[CrossRef]

Nat. Phys.

F. Tamburini, B. Thidé, G. Molina-Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys.7, 195–197 (2011).
[CrossRef]

Opt. Commun

G. Machavariani, N. Davidson, E. Hasman, S. Bilt, A. Ishaaya, and A. A. Friesem, “Efficient conversion of a Gaussian beam to a high purity helical beam,” Opt. Commun209, 265–271 (2002).
[CrossRef]

Opt. Commun.

S.-C. Chu and K. Otsuka, “Doughnut-like beam generation of Laguerre-Gaussian mode with extremely high mode purity,” Opt. Commun.281, 1647–1653 (2008).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun.96, 123–132 (1993).
[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun.112, 321–327 (1994).
[CrossRef]

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun.127, 183–188 (1996).
[CrossRef]

J. Sato, M. Endo, S. Yamaguchi, K. Nanri, and T. Fujioka, “Simple annular-beam generator with a laser-diode-pumped axially off-set power build-up cavity,” Opt. Commun.277, 342–348 (2007).
[CrossRef]

E. Abramochkin and V. Volostnikov, “Beam transformation and nontransformed beams,” Opt. Commun.83, 123–125 (1991).
[CrossRef]

A. T. O’Neil and J. Courtial, “Mode transformations in terms of the constituent Hermite-Gaussian or LaguerreGaussian modes and the variable-phase mode converter,” Opt. Commun.181, 35–45 (2000).
[CrossRef]

Opt. Express

Opt. Lett

T. Ando, Y. Ohtake, N. Matsumoto, T. Inoue, and N. Fukuchi, “Mode purities of Laguerre–Gaussian beams generated via complex-amplitude modulation using phase-only spatial light modulators,” Opt. Lett34, 34–36 (2009).
[CrossRef]

Opt. Lett.

Phys. Rev. A

J. Visser and G. Nienhuis, “Orbital angular momentum of general astigmatic modes,” Phys. Rev. A70, 013809 (2004).
[CrossRef]

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, “Creation of Laguerre-Gaussian laser modes using diffractive optics,” Phys. Rev. A66, 043801 (2002).
[CrossRef]

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A82, 023817 (2010).
[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. A45, 8185–8189 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. ’tHooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett.95, 240501 (2005).
[CrossRef] [PubMed]

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett.96, 163905 (2006).
[CrossRef] [PubMed]

Other

S. J. M. Habraken, “Cylindrical lens mode converters and OAM,” Personal Communication (2010).

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Figures (7)

Fig. 1
Fig. 1

Our experimental set-up to generate HLG modes as non-integer OAM beams, equipped with a quadrant detector for measuring the beam positional shifts, discussed in Section 3.

Fig. 2
Fig. 2

An incoming HG0,1 mode at varying orientation angle α projected onto the orthogonal symmetry axes of the cylindrical lenses of a ‘π/2-mode converter’. The symmetry axes of the outgoing HLG modes are always aligned to the projection axes. The outgoing HLG modes experience Gouy phase φ = 2α.

Fig. 3
Fig. 3

(a) Measured intensity profiles of the impinging HG0,1 mode as a function of the orientation angle α with respect to the symmetry axes of the ‘π/2-mode converter’; the white lines correspond to the wire orientation in the open laser cavity of Fig. 1. (b) Measured far-field intensity profiles after the collimating lens of the outgoing Hermite-Laguerre-Gauss (HLG) modes. (c) Calculated intensity profiles to compare with the measurement results in (b). The color map in the calculated intensity profiles (c) corresponds to the HLG phase profile that gradually increases from 0 to 2π.

Fig. 4
Fig. 4

Mode profiles at several Rayleigh distance zR, representing the near- and far-field planes for the outgoing HLG0,1|[α:60°] mode.

Fig. 5
Fig. 5

The (a) measured and (b) calculated interference patterns showing the phase singularity of the HLG beams. The black color corresponds to zero intensity and zero phase, whereas the white color corresponds to maximal intensity and phase ϕ = 2π.

Fig. 6
Fig. 6

(a) The cross section of the HLG0,1|α mode profile along the x-axis. (b) The corresponding response of a quadrant detector for beam displacement along the x–axis. Lines (both solid and dashed) and data points correspond to the analytical solution and experimental data, respectively.

Fig. 7
Fig. 7

The calibration constant K as a function of non-integer OAM is derived analytically for HLG0,1 modes with varying α. The white lines on the top row images illustrate the x-positions at which K is derived for several α values.

Equations (3)

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

I x I Σ = I A + I D ( I B + I C ) I A + I D + I B + I C = x | U ( x , y ) | 2 d y d x x | U ( x , y ) | 2 d y d x | U ( x , y ) | 2 d y d x = 2 0 x 0 | U ( x , y ) | 2 d y d x 2 0 0 | U ( x , y ) | 2 d y d x = 0 x 0 | U ( x , y ) | 2 d y d x 0 0 | U ( x , y ) | 2 d y d x ,
I y I Σ = I A + I B ( I C + I D ) I A + I B + I C + I D = 0 y 0 | U ( x , y ) | 2 d x d y 0 0 | U ( x , y ) | 2 d y d x ,
I x I Σ = 2 2 x π w exp [ 2 ( x w ) 2 ] cos 2 ( α ) + erf ( 2 x w ) .

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