Abstract

Proof of concept measurements of a modular spiral phase plate design able to generate millimetre wavelength beams with an azimuthal mode number of l = ±10 are presented. The plate is comprised of ten single modules that interlock to create the full plate assembly, allowing improved machining accuracy compared to standard techniques. Therefore, this design could be used in millimetre wavelength systems that require the manipulation of large OAM modes. The plate was manufactured from polypropylene (index of refraction n ≈ 1.5), and was measured at 100GHz. A three dimensional field scanner was used to measure three near field surfaces behind the plate. Intensity measurements showed the expected OAM intensity ring, and phase measurements showed ten phase dislocations, implying proper functionality.

© 2014 Optical Society of America

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  1. J. Wang, J. Yang, I.M. Frazal, 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,” Nature Photon. 6, 488–496 (2012).
    [CrossRef]
  2. H. Huang, G. Xie, Y. Yan, N. Ahmed, Y. Ren, Y. Yue, D. Rogawski, M. J. Willner, B. I. Erkmen, K. M. Birnbaum, S. J. Dolinar, M. P. J. Lavery, M. J. Padgett, M. Tur, and A. E. Willner, “100 Tbit/s free-space data link enabled by three-dimensional multiplexing of orbital angular momentum, polarization and wavelength,” Opt. Lett. 39, 197–200 (2014).
    [CrossRef] [PubMed]
  3. I. M. Frazal, N. Ahmed, J. Wang, J. Y. Yang, Y. Yan, B. Shamee, H. Huang, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “2 Tbit/s free-space data transmission on two orthogonal orbital-angular-momentum beams each carrying 25 WDM channels,” Opt. Lett. 37, 4753–4755 (2012).
    [CrossRef]
  4. F. Tamburini, E. Mari, A. Sponselli, B. Thidé, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14, 033001 (2012).
    [CrossRef]
  5. D. J. Sanchez, D. W. Oesch, and O. R. Reynolds, “The creation of photonic orbital angular momentum in electromagnetic waves propagating through turbulence,” Astron. Astrophys. 556, A130 (2013).
    [CrossRef]
  6. M. Harwit, “Photon Orbital Angular Momentum in Astrophysics,” Astrophys. J. 597, 1266 (2003).
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  7. M. Gray, Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK, is preparing a manuscript to be called “A photon orbital angular momentum model in an astrophysical maser.”
  8. B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T.D. Carozzi, Ya. N. Istomin, N.H. Ibragimov, and R. Khamitova, “Utilization of Photon Orbital Angular Momentum in the Low-Frequency Radio Domain,” Phys. Rev. Lett. 99, 087701 (2007).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  13. P. Schemmel, S. Maccalli, G. Pisano, and B. Maffei, “Three dimensional measurements of a millimetre wave orbital angular momentum vortex,” Opt. Lett. 39, 626–629 (2014).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  16. M.V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A: Pure Appl. Opt. 6, 259–268 (2004).
    [CrossRef]
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    [CrossRef]
  18. P. Goldsmith, Quasioptical Systems: Gaussian Beam Quasioptical Propagation and Applications, (IEEE Press, 1998).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  23. Y.S. Rumala, “Structured light interference due to multiple reflections in a spiral phase plate device and its propagation,” Proc. SPIE 8999, 899912 (2014).
    [CrossRef]
  24. R. L. Phillips and L. C. Andrews, “Spot size and divergence for Laguerre Gaussian beams of any order,” Appl. Opt. 22, 643 (1982).
    [CrossRef]
  25. V. Kotlyar and A. Kovalev, “Fraunhofer diffraction of the plane wave by a multilevel (quantised) spiral phase plate,” Opt. Lett. 33, 189–191 (2008).
    [CrossRef] [PubMed]
  26. P. Schemmel, S. Maccalli, B. Maffei, F. Ozturk, G. Pisano, and M.W. Ng, “A Near Field 3D Scanner for Millimetre Wavelengths,” in Proceedings of the 35th ESA Antenna Workshop on Antenna and Free Space RF Measurements, 10 – 13 September (2013), ESTEC, Noordwijk, The Netherlands.
  27. F. Ozturk, B. Maffei, and M. W. Ng, “A quasi-optical free-space s-parameters measurement system for material characterisation in W and Ka bands,” in Proceedings of the 33rd ESA Antenna Workshop on Antenna and Free Space RF Measurements, 18 – 21 October (2011), ESTEC, Noordwijk, The Netherlands.
  28. B. Maffei, S. Legg, M. Robinson, F. Ozturk, M. W. Ng, P. Schemmel, and G. Pisano, “Implementation of a quasi-optical free-space s-parameter measurement system,” in Proceedings of the 35th ESA Antenna Workshop on Antenna and Free Space RF Measurements, 10 – 13 September (2013), ESTEC, Noordwijk, The Netherlands.
  29. P. Schemmel, Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK, is preparing a manuscript to be called , “Systematics Study of Spiral Phase Plate Designs for Millimetre Wave Orbital Angular Momentum State Manipulation.”
  30. M.S. Soskin, V. N. Gorshkov, 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 (1997).
    [CrossRef]

2014 (3)

2013 (3)

Y.S. Rumala and A.E. Leanhardt, “Multiple-beam interference in a spiral phase plate,” J. Opt. Soc. Am. B. 30, 615–621 (2013).
[CrossRef]

Y.S. Rumala, “Interference theory of multiple optical vortex states in spiral phase plate etalon: thick-plate and thin-plate approximation,” J. Opt. Soc. Am. B. 31, 615–621 (2013).
[CrossRef]

D. J. Sanchez, D. W. Oesch, and O. R. Reynolds, “The creation of photonic orbital angular momentum in electromagnetic waves propagating through turbulence,” Astron. Astrophys. 556, A130 (2013).
[CrossRef]

2012 (3)

F. Tamburini, E. Mari, A. Sponselli, B. Thidé, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14, 033001 (2012).
[CrossRef]

J. Wang, J. Yang, I.M. Frazal, 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,” Nature Photon. 6, 488–496 (2012).
[CrossRef]

I. M. Frazal, N. Ahmed, J. Wang, J. Y. Yang, Y. Yan, B. Shamee, H. Huang, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “2 Tbit/s free-space data transmission on two orthogonal orbital-angular-momentum beams each carrying 25 WDM channels,” Opt. Lett. 37, 4753–4755 (2012).
[CrossRef]

2011 (1)

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

2008 (2)

A. V. Carpentier, H. Michinel, and J. R. Salgueiro, “Making optical vortices with computer-generated holograms,” Am. J. Phys. 76, 916–921 (2008).
[CrossRef]

V. Kotlyar and A. Kovalev, “Fraunhofer diffraction of the plane wave by a multilevel (quantised) spiral phase plate,” Opt. Lett. 33, 189–191 (2008).
[CrossRef] [PubMed]

2007 (1)

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T.D. Carozzi, Ya. N. Istomin, N.H. Ibragimov, and R. Khamitova, “Utilization of Photon Orbital Angular Momentum in the Low-Frequency Radio Domain,” Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef] [PubMed]

2004 (1)

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

2003 (2)

N. Trappe, J. A. Murphy, and S. Withington, “The Gaussian beam mode analysis of classical phase aberrations in diffraction-limited optical systems,” Eur. J. Phys. 24, 403–412 (2003).
[CrossRef]

M. Harwit, “Photon Orbital Angular Momentum in Astrophysics,” Astrophys. J. 597, 1266 (2003).
[CrossRef]

1997 (1)

M.S. Soskin, V. N. Gorshkov, 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 (1997).
[CrossRef]

1996 (1)

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 (1)

M.J. Padgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Optics Commun. 121, 36–40 (1995).
[CrossRef]

1994 (1)

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 (1)

D. Martin and J. Bowen, “Long-Wave Optics,” IEEE Trans. Microw. Theory Tech. 41, 1676–1689 (1993).
[CrossRef]

1992 (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]

1982 (1)

Ahmed, N.

Allen, L.

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.J. Padgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Optics Commun. 121, 36–40 (1995).
[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] [PubMed]

Andrews, L. C.

Anzolin, G.

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

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] [PubMed]

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]

Bergman, J.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T.D. Carozzi, Ya. N. Istomin, N.H. Ibragimov, and R. Khamitova, “Utilization of Photon Orbital Angular Momentum in the Low-Frequency Radio Domain,” Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef] [PubMed]

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]

Bianchini, A.

F. Tamburini, E. Mari, A. Sponselli, B. Thidé, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14, 033001 (2012).
[CrossRef]

Birnbaum, K. M.

Bowen, J.

D. Martin and J. Bowen, “Long-Wave Optics,” IEEE Trans. Microw. Theory Tech. 41, 1676–1689 (1993).
[CrossRef]

Carozzi, T.D.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T.D. Carozzi, Ya. N. Istomin, N.H. Ibragimov, and R. Khamitova, “Utilization of Photon Orbital Angular Momentum in the Low-Frequency Radio Domain,” Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef] [PubMed]

Carpentier, A. V.

A. V. Carpentier, H. Michinel, and J. R. Salgueiro, “Making optical vortices with computer-generated holograms,” Am. J. Phys. 76, 916–921 (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]

Dolinar, S.

J. Wang, J. Yang, I.M. Frazal, 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,” Nature Photon. 6, 488–496 (2012).
[CrossRef]

I. M. Frazal, N. Ahmed, J. Wang, J. Y. Yang, Y. Yan, B. Shamee, H. Huang, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “2 Tbit/s free-space data transmission on two orthogonal orbital-angular-momentum beams each carrying 25 WDM channels,” Opt. Lett. 37, 4753–4755 (2012).
[CrossRef]

Dolinar, S. J.

Erkmen, B. I.

Frazal, I. M.

Frazal, I.M.

J. Wang, J. Yang, I.M. Frazal, 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,” Nature Photon. 6, 488–496 (2012).
[CrossRef]

Goldsmith, P.

P. Goldsmith, Quasioptical Systems: Gaussian Beam Quasioptical Propagation and Applications, (IEEE Press, 1998).
[CrossRef]

Gorshkov, V. N.

M.S. Soskin, V. N. Gorshkov, 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 (1997).
[CrossRef]

Gray, M.

M. Gray, Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK, is preparing a manuscript to be called “A photon orbital angular momentum model in an astrophysical maser.”

Harwit, M.

M. Harwit, “Photon Orbital Angular Momentum in Astrophysics,” Astrophys. J. 597, 1266 (2003).
[CrossRef]

Heckenberg, N. R.

M.S. Soskin, V. N. Gorshkov, 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 (1997).
[CrossRef]

Huang, H.

Ibragimov, N.H.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T.D. Carozzi, Ya. N. Istomin, N.H. Ibragimov, and R. Khamitova, “Utilization of Photon Orbital Angular Momentum in the Low-Frequency Radio Domain,” Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef] [PubMed]

Istomin, Ya. N.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T.D. Carozzi, Ya. N. Istomin, N.H. Ibragimov, and R. Khamitova, “Utilization of Photon Orbital Angular Momentum in the Low-Frequency Radio Domain,” Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef] [PubMed]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics Third Edition, (John Wiley and Sons, Inc., 1998).

Khamitova, R.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T.D. Carozzi, Ya. N. Istomin, N.H. Ibragimov, and R. Khamitova, “Utilization of Photon Orbital Angular Momentum in the Low-Frequency Radio Domain,” Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef] [PubMed]

Kotlyar, V.

Kovalev, A.

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]

Lavery, M. P. J.

Leanhardt, A.E.

Y.S. Rumala and A.E. Leanhardt, “Multiple-beam interference in a spiral phase plate,” J. Opt. Soc. Am. B. 30, 615–621 (2013).
[CrossRef]

Legg, S.

B. Maffei, S. Legg, M. Robinson, F. Ozturk, M. W. Ng, P. Schemmel, and G. Pisano, “Implementation of a quasi-optical free-space s-parameter measurement system,” in Proceedings of the 35th ESA Antenna Workshop on Antenna and Free Space RF Measurements, 10 – 13 September (2013), ESTEC, Noordwijk, The Netherlands.

Maccalli, S.

P. Schemmel, S. Maccalli, G. Pisano, and B. Maffei, “Three dimensional measurements of a millimetre wave orbital angular momentum vortex,” Opt. Lett. 39, 626–629 (2014).
[CrossRef] [PubMed]

P. Schemmel, S. Maccalli, B. Maffei, F. Ozturk, G. Pisano, and M.W. Ng, “A Near Field 3D Scanner for Millimetre Wavelengths,” in Proceedings of the 35th ESA Antenna Workshop on Antenna and Free Space RF Measurements, 10 – 13 September (2013), ESTEC, Noordwijk, The Netherlands.

Maffei, B.

P. Schemmel, S. Maccalli, G. Pisano, and B. Maffei, “Three dimensional measurements of a millimetre wave orbital angular momentum vortex,” Opt. Lett. 39, 626–629 (2014).
[CrossRef] [PubMed]

B. Maffei, S. Legg, M. Robinson, F. Ozturk, M. W. Ng, P. Schemmel, and G. Pisano, “Implementation of a quasi-optical free-space s-parameter measurement system,” in Proceedings of the 35th ESA Antenna Workshop on Antenna and Free Space RF Measurements, 10 – 13 September (2013), ESTEC, Noordwijk, The Netherlands.

P. Schemmel, S. Maccalli, B. Maffei, F. Ozturk, G. Pisano, and M.W. Ng, “A Near Field 3D Scanner for Millimetre Wavelengths,” in Proceedings of the 35th ESA Antenna Workshop on Antenna and Free Space RF Measurements, 10 – 13 September (2013), ESTEC, Noordwijk, The Netherlands.

F. Ozturk, B. Maffei, and M. W. Ng, “A quasi-optical free-space s-parameters measurement system for material characterisation in W and Ka bands,” in Proceedings of the 33rd ESA Antenna Workshop on Antenna and Free Space RF Measurements, 18 – 21 October (2011), ESTEC, Noordwijk, The Netherlands.

Malos, J. T.

M.S. Soskin, V. N. Gorshkov, 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 (1997).
[CrossRef]

Mari, E.

F. Tamburini, E. Mari, A. Sponselli, B. Thidé, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14, 033001 (2012).
[CrossRef]

Martin, D.

D. Martin and J. Bowen, “Long-Wave Optics,” IEEE Trans. Microw. Theory Tech. 41, 1676–1689 (1993).
[CrossRef]

Michinel, H.

A. V. Carpentier, H. Michinel, and J. R. Salgueiro, “Making optical vortices with computer-generated holograms,” Am. J. Phys. 76, 916–921 (2008).
[CrossRef]

Molina-Terriza, G

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

Murphy, J. A.

N. Trappe, J. A. Murphy, and S. Withington, “The Gaussian beam mode analysis of classical phase aberrations in diffraction-limited optical systems,” Eur. J. Phys. 24, 403–412 (2003).
[CrossRef]

Ng, M. W.

B. Maffei, S. Legg, M. Robinson, F. Ozturk, M. W. Ng, P. Schemmel, and G. Pisano, “Implementation of a quasi-optical free-space s-parameter measurement system,” in Proceedings of the 35th ESA Antenna Workshop on Antenna and Free Space RF Measurements, 10 – 13 September (2013), ESTEC, Noordwijk, The Netherlands.

F. Ozturk, B. Maffei, and M. W. Ng, “A quasi-optical free-space s-parameters measurement system for material characterisation in W and Ka bands,” in Proceedings of the 33rd ESA Antenna Workshop on Antenna and Free Space RF Measurements, 18 – 21 October (2011), ESTEC, Noordwijk, The Netherlands.

Ng, M.W.

P. Schemmel, S. Maccalli, B. Maffei, F. Ozturk, G. Pisano, and M.W. Ng, “A Near Field 3D Scanner for Millimetre Wavelengths,” in Proceedings of the 35th ESA Antenna Workshop on Antenna and Free Space RF Measurements, 10 – 13 September (2013), ESTEC, Noordwijk, The Netherlands.

Oesch, D. W.

D. J. Sanchez, D. W. Oesch, and O. R. Reynolds, “The creation of photonic orbital angular momentum in electromagnetic waves propagating through turbulence,” Astron. Astrophys. 556, A130 (2013).
[CrossRef]

Ozturk, F.

B. Maffei, S. Legg, M. Robinson, F. Ozturk, M. W. Ng, P. Schemmel, and G. Pisano, “Implementation of a quasi-optical free-space s-parameter measurement system,” in Proceedings of the 35th ESA Antenna Workshop on Antenna and Free Space RF Measurements, 10 – 13 September (2013), ESTEC, Noordwijk, The Netherlands.

P. Schemmel, S. Maccalli, B. Maffei, F. Ozturk, G. Pisano, and M.W. Ng, “A Near Field 3D Scanner for Millimetre Wavelengths,” in Proceedings of the 35th ESA Antenna Workshop on Antenna and Free Space RF Measurements, 10 – 13 September (2013), ESTEC, Noordwijk, The Netherlands.

F. Ozturk, B. Maffei, and M. W. Ng, “A quasi-optical free-space s-parameters measurement system for material characterisation in W and Ka bands,” in Proceedings of the 33rd ESA Antenna Workshop on Antenna and Free Space RF Measurements, 18 – 21 October (2011), ESTEC, Noordwijk, The Netherlands.

Padgett, M. J.

Padgett, M.J.

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.J. Padgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Optics Commun. 121, 36–40 (1995).
[CrossRef]

Palmer, K.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T.D. Carozzi, Ya. N. Istomin, N.H. Ibragimov, and R. Khamitova, “Utilization of Photon Orbital Angular Momentum in the Low-Frequency Radio Domain,” Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef] [PubMed]

Phillips, R. L.

Pisano, G.

P. Schemmel, S. Maccalli, G. Pisano, and B. Maffei, “Three dimensional measurements of a millimetre wave orbital angular momentum vortex,” Opt. Lett. 39, 626–629 (2014).
[CrossRef] [PubMed]

B. Maffei, S. Legg, M. Robinson, F. Ozturk, M. W. Ng, P. Schemmel, and G. Pisano, “Implementation of a quasi-optical free-space s-parameter measurement system,” in Proceedings of the 35th ESA Antenna Workshop on Antenna and Free Space RF Measurements, 10 – 13 September (2013), ESTEC, Noordwijk, The Netherlands.

P. Schemmel, S. Maccalli, B. Maffei, F. Ozturk, G. Pisano, and M.W. Ng, “A Near Field 3D Scanner for Millimetre Wavelengths,” in Proceedings of the 35th ESA Antenna Workshop on Antenna and Free Space RF Measurements, 10 – 13 September (2013), ESTEC, Noordwijk, The Netherlands.

Ren, Y.

Reynolds, O. R.

D. J. Sanchez, D. W. Oesch, and O. R. Reynolds, “The creation of photonic orbital angular momentum in electromagnetic waves propagating through turbulence,” Astron. Astrophys. 556, A130 (2013).
[CrossRef]

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.

B. Maffei, S. Legg, M. Robinson, F. Ozturk, M. W. Ng, P. Schemmel, and G. Pisano, “Implementation of a quasi-optical free-space s-parameter measurement system,” in Proceedings of the 35th ESA Antenna Workshop on Antenna and Free Space RF Measurements, 10 – 13 September (2013), ESTEC, Noordwijk, The Netherlands.

Rogawski, D.

Romanato, F.

F. Tamburini, E. Mari, A. Sponselli, B. Thidé, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14, 033001 (2012).
[CrossRef]

Rumala, Y.S.

Y.S. Rumala, “Structured light interference due to multiple reflections in a spiral phase plate device and its propagation,” Proc. SPIE 8999, 899912 (2014).
[CrossRef]

Y.S. Rumala and A.E. Leanhardt, “Multiple-beam interference in a spiral phase plate,” J. Opt. Soc. Am. B. 30, 615–621 (2013).
[CrossRef]

Y.S. Rumala, “Interference theory of multiple optical vortex states in spiral phase plate etalon: thick-plate and thin-plate approximation,” J. Opt. Soc. Am. B. 31, 615–621 (2013).
[CrossRef]

Salgueiro, J. R.

A. V. Carpentier, H. Michinel, and J. R. Salgueiro, “Making optical vortices with computer-generated holograms,” Am. J. Phys. 76, 916–921 (2008).
[CrossRef]

Sanchez, D. J.

D. J. Sanchez, D. W. Oesch, and O. R. Reynolds, “The creation of photonic orbital angular momentum in electromagnetic waves propagating through turbulence,” Astron. Astrophys. 556, A130 (2013).
[CrossRef]

Schemmel, P.

P. Schemmel, S. Maccalli, G. Pisano, and B. Maffei, “Three dimensional measurements of a millimetre wave orbital angular momentum vortex,” Opt. Lett. 39, 626–629 (2014).
[CrossRef] [PubMed]

B. Maffei, S. Legg, M. Robinson, F. Ozturk, M. W. Ng, P. Schemmel, and G. Pisano, “Implementation of a quasi-optical free-space s-parameter measurement system,” in Proceedings of the 35th ESA Antenna Workshop on Antenna and Free Space RF Measurements, 10 – 13 September (2013), ESTEC, Noordwijk, The Netherlands.

P. Schemmel, S. Maccalli, B. Maffei, F. Ozturk, G. Pisano, and M.W. Ng, “A Near Field 3D Scanner for Millimetre Wavelengths,” in Proceedings of the 35th ESA Antenna Workshop on Antenna and Free Space RF Measurements, 10 – 13 September (2013), ESTEC, Noordwijk, The Netherlands.

P. Schemmel, Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK, is preparing a manuscript to be called , “Systematics Study of Spiral Phase Plate Designs for Millimetre Wave Orbital Angular Momentum State Manipulation.”

Shamee, B.

Sjöholm, J.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T.D. Carozzi, Ya. N. Istomin, N.H. Ibragimov, and R. Khamitova, “Utilization of Photon Orbital Angular Momentum in the Low-Frequency Radio Domain,” Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef] [PubMed]

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]

Soskin, M.S.

M.S. Soskin, V. N. Gorshkov, 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 (1997).
[CrossRef]

Sponselli, A.

F. Tamburini, E. Mari, A. Sponselli, B. Thidé, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14, 033001 (2012).
[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. A. 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Tamburini, F.

F. Tamburini, E. Mari, A. Sponselli, B. Thidé, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14, 033001 (2012).
[CrossRef]

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

Then, H.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T.D. Carozzi, Ya. N. Istomin, N.H. Ibragimov, and R. Khamitova, “Utilization of Photon Orbital Angular Momentum in the Low-Frequency Radio Domain,” Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef] [PubMed]

Thidé, B.

F. Tamburini, E. Mari, A. Sponselli, B. Thidé, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14, 033001 (2012).
[CrossRef]

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

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T.D. Carozzi, Ya. N. Istomin, N.H. Ibragimov, and R. Khamitova, “Utilization of Photon Orbital Angular Momentum in the Low-Frequency Radio Domain,” Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef] [PubMed]

Trappe, N.

N. Trappe, J. A. Murphy, and S. Withington, “The Gaussian beam mode analysis of classical phase aberrations in diffraction-limited optical systems,” Eur. J. Phys. 24, 403–412 (2003).
[CrossRef]

Tur, M.

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]

Vasnetsov, M. V.

M.S. Soskin, V. N. Gorshkov, 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 (1997).
[CrossRef]

Wang, J.

J. Wang, J. Yang, I.M. Frazal, 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,” Nature Photon. 6, 488–496 (2012).
[CrossRef]

I. M. Frazal, N. Ahmed, J. Wang, J. Y. Yang, Y. Yan, B. Shamee, H. Huang, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “2 Tbit/s free-space data transmission on two orthogonal orbital-angular-momentum beams each carrying 25 WDM channels,” Opt. Lett. 37, 4753–4755 (2012).
[CrossRef]

Willner, A. E.

Willner, A.E.

J. Wang, J. Yang, I.M. Frazal, 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,” Nature Photon. 6, 488–496 (2012).
[CrossRef]

Willner, M. J.

Withington, S.

N. Trappe, J. A. Murphy, and S. Withington, “The Gaussian beam mode analysis of classical phase aberrations in diffraction-limited optical systems,” Eur. J. Phys. 24, 403–412 (2003).
[CrossRef]

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]

Woerdman, J.P.

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]

Xie, G.

Yan, Y.

Yang, J.

J. Wang, J. Yang, I.M. Frazal, 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,” Nature Photon. 6, 488–496 (2012).
[CrossRef]

Yang, J. Y.

Yue, Y.

Am. J. Phys. (1)

A. V. Carpentier, H. Michinel, and J. R. Salgueiro, “Making optical vortices with computer-generated holograms,” Am. J. Phys. 76, 916–921 (2008).
[CrossRef]

Appl. Opt. (1)

Astron. Astrophys. (1)

D. J. Sanchez, D. W. Oesch, and O. R. Reynolds, “The creation of photonic orbital angular momentum in electromagnetic waves propagating through turbulence,” Astron. Astrophys. 556, A130 (2013).
[CrossRef]

Astrophys. J. (1)

M. Harwit, “Photon Orbital Angular Momentum in Astrophysics,” Astrophys. J. 597, 1266 (2003).
[CrossRef]

Eur. J. Phys. (1)

N. Trappe, J. A. Murphy, and S. Withington, “The Gaussian beam mode analysis of classical phase aberrations in diffraction-limited optical systems,” Eur. J. Phys. 24, 403–412 (2003).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (1)

D. Martin and J. Bowen, “Long-Wave Optics,” IEEE Trans. Microw. Theory Tech. 41, 1676–1689 (1993).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

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

J. Opt. Soc. Am. B. (2)

Y.S. Rumala and A.E. Leanhardt, “Multiple-beam interference in a spiral phase plate,” J. Opt. Soc. Am. B. 30, 615–621 (2013).
[CrossRef]

Y.S. Rumala, “Interference theory of multiple optical vortex states in spiral phase plate etalon: thick-plate and thin-plate approximation,” J. Opt. Soc. Am. B. 31, 615–621 (2013).
[CrossRef]

Nature Photon. (1)

J. Wang, J. Yang, I.M. Frazal, 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,” Nature Photon. 6, 488–496 (2012).
[CrossRef]

Nature Phys. (1)

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

New J. Phys. (1)

F. Tamburini, E. Mari, A. Sponselli, B. Thidé, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14, 033001 (2012).
[CrossRef]

Opt. Commun. (2)

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, 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]

Opt. Lett. (4)

Optics Commun. (1)

M.J. Padgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Optics Commun. 121, 36–40 (1995).
[CrossRef]

Phys. Rev. A. (2)

M.S. Soskin, V. N. Gorshkov, 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 (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] [PubMed]

Phys. Rev. Lett. (1)

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T.D. Carozzi, Ya. N. Istomin, N.H. Ibragimov, and R. Khamitova, “Utilization of Photon Orbital Angular Momentum in the Low-Frequency Radio Domain,” Phys. Rev. Lett. 99, 087701 (2007).
[CrossRef] [PubMed]

Proc. SPIE (1)

Y.S. Rumala, “Structured light interference due to multiple reflections in a spiral phase plate device and its propagation,” Proc. SPIE 8999, 899912 (2014).
[CrossRef]

Other (7)

P. Schemmel, S. Maccalli, B. Maffei, F. Ozturk, G. Pisano, and M.W. Ng, “A Near Field 3D Scanner for Millimetre Wavelengths,” in Proceedings of the 35th ESA Antenna Workshop on Antenna and Free Space RF Measurements, 10 – 13 September (2013), ESTEC, Noordwijk, The Netherlands.

F. Ozturk, B. Maffei, and M. W. Ng, “A quasi-optical free-space s-parameters measurement system for material characterisation in W and Ka bands,” in Proceedings of the 33rd ESA Antenna Workshop on Antenna and Free Space RF Measurements, 18 – 21 October (2011), ESTEC, Noordwijk, The Netherlands.

B. Maffei, S. Legg, M. Robinson, F. Ozturk, M. W. Ng, P. Schemmel, and G. Pisano, “Implementation of a quasi-optical free-space s-parameter measurement system,” in Proceedings of the 35th ESA Antenna Workshop on Antenna and Free Space RF Measurements, 10 – 13 September (2013), ESTEC, Noordwijk, The Netherlands.

P. Schemmel, Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK, is preparing a manuscript to be called , “Systematics Study of Spiral Phase Plate Designs for Millimetre Wave Orbital Angular Momentum State Manipulation.”

M. Gray, Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK, is preparing a manuscript to be called “A photon orbital angular momentum model in an astrophysical maser.”

P. Goldsmith, Quasioptical Systems: Gaussian Beam Quasioptical Propagation and Applications, (IEEE Press, 1998).
[CrossRef]

J. D. Jackson, Classical Electrodynamics Third Edition, (John Wiley and Sons, Inc., 1998).

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Figures (11)

Fig. 1
Fig. 1

Expected phase (a), dB intensity (b) and linear intensity (b) patterns of a numerically generated LG beam with l = 10 and ρ = 0. The central intensity null is caused by the undefined phase at the end of each phase dislocation. Each dislocation is curved because the LG mode was plotted away from the beam waist.

Fig. 2
Fig. 2

A CAD model of a smooth surfaced Δl = ±1 SPP.

Fig. 3
Fig. 3

A CAD model of a “split stepped,” SPP. Here two Δl = ±1 SPPs were compressed from an angular range of [0, 2π] to [0, π] and pushed together in order to generate an l = ±2 LG beam.

Fig. 4
Fig. 4

A full Δl = ±10 SPP (a). A single module from the full SPP showing the tongue and groove interlocking system (b).

Fig. 5
Fig. 5

Maximum mode content as a function of the decomposition beam waist has a maximum of 52.01% at 7.5mm.

Fig. 6
Fig. 6

Numerical simulations of a Δl = 10 stepped SPP in a split configuration. The normalised linear intensity on both the 40λ (120mm) [Fig. 6(a)] and 73.3λ (220mm) [Fig. 6(c)] measurement surfaces display a discontinuous intensity ring when compared with Fig. 1(c). The calculated phase on both surfaces also differs from the pure (l = 10, ρ = 0) pattern [Fig. 1(a)]. In both Fig. 6(b) and Fig. 6(d) radial modes generate discontinuities in the phase dislocation lines.

Fig. 7
Fig. 7

Transmission coefficients calculated as a function of SPP thickness (red line). Black dots indicate the eight individual step heights that make up the modular SPP.

Fig. 8
Fig. 8

A Gaussian beam is generated by the feed horn and is reflected by both CTRA mirrors. The beam then propagates to the SPP mount and is measured by the WR-10 probe [Fig. 8(a)]. (Not pictured is the absorbing material surrounding the mounting structure.) The measured incident Gaussian beam created by the CTRA source with vertical error bars denoting one standard deviation of the five measurement sweeps [Fig. 8(b)]. Measured near planar phase front at the beam waist created by the CTRA source with vertical error bars denoting one standard deviation of the five measurement sweeps [Fig. 8(c)].

Fig. 9
Fig. 9

Measured 6.7λ (20mm) surface normalised intensity pattern (Units in (V/m)) [Fig. 9(a)] shows a near field “image,” of the modular SPP is a result of the variable transmission through the SPP dielectric. Background normalised phase data (Units in degrees) for the 6.7λ (20mm) surface [Fig. 9(b)] contains ten phase dislocations, indicating that the modular SPP imparts a change in mode number of Δl = ±10.

Fig. 10
Fig. 10

Normalised linear intensity pattern (Units in V/m) for the 40λ (120mm) surface [Fig. 10(a)]. The expected intensity ring has developed and is clearly visible, although it remains discontinuous. Phase (Units in degrees) measured on the 40λ (120mm) surface [Fig. 10(b)] shows ten outer phase dislocations and a largely distorted centre. Phase distortions in the centre of the pattern are produced by complex interference as the width of each SPP step decreases with a decreasing radius and machining imperfections.

Fig. 11
Fig. 11

Measured normalised linear intensity (Units in V/m) of the 73.3λ (220mm) surface [Fig. 11(a)], showing the OAM intensity ring resulting from the undefined phase at the termination point of the dislocation lines. Background normalised phase (Units in degrees) on the 73.3λ (220mm) surface [Fig. 11(b)] contains ten outer phase dislocations at radial distances greater then 30mm. The clean central region, especially compared to that in Fig. 10, indicates the possible annihilation of phase vortices.

Tables (5)

Tables Icon

Table 1 Mode content, in percentages, of a U 0 0 beam passed through a smooth and a sixteen stepped Δl = 1 SPP.

Tables Icon

Table 2 Mode content, in percentages, of a U 0 0 beam passed through a smooth and an eight-steps-per-mode Δl = 10 SPP.

Tables Icon

Table 3 Mode content, in percentages, of a U 0 0 beam passed through a smooth and an eight-steps-per-mode Δl = 10 SPP, with an optimised decomposition mode beamwaist of 7.5mm.

Tables Icon

Table 5 Measured average and standard deviation step heights for the manufactured Δl = ±10 modular split stepped SPP.

Tables Icon

Table 4 RMS intensity pattern error as a function of the number of steps per mode between a perfect and modular split stepped Δl = ±10 SPP.

Equations (8)

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

U ρ l ( r , ϕ , z ) = A ρ l ( r , z ) L ρ | l | ( 2 r 2 w 2 ( z ) ) exp ( i l ϕ ) exp [ ( i k 0 r 2 z 2 ( z 2 + z R 2 ) ) i ( 2 ρ + | l | + 1 ) ϕ 0 ( z ) ]
r max = w ( z ) l 2
Δ l = h Δ n λ
U m n ( r , ϕ , z ) = l = ρ = 0 a ρ , m l , n U ρ l ( r , ϕ , z )
a ρ , m l , n = U ρ l | U m n
U m n ( r , ϕ , z ) = l = ρ = 0 a ρ , m l , n U ρ l ( r , ϕ , z ) exp ( i Δ l ϕ )
a ρ , m l , n = U ρ l | exp ( i Δ l ϕ ) | U m n
| C ρ , m l , n | 2 = | U ρ l | exp ( i Δ l ϕ ) | U m n | 2 | U m n | U m n | 2

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