Abstract

Optical transmission through a spiral phase plate is analyzed by treating the device as a Fabry–Perot etalon with an azimuthally varying thickness. The transmitted beam is calculated to contain a coherent superposition of optical vortices with different winding numbers. This yields an intensity profile with a periodic modulation as a function of azimuthal angle where the orientation rotates as a function of the laser frequency. These effects are quantified experimentally and theoretically.

© 2013 Optical Society of America

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    [CrossRef]
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  9. S. Franke-Arnold and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–313 (2008).
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  10. M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5, 343–348 (2011).
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  11. J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90, 133901 (2003).
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  13. M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
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  14. R. Kanamoto, E. M. Wright, and P. Meystre, “Quantum dynamics of Raman-coupled Bose–Einstein condensates using Laguerre–Gaussian beams,” Phys. Rev. A 75, 063623 (2007).
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  26. S. Thanvanthri, K. T. Kapale, and J. P. Dowling, “Arbitrary coherent superpositions of quantized vortices in Bose–Einstein condensates via orbital angular momentum of light,” Phys. Rev. A 77, 053825 (2008).
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    [CrossRef]
  30. N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
    [CrossRef]
  31. 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]
  32. S. van Enk and G. Nienhuis, “Eigenfunction description of laser beams and orbital angular momentum of light,” Opt. Commun. 94, 147–158 (1992).
    [CrossRef]
  33. 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]
  34. M. J. Padgett and L. Allen, “Orbital angular momentum exchange in cylindrical-lens mode converters,” J. Opt. B 4, S17–S19 (2002).
    [CrossRef]
  35. 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]
  36. F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, “Transverse modes, vortices and vertical-cavity surface-emitting Lasers,” Chaos, Solitons & Fractals 4, 1575–1596 (1994).
  37. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
    [CrossRef]
  38. 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, “Production and characterization of spiral phase plates for optical wavelengths,” Appl. Opt. 43, 688–694 (2004).
    [CrossRef]
  39. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
    [CrossRef]
  40. P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100, 13101 (2012).
    [CrossRef]
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  43. M. A. Rob, “Limitation of a wedge etalon for high resolution linewidth measurements,” Opt. Lett. 15, 604–606 (1990).
    [CrossRef]
  44. M. Dobosz and M. Kozuchowski, “Frequency stabilization of a diode by means of an optical wedge,” Meas. Sci. Technol. 23, 035202 (2012).
    [CrossRef]
  45. J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts & Company, 2005).
  46. The angle between the two surfaces of the spiral phase plate depends on radial position: tan(θ(r))=Δh/2πr. The surfaces are approximately parallel, i.e., θ(r)≪1, for r≫Δh, where Δh∼O(λ). For r≤O(λ), fabrication limitations often cause the actual thickness profile of the spiral phase plate to deviate from the ideal profile in Eq. (1). Accordingly, θ(r)≪1 over the same area where Eq. (1) accurately represents the surface of the device.
  47. S. Franke-Arnold, S. M. Barnett, E. Yao, J. Leach, J. Courtial, and M. Padgett, “Uncertainty principle for angular position and angular momentum,” New J. Phys. 6, 103 (2004).
    [CrossRef]
  48. E. Yao, S. Franke-Arnold, J. Courtial, S. Barnett, and M. Padgett, “Fourier relationship between angular position and optical orbital angular momentum,” Opt. Express 14, 9071–9076 (2006).
    [CrossRef]
  49. B. Jack, M. J. Padgett, and S. Franke-Arnold, “Angular diffraction,” New J. Phys. 10, 103013 (2008).
    [CrossRef]
  50. M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A 6, 259–268(2004).
    [CrossRef]
  51. J. B. Götte, S. Franke-Arnold, R. Zambrini, and S. M. Barnett, “Quantum formulation of fractional orbital angular momentum,” J. Mod. Opt. 54, 1723–1738 (2007).
    [CrossRef]
  52. J. B. Götte, K. O’Holleran, D. Preece, F. Flossmann, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Light beams with fractional orbital angular momentum and their vortex structure,” Opt. Express 16, 993–1006 (2008).
    [CrossRef]
  53. Spiral phase plates are purchased from RPC Photonics, www.rpcphotonics.com. The refractive index is calculated from the dispersion equation of the material used to manufacture the spiral phase plate, and its uncertainty is calculated from the wavelength dependence of the dispersion equation. The spiral step height with uncertainty are experimentally measured values by RPC Photonics. The thickness of the glass substrate and its uncertainty is provided by RPC Photonics. The coefficient of thermal expansion and the thermal coefficient of the refractive index is also provided by RPC Photonics.
  54. Y. S. Rumala, “A new etalon geometry: the spiral phase plate etalon,” Ph.D. thesis (University of Michigan, 2012).

2012 (2)

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100, 13101 (2012).
[CrossRef]

M. Dobosz and M. Kozuchowski, “Frequency stabilization of a diode by means of an optical wedge,” Meas. Sci. Technol. 23, 035202 (2012).
[CrossRef]

2011 (2)

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[CrossRef]

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

2009 (1)

K. C. Wright, L. S. Leslie, A. Hansen, and N. P. Bigelow, “Sculpting the vortex state of a spinor BEC,” Phys. Rev. Lett. 102, 030405 (2009).
[CrossRef]

2008 (6)

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

T. P. Simula, N. Nygaard, S. X. Hu, L. A. Collins, B. I. Schneider, and K. Mølmer, “Angular momentum exchange between coherent light and matter fields,” Phys. Rev. A 77, 015401 (2008).
[CrossRef]

K. C. Wright, L. S. Leslie, and N. P. Bigelow, “Optical control of the internal and external angular momentum of a Bose–Einstein condensate,” Phys. Rev. A 77, 041601 (2008).
[CrossRef]

B. Jack, M. J. Padgett, and S. Franke-Arnold, “Angular diffraction,” New J. Phys. 10, 103013 (2008).
[CrossRef]

S. Thanvanthri, K. T. Kapale, and J. P. Dowling, “Arbitrary coherent superpositions of quantized vortices in Bose–Einstein condensates via orbital angular momentum of light,” Phys. Rev. A 77, 053825 (2008).
[CrossRef]

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

2007 (4)

J. B. Götte, S. Franke-Arnold, R. Zambrini, and S. M. Barnett, “Quantum formulation of fractional orbital angular momentum,” J. Mod. Opt. 54, 1723–1738 (2007).
[CrossRef]

S. Franke-Arnold, J. Leach, M. J. Padgett, V. E. Lembessis, D. Ellinas, A. J. Wright, J. M. Girkin, P. Ohberg, and A. S. Arnold, “Optical ferris wheel for ultracold atoms,” Opt. Express 15, 8619–8625 (2007).
[CrossRef]

R. Kanamoto, E. M. Wright, and P. Meystre, “Quantum dynamics of Raman-coupled Bose–Einstein condensates using Laguerre–Gaussian beams,” Phys. Rev. A 75, 063623 (2007).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[CrossRef]

2006 (3)

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef]

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]

E. Yao, S. Franke-Arnold, J. Courtial, S. Barnett, and M. Padgett, “Fourier relationship between angular position and optical orbital angular momentum,” Opt. Express 14, 9071–9076 (2006).
[CrossRef]

2005 (3)

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

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, E. R. Eliel, G. W. ’t Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95, 240501 (2005).
[CrossRef]

K. T. Kapale and J. P. Dowling, “Vortex phase qubit: generating arbitrary, counter-rotating, coherent superpositions in Bose–Einstein condensates via optical angular momentum beams,” Phys. Rev. Lett. 95, 173601 (2005).
[CrossRef]

2004 (6)

Z. Dutton and J. Ruostekoski, “Transfer and storage of vortex states in light and matter waves,” Phys. Rev. Lett. 93, 193602 (2004).
[CrossRef]

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

S. Franke-Arnold, S. M. Barnett, E. Yao, J. Leach, J. Courtial, and M. Padgett, “Uncertainty principle for angular position and angular momentum,” New J. Phys. 6, 103 (2004).
[CrossRef]

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

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, “Production and characterization of spiral phase plates for optical wavelengths,” Appl. Opt. 43, 688–694 (2004).
[CrossRef]

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
[CrossRef]

2003 (2)

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

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

2002 (2)

S. M. Barnett, “Optical angular-momentum flux,” J. Opt. B 4, S7–S16 (2002).
[CrossRef]

M. J. Padgett and L. Allen, “Orbital angular momentum exchange in cylindrical-lens mode converters,” J. Opt. B 4, S17–S19 (2002).
[CrossRef]

2001 (1)

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

1994 (3)

S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110, 670–678 (1994).
[CrossRef]

F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, “Transverse modes, vortices and vertical-cavity surface-emitting Lasers,” Chaos, Solitons & Fractals 4, 1575–1596 (1994).

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

1993 (1)

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 (5)

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

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[CrossRef]

S. van Enk and G. Nienhuis, “Eigenfunction description of laser beams and orbital angular momentum of light,” Opt. Commun. 94, 147–158 (1992).
[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 modes,” Phys. Rev. A 45, 8185–8189 (1992).
[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]

1990 (2)

M. A. Rob, “Limitation of a wedge etalon for high resolution linewidth measurements,” Opt. Lett. 15, 604–606 (1990).
[CrossRef]

V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52, 429–431 (1990).

1983 (1)

1936 (1)

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936).
[CrossRef]

1935 (1)

R. A. Beth, “Direct detection of the angular momentum of light,” Phys. Rev. 48, 471 (1935).
[CrossRef]

’t Hooft, G. W.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, E. R. Eliel, G. W. ’t Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95, 240501 (2005).
[CrossRef]

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, “Production and characterization of spiral phase plates for optical wavelengths,” Appl. Opt. 43, 688–694 (2004).
[CrossRef]

Aiello, A.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, E. R. Eliel, G. W. ’t Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95, 240501 (2005).
[CrossRef]

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

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

Aieta, F.

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100, 13101 (2012).
[CrossRef]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[CrossRef]

Allen, L.

M. J. Padgett and L. Allen, “Orbital angular momentum exchange in cylindrical-lens mode converters,” J. Opt. B 4, S17–S19 (2002).
[CrossRef]

S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110, 670–678 (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 modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef]

Andersen, M. F.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef]

Arnold, A. S.

Barnett, S.

Barnett, S. M.

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

J. B. Götte, S. Franke-Arnold, R. Zambrini, and S. M. Barnett, “Quantum formulation of fractional orbital angular momentum,” J. Mod. Opt. 54, 1723–1738 (2007).
[CrossRef]

S. Franke-Arnold, S. M. Barnett, E. Yao, J. Leach, J. Courtial, and M. Padgett, “Uncertainty principle for angular position and angular momentum,” New J. Phys. 6, 103 (2004).
[CrossRef]

S. M. Barnett, “Optical angular-momentum flux,” J. Opt. B 4, S7–S16 (2002).
[CrossRef]

S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110, 670–678 (1994).
[CrossRef]

Bazhenov, V. Yu.

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

V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52, 429–431 (1990).

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” 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 modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef]

Berry, M. V.

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

Beth, R. A.

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936).
[CrossRef]

R. A. Beth, “Direct detection of the angular momentum of light,” Phys. Rev. 48, 471 (1935).
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S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, E. R. Eliel, G. W. ’t Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95, 240501 (2005).
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Appl. Opt. (1)

Appl. Phys. Lett. (1)

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100, 13101 (2012).
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V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52, 429–431 (1990).

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Opt. Express (4)

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Phys. Rev. Lett. (8)

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, E. R. Eliel, G. W. ’t Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95, 240501 (2005).
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K. C. Wright, L. S. Leslie, A. Hansen, and N. P. Bigelow, “Sculpting the vortex state of a spinor BEC,” Phys. Rev. Lett. 102, 030405 (2009).
[CrossRef]

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

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
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Science (1)

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[CrossRef]

Other (8)

A. E. Siegman, Lasers (University Science Books, 1986).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

D. L. Andrews, ed., Structured Light and Its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces (Elsevier, 2008).

J. P. Torres and L. Torner, Twisted Photons: Applications of Light with Orbital Angular Momentum (Wiley-VCH, 2011).

Spiral phase plates are purchased from RPC Photonics, www.rpcphotonics.com. The refractive index is calculated from the dispersion equation of the material used to manufacture the spiral phase plate, and its uncertainty is calculated from the wavelength dependence of the dispersion equation. The spiral step height with uncertainty are experimentally measured values by RPC Photonics. The thickness of the glass substrate and its uncertainty is provided by RPC Photonics. The coefficient of thermal expansion and the thermal coefficient of the refractive index is also provided by RPC Photonics.

Y. S. Rumala, “A new etalon geometry: the spiral phase plate etalon,” Ph.D. thesis (University of Michigan, 2012).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts & Company, 2005).

The angle between the two surfaces of the spiral phase plate depends on radial position: tan(θ(r))=Δh/2πr. The surfaces are approximately parallel, i.e., θ(r)≪1, for r≫Δh, where Δh∼O(λ). For r≤O(λ), fabrication limitations often cause the actual thickness profile of the spiral phase plate to deviate from the ideal profile in Eq. (1). Accordingly, θ(r)≪1 over the same area where Eq. (1) accurately represents the surface of the device.

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