Abstract

The spiral phase plate etalon transmission function is calculated from the low-reflectivity to high-reflectivity regime. Two approximations are considered: thick-plate approximation and thin-plate approximation. The thick-plate approximation explicitly takes into account the angle between the azimuthally increasing surface and the flat surface, while the thin-plate approximation does not. The two results are in agreement in the low-reflectivity regime, but not in the high-reflectivity regime. The thick-plate approximation is expected to provide a more accurate and general description of the device in all regimes. Origins of the device output intensity dependence on angle due to multiple vortex states present in the device are discussed, and a constraint on the number of internal reflections due to device geometry is also discussed.

© 2014 Optical Society of America

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    [CrossRef]
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  34. M. Eggleston, T. Godat, E. Munro, M. A. Alonso, H. Shi, and M. Bhattacharya, “Ray transfer matrix for a spiral phase plate,” J. Opt. Soc. Am. A 30, 2526–2530 (2013).
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  38. M. A. Kats, D. Sharma, J. Lin, P. Genevet, R. Blanchard, Z. Yang, M. M. Qazilbash, D. N. Basov, S. Ramanathan, and F. Capasso, “Ultra-thin perfect absorber employing a tunable phase change material,” Appl. Phys. Lett. 101, 221101 (2012).
    [CrossRef]
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  47. Note that r2=0.21 corresponds to a piece of glass that does not have antireflection coating. Therefore, an SPP that does not have antireflection coating will have an intensity modulation as a function of angle with amplitude of about 4% of total intensity as presented in Figs. 2(a) and 3, and the probability of generating OAM in an undesired state will be approximately 0.00194 as presented in Table 1. More generally, these effects ought to be taken into account in devices or structured media (e.g., phase grating) used to generate OAM based on transmission of light through it.
  48. 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).
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  49. 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).
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    [CrossRef]

2014 (2)

Y. S. Rumala, “Structured light interference due to multiple reflections in a spiral phase plate device and its propagation,” Proc. SPIE 8999, 899936 (2014).

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

2013 (6)

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]

R. Steiger, S. Bernet, and M. Ritsch-Marte, “Mapping of phase singularities with spiral phase contrast microscopy,” Opt. Express 21, 16282–16289 (2013).
[CrossRef]

M. Eggleston, T. Godat, E. Munro, M. A. Alonso, H. Shi, and M. Bhattacharya, “Ray transfer matrix for a spiral phase plate,” J. Opt. Soc. Am. A 30, 2526–2530 (2013).
[CrossRef]

M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nat. Mater. 12, 20–24 (2013).
[CrossRef]

K. C. Wright, R. B. Blakestad, C. J. Lobb, W. D. Phillips, and G. K. Campbell, “Driving phase slips in a superfluid atom circuit with a rotating weak link,” Phys. Rev. Lett. 110, 025302 (2013).
[CrossRef]

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
[CrossRef]

2012 (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]

M. A. Kats, D. Sharma, J. Lin, P. Genevet, R. Blanchard, Z. Yang, M. M. Qazilbash, D. N. Basov, S. Ramanathan, and F. Capasso, “Ultra-thin perfect absorber employing a tunable phase change material,” Appl. Phys. Lett. 101, 221101 (2012).
[CrossRef]

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, 013101 (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 (3)

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]

D. J. Alton, N. P. Stern, T. Aoki, H. Lee, E. Ostby, K. J. Vahala, and H. J. Kimble, “Strong interactions of single atoms and photons near a dielectric boundary,” Nat. Phys. 7, 159–165 (2011).
[CrossRef]

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Superflow in a toroidal Bose-Einstein condensate: an atom circuit with a tunable weak link,” Phys. Rev. Lett. 106, 130401 (2011).
[CrossRef]

2010 (2)

E. Brasselet, M. Malinauskas, A. Zukauskas, and S. Juodkazis, “Photopolymerized microscopic vortex beam generators: precise delivery of optical orbital angular momentum,” Appl. Phys. Lett. 97, 211108 (2010).
[CrossRef]

N. Zhang, J. A. Davis, I. Moreno, D. M. Cottrell, and X. C. Yuan, “Analysis of multilevel spiral phase plates using a dammann vortex sensing grating,” Opt. Express 18, 25987–25992 (2010).
[CrossRef]

2009 (1)

C. Jun, K. Deng-Feng, G. Min, and F. Zhi-Liang, “Generation of optical vortex using a spiral phase plate fabricated in quartz by direct laser writing and inductively coupled plasma etching,” Chin. Phys. Lett. 26, 014202 (2009).
[CrossRef]

2008 (4)

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

C. Maurer, A. Jesacher, S. Furhapter, S. Bernet, and M. Ritch-Marte, “Upgrading a microscope with a spiral phase plate,” J. Microsc. 230, 134–142 (2008).
[CrossRef]

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

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

2007 (3)

V. V. Kotlyar, A. A. Kovalev, R. V. Skidanov, S. N. Khonina, O. Yu. Moiseev, and V. A. Soifer, “Simple optical vortices formed by a spiral phase plate,” J. Opt. Technol. 74, 686–693 (2007).
[CrossRef]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[CrossRef]

H. Tsai, H. I. Smith, and R. Menon, “Fabrication of spiral-phase diffractive elements using scanning-electron-beam lithography,” J. Vac. Sci. Technol. B 25, 2068–2071 (2007).
[CrossRef]

2006 (2)

2005 (2)

A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Spiral phase elements obtained by use of discrete space-variant subwavelength gratings,” Opt. Commun. 251, 306–314 (2005).
[CrossRef]

G. Foo, D. M. Palacios, and G. A. Swartzlander, “Optical vortex coronagraph,” Opt. Lett. 30, 3308–3310 (2005).
[CrossRef]

2004 (7)

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]

C. Rotschild, S. Zommer, S. Moed, O. Hershcovitz, and S. G. Lipson, “Adjustable spiral phase plate,” Appl. Opt. 43, 2397–2399 (2004).
[CrossRef]

W. M. Lee, X.-C. Yuan, and W. C. Cheong, “Optical vortex beam shaping by use of highly efficient irregular spiral phase plates for optical micromanipulation,” Opt. Lett. 29, 1796–1798 (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, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, and G. W’t Hooft, “Half-integral spiral phase plates for optical wavelengths,” J. Opt. A 6, S288–S290 (2004).
[CrossRef]

T. Watanabe, M. Fujii, Y. Watanabe, N. Toyama, and Y. Iketaki, “Generation of a doughnut-shaped beam using a spiral phase plate,” Rev. Sci. Instrum. 75, 5131–5135 (2004).
[CrossRef]

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

2000 (1)

S. A. Diddams, D. J. Jones, J. Ye, T. M. Fortier, R. S. Windeler, S. T. Cundiff, T. W. Hansch, and J. L. Hall, “Towards the ultimate control of light optical frequency metrology and the phase control of femtosecond pulses,” Optics Photonics News 11 (10), 16–22 (2000).
[CrossRef]

1998 (1)

1994 (1)

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)

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 modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef]

1990 (1)

1953 (1)

K. Kinosita, “Numerical evaluation of the intensity curve of a multiple-beam Fizeau fringe,” J. Phys. Soc. Jpn. 8, 219–225 (1953).
[CrossRef]

1947 (1)

J. Brossel, “Multiple-beam localized fringes. Part I. Intensity distribution and localization,” Proc. Phys. Math. Soc. Jpn. 59, 224–234 (1947).
[CrossRef]

’t Hooft, G. W.

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, 013101 (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.

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

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (Institute of Physics, 2003).

Alonso, M. A.

Alton, D. J.

D. J. Alton, N. P. Stern, T. Aoki, H. Lee, E. Ostby, K. J. Vahala, and H. J. Kimble, “Strong interactions of single atoms and photons near a dielectric boundary,” Nat. Phys. 7, 159–165 (2011).
[CrossRef]

Andrews, D. L.

D. L. Andrews and M. Babiker, The Angular Momentum of Light (Cambridge University, 2012).

Aoki, T.

D. J. Alton, N. P. Stern, T. Aoki, H. Lee, E. Ostby, K. J. Vahala, and H. J. Kimble, “Strong interactions of single atoms and photons near a dielectric boundary,” Nat. Phys. 7, 159–165 (2011).
[CrossRef]

Arcizet, O.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[CrossRef]

Babiker, M.

D. L. Andrews and M. Babiker, The Angular Momentum of Light (Cambridge University, 2012).

Barnett, S.

Barnett, S. M.

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]

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (Institute of Physics, 2003).

Basov, D. N.

M. A. Kats, D. Sharma, J. Lin, P. Genevet, R. Blanchard, Z. Yang, M. M. Qazilbash, D. N. Basov, S. Ramanathan, and F. Capasso, “Ultra-thin perfect absorber employing a tunable phase change material,” Appl. Phys. Lett. 101, 221101 (2012).
[CrossRef]

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]

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]

Bernet, S.

R. Steiger, S. Bernet, and M. Ritsch-Marte, “Mapping of phase singularities with spiral phase contrast microscopy,” Opt. Express 21, 16282–16289 (2013).
[CrossRef]

C. Maurer, A. Jesacher, S. Furhapter, S. Bernet, and M. Ritch-Marte, “Upgrading a microscope with a spiral phase plate,” J. Microsc. 230, 134–142 (2008).
[CrossRef]

Berry, M. V.

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

Bhattacharya, M.

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]

Biener, G.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Spiral phase elements obtained by use of discrete space-variant subwavelength gratings,” Opt. Commun. 251, 306–314 (2005).
[CrossRef]

Blakestad, R. B.

K. C. Wright, R. B. Blakestad, C. J. Lobb, W. D. Phillips, and G. K. Campbell, “Driving phase slips in a superfluid atom circuit with a rotating weak link,” Phys. Rev. Lett. 110, 025302 (2013).
[CrossRef]

Blanchard, R.

M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nat. Mater. 12, 20–24 (2013).
[CrossRef]

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, 013101 (2012).
[CrossRef]

M. A. Kats, D. Sharma, J. Lin, P. Genevet, R. Blanchard, Z. Yang, M. M. Qazilbash, D. N. Basov, S. Ramanathan, and F. Capasso, “Ultra-thin perfect absorber employing a tunable phase change material,” Appl. Phys. Lett. 101, 221101 (2012).
[CrossRef]

Born, M.

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

Boyd, R. W.

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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).
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[CrossRef]

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E. Brasselet, M. Malinauskas, A. Zukauskas, and S. Juodkazis, “Photopolymerized microscopic vortex beam generators: precise delivery of optical orbital angular momentum,” Appl. Phys. Lett. 97, 211108 (2010).
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[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).
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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).
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Lin, J.

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, 013101 (2012).
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M. A. Kats, D. Sharma, J. Lin, P. Genevet, R. Blanchard, Z. Yang, M. M. Qazilbash, D. N. Basov, S. Ramanathan, and F. Capasso, “Ultra-thin perfect absorber employing a tunable phase change material,” Appl. Phys. Lett. 101, 221101 (2012).
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M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
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E. Brasselet, M. Malinauskas, A. Zukauskas, and S. Juodkazis, “Photopolymerized microscopic vortex beam generators: precise delivery of optical orbital angular momentum,” Appl. Phys. Lett. 97, 211108 (2010).
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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).
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C. Maurer, A. Jesacher, S. Furhapter, S. Bernet, and M. Ritch-Marte, “Upgrading a microscope with a spiral phase plate,” J. Microsc. 230, 134–142 (2008).
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[CrossRef]

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C. Jun, K. Deng-Feng, G. Min, and F. Zhi-Liang, “Generation of optical vortex using a spiral phase plate fabricated in quartz by direct laser writing and inductively coupled plasma etching,” Chin. Phys. Lett. 26, 014202 (2009).
[CrossRef]

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M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
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A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Superflow in a toroidal Bose-Einstein condensate: an atom circuit with a tunable weak link,” Phys. Rev. Lett. 106, 130401 (2011).
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S. S. R. Oemrawsingh, J. A. W. van Houwelingen, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, and G. W. ’t Hooft, “Production and characterization of spiral phase plates for optical wavelengths,” Appl. Opt. 43, 688–694 (2004).
[CrossRef]

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[CrossRef]

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D. J. Alton, N. P. Stern, T. Aoki, H. Lee, E. Ostby, K. J. Vahala, and H. J. Kimble, “Strong interactions of single atoms and photons near a dielectric boundary,” Nat. Phys. 7, 159–165 (2011).
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S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–313 (2008).
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[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).
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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).
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P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
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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, 013101 (2012).
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M. A. Kats, D. Sharma, J. Lin, P. Genevet, R. Blanchard, Z. Yang, M. M. Qazilbash, D. N. Basov, S. Ramanathan, and F. Capasso, “Ultra-thin perfect absorber employing a tunable phase change material,” Appl. Phys. Lett. 101, 221101 (2012).
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M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
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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).
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A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Superflow in a toroidal Bose-Einstein condensate: an atom circuit with a tunable weak link,” Phys. Rev. Lett. 106, 130401 (2011).
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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, 013101 (2012).
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Yuan, X.-C.

Zelan, M.

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E. Brasselet, M. Malinauskas, A. Zukauskas, and S. Juodkazis, “Photopolymerized microscopic vortex beam generators: precise delivery of optical orbital angular momentum,” Appl. Phys. Lett. 97, 211108 (2010).
[CrossRef]

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, 013101 (2012).
[CrossRef]

M. A. Kats, D. Sharma, J. Lin, P. Genevet, R. Blanchard, Z. Yang, M. M. Qazilbash, D. N. Basov, S. Ramanathan, and F. Capasso, “Ultra-thin perfect absorber employing a tunable phase change material,” Appl. Phys. Lett. 101, 221101 (2012).
[CrossRef]

Chin. Phys. Lett. (1)

C. Jun, K. Deng-Feng, G. Min, and F. Zhi-Liang, “Generation of optical vortex using a spiral phase plate fabricated in quartz by direct laser writing and inductively coupled plasma etching,” Chin. Phys. Lett. 26, 014202 (2009).
[CrossRef]

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C. Maurer, A. Jesacher, S. Furhapter, S. Bernet, and M. Ritch-Marte, “Upgrading a microscope with a spiral phase plate,” J. Microsc. 230, 134–142 (2008).
[CrossRef]

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M. V. Berry, “Optical vortices evolving from integer and fractional phase steps,” J. Opt. A 6, 259–268 (2004).
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S. S. R. Oemrawsingh, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, and G. W’t Hooft, “Half-integral spiral phase plates for optical wavelengths,” J. Opt. A 6, S288–S290 (2004).
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H. Tsai, H. I. Smith, and R. Menon, “Fabrication of spiral-phase diffractive elements using scanning-electron-beam lithography,” J. Vac. Sci. Technol. B 25, 2068–2071 (2007).
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S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–313 (2008).
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Meas. Sci. Technol. (1)

M. Dobosz and M. Kozuchowski, “Frequency stabilization of a diode by means of an optical wedge,” Meas. Sci. Technol. 23, 035202 (2012).
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M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nat. Mater. 12, 20–24 (2013).
[CrossRef]

Nat. Phys. (1)

D. J. Alton, N. P. Stern, T. Aoki, H. Lee, E. Ostby, K. J. Vahala, and H. J. Kimble, “Strong interactions of single atoms and photons near a dielectric boundary,” Nat. Phys. 7, 159–165 (2011).
[CrossRef]

Nature (1)

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[CrossRef]

New J. Phys. (3)

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]

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

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)

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).
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A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Spiral phase elements obtained by use of discrete space-variant subwavelength gratings,” Opt. Commun. 251, 306–314 (2005).
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Opt. Express (3)

Opt. Lett. (6)

Optics Photonics News (1)

S. A. Diddams, D. J. Jones, J. Ye, T. M. Fortier, R. S. Windeler, S. T. Cundiff, T. W. Hansch, and J. L. Hall, “Towards the ultimate control of light optical frequency metrology and the phase control of femtosecond pulses,” Optics Photonics News 11 (10), 16–22 (2000).
[CrossRef]

Phys. Rev. A (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 modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef]

Phys. Rev. Lett. (2)

K. C. Wright, R. B. Blakestad, C. J. Lobb, W. D. Phillips, and G. K. Campbell, “Driving phase slips in a superfluid atom circuit with a rotating weak link,” Phys. Rev. Lett. 110, 025302 (2013).
[CrossRef]

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Superflow in a toroidal Bose-Einstein condensate: an atom circuit with a tunable weak link,” Phys. Rev. Lett. 106, 130401 (2011).
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Y. S. Rumala, “Structured light interference due to multiple reflections in a spiral phase plate device and its propagation,” Proc. SPIE 8999, 899936 (2014).

Rev. Sci. Instrum. (1)

T. Watanabe, M. Fujii, Y. Watanabe, N. Toyama, and Y. Iketaki, “Generation of a doughnut-shaped beam using a spiral phase plate,” Rev. Sci. Instrum. 75, 5131–5135 (2004).
[CrossRef]

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 (7)

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

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (Institute of Physics, 2003).

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

D. L. Andrews and M. Babiker, The Angular Momentum of Light (Cambridge University, 2012).

Note that r2=0.21 corresponds to a piece of glass that does not have antireflection coating. Therefore, an SPP that does not have antireflection coating will have an intensity modulation as a function of angle with amplitude of about 4% of total intensity as presented in Figs. 2(a) and 3, and the probability of generating OAM in an undesired state will be approximately 0.00194 as presented in Table 1. More generally, these effects ought to be taken into account in devices or structured media (e.g., phase grating) used to generate OAM based on transmission of light through it.

J. Ye and S. Cudniff, Femtosecond Optical Frequency Comb: Principle, Operation and Applications (Kluwer, 2004).

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

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Figures (4)

Fig. 1.
Fig. 1.

(a) SPP etalon. (b) Wedge that varies as a function of angle to model transmission function in the thick-plate approximation. The azimuthal step height goes from ϕ=0 to ϕ=2π over a 2πr circumference of the input optical beam. r=ω0 is the beam waist. The transmitted field on the output plane of the device is a superposition of electric field amplitudes, tthick(ϕ)=ut2+ut4+ut6+. The field is calculated at a point where the light wave amplitudes ut2,ut4,ut6, enter at different points on the input plane, uthick(r,ϕ,0), and meet at a point on the uniform output plane, uthick(r,ϕ,h0+Δh) (dashed line).

Fig. 2.
Fig. 2.

SPP etalon resonances as a function of azimuthal angle. The peak value of the transmission function in the thin-plate approximation [modulus square of Eq. (4); black dashed line] is normalized by the amplitude factor to 1, and the thick-plate approximation [modulus square of Eq. (3); solid blue line] is normalized by the same amplitude factor, for an SPP etalon of β=5.55, γ=1.21×104rad, and M=79. The values for the reflection coefficient are (a) r2=0.21 [47], r2=0.50, r2=0.90, and (b) r2=0.73, r2=0.99. The point at which the thick-plate approximation starts to deviate from the thin-plate approximation is around r2=0.73. This is characterized by smaller peak heights, and at even higher reflection coefficient (i.e., r2=0.9, r2=0.99) there are additional interference peaks at the base of the principal intensity peaks, and lower peak intensity heights.

Fig. 3.
Fig. 3.

Transverse optical intensity profile showing SPP etalon resonances for thin-plate approximation (left) and thick-plate approximation (right) corresponding to Fig. 2. There appears to be a limit in the transmission linewidth in the high-reflectivity limit as seen in the thick-plate approximation.

Fig. 4.
Fig. 4.

As wave amplitude, u0, make multiple reflections with the azimuthally increasing surface, the light waves come out at larger angles and are bent toward the direction of increasing height. The successive distance, La,b,c, by which the light beam exits the surface of the etalon also gets larger. Angles “a”, “b”, and “c” are (π/2)nγ, (π/2)3nγ, and (π/2)5nγrad, respectively.

Tables (1)

Tables Icon

Table 1. Probability of Detecting OAM in Various States

Equations (19)

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

ut2=t1t2eikd1einkd2.
ut4=t1t2r22eikd1(1+4(nγ)2)einkd2(34γ2)eink6nγ2d11+(nγγ)22!,
ut6=t1t2r24eikd1(1+12(nγ)2)einkd2(520γ2)eink20nγ2d11+(nγγ)22!,
ut8=t1t2r26eikd1(1+24(nγ)2)einkd2(756γ2)eink42nγ2d11+(nγγ)22!.
tthick(ϕ)=uthick(r,ϕ,h0+Δh)uthick(r,ϕ,0)=ut2+ut4+ut6+
=t1t2eikd1einkd2m=0m=M[r22mΘ1Θ2Θ3]Θ4
=t1t2eikd1einkd2m=0m=M[r22mΘ2Θ3]
=t1t2t0e+iαϕm=0m=M[r22meim(βϕ+ϕ0)(1γ213(m+1)(2m+1))].
tthin(ϕ)=t2t1t0e+iαϕm=0m=Mr22meim2nk(h0+Δh)
=t2t1t0e+iαϕm=0m=Mr22meim(βϕ+ϕ0)
=t2t1t0e+iαϕ(1ei(βϕ+ϕ0)(1+M)r22+2M)1r22e+i(βϕ+ϕ0).
LN+1=(h0+Δhϕ2π)2N(N+1)γN=1,2,3,
LN+1=h02N(N+1)γN=1,2,3,
N=h0γ±h02γ2+(2h0γ)(2πω0)2h0γ.
p=1N|12π02πtthick(ϕ)eiϕdϕ|2
=1N|12π02πt2t1t0eiαϕmm=M(r22mΘ2Θ3)eiϕdϕ|2
=1N(|t2t1t0|2|r22m|2).
=α+m(1γ213(m+1)(2m+1))β,m=0,1,2,,M
pm=(|r2|41r24+4M1)|r2|4m.

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