Abstract

A novel method to generate and manipulate vector vortex beams in an integrated, ring resonator based geometry is proposed. We show numerically that a ring resonator, with an appropriate grating, addressed by a vertically displaced access waveguide emits a complex optical field. The emitted beam possesses a specific polarization topology, and consequently a transverse intensity profile and orbital angular momentum. We propose a combination of several concentric ring resonators, addressed with different bus guides, to generate arbitrary orbital angular momentum qudit states, which could potentially be used for classical and quantum communications. Finally, we demonstrate numerically that this device works as an orbital angular momentum sorter with an average cross-talk of −10dB between different orbital angular momentum channels.

© 2013 OSA

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    [CrossRef] [PubMed]
  34. M. J. Padgett and J. Courtial, “Poincaré-sphere equivalent for light beams containing orbital angular momentum,” Opt. Lett.24, 430–432 (1999).
    [CrossRef]
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    [CrossRef]
  36. J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett.88, 257901 (2002).
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    [CrossRef]
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    [CrossRef]

2013

2012

2011

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt.13, 064001 (2011).
[CrossRef]

R. W. Boyd, A. Jha, M. Malik, C. O’Sullivan, B. Rodenburg, and D. J. Gauthier, “Quantum key distribution in a high-dimensional state space: exploiting the transverse degree of freedom of the photon,” Proc. of SPIE794879480L–1 (2011).
[CrossRef]

2010

Y. F. Yu, Y. H. Fu, X. M. Zhang, A. Q. Liu, T. Bourouina, T. Mei, Z. X. Shen, and D. P. Tsai, “Pure angular momentum generator using a ring resonator,” œ18, 21651–21662 (2010).

A. M. Beckley, T. G. Brown, and M. A. Alonso, “Poincaré beam,” œ18, 10777–10785 (2010).

G. Berkhout, M. Lavery, J. Courtial, M. Beijersbergen, and M. Padgett, “Efficient Sorting of orbital angular momentum states of light,” Phys. Rev. Lett.105, 105601 (2010).
[CrossRef]

2009

E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, “Efficient generation and sorting of orbital angular momentum eigenmodes of light by thermally tuned q-plates,” Appl. Phys. Lett.94, 231124 (2009).
[CrossRef]

E. Brasselet, N. Murazawa, H. Misawa, and S. Juodkazis, “Optical vortices from liquid crystal droplets,” Phys. Rev. Lett.103, 103903 (2009).
[CrossRef] [PubMed]

J. L. O’Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics3, 687–695 (2009).
[CrossRef]

2008

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science320, 646–649 (2008).
[CrossRef] [PubMed]

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

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys.4, 282–286 (2008).
[CrossRef]

H. Wang, L. Shi, B. Luk̀yanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2, 501–505 (2008).
[CrossRef]

2007

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-Orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett.99, 073901 (2007).
[CrossRef] [PubMed]

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

W. S. Hell, “Far-field optical nanoscopy,” Science316, 1153–1158 (2007).
[CrossRef] [PubMed]

2006

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

2005

2004

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pasko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” œ12, 5448–5456 (2004).

2003

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett.91, 233901 (2003).
[CrossRef] [PubMed]

2002

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett.88, 257901 (2002).
[CrossRef] [PubMed]

2001

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412, 313–316 (2001).
[CrossRef] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science292, 912–914 (2001).
[CrossRef] [PubMed]

1999

1995

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

1994

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

1992

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

L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8189 (1992).
[CrossRef] [PubMed]

S. Suzuki, K. Shuto, and Y. Hibino, “Integrated-Optic Ring Resonators with Two Stacked Layers of Silica Waveguide on Si,” IEEE Photon. Technol. Lett.4, 1256–1258 (1992).
[CrossRef]

1935

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

1909

H. Poynting, “The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly polarised light,” Proc. R. Soc. Lond. A82, 560–567 (1909).
[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. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8189 (1992).
[CrossRef] [PubMed]

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (Bristol: Institute of Physics2003).
[CrossRef]

Alonso, M. A.

A. M. Beckley, T. G. Brown, and M. A. Alonso, “Poincaré beam,” œ18, 10777–10785 (2010).

Arlt, J.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science292, 912–914 (2001).
[CrossRef] [PubMed]

Barnett, S. M.

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pasko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” œ12, 5448–5456 (2004).

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett.88, 257901 (2002).
[CrossRef] [PubMed]

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (Bristol: Institute of Physics2003).
[CrossRef]

Barreiro, J. T.

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys.4, 282–286 (2008).
[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]

Beckley, A. M.

A. M. Beckley, T. G. Brown, and M. A. Alonso, “Poincaré beam,” œ18, 10777–10785 (2010).

Beijersbergen, M.

G. Berkhout, M. Lavery, J. Courtial, M. Beijersbergen, and M. Padgett, “Efficient Sorting of orbital angular momentum states of light,” Phys. Rev. Lett.105, 105601 (2010).
[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. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8189 (1992).
[CrossRef] [PubMed]

Berkhout, G.

G. Berkhout, M. Lavery, J. Courtial, M. Beijersbergen, and M. Padgett, “Efficient Sorting of orbital angular momentum states of light,” Phys. Rev. Lett.105, 105601 (2010).
[CrossRef]

Berry, M. V.

M. V. Berry, “Paraxial beams of spinning light,” in Singular optics, (Ed, M. S. Soskin, ) SPIE, 3487, 6–11 (1998).

Beth, R. A.

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

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University; 7 edition1999).

Bourouina, T.

Y. F. Yu, Y. H. Fu, X. M. Zhang, A. Q. Liu, T. Bourouina, T. Mei, Z. X. Shen, and D. P. Tsai, “Pure angular momentum generator using a ring resonator,” œ18, 21651–21662 (2010).

Boyd, R. W.

M. N. O’Sullivan, M. Mirhosseini, M. Malik, and R. W. Boyd, “Near-perfect sorting of orbital angular momentum and angular position states of light,” Opt. Express20, 24444–24449 (2012).
[CrossRef]

R. W. Boyd, A. Jha, M. Malik, C. O’Sullivan, B. Rodenburg, and D. J. Gauthier, “Quantum key distribution in a high-dimensional state space: exploiting the transverse degree of freedom of the photon,” Proc. of SPIE794879480L–1 (2011).
[CrossRef]

Brasselet, E.

E. Brasselet, N. Murazawa, H. Misawa, and S. Juodkazis, “Optical vortices from liquid crystal droplets,” Phys. Rev. Lett.103, 103903 (2009).
[CrossRef] [PubMed]

Brown, T. G.

A. M. Beckley, T. G. Brown, and M. A. Alonso, “Poincaré beam,” œ18, 10777–10785 (2010).

Bryant, P. E.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science292, 912–914 (2001).
[CrossRef] [PubMed]

Cai, X.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated Compact Optical Vortex Beam Emitters,” Science338, 363–366 (2012).
[CrossRef] [PubMed]

Cardano, F.

Chiu, D. T.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-Orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett.99, 073901 (2007).
[CrossRef] [PubMed]

Chong, C. T.

H. Wang, L. Shi, B. Luk̀yanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2, 501–505 (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 phase plate,” Opt. Commun.112, 321–327 (1994).
[CrossRef]

Courtial, J.

G. Berkhout, M. Lavery, J. Courtial, M. Beijersbergen, and M. Padgett, “Efficient Sorting of orbital angular momentum states of light,” Phys. Rev. Lett.105, 105601 (2010).
[CrossRef]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pasko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” œ12, 5448–5456 (2004).

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett.88, 257901 (2002).
[CrossRef] [PubMed]

M. J. Padgett and J. Courtial, “Poincaré-sphere equivalent for light beams containing orbital angular momentum,” Opt. Lett.24, 430–432 (1999).
[CrossRef]

Cryan, M. J.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science320, 646–649 (2008).
[CrossRef] [PubMed]

de Lisio, C.

Dholakia, K.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science292, 912–914 (2001).
[CrossRef] [PubMed]

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett.91, 233901 (2003).
[CrossRef] [PubMed]

Edgar, J. S.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-Orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett.99, 073901 (2007).
[CrossRef] [PubMed]

Foo, G.

Franke-Arnold, S.

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

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pasko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” œ12, 5448–5456 (2004).

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett.88, 257901 (2002).
[CrossRef] [PubMed]

Fu, Y. H.

Y. F. Yu, Y. H. Fu, X. M. Zhang, A. Q. Liu, T. Bourouina, T. Mei, Z. X. Shen, and D. P. Tsai, “Pure angular momentum generator using a ring resonator,” œ18, 21651–21662 (2010).

Furusawa, A.

J. L. O’Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics3, 687–695 (2009).
[CrossRef]

Galvez, E. J.

Gauthier, D. J.

R. W. Boyd, A. Jha, M. Malik, C. O’Sullivan, B. Rodenburg, and D. J. Gauthier, “Quantum key distribution in a high-dimensional state space: exploiting the transverse degree of freedom of the photon,” Proc. of SPIE794879480L–1 (2011).
[CrossRef]

Gibson, G.

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pasko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” œ12, 5448–5456 (2004).

He, H.

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

Heckenberg, N. R.

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

Hell, W. S.

W. S. Hell, “Far-field optical nanoscopy,” Science316, 1153–1158 (2007).
[CrossRef] [PubMed]

Hibino, Y.

S. Suzuki, K. Shuto, and Y. Hibino, “Integrated-Optic Ring Resonators with Two Stacked Layers of Silica Waveguide on Si,” IEEE Photon. Technol. Lett.4, 1256–1258 (1992).
[CrossRef]

Jeffries, G. D. M.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-Orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett.99, 073901 (2007).
[CrossRef] [PubMed]

Jha, A.

R. W. Boyd, A. Jha, M. Malik, C. O’Sullivan, B. Rodenburg, and D. J. Gauthier, “Quantum key distribution in a high-dimensional state space: exploiting the transverse degree of freedom of the photon,” Proc. of SPIE794879480L–1 (2011).
[CrossRef]

Johnson-Morris, B.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated Compact Optical Vortex Beam Emitters,” Science338, 363–366 (2012).
[CrossRef] [PubMed]

Juodkazis, S.

E. Brasselet, N. Murazawa, H. Misawa, and S. Juodkazis, “Optical vortices from liquid crystal droplets,” Phys. Rev. Lett.103, 103903 (2009).
[CrossRef] [PubMed]

Karimi, E.

F. Cardano, E. Karimi, L. Marrucci, C. de Lisio, and E. Santamato, “Generation and dynamics of optical beams with polarization singularities,” Opt. Express21, 8815–8820 (2013).
[CrossRef] [PubMed]

E. Karimi, L. Marrucci, C. de Lisio, and E. Santamato, “Time-division multiplexing of the orbital angular momentum states of light,” Opt. Lett.37, 127–129 (2012).
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L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt.13, 064001 (2011).
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E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, “Efficient generation and sorting of orbital angular momentum eigenmodes of light by thermally tuned q-plates,” Appl. Phys. Lett.94, 231124 (2009).
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Kristensen, M.

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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J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys.4, 282–286 (2008).
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G. Berkhout, M. Lavery, J. Courtial, M. Beijersbergen, and M. Padgett, “Efficient Sorting of orbital angular momentum states of light,” Phys. Rev. Lett.105, 105601 (2010).
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J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett.88, 257901 (2002).
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R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett.91, 233901 (2003).
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Y. F. Yu, Y. H. Fu, X. M. Zhang, A. Q. Liu, T. Bourouina, T. Mei, Z. X. Shen, and D. P. Tsai, “Pure angular momentum generator using a ring resonator,” œ18, 21651–21662 (2010).

Luk`yanchuk, B.

H. Wang, L. Shi, B. Luk̀yanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2, 501–505 (2008).
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L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science292, 912–914 (2001).
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R. W. Boyd, A. Jha, M. Malik, C. O’Sullivan, B. Rodenburg, and D. J. Gauthier, “Quantum key distribution in a high-dimensional state space: exploiting the transverse degree of freedom of the photon,” Proc. of SPIE794879480L–1 (2011).
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L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett.96, 163905 (2006).
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F. Cardano, E. Karimi, L. Marrucci, C. de Lisio, and E. Santamato, “Generation and dynamics of optical beams with polarization singularities,” Opt. Express21, 8815–8820 (2013).
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E. Karimi, L. Marrucci, C. de Lisio, and E. Santamato, “Time-division multiplexing of the orbital angular momentum states of light,” Opt. Lett.37, 127–129 (2012).
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L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt.13, 064001 (2011).
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E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, “Efficient generation and sorting of orbital angular momentum eigenmodes of light by thermally tuned q-plates,” Appl. Phys. Lett.94, 231124 (2009).
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L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett.96, 163905 (2006).
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Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-Orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett.99, 073901 (2007).
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Y. F. Yu, Y. H. Fu, X. M. Zhang, A. Q. Liu, T. Bourouina, T. Mei, Z. X. Shen, and D. P. Tsai, “Pure angular momentum generator using a ring resonator,” œ18, 21651–21662 (2010).

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E. Brasselet, N. Murazawa, H. Misawa, and S. Juodkazis, “Optical vortices from liquid crystal droplets,” Phys. Rev. Lett.103, 103903 (2009).
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G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys.3, 305–310 (2007).
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L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt.13, 064001 (2011).
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E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, “Efficient generation and sorting of orbital angular momentum eigenmodes of light by thermally tuned q-plates,” Appl. Phys. Lett.94, 231124 (2009).
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X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated Compact Optical Vortex Beam Emitters,” Science338, 363–366 (2012).
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J. L. O’Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics3, 687–695 (2009).
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A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science320, 646–649 (2008).
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R. W. Boyd, A. Jha, M. Malik, C. O’Sullivan, B. Rodenburg, and D. J. Gauthier, “Quantum key distribution in a high-dimensional state space: exploiting the transverse degree of freedom of the photon,” Proc. of SPIE794879480L–1 (2011).
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Padgett, M.

G. Berkhout, M. Lavery, J. Courtial, M. Beijersbergen, and M. Padgett, “Efficient Sorting of orbital angular momentum states of light,” Phys. Rev. Lett.105, 105601 (2010).
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G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pasko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” œ12, 5448–5456 (2004).

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett.88, 257901 (2002).
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L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett.96, 163905 (2006).
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G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pasko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” œ12, 5448–5456 (2004).

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L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science292, 912–914 (2001).
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L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt.13, 064001 (2011).
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E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, “Efficient generation and sorting of orbital angular momentum eigenmodes of light by thermally tuned q-plates,” Appl. Phys. Lett.94, 231124 (2009).
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A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science320, 646–649 (2008).
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H. Poynting, “The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly polarised light,” Proc. R. Soc. Lond. A82, 560–567 (1909).
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R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett.91, 233901 (2003).
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A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science320, 646–649 (2008).
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R. W. Boyd, A. Jha, M. Malik, C. O’Sullivan, B. Rodenburg, and D. J. Gauthier, “Quantum key distribution in a high-dimensional state space: exploiting the transverse degree of freedom of the photon,” Proc. of SPIE794879480L–1 (2011).
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F. Cardano, E. Karimi, L. Marrucci, C. de Lisio, and E. Santamato, “Generation and dynamics of optical beams with polarization singularities,” Opt. Express21, 8815–8820 (2013).
[CrossRef] [PubMed]

E. Karimi, L. Marrucci, C. de Lisio, and E. Santamato, “Time-division multiplexing of the orbital angular momentum states of light,” Opt. Lett.37, 127–129 (2012).
[CrossRef] [PubMed]

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt.13, 064001 (2011).
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E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, “Efficient generation and sorting of orbital angular momentum eigenmodes of light by thermally tuned q-plates,” Appl. Phys. Lett.94, 231124 (2009).
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L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt.13, 064001 (2011).
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Y. F. Yu, Y. H. Fu, X. M. Zhang, A. Q. Liu, T. Bourouina, T. Mei, Z. X. Shen, and D. P. Tsai, “Pure angular momentum generator using a ring resonator,” œ18, 21651–21662 (2010).

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H. Wang, L. Shi, B. Luk̀yanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2, 501–505 (2008).
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H. Wang, L. Shi, B. Luk̀yanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2, 501–505 (2008).
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L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8189 (1992).
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X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated Compact Optical Vortex Beam Emitters,” Science338, 363–366 (2012).
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X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated Compact Optical Vortex Beam Emitters,” Science338, 363–366 (2012).
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Y. F. Yu, Y. H. Fu, X. M. Zhang, A. Q. Liu, T. Bourouina, T. Mei, Z. X. Shen, and D. P. Tsai, “Pure angular momentum generator using a ring resonator,” œ18, 21651–21662 (2010).

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G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pasko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” œ12, 5448–5456 (2004).

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J. L. O’Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics3, 687–695 (2009).
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H. Wang, L. Shi, B. Luk̀yanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2, 501–505 (2008).
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Y. F. Yu, Y. H. Fu, X. M. Zhang, A. Q. Liu, T. Bourouina, T. Mei, Z. X. Shen, and D. P. Tsai, “Pure angular momentum generator using a ring resonator,” œ18, 21651–21662 (2010).

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Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-Orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett.99, 073901 (2007).
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E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, “Efficient generation and sorting of orbital angular momentum eigenmodes of light by thermally tuned q-plates,” Appl. Phys. Lett.94, 231124 (2009).
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S. Suzuki, K. Shuto, and Y. Hibino, “Integrated-Optic Ring Resonators with Two Stacked Layers of Silica Waveguide on Si,” IEEE Photon. Technol. Lett.4, 1256–1258 (1992).
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J. Opt.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt.13, 064001 (2011).
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Nat. Phys.

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

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Opt. Commun.

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Phys. Rev. Lett.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-Orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett.99, 073901 (2007).
[CrossRef] [PubMed]

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Proc. of SPIE

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X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated Compact Optical Vortex Beam Emitters,” Science338, 363–366 (2012).
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Figures (7)

Fig. 1
Fig. 1

Schematic of the proposed configuration of a silicon bus wave-guide and ring resonator. The ring resonator is on top of the access waveguide, separated by a 275 nm thick layer of silica. The angular grating inside the ring resonator is similar to that suggested in Ref. [27].

Fig. 2
Fig. 2

Theoretical intensity and polarization patterns for a beam emitted from a ring resonator. The upper row is for light polarized perpendicular to the waveguide, yet in the plane of the resonator, while the lower row is for light polarized parallel to the waveguide, leading to a radial and an azimuthal polarization distribution inside the ring resonator respectively. Each column corresponds to a specific angular phase matching condition and consequently value of OAM. Interestingly, for the case where = ±1, the intensity pattern of the outgoing beam does not form a doughnut shape, and its polarization switches from radial to azimuthal and vice versa. This type of beam is know as the Poincaré or polarization-singular beam. In this analysis, we have neglected any possible variations in the radial beam profile due to confinement of the scattering sources and instead a Laguerre-Gauss mode of radial order zero was assumed.

Fig. 3
Fig. 3

Sketch showing the stereoscopic mapping of the polarization Poincaré sphere on a beam transverse plane for the case of radially polarized beam with = −1. The beam possesses a right-handed circular polarization at the center (named C-point), tangent to the sphere’s south pole. From this point the polarization transitions through right handed elliptical to linear polarization at the so called L-line, a mapping of the Poincaré sphere’s equator. The upper hemisphere of the Poincaré sphere, however, is mapped to the region outside of the L-line, which therefore has a left handed polarization (initially elliptical, then circular). In the case of a radially polarized beam with = +1, the stereoscopic mapping is on the north pole, consequently the polarization handedness changes from right to left handed.

Fig. 4
Fig. 4

Simulated far-field intensity distribution of the beam emitted from a ring resonator, for (a) = 1 and (b) = 2. The absence/existence of a doughnut pattern prove the vortex properties of these beam. However, the radial patterns show additional maxima due to angular diffraction for the finite sized source.

Fig. 5
Fig. 5

Spectrum of three concentric ring resonators: green dot-dashed, red dashed and blue solid lines correspond to inner, middle and outer resonators, respectively. All resonators have a resonance at 1542 nm, allowing for the formation of a superposition state. The resonator Q factors are between 700 and 1000.

Fig. 6
Fig. 6

Simulated intensity pattern of a superposition state generated by two concentric ring resonators. (a) The beam is a superposition of = +2 and ℓ′ = −2, and (b) = +2 and ℓ′ = +1, respectively. In (b) the relative phase of the input signals for the two waveguides is varied, leading to a rotation of the superposition pattern. In (b), the intensity patterns, from left to right, correspond to relative phase of χ = 0°, χ = 120°, and χ = 240°, respectively.

Fig. 7
Fig. 7

Optical output power of the access waveguides for ring resonators that are set up for = +1 (inner ring) and = +2 (outer ring) at 1542 nm. Red dashed and blue solid curves correspond to the output power from the access waveguide of the inner and outer ring resonators, respectively. (a) Shows the output beam power from access waveguides when illuminated with an equal superposition of = +1 and = +2. The power unbalance is due to different out-coupling efficiencies for the outer and inner resonators. We can see a clear peak at the resonance of 1542 nm. (b) Output power when illuminated with a superposition of = −2 and = +2 beams. The matched ring resonator (outer) couples at the correct resonance, while the other ring resonator (inner) couples at resonances for which the angular phase matching condition is met. Here we should note that the large bandwidth of the illumination is necessary for a shorter FDTD simulation time, however, experimentally the input could be chosen such that only the resonance of interest (here 1542 nm) would be excited.

Equations (6)

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R 0 = m λ / ( 2 π n eff ) ,
= m q ,
E ( r ) = A ( r 0 ) e i k r r B ( r ) = k c × A ( r 0 ) e i k r r ,
E r ( r ) = E 0 ( r , z ) e i φ r ^ = E 0 ( r , z ) 2 [ | L π | 1 o + | R π | + 1 o ] ,
E φ ( r ) = E 0 ( r , z ) e i φ φ ^ = i E 0 ( r , z ) 2 [ | L π | 1 o + | R π | + 1 o ] ,
| ψ = cos ( θ 2 ) | + e i χ sin ( θ 2 ) | ,

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