Abstract

We present a novel method for efficient sorting of photons prepared in states of orbital angular momentum (OAM) and angular position (ANG). A log-polar optical transform is used in combination with a holographic beam-splitting method to achieve better mode discrimination and reduced cross-talk than reported previously. Simulating this method for 7 modes, we have calculated an improved mutual information of 2.43 bits/photon and 2.29 bits/photon for OAM and ANG modes respectively. In addition, we present preliminary results from an experimental implementation of this technique. This method is expected to have important applications for high-dimensional quantum key distribution systems.

© 2012 OSA

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  1. R. Piestun and D. A. B. Miller, “Electromagnetic degrees of freedom of an optical system,” J. Opt. Soc. Am. A17, 892–902 (2000).
    [CrossRef]
  2. L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8189 (1992).
    [CrossRef] [PubMed]
  3. A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photon.3, 161–204 (2011).
    [CrossRef]
  4. M. Malik, M. OSullivan, B. Rodenburg, M. Mirhosseini, J. Leach, M. P. J. Lavery, M. J. Padgett, and R. W. Boyd, “Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding,” Opt. Express20, 13195 (2012).
    [CrossRef] [PubMed]
  5. G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express12, 5448–5456 (2004).
    [CrossRef] [PubMed]
  6. J. Wang, J.-Y. Yang, I. M. Fazal, 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,” Nat. Photon.6, 488–496 (2012).
    [CrossRef]
  7. S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys.8, 75–75 (2006).
    [CrossRef]
  8. J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric Methods to Measure Orbital and Spin, or the Total Angular Momentum of a Single Photon,” Phys. Rev. Lett.92, 013601 (2004).
    [CrossRef] [PubMed]
  9. 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]
  10. M. T. Gruneisen, R. C. Dymale, K. E. Stoltenberg, and N. Steinhoff, “Optical vortex discrimination with a transmission volume hologram,” New J. Phys.13, 083030 (2011).
    [CrossRef]
  11. M. P. J. Lavery, D. J. Robertson, G. C. G. Berkhout, G. D. Love, M. J. Padgett, and J. Courtial, “Refractive elements for the measurement of the orbital angular momentum of a single photon,” Opt. Express20, 2110–2115 (2012).
    [CrossRef] [PubMed]
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    [CrossRef]
  13. Y. Saito, S.-i. Komatsu, and H. Ohzu, “Scale and rotation invariant real time optical correlator using computer generated hologram,” Opt. Commun.47, 8–11 (1983).
    [CrossRef]
  14. C. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in “Proc. IEEE Int. Conf.”, (Bangalore, 1984), pp. 175–179.
  15. D. Prongué, H. P. Herzig, R. Dändliker, and M. T. Gale, “Optimized kinoform structures for highly efficient fan-out elements,” Appl. Opt.31, 5706–5711 (1992).
    [CrossRef] [PubMed]
  16. L. A. Romero and F. M. Dickey, “Theory of optimal beam splitting by phase gratings. I. One-dimensional gratings,” J. Opt. Soc. Am. A24, 2280–2295 (2007).
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  17. M. Krenn, R. Fickler, M. Huber, R. Lapkiewicz, W. Plick, S. Ramelow, and A. Zeilinger, “Entanglement of Photons with Tunable Singularities,” arXiv:quant-ph/1205.2514 (2012).

2012 (3)

2011 (2)

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photon.3, 161–204 (2011).
[CrossRef]

M. T. Gruneisen, R. C. Dymale, K. E. Stoltenberg, and N. Steinhoff, “Optical vortex discrimination with a transmission volume hologram,” New J. Phys.13, 083030 (2011).
[CrossRef]

2010 (1)

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]

2007 (1)

2006 (1)

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys.8, 75–75 (2006).
[CrossRef]

2004 (2)

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric Methods to Measure Orbital and Spin, or the Total Angular Momentum of a Single Photon,” Phys. Rev. Lett.92, 013601 (2004).
[CrossRef] [PubMed]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express12, 5448–5456 (2004).
[CrossRef] [PubMed]

2000 (1)

1992 (2)

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

D. Prongué, H. P. Herzig, R. Dändliker, and M. T. Gale, “Optimized kinoform structures for highly efficient fan-out elements,” Appl. Opt.31, 5706–5711 (1992).
[CrossRef] [PubMed]

1983 (1)

Y. Saito, S.-i. Komatsu, and H. Ohzu, “Scale and rotation invariant real time optical correlator using computer generated hologram,” Opt. Commun.47, 8–11 (1983).
[CrossRef]

1974 (1)

Ahmed, N.

J. Wang, J.-Y. Yang, I. M. Fazal, 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,” Nat. Photon.6, 488–496 (2012).
[CrossRef]

Allen, L.

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

Barnett, S. M.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric Methods to Measure Orbital and Spin, or the Total Angular Momentum of a Single Photon,” Phys. Rev. Lett.92, 013601 (2004).
[CrossRef] [PubMed]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express12, 5448–5456 (2004).
[CrossRef] [PubMed]

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]

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

Bennett, C.

C. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in “Proc. IEEE Int. Conf.”, (Bangalore, 1984), pp. 175–179.

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]

Berkhout, G. C. G.

Boyd, R. W.

Brassard, G.

C. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in “Proc. IEEE Int. Conf.”, (Bangalore, 1984), pp. 175–179.

Bryngdahl, O.

Courtial, J.

M. P. J. Lavery, D. J. Robertson, G. C. G. Berkhout, G. D. Love, M. J. Padgett, and J. Courtial, “Refractive elements for the measurement of the orbital angular momentum of a single photon,” Opt. Express20, 2110–2115 (2012).
[CrossRef] [PubMed]

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. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express12, 5448–5456 (2004).
[CrossRef] [PubMed]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric Methods to Measure Orbital and Spin, or the Total Angular Momentum of a Single Photon,” Phys. Rev. Lett.92, 013601 (2004).
[CrossRef] [PubMed]

Dändliker, R.

Dickey, F. M.

Dolinar, S.

J. Wang, J.-Y. Yang, I. M. Fazal, 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,” Nat. Photon.6, 488–496 (2012).
[CrossRef]

Dymale, R. C.

M. T. Gruneisen, R. C. Dymale, K. E. Stoltenberg, and N. Steinhoff, “Optical vortex discrimination with a transmission volume hologram,” New J. Phys.13, 083030 (2011).
[CrossRef]

Fazal, I. M.

J. Wang, J.-Y. Yang, I. M. Fazal, 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,” Nat. Photon.6, 488–496 (2012).
[CrossRef]

Fickler, R.

M. Krenn, R. Fickler, M. Huber, R. Lapkiewicz, W. Plick, S. Ramelow, and A. Zeilinger, “Entanglement of Photons with Tunable Singularities,” arXiv:quant-ph/1205.2514 (2012).

Franke-Arnold, S.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric Methods to Measure Orbital and Spin, or the Total Angular Momentum of a Single Photon,” Phys. Rev. Lett.92, 013601 (2004).
[CrossRef] [PubMed]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express12, 5448–5456 (2004).
[CrossRef] [PubMed]

Gale, M. T.

Gibson, G.

Gröblacher, S.

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys.8, 75–75 (2006).
[CrossRef]

Gruneisen, M. T.

M. T. Gruneisen, R. C. Dymale, K. E. Stoltenberg, and N. Steinhoff, “Optical vortex discrimination with a transmission volume hologram,” New J. Phys.13, 083030 (2011).
[CrossRef]

Herzig, H. P.

Huang, H.

J. Wang, J.-Y. Yang, I. M. Fazal, 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,” Nat. Photon.6, 488–496 (2012).
[CrossRef]

Huber, M.

M. Krenn, R. Fickler, M. Huber, R. Lapkiewicz, W. Plick, S. Ramelow, and A. Zeilinger, “Entanglement of Photons with Tunable Singularities,” arXiv:quant-ph/1205.2514 (2012).

Jennewein, T.

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys.8, 75–75 (2006).
[CrossRef]

Komatsu, S.-i.

Y. Saito, S.-i. Komatsu, and H. Ohzu, “Scale and rotation invariant real time optical correlator using computer generated hologram,” Opt. Commun.47, 8–11 (1983).
[CrossRef]

Krenn, M.

M. Krenn, R. Fickler, M. Huber, R. Lapkiewicz, W. Plick, S. Ramelow, and A. Zeilinger, “Entanglement of Photons with Tunable Singularities,” arXiv:quant-ph/1205.2514 (2012).

Lapkiewicz, R.

M. Krenn, R. Fickler, M. Huber, R. Lapkiewicz, W. Plick, S. Ramelow, and A. Zeilinger, “Entanglement of Photons with Tunable Singularities,” arXiv:quant-ph/1205.2514 (2012).

Lavery, 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]

Lavery, M. P. J.

Leach, J.

M. Malik, M. OSullivan, B. Rodenburg, M. Mirhosseini, J. Leach, M. P. J. Lavery, M. J. Padgett, and R. W. Boyd, “Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding,” Opt. Express20, 13195 (2012).
[CrossRef] [PubMed]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric Methods to Measure Orbital and Spin, or the Total Angular Momentum of a Single Photon,” Phys. Rev. Lett.92, 013601 (2004).
[CrossRef] [PubMed]

Love, G. D.

Malik, M.

Miller, D. A. B.

Mirhosseini, M.

Ohzu, H.

Y. Saito, S.-i. Komatsu, and H. Ohzu, “Scale and rotation invariant real time optical correlator using computer generated hologram,” Opt. Commun.47, 8–11 (1983).
[CrossRef]

OSullivan, M.

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).
[CrossRef]

Padgett, M. J.

Pas’ko, V.

Piestun, R.

Plick, W.

M. Krenn, R. Fickler, M. Huber, R. Lapkiewicz, W. Plick, S. Ramelow, and A. Zeilinger, “Entanglement of Photons with Tunable Singularities,” arXiv:quant-ph/1205.2514 (2012).

Prongué, D.

Ramelow, S.

M. Krenn, R. Fickler, M. Huber, R. Lapkiewicz, W. Plick, S. Ramelow, and A. Zeilinger, “Entanglement of Photons with Tunable Singularities,” arXiv:quant-ph/1205.2514 (2012).

Ren, Y.

J. Wang, J.-Y. Yang, I. M. Fazal, 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,” Nat. Photon.6, 488–496 (2012).
[CrossRef]

Robertson, D. J.

Rodenburg, B.

Romero, L. A.

Saito, Y.

Y. Saito, S.-i. Komatsu, and H. Ohzu, “Scale and rotation invariant real time optical correlator using computer generated hologram,” Opt. Commun.47, 8–11 (1983).
[CrossRef]

Skeldon, K.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric Methods to Measure Orbital and Spin, or the Total Angular Momentum of a Single Photon,” Phys. Rev. Lett.92, 013601 (2004).
[CrossRef] [PubMed]

Spreeuw, R.

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

Steinhoff, N.

M. T. Gruneisen, R. C. Dymale, K. E. Stoltenberg, and N. Steinhoff, “Optical vortex discrimination with a transmission volume hologram,” New J. Phys.13, 083030 (2011).
[CrossRef]

Stoltenberg, K. E.

M. T. Gruneisen, R. C. Dymale, K. E. Stoltenberg, and N. Steinhoff, “Optical vortex discrimination with a transmission volume hologram,” New J. Phys.13, 083030 (2011).
[CrossRef]

Tur, M.

J. Wang, J.-Y. Yang, I. M. Fazal, 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,” Nat. Photon.6, 488–496 (2012).
[CrossRef]

Vasnetsov, M.

Vaziri, A.

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys.8, 75–75 (2006).
[CrossRef]

Wang, J.

J. Wang, J.-Y. Yang, I. M. Fazal, 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,” Nat. Photon.6, 488–496 (2012).
[CrossRef]

Weihs, G.

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys.8, 75–75 (2006).
[CrossRef]

Willner, A. E.

J. Wang, J.-Y. Yang, I. M. Fazal, 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,” Nat. Photon.6, 488–496 (2012).
[CrossRef]

Woerdman, J.

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

Yan, Y.

J. Wang, J.-Y. Yang, I. M. Fazal, 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,” Nat. Photon.6, 488–496 (2012).
[CrossRef]

Yang, J.-Y.

J. Wang, J.-Y. Yang, I. M. Fazal, 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,” Nat. Photon.6, 488–496 (2012).
[CrossRef]

Yao, A. M.

Yue, Y.

J. Wang, J.-Y. Yang, I. M. Fazal, 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,” Nat. Photon.6, 488–496 (2012).
[CrossRef]

Zeilinger, A.

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys.8, 75–75 (2006).
[CrossRef]

M. Krenn, R. Fickler, M. Huber, R. Lapkiewicz, W. Plick, S. Ramelow, and A. Zeilinger, “Entanglement of Photons with Tunable Singularities,” arXiv:quant-ph/1205.2514 (2012).

Adv. Opt. Photon. (1)

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

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

Nat. Photon. (1)

J. Wang, J.-Y. Yang, I. M. Fazal, 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,” Nat. Photon.6, 488–496 (2012).
[CrossRef]

New J. Phys. (2)

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys.8, 75–75 (2006).
[CrossRef]

M. T. Gruneisen, R. C. Dymale, K. E. Stoltenberg, and N. Steinhoff, “Optical vortex discrimination with a transmission volume hologram,” New J. Phys.13, 083030 (2011).
[CrossRef]

Opt. Commun. (1)

Y. Saito, S.-i. Komatsu, and H. Ohzu, “Scale and rotation invariant real time optical correlator using computer generated hologram,” Opt. Commun.47, 8–11 (1983).
[CrossRef]

Opt. Express (3)

Phys. Rev. A (1)

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

Phys. Rev. Lett. (2)

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric Methods to Measure Orbital and Spin, or the Total Angular Momentum of a Single Photon,” Phys. Rev. Lett.92, 013601 (2004).
[CrossRef] [PubMed]

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]

Other (2)

C. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in “Proc. IEEE Int. Conf.”, (Bangalore, 1984), pp. 175–179.

M. Krenn, R. Fickler, M. Huber, R. Lapkiewicz, W. Plick, S. Ramelow, and A. Zeilinger, “Entanglement of Photons with Tunable Singularities,” arXiv:quant-ph/1205.2514 (2012).

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Figures (3)

Fig. 1
Fig. 1

Schematic showing the configuration for enhanced sorting of 1(a) OAM and 1(b) ANG modes. The OAM sorter shown here is from Ref. [9]. The fan-out phase element is combined with the second element of the OAM sorter to create multiple copies of the transformed beam. A phase-correcting element then corrects the relative phases introduced between the copies.

Fig. 2
Fig. 2

Simulation results comparing 2(a) the output from the OAM sorter with 2(b) the output from the N = 9 fan-out-enhanced OAM sorter for 7 input OAM modes and comparing 2(c) the output from the ANG sorter with 2(d) the output from the fan-out-enhanced ANG sorter for 7 input ANG modes. Different colors correspond to different modes.

Fig. 3
Fig. 3

Preliminary results from an experimental implementation of our sorting method. 3(a) Output from the OAM sorter [11] for different input OAM modes. 3(b) Output from the fan-out-enhanced OAM sorter proposed in this paper. Here, we used a fan-out element that creates 3 copies of the beam.

Tables (1)

Tables Icon

Table 1 Mutual information (in bits/photon) and error percentages calculated for the OAM and ANG sorters and the fan-out-enhanced (N=9) OAM and ANG sorters when sorting 7 modes. The theoretical limit is shown in the second column and is equal to log2(7) = 2.81.

Equations (9)

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

u ( r , φ ) = R ( r ) e i φ ,
θ j ( r , φ ) = 1 2 L + 1 = L L u ( r , φ ) e i 2 π j / ( 2 L + 1 ) .
U ( x ) = e i x / a rect ( x 2 π a ) ,
U ˜ ( x ) = ( 2 π a ) sinc ( x Δ Δ ) ,
U ˜ ( x ) = 2 π a N sinc ( x Δ Δ / N ) .
Θ j ( x ) = 1 2 L + 1 rect ( x 2 π a ) δ L ( x Δ θ j a )
Θ ˜ j ( k ) = 2 π a 2 L + 1 = L L sinc ( a k ) e i 2 π j ( 2 L + 1 ) .
Θ j ( x ) = 1 N ( 2 L + 1 ) rect ( x 2 π a ) δ n L ( x Δ θ j a ) ,
U ( x , y ) = m = 1 N A m e i ϕ m e i 2 π s m x / λ ,

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