Abstract

Transformation and detection of photons in higher-order spatial modes usually requires complicated holographic techniques. Detectors based on spatial holograms suffer from non-idealities and should be carefully calibrated. We report a novel method for analyzing the quality of projective measurements in spatial mode basis inspired by quantum detector tomography. It allows us to calibrate the detector response using only gaussian beams. We experimentally investigate the inherent inaccuracy of the existing methods of mode transformation and provide a full statistical reconstruction of the POVM (positive operator valued measure) elements for holographic spatial mode detectors.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Creation and detection of optical modes with spatial light modulators

Andrew Forbes, Angela Dudley, and Melanie McLaren
Adv. Opt. Photon. 8(2) 200-227 (2016)

Quantum state discrimination

Stephen M. Barnett and Sarah Croke
Adv. Opt. Photon. 1(2) 238-278 (2009)

Self-healing high-dimensional quantum key distribution using hybrid spin-orbit Bessel states

Isaac Nape, Eileen Otte, Adam Vallés, Carmelo Rosales-Guzmán, Filippo Cardano, Cornelia Denz, and Andrew Forbes
Opt. Express 26(21) 26946-26960 (2018)

References

  • View by:
  • |
  • |
  • |

  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. Photonics 6, 488–496 (2012).
    [Crossref]
  2. N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
    [Crossref] [PubMed]
  3. G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
    [Crossref]
  4. H. Qassim, F. M. Miatto, J. P. Torres, M. J. Padgett, E. Karimi, and R. W. Boyd, “Limitations to the determination of a Laguerre-Gauss spectrum via projective, phase-flattening measurement,” J. Opt. Soc. Am. B 31, A20–A23 (2014).
    [Crossref]
  5. J. P. Kirk and A. L. Jones, “Phase-only complex-valued spatial filter,” J. Opt. Soc. Am. 61, 1023–1028 (1971).
    [Crossref]
  6. J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38, 5004–5013 (1999).
    [Crossref]
  7. E. Bolduc, N. Bent, E. Santamato, E. Karimi, and R. W. Boyd, “Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram,” Opt. Lett.  38, 3546–3549 (2013).
    [Crossref] [PubMed]
  8. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
    [Crossref] [PubMed]
  9. A. Syouji, K. Kurihara, A. Otomo, and S. Saito, “Diffraction-grating-type phase converters for conversion of hermite-laguerre-gaussian mode into gaussian mode,” Appl. Opt. 49, 1513–1517 (2010).
    [Crossref] [PubMed]
  10. B. Jack, A. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. Ireland, S. Barnett, and M. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81, 043844 (2010).
    [Crossref]
  11. V. Salakhutdinov, E. Eliel, and W. Löffler, “Full-field quantum correlations of spatially entangled photons,” Phys. Rev. Lett. 108, 173604 (2012).
    [Crossref] [PubMed]
  12. J. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. Pregnell, C. Silberhorn, T. Ralph, J. Eisert, M. Plenio, and I. Walmsley, “Tomography of quantum detectors,” Nat. Phys. 5, 27–30 (2008).
    [Crossref]
  13. A. Feito, J. Lundeen, H. Coldenstrodt-Ronge, J. Eisert, M. Plenio, and I. Walmsley, “Measuring measurement: theory and practice,” New J. Phys. 11, 093038 (2009).
    [Crossref]

2014 (1)

2013 (2)

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

E. Bolduc, N. Bent, E. Santamato, E. Karimi, and R. W. Boyd, “Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram,” Opt. Lett.  38, 3546–3549 (2013).
[Crossref] [PubMed]

2012 (2)

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. Photonics 6, 488–496 (2012).
[Crossref]

V. Salakhutdinov, E. Eliel, and W. Löffler, “Full-field quantum correlations of spatially entangled photons,” Phys. Rev. Lett. 108, 173604 (2012).
[Crossref] [PubMed]

2010 (2)

A. Syouji, K. Kurihara, A. Otomo, and S. Saito, “Diffraction-grating-type phase converters for conversion of hermite-laguerre-gaussian mode into gaussian mode,” Appl. Opt. 49, 1513–1517 (2010).
[Crossref] [PubMed]

B. Jack, A. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. Ireland, S. Barnett, and M. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81, 043844 (2010).
[Crossref]

2009 (1)

A. Feito, J. Lundeen, H. Coldenstrodt-Ronge, J. Eisert, M. Plenio, and I. Walmsley, “Measuring measurement: theory and practice,” New J. Phys. 11, 093038 (2009).
[Crossref]

2008 (1)

J. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. Pregnell, C. Silberhorn, T. Ralph, J. Eisert, M. Plenio, and I. Walmsley, “Tomography of quantum detectors,” Nat. Phys. 5, 27–30 (2008).
[Crossref]

2007 (1)

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

1999 (1)

1971 (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. Photonics 6, 488–496 (2012).
[Crossref]

Barnett, S.

B. Jack, A. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. Ireland, S. Barnett, and M. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81, 043844 (2010).
[Crossref]

Bent, N.

E. Bolduc, N. Bent, E. Santamato, E. Karimi, and R. W. Boyd, “Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram,” Opt. Lett.  38, 3546–3549 (2013).
[Crossref] [PubMed]

Bolduc, E.

E. Bolduc, N. Bent, E. Santamato, E. Karimi, and R. W. Boyd, “Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram,” Opt. Lett.  38, 3546–3549 (2013).
[Crossref] [PubMed]

Boyd, R. W.

H. Qassim, F. M. Miatto, J. P. Torres, M. J. Padgett, E. Karimi, and R. W. Boyd, “Limitations to the determination of a Laguerre-Gauss spectrum via projective, phase-flattening measurement,” J. Opt. Soc. Am. B 31, A20–A23 (2014).
[Crossref]

E. Bolduc, N. Bent, E. Santamato, E. Karimi, and R. W. Boyd, “Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram,” Opt. Lett.  38, 3546–3549 (2013).
[Crossref] [PubMed]

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

Campos, J.

Coldenstrodt-Ronge, H.

A. Feito, J. Lundeen, H. Coldenstrodt-Ronge, J. Eisert, M. Plenio, and I. Walmsley, “Measuring measurement: theory and practice,” New J. Phys. 11, 093038 (2009).
[Crossref]

J. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. Pregnell, C. Silberhorn, T. Ralph, J. Eisert, M. Plenio, and I. Walmsley, “Tomography of quantum detectors,” Nat. Phys. 5, 27–30 (2008).
[Crossref]

Cottrell, D. M.

Davis, J. A.

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. Photonics 6, 488–496 (2012).
[Crossref]

Eisert, J.

A. Feito, J. Lundeen, H. Coldenstrodt-Ronge, J. Eisert, M. Plenio, and I. Walmsley, “Measuring measurement: theory and practice,” New J. Phys. 11, 093038 (2009).
[Crossref]

J. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. Pregnell, C. Silberhorn, T. Ralph, J. Eisert, M. Plenio, and I. Walmsley, “Tomography of quantum detectors,” Nat. Phys. 5, 27–30 (2008).
[Crossref]

Eliel, E.

V. Salakhutdinov, E. Eliel, and W. Löffler, “Full-field quantum correlations of spatially entangled photons,” Phys. Rev. Lett. 108, 173604 (2012).
[Crossref] [PubMed]

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. Photonics 6, 488–496 (2012).
[Crossref]

Feito, A.

A. Feito, J. Lundeen, H. Coldenstrodt-Ronge, J. Eisert, M. Plenio, and I. Walmsley, “Measuring measurement: theory and practice,” New J. Phys. 11, 093038 (2009).
[Crossref]

J. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. Pregnell, C. Silberhorn, T. Ralph, J. Eisert, M. Plenio, and I. Walmsley, “Tomography of quantum detectors,” Nat. Phys. 5, 27–30 (2008).
[Crossref]

Franke-Arnold, S.

B. Jack, A. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. Ireland, S. Barnett, and M. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81, 043844 (2010).
[Crossref]

Huang, H.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

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. Photonics 6, 488–496 (2012).
[Crossref]

Ireland, D.

B. Jack, A. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. Ireland, S. Barnett, and M. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81, 043844 (2010).
[Crossref]

Jack, B.

B. Jack, A. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. Ireland, S. Barnett, and M. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81, 043844 (2010).
[Crossref]

Jones, A. L.

Karimi, E.

H. Qassim, F. M. Miatto, J. P. Torres, M. J. Padgett, E. Karimi, and R. W. Boyd, “Limitations to the determination of a Laguerre-Gauss spectrum via projective, phase-flattening measurement,” J. Opt. Soc. Am. B 31, A20–A23 (2014).
[Crossref]

E. Bolduc, N. Bent, E. Santamato, E. Karimi, and R. W. Boyd, “Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram,” Opt. Lett.  38, 3546–3549 (2013).
[Crossref] [PubMed]

Kirk, J. P.

Kristensen, P.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

Kurihara, K.

Leach, J.

B. Jack, A. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. Ireland, S. Barnett, and M. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81, 043844 (2010).
[Crossref]

Löffler, W.

V. Salakhutdinov, E. Eliel, and W. Löffler, “Full-field quantum correlations of spatially entangled photons,” Phys. Rev. Lett. 108, 173604 (2012).
[Crossref] [PubMed]

Lundeen, J.

A. Feito, J. Lundeen, H. Coldenstrodt-Ronge, J. Eisert, M. Plenio, and I. Walmsley, “Measuring measurement: theory and practice,” New J. Phys. 11, 093038 (2009).
[Crossref]

J. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. Pregnell, C. Silberhorn, T. Ralph, J. Eisert, M. Plenio, and I. Walmsley, “Tomography of quantum detectors,” Nat. Phys. 5, 27–30 (2008).
[Crossref]

Mair, A.

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

Miatto, F. M.

Molina-Terriza, G.

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

Moreno, I.

Otomo, A.

Padgett, M.

B. Jack, A. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. Ireland, S. Barnett, and M. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81, 043844 (2010).
[Crossref]

Padgett, M. J.

Plenio, M.

A. Feito, J. Lundeen, H. Coldenstrodt-Ronge, J. Eisert, M. Plenio, and I. Walmsley, “Measuring measurement: theory and practice,” New J. Phys. 11, 093038 (2009).
[Crossref]

J. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. Pregnell, C. Silberhorn, T. Ralph, J. Eisert, M. Plenio, and I. Walmsley, “Tomography of quantum detectors,” Nat. Phys. 5, 27–30 (2008).
[Crossref]

Pregnell, K.

J. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. Pregnell, C. Silberhorn, T. Ralph, J. Eisert, M. Plenio, and I. Walmsley, “Tomography of quantum detectors,” Nat. Phys. 5, 27–30 (2008).
[Crossref]

Qassim, H.

Ralph, T.

J. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. Pregnell, C. Silberhorn, T. Ralph, J. Eisert, M. Plenio, and I. Walmsley, “Tomography of quantum detectors,” Nat. Phys. 5, 27–30 (2008).
[Crossref]

Ramachandran, S.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

Ren, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

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. Photonics 6, 488–496 (2012).
[Crossref]

Romero, J.

B. Jack, A. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. Ireland, S. Barnett, and M. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81, 043844 (2010).
[Crossref]

Saito, S.

Salakhutdinov, V.

V. Salakhutdinov, E. Eliel, and W. Löffler, “Full-field quantum correlations of spatially entangled photons,” Phys. Rev. Lett. 108, 173604 (2012).
[Crossref] [PubMed]

Santamato, E.

E. Bolduc, N. Bent, E. Santamato, E. Karimi, and R. W. Boyd, “Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram,” Opt. Lett.  38, 3546–3549 (2013).
[Crossref] [PubMed]

Silberhorn, C.

J. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. Pregnell, C. Silberhorn, T. Ralph, J. Eisert, M. Plenio, and I. Walmsley, “Tomography of quantum detectors,” Nat. Phys. 5, 27–30 (2008).
[Crossref]

Syouji, A.

Torner, L.

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

Torres, J. P.

Tur, M.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

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. Photonics 6, 488–496 (2012).
[Crossref]

Vaziri, A.

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

Walmsley, I.

A. Feito, J. Lundeen, H. Coldenstrodt-Ronge, J. Eisert, M. Plenio, and I. Walmsley, “Measuring measurement: theory and practice,” New J. Phys. 11, 093038 (2009).
[Crossref]

J. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. Pregnell, C. Silberhorn, T. Ralph, J. Eisert, M. Plenio, and I. Walmsley, “Tomography of quantum detectors,” Nat. Phys. 5, 27–30 (2008).
[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. Photonics 6, 488–496 (2012).
[Crossref]

Weihs, G.

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

Willner, A. E.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

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. Photonics 6, 488–496 (2012).
[Crossref]

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. Photonics 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. Photonics 6, 488–496 (2012).
[Crossref]

Yao, A.

B. Jack, A. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. Ireland, S. Barnett, and M. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81, 043844 (2010).
[Crossref]

Yue, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

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. Photonics 6, 488–496 (2012).
[Crossref]

Yzuel, M. J.

Zeilinger, A.

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

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (1)

Nat. Photonics (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. Photonics 6, 488–496 (2012).
[Crossref]

Nat. Phys. (2)

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

J. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. Pregnell, C. Silberhorn, T. Ralph, J. Eisert, M. Plenio, and I. Walmsley, “Tomography of quantum detectors,” Nat. Phys. 5, 27–30 (2008).
[Crossref]

Nature (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] [PubMed]

New J. Phys. (1)

A. Feito, J. Lundeen, H. Coldenstrodt-Ronge, J. Eisert, M. Plenio, and I. Walmsley, “Measuring measurement: theory and practice,” New J. Phys. 11, 093038 (2009).
[Crossref]

Opt. Lett (1)

E. Bolduc, N. Bent, E. Santamato, E. Karimi, and R. W. Boyd, “Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram,” Opt. Lett.  38, 3546–3549 (2013).
[Crossref] [PubMed]

Phys. Rev. A (1)

B. Jack, A. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. Ireland, S. Barnett, and M. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81, 043844 (2010).
[Crossref]

Phys. Rev. Lett. (1)

V. Salakhutdinov, E. Eliel, and W. Löffler, “Full-field quantum correlations of spatially entangled photons,” Phys. Rev. Lett. 108, 173604 (2012).
[Crossref] [PubMed]

Science (1)

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1 Experimental setup. A single phase-only SLM is used for both calibration beam preparation and as a part of the mode filter. The waist of the Gaussian beam is carefully controlled and mode-matched to the detection mode by the first phase hologram (right one on the inset). The mode-transforming hologram is displayed on the other part (left on the inset). The transformed beam is focused to a single mode fiber.
Fig. 2
Fig. 2 Detection probability distributions for five lower-order phase-only holograms, corresponding to n = 0…4 and m = 0. Horizontal axis represents the displacement of the detecting fiber in the far field of the hologram δi, corresponding to detection mode tilts θi = δi/f, where f = 8mm is the focal length of the focusing objective. Displacement is given in dimensionless units δi/w, where w = (1.871 ± 0.007)μm is the fiber mode waist. Points are experimentally measured data for holograms with no amplitude modulation, solid lines are theoretical distributions for ideal HG modes (a) and probability distributions for reconstructed POVM of the real detector (b).
Fig. 3
Fig. 3 Diagonal elements of the reconstructed POVM matrix in HG basis Πn,kk: reconstructed from experimental data for holograms with no amplitude modulation (a), and with both phase and amplitude modulation (b); reconstructed from numerical simulations of the far-field diffraction pattern for holograms without (c) and with (d) amplitude modulation.

Equations (7)

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

M ( x , y ) = sinc ( π ( A ( x , y ) 1 ) ) ,   F ( x , y ) = Φ ( x , y ) π A ( x , y ) .
φ m n ( x , y ) = 2 π w 2 2 m + n n ! m ! H m ( 2 x w ) H n ( 2 y w ) × exp ( x 2 + y 2 w 2 ) ,
π ˜ n = k , p θ k , p ( n ) | ψ k ψ p | .
φ 00 ( x d i , y ) = 2 π w 2 exp ( ( x d i ) 2 + y 2 w 2 ) ,
P d i , n = d i | π n | d i = | 2 π w 2 e ( x d i ) 2 + y 2 w 2 φ n 0 ( x , y ) d x d y | 2 = d i 2 n w 2 n n ! exp ( d i 2 w 2 ) .
P d i , n = d i | π ˜ n | d i = exp ( d i 2 w 2 ) k , p = 0 M d i k + p w k + p k ! p ! θ k p ( n ) = k , p = 0 M F i , k p Π k p , n ,
F i , k p = exp ( d i 2 w 2 ) d i k + p w k + p k ! p ! ; Π k p , n = θ k p ( n ) .

Metrics