Abstract

In recent years, mode-division multiplexing (MDM) has been proposed as a promising solution in order to increase the information capacity of optical networks both in free-space and in optical fiber transmission. Here we present the design, fabrication and test of diffractive optical elements for mode-division multiplexing based on optical transformations in the visible range. Diffractive optics have been fabricated by means of 3D high-resolution electron beam lithography on polymethylmethacrylate resist layer spun over a glass substrate. The same optical sequence was exploited both for input-mode multiplexing and for output-mode sorting after free-space propagation. Their high miniaturization level and efficiency make these optical devices ideal for integration into next-generation platforms for mode-division (de)multiplexing in telecom applications.

© 2017 Optical Society of America

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2017 (3)

H. Zhou, D. Fu, J. Dong, P. Zhang, D. Chen, X. Cai, F. Li, and X. Zhang, “Orbital angular momentum complex spectrum analyzer for vortex light based on the rotational Doppler effect,” Light Sci. Appl. 6, e16251 (2017).

C. Wan, J. Chen, and Q. Zhan, “Compact and high-resolution optical orbital angular momentum sorter,” APL Photonics 2(3), 031302 (2017).
[Crossref]

G. Ruffato, M. Massari, and F. Romanato, “Compact sorting of optical vortices by means of diffractive transformation optics,” Opt. Lett. 42(3), 551–554 (2017).
[Crossref] [PubMed]

2016 (6)

J. Wang, “Advances in communications using optical vortices,” Photon. Res. 4(5), B14–B28 (2016).
[Crossref]

J. Zhou, W. Zhang, and L. Chen, “Experimental detection of high-order or fractional orbital angular momentum of light based on a robust mode converter,” Appl. Phys. Lett. 108(11), 111108 (2016).
[Crossref]

S. Gao, T. Lei, Y. Li, Y. Yuan, Z. Xie, Z. Li, and X. Yuan, “OAM-labeled free-space optical flow routing,” Opt. Express 24(19), 21642–21651 (2016).
[Crossref] [PubMed]

G. Ruffato, M. Massari, and F. Romanato, “Diffractive optics for combined spatial- and mode- division demultiplexing of optical vortices: design, fabrication and optical characterization,” Sci. Rep. 6(1), 24760 (2016).
[Crossref] [PubMed]

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Rochardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fisher, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. B. Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
[Crossref]

A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. Ben Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6(1), 27674 (2016).
[Crossref] [PubMed]

2015 (7)

M. Mirhosseini, O. S. Magana-Loaiza, M. N. O’Sullivan, B. Rudenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17(3), 033033 (2015).
[Crossref]

S. Yu, “Potentials and challenges of using orbital angular momentum communications in optical interconnects,” Opt. Express 23(3), 3075–3087 (2015).
[Crossref] [PubMed]

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An Nguyen, D. A. Nolan, M.-J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
[Crossref] [PubMed]

K. S. Morgan, I. S. Raghu, and E. G. Johnson, “Design and fabrication of diffractive optics for orbital angular momentum space division multiplexing,” Proc. SPIE 9374, 93740Y (2015).
[Crossref]

M. Massari, G. Ruffato, M. Gintoli, F. Ricci, and F. Romanato, “Fabrication and characterization of high-quality spiral phase plates for optical applications,” Appl. Opt. 54(13), 4077–4083 (2015).
[Crossref]

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
[Crossref]

G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40(9), 1980–1983 (2015).
[Crossref] [PubMed]

2014 (4)

2013 (5)

P. Bierdz, M. Kwon, C. Roncaioli, and H. Deng, “High fidelity detection of the orbital angular momentum of light by time mapping,” New J. Phys. 15(11), 113062 (2013).
[Crossref]

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. E. Wilner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15(1), 013024 (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] [PubMed]

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(6140), 1545–1548 (2013).
[Crossref] [PubMed]

A. Belmonte and J. P. Torres, “Digital coherent receiver for orbital angular momentum demultiplexing,” Opt. Lett. 38(2), 241–243 (2013).
[Crossref] [PubMed]

2012 (6)

Y. Yan, Y. Yue, H. Huang, J. Y. Yang, M. R. Chitgarha, N. Ahmed, M. Tur, S. J. Dolinar, and A. E. Willner, “Efficient generation and multiplexing of optical orbital angular momentum modes in a ring fiber by using multiple coherent inputs,” Opt. Lett. 37(17), 3645–3647 (2012).
[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(7), 488–496 (2012).
[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(3), 033001 (2012).
[Crossref]

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. Express 20(3), 2110–2115 (2012).
[Crossref] [PubMed]

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. Express 20(22), 24444–24449 (2012).
[Crossref] [PubMed]

T. Su, R. P. Scott, S. S. Djordjevic, N. K. Fontaine, D. J. Geisler, X. Cai, and S. J. B. Yoo, “Demonstration of free space coherent optical communication using integrated silicon photonic orbital angular momentum devices,” Opt. Express 20(9), 9396–9402 (2012).
[Crossref] [PubMed]

2010 (3)

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[Crossref] [PubMed]

B. J. Wiley, D. Qin, and Y. Xia, “Nanofabrication at high throughput and low cost,” ACS Nano 4(7), 3554–3559 (2010).
[Crossref] [PubMed]

N. Zhang, X. C. Yuan, and R. E. Burge, “Extending the detection range of optical vortices by Dammann vortex gratings,” Opt. Lett. 35(20), 3495–3497 (2010).
[Crossref] [PubMed]

2004 (1)

2002 (1)

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(25), 257901 (2002).
[Crossref] [PubMed]

1998 (1)

V. V. Kotlyar, S. N. Khonina, and V. A. Soifer, “Light field decomposition in angular harmonics by means of diffractive optics,” J. Mod. Opt. 45(7), 1495–1506 (1998).
[Crossref]

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 laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Agrell, E.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Rochardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fisher, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. B. Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
[Crossref]

Ahmed, N.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An Nguyen, D. A. Nolan, M.-J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
[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(7), 488–496 (2012).
[Crossref]

Y. Yan, Y. Yue, H. Huang, J. Y. Yang, M. R. Chitgarha, N. Ahmed, M. Tur, S. J. Dolinar, and A. E. Willner, “Efficient generation and multiplexing of optical orbital angular momentum modes in a ring fiber by using multiple coherent inputs,” Opt. Lett. 37(17), 3645–3647 (2012).
[Crossref] [PubMed]

Alfano, R. R.

G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40(9), 1980–1983 (2015).
[Crossref] [PubMed]

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An Nguyen, D. A. Nolan, M.-J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
[Crossref] [PubMed]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

An Nguyen, T.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An Nguyen, D. A. Nolan, M.-J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
[Crossref] [PubMed]

Barnett, S.

Barnett, S. M.

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(25), 257901 (2002).
[Crossref] [PubMed]

Beijersbergen, M. W.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[Crossref] [PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Belmonte, A.

Ben Salem, A.

A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. Ben Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6(1), 27674 (2016).
[Crossref] [PubMed]

Berkhout, G. C. G.

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. Express 20(3), 2110–2115 (2012).
[Crossref] [PubMed]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[Crossref] [PubMed]

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(3), 033001 (2012).
[Crossref]

Bierdz, P.

P. Bierdz, M. Kwon, C. Roncaioli, and H. Deng, “High fidelity detection of the orbital angular momentum of light by time mapping,” New J. Phys. 15(11), 113062 (2013).
[Crossref]

Bowers, J. E.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Rochardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fisher, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. B. Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
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M. Mirhosseini, O. S. Magana-Loaiza, M. N. O’Sullivan, B. Rudenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17(3), 033033 (2015).
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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(6140), 1545–1548 (2013).
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Cai, X.

H. Zhou, D. Fu, J. Dong, P. Zhang, D. Chen, X. Cai, F. Li, and X. Zhang, “Orbital angular momentum complex spectrum analyzer for vortex light based on the rotational Doppler effect,” Light Sci. Appl. 6, e16251 (2017).

T. Su, R. P. Scott, S. S. Djordjevic, N. K. Fontaine, D. J. Geisler, X. Cai, and S. J. B. Yoo, “Demonstration of free space coherent optical communication using integrated silicon photonic orbital angular momentum devices,” Opt. Express 20(9), 9396–9402 (2012).
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H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An Nguyen, D. A. Nolan, M.-J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
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Chen, D.

H. Zhou, D. Fu, J. Dong, P. Zhang, D. Chen, X. Cai, F. Li, and X. Zhang, “Orbital angular momentum complex spectrum analyzer for vortex light based on the rotational Doppler effect,” Light Sci. Appl. 6, e16251 (2017).

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C. Wan, J. Chen, and Q. Zhan, “Compact and high-resolution optical orbital angular momentum sorter,” APL Photonics 2(3), 031302 (2017).
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J. Zhou, W. Zhang, and L. Chen, “Experimental detection of high-order or fractional orbital angular momentum of light based on a robust mode converter,” Appl. Phys. Lett. 108(11), 111108 (2016).
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W. Zhang, Q. Qi, J. Zhou, and L. Chen, “Mimicking Faraday Rotation to Sort the Orbital Angular Momentum of Light,” Phys. Rev. Lett. 112(15), 153601 (2014).
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Chraplyvy, A. R.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Rochardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fisher, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. B. Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
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M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. E. Wilner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15(1), 013024 (2013).
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G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
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G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004).
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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(25), 257901 (2002).
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P. Bierdz, M. Kwon, C. Roncaioli, and H. Deng, “High fidelity detection of the orbital angular momentum of light by time mapping,” New J. Phys. 15(11), 113062 (2013).
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Denolle, B.

Djordjevic, S. S.

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(7), 488–496 (2012).
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Dolinar, S. J.

Dong, J.

H. Zhou, D. Fu, J. Dong, P. Zhang, D. Chen, X. Cai, F. Li, and X. Zhang, “Orbital angular momentum complex spectrum analyzer for vortex light based on the rotational Doppler effect,” Light Sci. Appl. 6, e16251 (2017).

Dudley, A.

A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. Ben Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6(1), 27674 (2016).
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Earnshaw, M.

Eggleton, B. J.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Rochardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fisher, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. B. Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
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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(7), 488–496 (2012).
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Ferrari, C.

Fickler, R.

R. Fickler, R. Lapkiewicz, M. Huber, M. P. J. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nat. Commun. 5, 4502 (2014).
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Fisher, J. K.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Rochardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fisher, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. B. Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
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Fontaine, N. K.

Forbes, A.

A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. Ben Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6(1), 27674 (2016).
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Franke-Arnold, S.

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004).
[Crossref] [PubMed]

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(25), 257901 (2002).
[Crossref] [PubMed]

Fu, D.

H. Zhou, D. Fu, J. Dong, P. Zhang, D. Chen, X. Cai, F. Li, and X. Zhang, “Orbital angular momentum complex spectrum analyzer for vortex light based on the rotational Doppler effect,” Light Sci. Appl. 6, e16251 (2017).

Gao, S.

Gauthier, D. J.

M. Mirhosseini, O. S. Magana-Loaiza, M. N. O’Sullivan, B. Rudenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17(3), 033033 (2015).
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Geisler, D. J.

Genevaux, P.

Gibson, G.

Gintoli, M.

Gisin, N.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Rochardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fisher, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. B. Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
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Guan, B.

Huang, H.

G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40(9), 1980–1983 (2015).
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H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An Nguyen, D. A. Nolan, M.-J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
[Crossref] [PubMed]

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(6140), 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(7), 488–496 (2012).
[Crossref]

Y. Yan, Y. Yue, H. Huang, J. Y. Yang, M. R. Chitgarha, N. Ahmed, M. Tur, S. J. Dolinar, and A. E. Willner, “Efficient generation and multiplexing of optical orbital angular momentum modes in a ring fiber by using multiple coherent inputs,” Opt. Lett. 37(17), 3645–3647 (2012).
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Huber, M.

R. Fickler, R. Lapkiewicz, M. Huber, M. P. J. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nat. Commun. 5, 4502 (2014).
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Jia, P.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
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Jian, P.

Johnson, E. G.

K. S. Morgan, I. S. Raghu, and E. G. Johnson, “Design and fabrication of diffractive optics for orbital angular momentum space division multiplexing,” Proc. SPIE 9374, 93740Y (2015).
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Karimi, E.

Karlsson, M.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Rochardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fisher, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. B. Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
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Khonina, S. N.

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Kotlyar, V. V.

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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(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Krummrich, P. M.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Rochardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fisher, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. B. Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
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E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Rochardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fisher, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. B. Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
[Crossref]

Kwon, M.

P. Bierdz, M. Kwon, C. Roncaioli, and H. Deng, “High fidelity detection of the orbital angular momentum of light by time mapping,” New J. Phys. 15(11), 113062 (2013).
[Crossref]

Labroille, G.

Lapkiewicz, R.

R. Fickler, R. Lapkiewicz, M. Huber, M. P. J. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nat. Commun. 5, 4502 (2014).
[Crossref] [PubMed]

Lavery, M. P. J.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An Nguyen, D. A. Nolan, M.-J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
[Crossref] [PubMed]

M. Mirhosseini, O. S. Magana-Loaiza, M. N. O’Sullivan, B. Rudenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17(3), 033033 (2015).
[Crossref]

G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40(9), 1980–1983 (2015).
[Crossref] [PubMed]

R. Fickler, R. Lapkiewicz, M. Huber, M. P. J. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nat. Commun. 5, 4502 (2014).
[Crossref] [PubMed]

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. E. Wilner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15(1), 013024 (2013).
[Crossref]

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. Express 20(3), 2110–2115 (2012).
[Crossref] [PubMed]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[Crossref] [PubMed]

Leach, J.

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(25), 257901 (2002).
[Crossref] [PubMed]

Lei, T.

S. Gao, T. Lei, Y. Li, Y. Yuan, Z. Xie, Z. Li, and X. Yuan, “OAM-labeled free-space optical flow routing,” Opt. Express 24(19), 21642–21651 (2016).
[Crossref] [PubMed]

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
[Crossref]

Li, F.

H. Zhou, D. Fu, J. Dong, P. Zhang, D. Chen, X. Cai, F. Li, and X. Zhang, “Orbital angular momentum complex spectrum analyzer for vortex light based on the rotational Doppler effect,” Light Sci. Appl. 6, e16251 (2017).

Li, M.-J.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An Nguyen, D. A. Nolan, M.-J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
[Crossref] [PubMed]

Li, Y.

S. Gao, T. Lei, Y. Li, Y. Yuan, Z. Xie, Z. Li, and X. Yuan, “OAM-labeled free-space optical flow routing,” Opt. Express 24(19), 21642–21651 (2016).
[Crossref] [PubMed]

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
[Crossref]

Li, Z.

S. Gao, T. Lei, Y. Li, Y. Yuan, Z. Xie, Z. Li, and X. Yuan, “OAM-labeled free-space optical flow routing,” Opt. Express 24(19), 21642–21651 (2016).
[Crossref] [PubMed]

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
[Crossref]

Lin, J.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
[Crossref]

Liu, G. N.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
[Crossref]

Lord, A.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Rochardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fisher, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. B. Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
[Crossref]

Love, G. D.

Magana-Loaiza, O. S.

M. Mirhosseini, O. S. Magana-Loaiza, M. N. O’Sullivan, B. Rudenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17(3), 033033 (2015).
[Crossref]

Malik, M.

M. Mirhosseini, O. S. Magana-Loaiza, M. N. O’Sullivan, B. Rudenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17(3), 033033 (2015).
[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] [PubMed]

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. Express 20(22), 24444–24449 (2012).
[Crossref] [PubMed]

Mari, E.

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(3), 033001 (2012).
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Marrucci, L.

Massari, M.

Milione, G.

G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40(9), 1980–1983 (2015).
[Crossref] [PubMed]

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An Nguyen, D. A. Nolan, M.-J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
[Crossref] [PubMed]

Min, C.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
[Crossref]

Mirhosseini, M.

M. Mirhosseini, O. S. Magana-Loaiza, M. N. O’Sullivan, B. Rudenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17(3), 033033 (2015).
[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] [PubMed]

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. Express 20(22), 24444–24449 (2012).
[Crossref] [PubMed]

Morgan, K. S.

K. S. Morgan, I. S. Raghu, and E. G. Johnson, “Design and fabrication of diffractive optics for orbital angular momentum space division multiplexing,” Proc. SPIE 9374, 93740Y (2015).
[Crossref]

Morizur, J.-F.

Ndagano, B.

A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. Ben Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6(1), 27674 (2016).
[Crossref] [PubMed]

Nguyen, T. A.

Niu, H.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
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G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40(9), 1980–1983 (2015).
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H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An Nguyen, D. A. Nolan, M.-J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
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O’Sullivan, M. N.

M. Mirhosseini, O. S. Magana-Loaiza, M. N. O’Sullivan, B. Rudenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17(3), 033033 (2015).
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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. Express 20(22), 24444–24449 (2012).
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Padgett, M.

Padgett, M. J.

M. Mirhosseini, O. S. Magana-Loaiza, M. N. O’Sullivan, B. Rudenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17(3), 033033 (2015).
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R. Fickler, R. Lapkiewicz, M. Huber, M. P. J. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nat. Commun. 5, 4502 (2014).
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M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. E. Wilner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15(1), 013024 (2013).
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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. Express 20(3), 2110–2115 (2012).
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E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Rochardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fisher, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. B. Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
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W. Zhang, Q. Qi, J. Zhou, and L. Chen, “Mimicking Faraday Rotation to Sort the Orbital Angular Momentum of Light,” Phys. Rev. Lett. 112(15), 153601 (2014).
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B. J. Wiley, D. Qin, and Y. Xia, “Nanofabrication at high throughput and low cost,” ACS Nano 4(7), 3554–3559 (2010).
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K. S. Morgan, I. S. Raghu, and E. G. Johnson, “Design and fabrication of diffractive optics for orbital angular momentum space division multiplexing,” Proc. SPIE 9374, 93740Y (2015).
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H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An Nguyen, D. A. Nolan, M.-J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
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G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40(9), 1980–1983 (2015).
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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(6140), 1545–1548 (2013).
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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(7), 488–496 (2012).
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Roberts, K.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Rochardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fisher, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. B. Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
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M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. E. Wilner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15(1), 013024 (2013).
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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. Express 20(3), 2110–2115 (2012).
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E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Rochardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fisher, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. B. Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
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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(3), 033001 (2012).
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M. Mirhosseini, O. S. Magana-Loaiza, M. N. O’Sullivan, B. Rudenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17(3), 033033 (2015).
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Savory, S. J.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Rochardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fisher, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. B. Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
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M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. E. Wilner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15(1), 013024 (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(3), 033001 (2012).
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L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
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E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Rochardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fisher, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. B. Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
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M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. E. Wilner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15(1), 013024 (2013).
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Tamburini, F.

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(3), 033001 (2012).
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Thidé, B.

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(3), 033001 (2012).
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E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Rochardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fisher, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. B. Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
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Treps, N.

Trichili, A.

A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. Ben Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6(1), 27674 (2016).
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Tur, M.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An Nguyen, D. A. Nolan, M.-J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
[Crossref] [PubMed]

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(6140), 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(7), 488–496 (2012).
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Y. Yan, Y. Yue, H. Huang, J. Y. Yang, M. R. Chitgarha, N. Ahmed, M. Tur, S. J. Dolinar, and A. E. Willner, “Efficient generation and multiplexing of optical orbital angular momentum modes in a ring fiber by using multiple coherent inputs,” Opt. Lett. 37(17), 3645–3647 (2012).
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M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. E. Wilner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15(1), 013024 (2013).
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Wan, C.

C. Wan, J. Chen, and Q. Zhan, “Compact and high-resolution optical orbital angular momentum sorter,” APL Photonics 2(3), 031302 (2017).
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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(7), 488–496 (2012).
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B. J. Wiley, D. Qin, and Y. Xia, “Nanofabrication at high throughput and low cost,” ACS Nano 4(7), 3554–3559 (2010).
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G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40(9), 1980–1983 (2015).
[Crossref] [PubMed]

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An Nguyen, D. A. Nolan, M.-J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
[Crossref] [PubMed]

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(6140), 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(7), 488–496 (2012).
[Crossref]

Y. Yan, Y. Yue, H. Huang, J. Y. Yang, M. R. Chitgarha, N. Ahmed, M. Tur, S. J. Dolinar, and A. E. Willner, “Efficient generation and multiplexing of optical orbital angular momentum modes in a ring fiber by using multiple coherent inputs,” Opt. Lett. 37(17), 3645–3647 (2012).
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M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. E. Wilner, and M. J. Padgett, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15(1), 013024 (2013).
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E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Rochardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fisher, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. B. Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
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L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
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B. J. Wiley, D. Qin, and Y. Xia, “Nanofabrication at high throughput and low cost,” ACS Nano 4(7), 3554–3559 (2010).
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G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40(9), 1980–1983 (2015).
[Crossref] [PubMed]

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An Nguyen, D. A. Nolan, M.-J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
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Xu, X.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
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Y. Yan, Y. Yue, H. Huang, J. Y. Yang, M. R. Chitgarha, N. Ahmed, M. Tur, S. J. Dolinar, and A. E. Willner, “Efficient generation and multiplexing of optical orbital angular momentum modes in a ring fiber by using multiple coherent inputs,” Opt. Lett. 37(17), 3645–3647 (2012).
[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(7), 488–496 (2012).
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Yang, J. Y.

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(7), 488–496 (2012).
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Yu, C.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
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Yuan, X.

S. Gao, T. Lei, Y. Li, Y. Yuan, Z. Xie, Z. Li, and X. Yuan, “OAM-labeled free-space optical flow routing,” Opt. Express 24(19), 21642–21651 (2016).
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T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
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Yuan, X. C.

Yuan, Y.

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(6140), 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(7), 488–496 (2012).
[Crossref]

Y. Yan, Y. Yue, H. Huang, J. Y. Yang, M. R. Chitgarha, N. Ahmed, M. Tur, S. J. Dolinar, and A. E. Willner, “Efficient generation and multiplexing of optical orbital angular momentum modes in a ring fiber by using multiple coherent inputs,” Opt. Lett. 37(17), 3645–3647 (2012).
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Zeilinger, A.

R. Fickler, R. Lapkiewicz, M. Huber, M. P. J. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nat. Commun. 5, 4502 (2014).
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Zghal, M.

A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. Ben Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6(1), 27674 (2016).
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C. Wan, J. Chen, and Q. Zhan, “Compact and high-resolution optical orbital angular momentum sorter,” APL Photonics 2(3), 031302 (2017).
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T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
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Zhang, P.

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Zhang, W.

J. Zhou, W. Zhang, and L. Chen, “Experimental detection of high-order or fractional orbital angular momentum of light based on a robust mode converter,” Appl. Phys. Lett. 108(11), 111108 (2016).
[Crossref]

W. Zhang, Q. Qi, J. Zhou, and L. Chen, “Mimicking Faraday Rotation to Sort the Orbital Angular Momentum of Light,” Phys. Rev. Lett. 112(15), 153601 (2014).
[Crossref] [PubMed]

Zhang, X.

H. Zhou, D. Fu, J. Dong, P. Zhang, D. Chen, X. Cai, F. Li, and X. Zhang, “Orbital angular momentum complex spectrum analyzer for vortex light based on the rotational Doppler effect,” Light Sci. Appl. 6, e16251 (2017).

Zhou, H.

H. Zhou, D. Fu, J. Dong, P. Zhang, D. Chen, X. Cai, F. Li, and X. Zhang, “Orbital angular momentum complex spectrum analyzer for vortex light based on the rotational Doppler effect,” Light Sci. Appl. 6, e16251 (2017).

Zhou, J.

J. Zhou, W. Zhang, and L. Chen, “Experimental detection of high-order or fractional orbital angular momentum of light based on a robust mode converter,” Appl. Phys. Lett. 108(11), 111108 (2016).
[Crossref]

W. Zhang, Q. Qi, J. Zhou, and L. Chen, “Mimicking Faraday Rotation to Sort the Orbital Angular Momentum of Light,” Phys. Rev. Lett. 112(15), 153601 (2014).
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Figures (7)

Fig. 1
Fig. 1 Schematic of the (de)multiplexer working principle. From left to right: multiplexing. The input beam should be reshaped into an elongated form, for instance using a cylindrical lens. Then it is Fourier-transformed with a lens and it illuminates the first optical element with a tilted angle, depending on the initial axial displacement with respect to the axis of the lens. Then the beam is wrapped and illuminates the second optical element for phase correction. The system converts an input linear phase gradient, created by the tilted incidence, into an output azimuthal phase gradient. Beams with different axial displacements in input are converted into beams with different OAM content. From right to left: demultiplexing.
Fig. 2
Fig. 2 Diffractive optics for log-pol coordinate transformation. Computed phase patterns (a.1, b.1), optical microscope inspections and details: unwrapper (a.1, a.2, a.3) and phase-corrector (b.1, b.2, b.3). Design parameters: a = 220 μm, b = 50 μm, f1 = 9 mm, carrier spatial frequency in the phase-corrector for image tilt (in the demultiplexer): α = β = 0.1 μm−1. Optimized for wavelength λ = 632.8 nm. 256 phase levels. Total size: 1.6 x 1.6 mm2.
Fig. 3
Fig. 3 Experimental setup for OAM sorting with diffractive optical elements (DOE) implementing transformation optics. A laser (laser1) illuminates a cylindrical lens (CL1) for input beam reshaping. The input system can move perpendicularly to the propagation direction with a micrometric translator (T1). Then the beam is Fourier transformed with a lens (L) and illuminates the sequence of optical elements PC1-UW1 performing multiplexing. After travelling in free-space, the generated vortex is split with a 50:50 beam-splitter (BS) for beam analysis with a first camera (CCD1). The second part of the beam enters the demultiplexing sequence UW2-PC2. Finally, the beam is Fourier-transformed by a lens (L) and collected on a second camera (CCD2). A second input chain (laser2, CL2, T2) was added for the test of two-channel mode-division multiplexing. An iris diaphragm (D) can exclude this second beam. A third camera (CCD3) collects the interference pattern between the output laser beam and the output mode of the multiplexer (PC1-UW1) for the analysis of phase-pattern dislocations. For this purpose, additional beam-splitters and mirrors (M) are inserted for the design of the required Mach-Zehnder optical setup.
Fig. 4
Fig. 4 (a) Images recorded with a CCD camera are shown for various OAM states up to the 3rd order (white numbers), for translation of the laser towards opposite directions. The distance between the lateral positions of the laser that generate integer OAM states was around 35 μm. In between these positions, fractional OAM modes are generated. (b) Generation and detection of a beam corresponding to = −4. (c) Multiplexing and demultiplexing of two beams corresponding to = + 5 and = −5. (d) Output position as a function of input laser shift, experimental data for in the range {-14,…, + 14}, step Δ = 4.
Fig. 5
Fig. 5 Generated beams (a) and related interferograms (b) for input laser positions corresponding to OAM values from = 0 to = 5. Central fork-dislocations confirm the presence of a phase singularity along the axis of the beam.
Fig. 6
Fig. 6 Experimental intensity output and efficiency for 8 input modes, in the range = {-14,…, + 14}, step Δ = 4. Bar-plot: channels efficiency.
Fig. 7
Fig. 7 Efficiency (a) and cross-talk (b) for 8 channels in the set {-14, …, + 14}, step Δ = 4.

Equations (5)

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Ω 1 ( x,y )= 2πa λ f 1 [ yarctan( y x )xln( x 2 + y 2 b )+x+ x 2 + y 2 2a ]
Ω 2 ( u,v )= 2πab λ f 1 exp( u a )cos( v a )
Δs= f 2 λ 2πa
d k = λ n PMMA 1 k1 N
X T =* =10 log 10 I *,ALL\* I *,ALL

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