Abstract

A novel optical device is designed and fabricated in order to overcome the limits of the traditional sorter based on log-pol optical transformation for the demultiplexing of optical beams carrying orbital angular momentum (OAM). The proposed configuration simplifies the alignment procedure and significantly improves the compactness and miniaturization level of the optical architecture. Since the device requires to operate beyond the paraxial approximation, a rigorous formulation of transformation optics in the non-paraxial regime has been developed and applied. The sample has been fabricated as 256-level phase-only diffractive optics with high-resolution electron-beam lithography, and tested for the demultiplexing of OAM beams at the telecom wavelength of 1310 nm. The designed sorter can find promising applications in next-generation optical platforms for mode-division multiplexing based on OAM modes both for free-space and multi-mode fiber transmission.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2019 (4)

J. Wang, “Twisted optical communications using orbital angular momentum,” Sci. China: Phys., Mech. Astron. 62(3), 34201 (2019).
[Crossref]

C. Wan, G. Rui, J. Chen, and Q. Zhan, “Detection of photonic orbital angular momentum with micro- and nano-optical structures,” Front. Optoelectron. 12(1), 88–96 (2019).
[Crossref]

W. Li, K. S. Morgan, Y. Li, K. Miller, G. White, R. J. Watkins, and E. G. Johnson, “Rapidly tunable orbital angular momentum (OAM) system for higher order Bessel beams integrated in time (HOBBIT),” Opt. Express 27(4), 3920–3934 (2019).
[Crossref]

Y. Wen, I. Chremmos, Y. Chen, J. Zhu, Y. Zhang, and S. Yu, “A compact mode sorter for demultiplexing vortex light beams,” Proc. SPIE 11048, 1104820 (2019).
[Crossref]

2018 (4)

G. Ruffato, M. Girardi, M. Massari, E. Mafakheri, B. Sephton, P. Capaldo, A. Forbes, and F. Romanato, “A compact diffractive sorter for high-resolution demultiplexing of orbital angular momentum beams,” Sci. Rep. 8(1), 10248 (2018).
[Crossref]

Y. Wen Y, I. Chremmos, Y. Chen, J. Zhu, Y. Zhang, and S. Yu, “Spiral Transformation for High-Resolution and Efficient Sorting of Optical Vortex Modes,” Phys. Rev. Lett. 120(19), 193904 (2018).
[Crossref]

P. J. Winzer, D. T. Neilson, and A. R. Chraplyvy, “Fiber-optic transmission and networking: the previous 20 and the next 20 years,” Opt. Express 26(18), 24190–24239 (2018).
[Crossref]

G. Vicidomini, P. Bianchini, and A. Diaspro, “STED super-resolved microscopy,” Nat. Methods 15(3), 173–182 (2018).
[Crossref]

2017 (8)

M. J. Padgett, “Orbital angular momentum 25 years on,” Opt. Express 25(10), 11265–11274 (2017).
[Crossref]

M. Ritsch-Marte, “Orbital angular momentum light in microscopy,” Phil. Trans. R. Soc. A 375(2087), 20150437 (2017).
[Crossref]

G. Ruffato, R. Rossi, M. Massari, E. Mafakheri, P. Capaldo, and F. Romanato, “Design, fabrication and characterization of Computer-Generated Holograms for anti-counterfeiting applications using OAM beams as light decoders,” Sci. Rep. 7(1), 18011 (2017).
[Crossref]

A. E. Willner, Y. Ren, G. Xie, Y. Yan, L. Li, Z. Zhao, J. Wang, M. Tur, A. F. Molish, and S. Ashrafi, “Recent advances in high-capacity free-space optical and radio-frequency communications using orbital angular momentum multiplexing,” Phil. Trans. R. Soc. A 375(2087), 20150439 (2017).
[Crossref]

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

S. Lightman, G. Hurvitz, R. Gvishi, and A. Arie, “Miniature wide-spectrum mode sorter for vortex beams produced by 3D laser printing,” Optica 4(6), 605–610 (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]

G. Ruffato, M. Massari, G. Parisi, and F. Romanato, “Test of mode-division multiplexing and demultiplexing in free-space with diffractive transformation optics,” Opt. Express 25(7), 7859–7868 (2017).
[Crossref]

2016 (2)

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]

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

2015 (3)

2014 (1)

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(1), 4502 (2014).
[Crossref]

2013 (5)

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. E. Willner, 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(1), 2781 (2013).
[Crossref]

A. Dudley, T. Mhlanga, M. Lavery, A. McDonald, F. S. Roux, M. Padgett, and A. Forbes, “Efficient sorting of Bessel beams,” Opt. Express 21(1), 165–171 (2013).
[Crossref]

S. Ramachandran and P. Kristensen, “Optical vortices in fiber,” Nanophotonics 2(5-6), 455–474 (2013).
[Crossref]

N. Bozinovic, Y. Yue, Y. Ren, N. 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]

2012 (2)

2011 (1)

M. J. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
[Crossref]

2010 (2)

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]

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

2007 (1)

J. Li, Z. Peng, and Y. Fu, “Diffraction transfer function and its calculation of classic diffraction formula,” Opt. Commun. 280(2), 243–248 (2007).
[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 modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

1987 (1)

W. J. Hossack, A. M. Darling, and A. Dahdouh, “Coordinate transformations with multiple computer-generated optical elements,” J. Mod. Opt. 34(9), 1235–1250 (1987).
[Crossref]

1983 (1)

Y. Saito, S. Komatsu, and H. Ohzu, “Scale and rotation invariant real time optical correlator using computer generated hologram,” Opt. Commun. 47(1), 8–11 (1983).
[Crossref]

Agrell, E.

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

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

Andrews, D.

D. Andrews and M. Babiker, The angular momentum of light (Cambridge University, 2013).

Arie, A.

Ashrafi, S.

A. E. Willner, Y. Ren, G. Xie, Y. Yan, L. Li, Z. Zhao, J. Wang, M. Tur, A. F. Molish, and S. Ashrafi, “Recent advances in high-capacity free-space optical and radio-frequency communications using orbital angular momentum multiplexing,” Phil. Trans. R. Soc. A 375(2087), 20150439 (2017).
[Crossref]

Babiker, M.

D. Andrews and M. Babiker, The angular momentum of light (Cambridge University, 2013).

Barbieri, C.

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]

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

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]

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]

Bianchini, A.

Bianchini, P.

G. Vicidomini, P. Bianchini, and A. Diaspro, “STED super-resolved microscopy,” Nat. Methods 15(3), 173–182 (2018).
[Crossref]

Bowers, J. E.

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

Bowman, R.

M. J. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
[Crossref]

Boyd, R. W.

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4(1), 2781 (2013).
[Crossref]

Boyd, R.W.

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]

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. Ren, N. 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]

Brandt-Pearce, M.

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

Capaldo, P.

G. Ruffato, M. Girardi, M. Massari, E. Mafakheri, B. Sephton, P. Capaldo, A. Forbes, and F. Romanato, “A compact diffractive sorter for high-resolution demultiplexing of orbital angular momentum beams,” Sci. Rep. 8(1), 10248 (2018).
[Crossref]

G. Ruffato, R. Rossi, M. Massari, E. Mafakheri, P. Capaldo, and F. Romanato, “Design, fabrication and characterization of Computer-Generated Holograms for anti-counterfeiting applications using OAM beams as light decoders,” Sci. Rep. 7(1), 18011 (2017).
[Crossref]

Chen, J.

C. Wan, G. Rui, J. Chen, and Q. Zhan, “Detection of photonic orbital angular momentum with micro- and nano-optical structures,” Front. Optoelectron. 12(1), 88–96 (2019).
[Crossref]

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

Chen, Y.

Y. Wen, I. Chremmos, Y. Chen, J. Zhu, Y. Zhang, and S. Yu, “A compact mode sorter for demultiplexing vortex light beams,” Proc. SPIE 11048, 1104820 (2019).
[Crossref]

Y. Wen Y, I. Chremmos, Y. Chen, J. Zhu, Y. Zhang, and S. Yu, “Spiral Transformation for High-Resolution and Efficient Sorting of Optical Vortex Modes,” Phys. Rev. Lett. 120(19), 193904 (2018).
[Crossref]

Chraplyvy, A. R.

P. J. Winzer, D. T. Neilson, and A. R. Chraplyvy, “Fiber-optic transmission and networking: the previous 20 and the next 20 years,” Opt. Express 26(18), 24190–24239 (2018).
[Crossref]

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

Chremmos, I.

Y. Wen, I. Chremmos, Y. Chen, J. Zhu, Y. Zhang, and S. Yu, “A compact mode sorter for demultiplexing vortex light beams,” Proc. SPIE 11048, 1104820 (2019).
[Crossref]

Y. Wen Y, I. Chremmos, Y. Chen, J. Zhu, Y. Zhang, and S. Yu, “Spiral Transformation for High-Resolution and Efficient Sorting of Optical Vortex Modes,” Phys. Rev. Lett. 120(19), 193904 (2018).
[Crossref]

Courtial, J.

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. E. Willner, 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]

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]

Dahdouh, A.

W. J. Hossack, A. M. Darling, and A. Dahdouh, “Coordinate transformations with multiple computer-generated optical elements,” J. Mod. Opt. 34(9), 1235–1250 (1987).
[Crossref]

Darling, A. M.

W. J. Hossack, A. M. Darling, and A. Dahdouh, “Coordinate transformations with multiple computer-generated optical elements,” J. Mod. Opt. 34(9), 1235–1250 (1987).
[Crossref]

Diaspro, A.

G. Vicidomini, P. Bianchini, and A. Diaspro, “STED super-resolved microscopy,” Nat. Methods 15(3), 173–182 (2018).
[Crossref]

Dudley, A.

Eggleton, B. J.

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

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M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. E. Willner, 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]

Swartzlander, G.A.

Tamburini, F.

Thidé, B.

Tomkos, I.

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A. E. Willner, Y. Ren, G. Xie, Y. Yan, L. Li, Z. Zhao, J. Wang, M. Tur, A. F. Molish, and S. Ashrafi, “Recent advances in high-capacity free-space optical and radio-frequency communications using orbital angular momentum multiplexing,” Phil. Trans. R. Soc. A 375(2087), 20150439 (2017).
[Crossref]

Tur, N.

N. Bozinovic, Y. Yue, Y. Ren, N. 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]

Tyler, G. A.

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. E. Willner, 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. Vicidomini, P. Bianchini, and A. Diaspro, “STED super-resolved microscopy,” Nat. Methods 15(3), 173–182 (2018).
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C. Wan, G. Rui, J. Chen, and Q. Zhan, “Detection of photonic orbital angular momentum with micro- and nano-optical structures,” Front. Optoelectron. 12(1), 88–96 (2019).
[Crossref]

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

Wang, J.

J. Wang, “Twisted optical communications using orbital angular momentum,” Sci. China: Phys., Mech. Astron. 62(3), 34201 (2019).
[Crossref]

A. E. Willner, Y. Ren, G. Xie, Y. Yan, L. Li, Z. Zhao, J. Wang, M. Tur, A. F. Molish, and S. Ashrafi, “Recent advances in high-capacity free-space optical and radio-frequency communications using orbital angular momentum multiplexing,” Phil. Trans. R. Soc. A 375(2087), 20150439 (2017).
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Wen Y, Y.

Y. Wen Y, I. Chremmos, Y. Chen, J. Zhu, Y. Zhang, and S. Yu, “Spiral Transformation for High-Resolution and Efficient Sorting of Optical Vortex Modes,” Phys. Rev. Lett. 120(19), 193904 (2018).
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A. E. Willner, Y. Ren, G. Xie, Y. Yan, L. Li, Z. Zhao, J. Wang, M. Tur, A. F. Molish, and S. Ashrafi, “Recent advances in high-capacity free-space optical and radio-frequency communications using orbital angular momentum multiplexing,” Phil. Trans. R. Soc. A 375(2087), 20150439 (2017).
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M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. E. Willner, 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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N. Bozinovic, Y. Yue, Y. Ren, N. 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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E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
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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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A. E. Willner, Y. Ren, G. Xie, Y. Yan, L. Li, Z. Zhao, J. Wang, M. Tur, A. F. Molish, and S. Ashrafi, “Recent advances in high-capacity free-space optical and radio-frequency communications using orbital angular momentum multiplexing,” Phil. Trans. R. Soc. A 375(2087), 20150439 (2017).
[Crossref]

Yan, Y.

A. E. Willner, Y. Ren, G. Xie, Y. Yan, L. Li, Z. Zhao, J. Wang, M. Tur, A. F. Molish, and S. Ashrafi, “Recent advances in high-capacity free-space optical and radio-frequency communications using orbital angular momentum multiplexing,” Phil. Trans. R. Soc. A 375(2087), 20150439 (2017).
[Crossref]

Yu, S.

Y. Wen, I. Chremmos, Y. Chen, J. Zhu, Y. Zhang, and S. Yu, “A compact mode sorter for demultiplexing vortex light beams,” Proc. SPIE 11048, 1104820 (2019).
[Crossref]

Y. Wen Y, I. Chremmos, Y. Chen, J. Zhu, Y. Zhang, and S. Yu, “Spiral Transformation for High-Resolution and Efficient Sorting of Optical Vortex Modes,” Phys. Rev. Lett. 120(19), 193904 (2018).
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S. Yu, “Potentials and challenges of using orbital angular momentum communications in optical interconnects,” Opt. Express 23(3), 3075–3087 (2015).
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N. Bozinovic, Y. Yue, Y. Ren, N. 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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[Crossref]

Zhan, Q.

C. Wan, G. Rui, J. Chen, and Q. Zhan, “Detection of photonic orbital angular momentum with micro- and nano-optical structures,” Front. Optoelectron. 12(1), 88–96 (2019).
[Crossref]

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

Zhang, Y.

Y. Wen, I. Chremmos, Y. Chen, J. Zhu, Y. Zhang, and S. Yu, “A compact mode sorter for demultiplexing vortex light beams,” Proc. SPIE 11048, 1104820 (2019).
[Crossref]

Y. Wen Y, I. Chremmos, Y. Chen, J. Zhu, Y. Zhang, and S. Yu, “Spiral Transformation for High-Resolution and Efficient Sorting of Optical Vortex Modes,” Phys. Rev. Lett. 120(19), 193904 (2018).
[Crossref]

Zhao, Z.

A. E. Willner, Y. Ren, G. Xie, Y. Yan, L. Li, Z. Zhao, J. Wang, M. Tur, A. F. Molish, and S. Ashrafi, “Recent advances in high-capacity free-space optical and radio-frequency communications using orbital angular momentum multiplexing,” Phil. Trans. R. Soc. A 375(2087), 20150439 (2017).
[Crossref]

Zhu, J.

Y. Wen, I. Chremmos, Y. Chen, J. Zhu, Y. Zhang, and S. Yu, “A compact mode sorter for demultiplexing vortex light beams,” Proc. SPIE 11048, 1104820 (2019).
[Crossref]

Y. Wen Y, I. Chremmos, Y. Chen, J. Zhu, Y. Zhang, and S. Yu, “Spiral Transformation for High-Resolution and Efficient Sorting of Optical Vortex Modes,” Phys. Rev. Lett. 120(19), 193904 (2018).
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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).
[Crossref]

APL Photonics (1)

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

Appl. Opt. (1)

Front. Optoelectron. (1)

C. Wan, G. Rui, J. Chen, and Q. Zhan, “Detection of photonic orbital angular momentum with micro- and nano-optical structures,” Front. Optoelectron. 12(1), 88–96 (2019).
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[Crossref]

Nat. Methods (1)

G. Vicidomini, P. Bianchini, and A. Diaspro, “STED super-resolved microscopy,” Nat. Methods 15(3), 173–182 (2018).
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Nat. Photonics (1)

M. J. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
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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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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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Optica (1)

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A. E. Willner, Y. Ren, G. Xie, Y. Yan, L. Li, Z. Zhao, J. Wang, M. Tur, A. F. Molish, and S. Ashrafi, “Recent advances in high-capacity free-space optical and radio-frequency communications using orbital angular momentum multiplexing,” Phil. Trans. R. Soc. A 375(2087), 20150439 (2017).
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Proc. SPIE (1)

Y. Wen, I. Chremmos, Y. Chen, J. Zhu, Y. Zhang, and S. Yu, “A compact mode sorter for demultiplexing vortex light beams,” Proc. SPIE 11048, 1104820 (2019).
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Sci. China: Phys., Mech. Astron. (1)

J. Wang, “Twisted optical communications using orbital angular momentum,” Sci. China: Phys., Mech. Astron. 62(3), 34201 (2019).
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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).
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Science (1)

N. Bozinovic, Y. Yue, Y. Ren, N. 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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D. Andrews and M. Babiker, The angular momentum of light (Cambridge University, 2013).

C. Rosales-Guzmán and A. Forbes, How to Shape Light With Spatial Light Modulators (SPIE, 2017).
[Crossref]

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Figures (8)

Fig. 1.
Fig. 1. (a) Scheme of the traditional log-pol sorter working principle with separated and coaxial optical elements, i.e. un-wrapper and phase-corrector. The azimuthal phase gradients of the input OAM-beams are transformed into linear phase gradients and focused at distinct positions at the focal plane of a lens. (b) Non-paraxial compact configuration with the two elements fabricated on the same surface of a single transparent slab with a reflective back-side. By adding a tilt to the first phase pattern, i.e. the un-wrapper, the unwrapping beam propagates with a non-null angle and after back-reflection illuminates the second element performing phase-correction. The two elements are patterned side-by-side on the same facet of the optical device.
Fig. 2.
Fig. 2. (a) Simulation of the transformed beam for input LG mode with  = +5. Phase-corrected output beam assuming the traditional formulation of the un-wrapper in the paraxial approximation (Eq. (2)) for increasing values of the axial displacement c, in the range from 0 to 1250 µm, step 250 µm (a.1-6), and corresponding far-field spots (b.1-6). Parameters of the log-pol transformation: a = 120 µm, b = 700 µm, f = 4.572 mm. Working wavelength λ = 1310 nm. Refractive index of the medium n = 1.4467. In (a.1-6) brightness and colors refer to intensity and phase, respectively.
Fig. 3.
Fig. 3. Numerical simulation of a LG beam with  = +5 (a) after illuminating the un-wrapper element, placed in z = 0, calculated in the non-paraxial regime (b-g). With respect to Fig. 2(a.6), the beam is correctly transformed at the focal plane, and the linear phase gradient is retained after illuminating the corresponding phase-corrector (g). (h) Far-field spot. Parameters of the log-pol transformation: a = 120 µm, b = 700 µm, f = 4.572 mm, c = 1.250 mm. Working wavelength λ = 1310 nm. Refractive index of the medium n = 1.4467. In (a) and (g), brightness and colors refer to intensity and phase, respectively.
Fig. 4.
Fig. 4. (a) Picture of the fabricated sorter mounted on the sample holder of the experimental setup in Fig. 5. (b) SEM inspection of the zone between un-wrapper and phase-corrector and phase-corrector details at higher magnifications (c, d).
Fig. 5.
Fig. 5. Scheme of the experimental setup used for the optical characterization of the fabricated sorter. The DFB laser output (λ = 1310 nm) is collimated at the end of the single mode fiber with an aspheric lens with focal length fF = 7.5 mm, linearly polarized (P1) and expanded (f1 = 3.5 cm, f2 = 10.0 cm). The SLM first order is filtered (D1) and resized (f3 = 20.0 cm, f4 = 12.5 cm) before illuminating the sorter. A beam splitter (BS) is used both to check the input beam with a first camera (CCD#1) and collect the sorter output at the focal plane of a fifth Fourier lens (f5 = 7.5 cm) with a second camera (CCD#2). The compact diffractive sorter (CDS) is mounted on a 6-axis sample holder.
Fig. 6.
Fig. 6. Experimental data for input superposition of LG beams with opposite values of OAM (a) and corresponding output of the fabricated sorter (b). For each value increasing in modulus from 0 to 10, the superposition of two LG beams with opposite OAM generates a petalized beam with 2 petals. The two contributions are correctly detected and demultiplexed by the sorter at two distinct positions, proportionally to the value of .
Fig. 7.
Fig. 7. Positions of the far-field spots for input LG beams carrying OAM in in the range from −10 to +10. Experimental data (blue dots), linear fit (solid red line) and theoretical trend (dashed red line). The coordinate has been normalized by the parameter Δs = λf/2πa, therefore the theoretical slope equals +1. Experimental slope: +0.98 ± 0.02.
Fig. 8.
Fig. 8. Efficiency (η) of the sorter for input OAM beams with input OAM value in in the range from  = −10 to  = +10.

Equations (9)

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

{ u = a ln ( x 2 + y 2 b ) + c v = a arctan ( y x ) .
Ω U W ( p ) = 2 π a λ f [ y arctan ( y x ) x log ( x 2 + y 2 b ) + x ] 2 π λ x 2 + y 2 2 f + 2 π c λ f x ,
U ( u , v ) = f i λ U ( i n ) ( x , y ) e i Ω U W ( x , y ) e i k f 2 + ( x u ) 2 + ( y v ) 2 f 2 + ( x u ) 2 + ( y v ) 2 d x d y .
Φ ( x , y ) = Ω U W ( x , y ) + k f 2 + ( x u ) 2 + ( y v ) 2 .
{ Ω U W x = k x u f 2 + ( x u ) 2 + ( y v ) 2 Ω U W y = k y v f 2 + ( x u ) 2 + ( y v ) 2 .
U ( u , v ) = F T 1 { F T { U ( i n ) e i Ω U W ( x , y ) } F T { f i λ e i k f 2 + x 2 + y 2 f 2 + x 2 + y 2 } } ,
Ω P C ( u , v ) = 2 π arctan ( Im { U ( u , v ) } / Re { U ( u , v ) } ) .
t ( x , y ) = λ n R ( λ ) 1 2 π Ω ( x , y ) 2 π . .
X T j = 10 log 10 ( I j , A L L / j I j , A L L ) ,

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