Abstract

With the amplitude, time, wavelength/frequency, phase, and polarization/spin parameter dimensions of the light wave/photon almost fully utilized in both classical and quantum photonic information systems, orbital angular momentum (OAM) carried by optical vortex modes is regarded as a new modal parameter dimension for further boosting the capacity and performance of the systems. To exploit the OAM mode space for such systems, stringent performance requirements on a pair of OAM mode multiplexer and demultiplexer (also known as mode sorters) must be met. In this work, we implement a newly discovered optical spiral transformation to achieve a low-cross-talk, wide-optical-bandwidth, polarization-insensitive, compact, and robust OAM mode sorter that realizes the desired bidirectional conversion between seven co-axial OAM modes carried by a ring-core fiber and seven linearly displaced Gaussian-like modes in parallel single-mode fiber channels. We further apply the device to successfully demonstrate high-spectral-efficiency and high-capacity data transmission in a 50-km OAM fiber communication link for the first time, in which a multi-dimensional multiplexing scheme multiplexes eight orbital-spin vortex mode channels with each mode channel simultaneously carrying 10 wavelength-division multiplexing channels, demonstrating the promising potential of both the OAM mode sorter and the multi-dimensional multiplexed OAM fiber systems enabled by the device. Our results pave the way for future OAM-based multi-dimensional communication systems.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (7)

A. Sit, R. Fickler, F. Alsaiari, F. Bouchard, H. Larocque, P. Gregg, L. Yan, R. W. Boyd, S. Ramachandran, and E. Karimi, “Quantum cryptography with structured photons through a vortex fiber,” Opt. Lett. 43, 4108–4111 (2018).
[Crossref]

G. Zhu, Z. Hu, X. Wu, C. Du, W. Luo, Y. Chen, X. Cai, J. Liu, J. Zhu, and S. Yu, “Scalable mode division multiplexed transmission over a 10-km ring-core fiber using high-order orbital angular momentum modes,” Opt. Express 26, 594–604 (2018).
[Crossref]

M. Erhard, R. Fickler, M. Krenn, and A. Zeilinger, “Twisted photons: new quantum perspectives in high dimensions,” Light Sci. Appl. 7, 17146 (2018).
[Crossref]

N. Zhou, S. Zheng, X. Cao, S. Gao, S. Li, M. He, X. Cai, and J. Wang, “Generating and synthesizing ultrabroadband twisted light using a compact silicon chip,” Opt. Lett. 43, 3140–3143 (2018).
[Crossref]

Z. Xie, T. Lei, F. Li, H. Qiu, Z. Zhang, H. Wang, C. Min, L. Du, Z. Li, and X. Yuan, “Ultra-broadband on-chip twisted light emitter for optical communications,” Light Sci. Appl. 7, 18001 (2018).
[Crossref]

Y. Wen, 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, 193904 (2018).
[Crossref]

J. Zhang, G. Zhu, J. Liu, X. Wu, J. Zhu, C. Du, W. Luo, Y. Chen, and S. Yu, “Orbital-angular-momentum mode-group multiplexed transmission over a graded-index ring-core fiber based on receive diversity and maximal ratio combining,” Opt. Express 26, 4243–4257 (2018).
[Crossref]

2017 (8)

P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, and R. Devlin, “Recent advances in planar optics: from plasmonic to dielectric metasurfaces,” Optica 4, 139–152 (2017).
[Crossref]

G. Ruffato, M. Massari, and F. Romanato, “Compact sorting of optical vortices by means of diffractive transformation optics,” Opt. Lett. 42, 551–554 (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, 605–610 (2017).
[Crossref]

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

Y. Zhou, M. Mirhosseini, D. Fu, J. Zhao, S. M. H. Rafsanjani, A. E. Willner, and R. W. Boyd, “Sorting photons by radial quantum number,” Phys. Rev. Lett. 119, 263602 (2017).
[Crossref]

S. Pidishety, S. Pachava, P. Gregg, S. Ramachandran, G. Brambilla, and B. Srinivasan, “Orbital angular momentum beam excitation using an all-fiber weakly fused mode selective coupler,” Opt. Lett. 42, 4347–4350 (2017).
[Crossref]

J. M. Kahn and D. A. B. Miller, “Communications expands its space,” Nat. Photonics 11, 5–8 (2017).
[Crossref]

A. Sit, F. Bouchard, R. Fickler, J. Gagnon-Bischoff, H. Larocque, K. Heshami, D. Elser, C. Peuntinger, K. Gunthner, B. Heim, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “High-dimensional intracity quantum cryptography with structured photons,” Optica 4, 1006–1010 (2017).
[Crossref]

2016 (1)

A. Liu, C.-L. Zou, X. Ren, Q. Wang, and G.-C. Guo, “On-chip generation and control of the vortex beam,” Appl. Phys. Lett. 108, 181103 (2016).
[Crossref]

2015 (5)

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, e257 (2015).
[Crossref]

A. E. Willner, H. Huang, Y. Yan, Y. Ren, H. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7, 66–106 (2015).
[Crossref]

M. Krenn, J. Handsteiner, M. Fink, R. Fickler, and A. Zeilinger, “Twisted photon entanglement through turbulent air across Vienna,” Proc. Natl. Acad. Sci. U. S. A. 112, 14197–14201 (2015).
[Crossref]

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, 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, 033033 (2015).
[Crossref]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–944 (2015).
[Crossref]

2014 (5)

C. Brunet, P. Vaity, Y. Messaddeq, S. LaRochelle, and L. A. Rusch, “Design, fabrication and validation of an OAM fiber supporting 36 states,” Opt. Express 22, 26117–26127 (2014).
[Crossref]

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref]

E. Karimi, R. W. Boyd, P. de la Hoz, H. de Guise, J. Řeháček, Z. Hradil, A. Aiello, G. Leuchs, and L. L. Sánchez-Soto, “Radial quantum number of Laguerre-Gauss modes,” Phys. Rev. A 89, 063813 (2014).
[Crossref]

G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6, 413–487 (2014).
[Crossref]

G. Labroille, B. Denolle, P. Jian, P. Genevaux, N. Treps, and J.-F. Morizur, “Efficient and mode selective spatial mode multiplexer based on multi-plane light conversion,” Opt. Express 22, 15599–15607 (2014).
[Crossref]

2013 (5)

2012 (3)

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, 153601 (2010).
[Crossref]

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

2004 (1)

2002 (1)

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

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 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, 1235–1250 (1987).
[Crossref]

1976 (1)

Ahmed, H.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, H. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7, 66–106 (2015).
[Crossref]

Ahmed, N.

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref]

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]

Aiello, A.

E. Karimi, R. W. Boyd, P. de la Hoz, H. de Guise, J. Řeháček, Z. Hradil, A. Aiello, G. Leuchs, and L. L. Sánchez-Soto, “Radial quantum number of Laguerre-Gauss modes,” Phys. Rev. A 89, 063813 (2014).
[Crossref]

Aieta, F.

Allen, L.

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

Alsaiari, F.

Arbabi, A.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–944 (2015).
[Crossref]

Arie, A.

Arita, Y.

Arrizón, V.

Ashrafi, N.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, H. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7, 66–106 (2015).
[Crossref]

Ashrafi, S.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, H. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7, 66–106 (2015).
[Crossref]

Bagheri, M.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–944 (2015).
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Supplementary Material (1)

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» Supplement 1       More details on the design, fabrication, and characteriazation of the OAM mode sorter.

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Figures (4)

Fig. 1.
Fig. 1. Illustration of the OAM mode sorting concept and the corresponding compact device. (a) The principle of the OAM mode sorting is based on an optical coordinate transformation between two planes $x {- }y$ and $u {-} v$. Through a spiral transformation performed by a pair of phase masks that are integrated on the opposite sides of a thin dielectric slab, incident ring-shaped OAM modes with different angular phase gradients (topological charges) are transformed into stripe-shaped output modes with different linear phase gradients (tilted angles), which can then be spatially resolved in the focal plane of a lens. (b) A fabricated ${3} \times {4}$ array of OAM mode sorters based on the above principle, which consist of only three-plane phase elements, including (c) unwrappers, (d) phase correctors, and (e) elliptical lenses, all integrated on a 3D-printing base as a compact device.
Fig. 2.
Fig. 2. Numerical and experimental performance of the compact vortex mode sorter. (a) Incident perfect vortex beams with topological charges of $ - 3 \le \ell \le 3 $. (b), (c) Intensity distributions of the unwrapped vortex beams in the plane of the phase corrector after the log-polar (b) and the spiral transformation (c). (d), (e) Intensity distributions of the separated vortex beams in the focal plane of the lens based on the log-polar (d) and the spiral transformation (e) schemes. The corresponding intensity profiles along the middle horizontal lines (indicated with red dashed lines) are shown on the right, which illustrates the expected high modal resolution based on the spiral scheme (e) compared to the log-polar scheme (d).
Fig. 3.
Fig. 3. Bidirectional mapping between OAM modes and displaced Gaussian-like modes. OAM demultiplexing: (a) mode mapping from OAM modes with topological charges of $ - 3 \le \ell \le 3 $ in Fig. 2 to displaced Gaussian-like modes, which are coupled into the SMF. (b) Measured mode transfer matrix as an OAM demultiplexer (where L and R represent left- and right-handed circular polarizations), with cross-talk levels marked. OAM multiplexing: (c) reverse mapping of displaced Gaussian beams output from the SMF at different positions to seven co-axial ring-shaped OAM beams and their corresponding far field. (d) Measured mode transfer matrix as an OAM multiplexer with cross-talk levels marked.
Fig. 4.
Fig. 4. Data-transmission experiments in a 50-km OAM-MDM-WDM system. (a) Experimental setup of the OAM-MDM-WDM data transmission system. PC, polarization controller; OC, optical coupler; SMF, single-mode fiber; LP, linear polarizer; SLM, spatial light modulator; MR, mirror; QWP, quarter-wave plate; HWP, half-wave plate; Col., collimator; BS, beam splitter; ICR, integrated coherent receiver. (b) Optical spectra of the 10 wavelength channels used for WDM. (c) Mode demultiplexing of the 50-km RCF with the corresponding mode transfer matrix. (d) Constellations of the received signals with the best measured BERs at a wavelength of 1550 nm. (e) Measured BERs of all 80 channels after 50-km RCF transmission.

Equations (4)

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u ( r , θ ) = β 1 + a 2 [ a θ ln ( r r 0 ) ] , v ( r , θ ) = β 1 + a 2 [ θ + a ln ( r r 0 ) ] ,
Q ( x , y ) = k β d ( a 2 + 1 ) [ ( a y x ) ln ( r / r 0 ) + ( a x + y ) θ + x a y ] k r 2 2 d ,
P 1 ( u , v ) = Q ( x , y ) k ( x u ) 2 + ( y v ) 2 + d 2 ,
S = λ 0 f 2 π β ,