DOI: 10.1126/science.1237861, 1545 (2013);340 Science

et al.Nenad Bozinovicin FibersTerabit-Scale Orbital Angular Momentum Mode Division Multiplexing

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Terabit-Scale Orbital AngularMomentum Mode DivisionMultiplexing in FibersNenad Bozinovic,1* Yang Yue,2* Yongxiong Ren,2 Moshe Tur,3 Poul Kristensen,4 Hao Huang,2

Alan E. Willner,2† Siddharth Ramachandran1†

Internet data traffic capacity is rapidly reaching limits imposed by optical fiber nonlinear effects. Havingalmost exhausted available degrees of freedom to orthogonally multiplex data, the possibility is nowbeing explored of using spatial modes of fibers to enhance data capacity. We demonstrate the viability ofusing the orbital angular momentum (OAM) of light to create orthogonal, spatially distinct streams ofdata-transmitting channels that are multiplexed in a single fiber. Over 1.1 kilometers of a speciallydesigned optical fiber that minimizes mode coupling, we achieved 400-gigabits-per-second datatransmission using four angular momentum modes at a single wavelength, and 1.6 terabits persecond using two OAM modes over 10 wavelengths. These demonstrations suggest that OAM couldprovide an additional degree of freedom for data multiplexing in future fiber networks.

The data-carrying capacity of single-modeoptical fibers has increased by four ordersof magnitude in the past three decades (1),

primarily because of multiplexing techniques thatuse wavelength, amplitude, phase, and polariza-tion of light to encode information (Fig. 1A). As

the capacity of the current optical fiber systemsreaches limits imposed by nonlinear effects (2),the possibility of spatial-division–multiplexingmethods by use of multicore (3) and multimode(4) fibers has emerged to address the forthcomingcapacity crunch. Although multicore fiberspotentially require more complex manufacturingthan do circularly symmetric multimode fibers,conventional multimode fibers suffer from modecoupling caused by random perturbations in fi-bers or incomplete mode-conversion (5). Methodsthat have been developed to address the problemof mode coupling so far have been dependent oncomputationally intensive digital signal processing(DSP) algorithms, and have been based either on

adaptive optics feedback (6) or complex multiple-input multiple-output (MIMO) methodologies (4).

We show a method that offers a means of in-creasing network throughput without using com-plex DSP algorithms, but instead by using fibermodes that carry orbital angular momentum(OAM).As one of themost fundamental physicalquantities in classical and quantum electrody-namics, OAM of light has initiated widespreadinterest in many areas, including optical tweezers,atom manipulation, and optical communications(7). Photons that carry OAMhave a helical phaseof electric field proportional to exp(i‘f), where‘ is topological charge, and f is the azimuthalangle (7). Several classical (8) and quantum (9)communications experiments have exploited theinherent orthogonality ofOAMmodes in free spaceby multiplexing information in this additional de-gree of freedom, increasing the capacity of free-space communications links. In fibers, however,OAM beams were considered to be completelyunstable owing to mode coupling, and only short-length fiber propagation, without data transmis-sion, has been demonstrated (10–14).

The OAMmode-division multiplexing (OAM-MDM) concept used here is illustrated in Fig. 1Band is based on multiplexing two fundamentalfiber modes of opposite spins (circular polariza-tions), with the two OAM fiber modes of oppo-site topological charges ‘ = T1. The three keyenablers for our demonstration are (i) a multi-plexing setup, comprising spatial light modula-tors (SLMs) and conventional free-space optics(conceptually illustrated in Fig. 1, C and D), thatenabled <–21 dB of multiplexing crosstalk; (ii) acircularly symmetric specialty fiber fabricated ona commercial manufacturing setup that minimizedmode coupling, leading to <–10 dB of crosstalk

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1Department of Electrical and Computer Engineering and Pho-tonics Center, Boston University, Boston, MA 02215, USA.2Department of Electrical Engineering, University of SouthernCalifornia, Los Angeles, CA 90089, USA. 3School of ElectricalEngineering, Tel Aviv University, 69978 Tel Aviv, Israel. 4OFS-Fitel, 2605 Brøndby, Denmark.

*These authors contributed equally to this work.†Corresponding author. E-mail: sidr@bu.edu (S.R.); willner@usc.edu (A.E.W.)

Fig. 1. The OAM-MDM principle.(A) OAM may be considered as an or-thogonal degree of freedom for datamultiplexing. (B) Simplified OAM-MDMsetup: four modes with distinct valuesof OAM (ℓ) and spin (or circular polar-ization, s) are multiplexed into a specialtyfiber, transmitted for 1.1 km, demulti-plexed, and analyzed at the output byusing BER testers and cameras. (C) OAMconversion of ℓ = 0 → 1 is achievedby using spiral phase patterns (SPPs)(the spiral pattern has opposite helicityfor the ℓ = 0 → 1 case). (D) Spin con-version to s = T1 is implemented witha quarter wave plate (QWP) whose fastaxis is oriented T45° with respect tothe input (linear) polarization.

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among modes after 1.1 km of propagation; and(iii) a demultiplexing setup that enabled sorting ofthe modes with high purity at the output by usingfree-space polarization and OAM sorters. The de-tailed experimental setup is available in fig. S1 (15).

Conventional single-mode fibers (SMFs) sup-port propagation of two distinct, degenerate po-larization states of the fundamental mode ðLPT

01Þ,designated by their spin s = T1. The few-modefiber that we use (“vortex fiber”) additionallysupports the first-order antisymmetric modes:one transverse magnetic mode (TM01), two OAM

T

modes (denoted by their ‘ = T1 topological charge),and one transverse electric (TE01) mode (“0” and“1” in the subscript “01” refer to azimuthal andradial indices, respectively, denoting the numberof nulls in the electric field in the two orthogonaldirections). However, unlike traditional few-modefibers, the vortex fiber was designed to lift thenear-degeneracy between the desired OAM T andparasitic TM01 and TE01, hence minimizing modalcrosstalk between them (16). Thus, this fiber yieldstwo new degenerate states (OAM T) in additionto the conventional degenerate LPT

01 modes:

The index profile of our vortex fiber (Fig. 2,A and B) has a characteristic high-index ring thatserves to lift the debilitating near-degeneracybetween the desired OAM T and parasitic TM01

and TE01 responsible for mode coupling in con-ventional fibers (5). Effective index differences(Dneff) of the first-order modes with respect tothe LPT

01 modes were numerically calculated andcompared with the experimentally measured val-ues (Fig. 2C). In the vortex fiber, the OAM T statesare separated from the LP T

01 states by Dneff ≈ 3 ×10–3 (at 1550 nm) and from the parasitic TE01and TM01 states by Dneff ≈ 1.6 × 10–3. Thesevalues of Dneff are larger than those in polarization-maintaining fibers that preserve distinct polar-ization modes and, by analogy, indicate that alldistinct modes in the vortex fiber should be re-sistant to distributed mode coupling (16). This isin contrast to conventional fibers and hence in-dicative of the fact that OAM modes would bepreserved in these vortex fibers. The degeneratepair of OAM T states inevitably mix into eachother because of fiber birefringence (13). How-ever, this coupling can be compensated for by

using a fiber polarization controller (we achieve–20 dB of crosstalk between the twoOAM T statesat the output of the 1.1-km bare-fiber spool).Polarization controller feedback–based correctiontechniques are commonly used in conventionalpolarization-division multiplexed systems (17).

We used a previously developed mode-puritycharacterization technique that analyzes spatialintensity variations at the fiber output arising fromintermodal interference in order to study the ef-fects of distributed mode coupling (13). Relativemode powers as a function of a fiber length (iter-atively measured via cutback) is shown in Fig. 2Dfor the case of high-purity (>21 dB)OAM + modeexcitation at 1550 nm. After 1.1 km of propaga-tion of the desired OAMmodes, less than –10 dBof the input power leaked into the LP T

01 and theparasitic TM01 and TE01 modes. The relativemode powers are alsomeasured in time (Fig. 2E),indicating temporal stability on the order of hours,although polarization controller adjustments werenecessary for longer periods of time.

Having confirmed the capability of the fiberto carry individual OAM states over long distances

Fig. 2. Vortex fiber characteristics. (A) Microscope image of the vortex fiberfacet. (B) Measured fiber refractive index and numerically calculated modeprofiles. (C) Measured (open circles) and numerically calculated (solid lines)effective index differences (Dneff) of the first-order modes—TE01, OAM, andTM01—with respect to the fundamental mode (LP01); large Dneff betweenmodes lowers mode-coupling distortions. (D) Measured modal power ratios as

a function of fiber length for the case of OAM+ mode excitation at 1550 nm(OAM power refers to combined OAM+ and OAM– mode powers, and LP01refers to combined powers of the two LPT01 states). (E) Relative mode powerswith respect to time, showing the temporal stability of the OAM modes. (F)Table of vortex fiber properties at 1550 nm, including numerically calculatedeffective area and dispersion and experimentally measured loss.

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with low mode-coupling, we investigate the pros-pects of multiplexing four guided modes—namely,the two LP T

01 and the two OAM T modes—andusing them as four distinct channels for OAM-MDM data transmission. We used a commercialSLM and free-space optics for OAM mode gen-eration and multiplexing (Fig. 1, B and C, andfig. S1). The detailed alignment procedure is avail-able in (15).

After 1.1 km of propagation, the vortex fiberoutput is imaged onto a camera when only onechannel is enabled at a time. Examples of imagesfrom theLP T

01 and OAM + channels are shown inFig. 3, A and B (images from all four channelsare available in fig. S2). To reveal the transversephase of theOAM T channel outputs, interferencewith an expanded Gaussian beam reference wasrecorded (Fig. 3, C and D), with the vortex fiberpolarization controller adjusted to yield ≈–20 dBOAM T crosstalk. The spiral interference patternsclearly indicate that theOAM + (OAM –) state wasobtained at the output in the case when the in-dividual OAM + (OAM –) mode was sent at thechannel input.

With all four channels enabled simultaneous-ly, the demuxing system sorts the modes accord-ing to their OAM (l ) and spin (s) values, usinganother SLM and a combination of a quarter-wave plate and a polarizer, respectively (15). Inthe example of theOAM+ channel, the resultingoutput maps back into a conventional Gaussian-shaped beamwith a planar phase (Fig. 3, E and F),which we can now route to a coherent receiver by

coupling into an SMF. This enables a quantitativemeasure of mode purity by observing channeloutput power versus time (Fig. 3G), which re-veals how much power leaked into other chan-nels (crosstalk), as well as howmuch power leakedout-and-back, during fiber propagation, into anindividual channel [multi-path interference (MPI)](18, 19). MPI is a fundamental property arisingfrom fiber design, whereas crosstalk depends onboth the fiber and the multiplexing (or demulti-plexing) setup design. Both crosstalk and MPIincrease bit error rate (BER) in the absence ofMIMO corrective algorithms (measured valuesfor all the modes are given in Fig. 3E).

We have demonstrated OAM-MDM datatransmission feasibility of the system describedabove by sending 50-GBaud, quadrature-phase-shift-keyed (QPSK) data at a single wavelengthand over four mode channels (Fig. 4A) (15, 20).BERs were measured for two cases: when onlyone channel was used for data transmission (single-channel case) and when all four channels weresimultaneously populated with distinct (decor-related) data streams (all-channels case). In thesingle-channel case, the largest received powerpenalty for achieving a BER of 3.8 × 10–3 [thethreshold BER level at which forward-error-correction (FEC) algorithms ensure error-freedata transmission] is 2.5 dB, mainly due to MPI.In the all-channel case, this largest power penaltyincreased to 4.1 dB, mainly due to crosstalk. Inthe latter case, a total transmission capacity at400 Gbit/s below the FEC limit is achieved.

In addition to the single-wavelength demon-stration, we used wavelength-division multiplex-ing (WDM) to further extend the capacity of oursystem (Fig. 4C) (20). Recall that we used a con-ventional polarization controller to achieve≈–20dBcrosstalk between the OAM T modes. However,optimizing our system to yield two orthogonal,pureOAM T states at one wavelength implies thatat other wavelengths, the OAM T states will, toa certain extent, couple with each other. Amoreadvanced transmitter with individual wavelengthchannel polarization control could, in principle,be used to mitigate this effect. In addition, extra-neous contributory factors such as the wavelengthdependence of the SLM and other free-spaceoptical components can also affect the crosstalk.For these reasons, only two OAM modes and10 WDM channels (from 1546.64 to 1553.88 nm)were chosen for our WDM experiment (Fig. 4D,boxed region, which illustrates wavelengths atwhich crosstalk was low) (15). Reduction to twomodes allowed us to choose a more complexmod-ulation format (16-quadrature amplitude mod-ulation) for data transmission, yielding higherspectral efficiency, albeit at a lower baud rate of20 GBaud. Although the BER of the two modesvaried somewhat because of crosstalk (Fig. 4E),transmission of 20 channels (OAM-MDM andWDM) resulted in a total transmission capacityof 1.6 Tb/s under the FEC limit.

Our results indicate that simple, low-complexityDSP coherent detection methods can be used toachieveOAM-MDM in fibers. Our demonstration

Fig. 3. Transmission channel characterization. (A and B) Intensity of LPT01and OAM+ channel outputs (collimated). (C and D) Interference patterns betweenan expanded Gaussian beam reference and the OAM+ and OAM– channel outputs,respectively. The handedness of the spiral is indicative of the OAM value (l = +1or –1) carried by each beam. Clear spiral images are also indicative of high modepurity. (E and F) Intensity and phase of the OAM+ channel output after demulti-

plexing. All images taken when only one channel is enabled at a time. (G) Exampleof the LPT01 channel power drift (attributed to crosstalk and free-space optics) andpower fluctuations (due to MPI). (Inset) Illustration of crosstalk and MPI mechanisms;mode A can couple into mode B, producing crosstalk, but a certain amount of thepower can couple back into mode A, interfering with the original signal and producingMPI. (H) Table of measured values for crosstalk and MPI for all four modes.

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used no computationally intensive DSP correc-tive algorithms, such as MIMO. Furthermore,because our OAM-MDM scheme primarily re-quired that the vortex fiber we used enabledmode-coupling–free propagation of OAMmodes,we expect this scheme to be scalable in numberof modes, and thus data capacity, given recentdevelopments on fiber designs that may be ableto support propagation of multiple OAM modeswith ‘ >> 1 (22). Because our primary goal is thatof demonstrating the viability of fiber-based datatransmission of independent OAM modes, weused conventional, commercial components (SLMsand wave retarders) for muxing and demuxing,which are inherently lossy as the number of OAMmodes is scaled. Recent demonstrations of theo-retically lossless OAM muxing devices, basedon waveguides (23) or free-space optics (24), in-dicate that the required component technology isconcurrently developing to enable realistic deploy-ments of scalable networks based onOAM-MDM.

References and Notes1. R. Essiambre, R. Tkach, Proc. IEEE 100, 1035 (2012).2. D. J. Richardson, Science 330, 327 (2010).3. J. Sakaguchi et al., J. Lightwave Technol. 30, 658

(2012).4. R. Ryf et al., J. Lightwave Technol. 30, 521 (2012).

5. D. Marcuse, Appl. Opt. 23, 1082 (1984).6. J. Carpenter, B. C. Thomsen, T. D. Wilkinson, Degenerate

mode-group division multiplexing, J. Lightwave Technol.30, 3946 (2012).

7. D. Andrews, Structured Light and Its Applications(Academic Press, New York, 2008).

8. J. Wang et al., Nat. Photonics 6, 488 (2012).9. S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs,

A. Zeilinger, New J. Phys. 8, 75 (2006).10. D. McGloin, N. B. Simpson, M. J. Padgett, Appl. Opt.

37, 469 (1998).11. P. Z. Dashti, F. Alhassen, H. P. Lee, Phys. Rev. Lett.

96, 043604 (2006).12. N. Bozinovic, P. Kristensen, S. Ramachandran, in

Frontiers in Optics 2011/Laser Science XXVII, OSATechnical Digest (online) (Optical Society of America,2011), paper LWL3; available at http://dx.doi.org/10.1364/LS.2011.LWL3.

13. N. Bozinovic, S. Golowich, P. Kristensen, S. Ramachandran,Opt. Lett. 37, 2451 (2012).

14. G. K. L. Wong et al., Science 337, 446 (2012).15. Materials and methods are available as supplementary

materials on Science Online.16. S. Ramachandran, P. Kristensen, M. F. Yan, Opt. Lett.

34, 2525 (2009).17. H. Sunnerud, C. Xie, M. Karlsson, R. Samuelsson,

P. A. Andrekson, J. Lightwave Technol. 20, 368(2002).

18. S. Ramachandran, J. W. Nicholson, S. Ghalmi, M. F. Yan,IEEE Photon. Technol. Lett. 15, 1171 (2003).

19. S. Ramachandran, S. Ghalmi, J. Bromage,S. Chandrasekhar, L. L. Buhl, IEEE Photon. Technol. Lett.17, 238 (2005).

20. N. Bozinovic et al., in European Conference and Exhibitionon Optical Communication, OSA Technical Digest (online),(Optical Society of America, 2013), paper Th.3.C.6;available at http://dx.doi.org/10.1364/ECEOC.2012.Th.3.C.6.

21. Y. Yue et al., in Conference on Optical Fiber Communications,OSA Technical Digest, paper OTh4G.2 (Optical Society ofAmerica, Washington, DC, 2013).

22. P. Gregg et al., in Conference on Lasers and Electro-Optics2013, OSA Technical Digest (online) (Optical Society ofAmerica, 2013), paper CTu2K.2.

23. T. Su et al., Opt. Express 20, 9396 (2012).24. G. C. Berkhout, M. P. Lavery, J. Courtial,

M. W. Beijersbergen, M. J. Padgett, Phys. Rev. Lett. 105,153601 (2010).

Acknowledgments: We thank S. Golowich, P. Gregg, andP. Steinvurzel for insightful discussions and M. V. Pedersenfor the numerical waveguide simulation tool. This workwas funded by the Defense Advanced Research ProjectsAgency–InPho program. M.T. acknowledges support from theChief Scientist Office of the Israeli Ministry of Industry, Tradeand Labor within the “Tera Santa” consortium. All data relatedto the experiments described in this manuscript are recordedin laboratory notebooks of members in S.R.’s group, and allassociated digital data are stored on networked computers atBoston University, whose contents are archived daily.

Supplementary Materialswww.sciencemag.org/cgi/content/full/340/6140/1545/DC1Materials and MethodsFigs. S1 to S6

15 March 2013; accepted 29 May 201310.1126/science.1237861

Fig. 4. Data-transmission experiments. (A) Block diagram of 50 × 2 GbaudQPSK signal transmission over a single wavelength carrying four modes inthe vortex fiber. (B) Measured BER as a function of received power for thesingle-channel (SC) and all-channels (AC) transmission case. (C) Block diagram

of 20 × 4 Gbaud 16-QAM signal transmission over 10 wavelengths carryingtwo modes in the vortex fiber. (D) Measured crosstalk between OAMT modesas a function of wavelength. (E) BER as a function of wavelength for OAMT

modes in the WDM system.

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