www.sciencemag.org/cgi/content/full/340/6140/1545/DC1

Supplementary Material for

Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers

Nenad Bozinovic, Yang Yue, Yongxiong Ren, Moshe Tur, Poul Kristensen, Hao Huang, Alan E. Willner, Siddharth Ramachandran*

*Corresponding author. E-mail: sidr@bu.edu

Published 28 June 2013, Science 340, 1545 (2013)

DOI: 10.1126/science.1237861

This PDF file includes:

Materials and Methods

Figs. S1 to S6

1

Supplementary Materials for

Terabit-scale orbital angular momentum mode division multiplexing in fibers

Nenad Bozinovic, Yang Yue, Yongxiong Ren, Moshe Tur, Poul Kristensen, Hao Huang,

Alan E. Willner, Siddharth Ramachandran*

*To whom correspondence should be addressed. E-mail: sidr@bu.edu

This PDF file includes:

Materials and Methods Fig. S1-S6

The supplementary materials are organized as follows; In §1 we provide details on the methods used to obtain data in Fig. 2. In §2 we give a detailed description of the setup used for imaging and data transmission. The adjustment procedure using polarization controllers is described in §3. Additional imaging results of the modes are given in §4. In §5 we provide additional information on the demultiplexing procedure. In §6, we give additional information on the data transmission procedure. §7 provides phase imaging results using the WDM system.

2

Materials and Methods 1) Explanation of methods used for data in Fig. 2

The fiber index profile in Fig. 2B was obtained using an interferometry-based fiber profiler (IFA-100, Interfiber Analysis) at 633 nm, and is plotted with respect to the refractive index of silica. For Fig. 2C, numerical calculations were done using a numerical finite-difference method. Experimental values in Fig. 2C were obtained by observing resonance-loss-spectrum of a microbend grating induced in the fiber (for more details on the method see (16)). Cut-back results (Fig. 2D) were obtained by measuring modal power ratios for a long fiber length first, which was then sequentially shortened. Thus, we ensured that the same input launch conditions existed for all the lengths that were measured. We used a microbend-induced grating with length 𝐿 = 40𝑚𝑚 and grating-period Λ = 475µm as a mode converter, prior to which fiber was securely taped to be free of any perturbations that would change phase or polarization, and therefore coupling conditions, at the grating input. For the data in Fig. 2D-E, we use a tunable continuous wave external cavity laser (CW-ECL, Agilent 8168F) with 100-kHz linewidth (coherence length ~ 3km) to capture necessary modal interference effects between the modes after 1.1-km of propagation in the vortex fiber (the maximum optical-path length delay, given by Δ𝑛𝑔𝐿, where Δ𝑛𝑔 is the difference in group index between modes, is ≈ 3 meters). Mode coupling is affected by the wavelength of light as well as the fiber temperature (5). For this reason, at a particular fiber length, relative modal powers were determined for 500 different wavelengths within a 0.5 𝑛𝑚 range (each point on Fig. 2D denotes a mean value with one standard deviation from the mean). We note that the linewidth of our source was on the order of 𝑓𝑚 ensuring visibility of the modal interference necessary for power calculations (in contrast, the data-carrying source used to obtain BERs had a linewidth on the order of a 𝑛𝑚).

2) Explanation of the setup used for imaging and data transmission The detailed experimental OAM-MDM setup is shown in Fig. S1. For the single wavelength experiments, a CW-ECL operating at 1550 nm was first modulated using a 50 GBaud QPSK signal, and subsequently split into four arms that were delayed sufficiently to obtain four de-correlated data channels (two for the WDM experiments). Two of the four channels were converted into the 𝑂𝐴𝑀± modes (modes A and B) using reflection off fork-holograms of topological charge ±1, created using the LCOS-SLM (X10468-8, Hamamatsu). In order to create only the 𝑂𝐴𝑀± states and avoid creating spurious 𝑇𝐸01 and 𝑇𝑀01 modes when coupling into the fiber, we note that it is critical to generate circularly polarized free-space 𝑂𝐴𝑀± states, before coupling into the fiber (13). The other two 𝐿𝑃01 modes (C and D) were left unchanged. A 6-axis fiber stage positioner (Thorlabs, MAX601D) was used for input coupling. Precise optical alignment enabled avoiding any offset coupling, which can otherwise introduce strong crosstalk (offset coupling of <50nm was necessary and achieved). We found the incident angle (of light on the fiber facet) to also be important for input coupling, but less critical than the offset. Fiber coupling losses were 0.7dB for the 𝐿𝑃01 mode and 1.1dB for the OAM modes.

3

3) Polarization controllers adjustments procedure After alignment, the four polarization controllers at the channel inputs (A, B, C and D on Fig. S1) were first adjusted to equalize the output channel powers. Next, the polarization controller on the vortex fiber (PC-VF in Fig. S1) was adjusted to obtain the 𝑂𝐴𝑀± states at the vortex fiber input with the smallest possible cross-talk (a minimum value of −20𝑑𝐵 was obtained; Fig. 4D). In order to create only the 𝑂𝐴𝑀± states when coupling into the fiber and avoid creating spurious 𝑇𝐸01 and 𝑇𝑀01 modes, we note that it is critical to generate circularly polarized free-space 𝑂𝐴𝑀± states, before coupling into the fiber (13). Finally, the polarization controller on the input SMF (PC-SMF) was adjusted to obtain 𝐿𝑃01

± modes at the output with the smallest crosstalk (< −30𝑑𝐵 was achieved). Note that we did not necessarily have 𝐿𝑃01

± states at the channel inputs (C, D) but rather states with arbitrary polarizations; however, 𝑂𝐴𝑀± states were ensured at both input and output. The vortex fiber spool was thermally isolated using a custom-made Styrofoam box. Polarization controllers needed adjustments in roughly one–hour increments to account for components drifts and temperature fluctuations. We note that automated polarization controller feedback corrections are commonly used techniques in conventional polarization-division multiplexed systems (17).

4) Additional mode imaging results

Intensity images in Fig. 3 were obtained using 50 GBaud, QPSK modulated source and an near-infrared (NIR) camera (NIR-300, VDS Vosskühler GmbH). Interference patterns in Fig. 3 were obtained using an unmodulated CW-ECL (100 kHz linewidth) source and a 60 µs camera exposure time. Intensities of all four modes are shown in Fig. S2.

5) Additional demultiplexing setup information

At the demultiplexing port, a spin sorter was constructed from a quarter wave plate and a polarizer, while another LCOS-SLM was used as the OAM sorter. To demultiplex the four modes, we used two orientations of a demultiplexing quarter-wave-plate (±45o), and three SLM holograms (ℓ=0, ±1). The mode demuxing schematic is illustrated in Fig. S3A. An illustrative method for measuring crosstalk is shown in Fig. S3B. Crosstalk (XT) and multipath interference (MPI) (18, 19) for each of the four channels were measured using:

𝑋𝑇 𝑖 [𝑑𝐵] = 𝑃𝑖∗[𝑑𝐵𝑚]− 𝑃𝑖 [𝑑𝐵𝑚], (1)

𝑀𝑃𝐼𝑖[𝑑𝐵] = 20 𝑙𝑜𝑔1010∆𝑖/20 − 110∆𝑖/20 + 1

, (2)

where the index i represents four channels (𝐴,𝐵,𝐶,𝐷 in Fig. S1), 𝑃𝑖 is the output power at the channel 𝑖 when all the input channels are on, 𝑃𝑖∗ is the power output for the channel 𝑖 when the input channel 𝑖 is off, and ∆𝑖 denotes the peak-to-peak power output fluctuations for channel 𝑖, when all the input channels are on (all power values given in dB).

4

6) Additional data transmission information

Figure S4 shows constellation diagrams in the case of the 4-mode OAM-MDM experiment in the single-channel as well as the all-channel case, using 50 GBaud non-return-to-zero (NRZ) QPSK at 1550 nm. Figure S5 shows additional results of the transmission experiment with 2-OAM modes, 10 wavelengths and 16-QAM signal modulation. The optical spectra of the modulated signal just before the input at the fiber, and after transmission in the 𝑂𝐴𝑀+ mode followed by the demux, are plotted in Fig. S5A. We can see that all WDM channels have ~25dB OSNR after demultiplexing. Figure S5B shows constellations for a) 16-QAM back-to-back (B2B) data transmission, b) 𝑂𝐴𝑀+ mode at 1550.64 nm w/o crosstalk (XT) (one wavelength is on, one mode is on), c) 𝑂𝐴𝑀+ mode at 1550.64 nm w/ WDM XT (10 wavelengths are on, one mode is on), and d) 𝑂𝐴𝑀+ mode for WDM source w/ all XT (10 wavelengths are on, two mode are on). Note the gradual increase in distortion of the constellations as wavelengths and modes are added to the fiber. Figure S5C shows measured BER curves for the OAM modes at 1550.64 nm, in the WDM case, as a function of received power. At the optimal wavelength, crosstalk for the two OAM modes was −21.4 𝑑𝐵 and −20.2 𝑑𝐵, respectively. We can see that the BER for the mode 𝑂𝐴𝑀+ is slightly better than that for the mode 𝑂𝐴𝑀− mode, mainly due to differences in alignment of the optical components. At the FEC limit (3.8 × 10−3 according to the ITU-T Recommendation G.975.1, Appendix I.9, 2004), the average power penalty of mode 𝑂𝐴𝑀+ and 𝑂𝐴𝑀− for the cases w/o XT, w/ WDM XT and w/ all XT are 1.8 𝑑𝐵, 2.4 𝑑𝐵 and 4.55 𝑑𝐵, respectively.

7) Phase imaging in the WDM case Despite the higher cross-talk between the two 𝑂𝐴𝑀± modes as we move away from the optimal wavelength, spiral interference patterns were observed throughout the 1540-1570 nm wavelength range. Figure S6 demonstrates this for the 𝑂𝐴𝑀+ case; for brevity, only a few wavelengths, spaced in 10pm, 100pm, 1000pm and 10nm steps are shown (as before, a CW-ECL with 100 kHz linewidth and a 60 µs camera exposure time was used for this measurement). The 𝑂𝐴𝑀+ mode purity (and hence spiral quality) degrades for some intermediate wavelengths, but the fact that it generally maintains a spiral pattern is indicative of a substantially pure OAM mode over a 30-nm spectral range.

5

Fig. S1 Systems experiment setup: signal from the laser or WDM source is modulated, amplified using an erbium doped fiber amplifier (EDFA), filtered using a band pass filter (BPF) and split into four individual fiber arms (two in the case of the WDM experiment). Two of the arms were converted into OAM modes using the input SLM. Two fundamental modes were also collinearly aligned with the two OAM modes using a beam-splitter, and all four modes were coupled into the fiber. After propagation, the modes are demultiplexed sequentially and sent for coherent detection and offline digital signal processing (DSP). Acronyms: ADC - analog digital convertor, Att - attenuator, FM - flip mirror, LO - local oscillator, OC - optical coupler, (N)PBS: (non)-polarizing beam-splitter, PBC - polarization beam combiner, PC - polarization controllers, PC-SMF - polarization controller on SMF, PC-VF - polarization controller on vortex fiber. OC: optical coupler, (N)PBS: (non-)polarizing beam-splitter, PBC: polarization beam combiner, PC: polarization controller.

6

Fig. S2 Collimated single-channel images recorded with the NIR camera after 1.1km fiber propagation using the 50 GBaud, QPSK modulated source. (A, B) Doughnut shaped mode images result from the phase singularity in the center of OAM modes. (C, D) 𝐿𝑃01 mode intensity images.

7

Fig. S3 (A) Example of an SLM-based demux pattern of an OAM mode without (ℓ=0) and with (ℓ=+1) fork holograms, respectively. (B) Example of crosstalk measurement for one mode. Power at the demultiplexed channel is shown for a short time scale when all the modes are on, and where the dominant mode is off. The dip in power denotes how much of a crosstalk is present between, in this case, the 𝐿𝑃01+ mode and all the other modes.

8

Fig. S4 Constellation diagrams in the case of 4-mode OAM-MDM, with 50 GBaud NRZ-QPSK, λ = 1550nm, for the single-channel, and all-channel cases. Note the larger distortion of the constellations in the all-channel case.

9

Fig. S5 Additional experimental results of the 2-OAM modes, 10 wavelengths, 16-QAM transmission experiments. (A) Spectrum of the modulated signal at the output of the WDM 16-QAM Tx, and spectrum of the 𝑂𝐴𝑀+ mode at the receiver after demultiplexing. (B) Constellations of 16-QAM modulation for the demultiplexed 𝑂𝐴𝑀+ mode at 1550.64 nm, for several cases (without and with crosstalk). (C) BER as a function of received power at 1550.64 nm, for B2B, and OAM modes without and with XT from WDM channels or the other OAM mode.

10

Fig. S6 Spiral interference patterns, showing helical phase, of the 𝑂𝐴𝑀+ mode at different wavelengths for the same vortex fiber conditions (no polarization controller adjustments). (A-D) Spiral patterns for the wavelengths spaced in 10pm, 100pm, and 1000pm. (E-H) Spirals for the wavelengths spaced in 10nm.

References and Notes 1. R. Essiambre, R. Tkach, Capacity trends and limits of optical communication networks. Proc.

IEEE 100, 1035 (2012). doi:10.1109/JPROC.2012.2182970

2. D. J. Richardson, Filling the light pipe. Science 330, 327 (2010). doi:10.1126/science.1191708 Medline

3. J. Sakaguchi et al., Space division multiplexed transmission of 109-Tb/s data signals using homogeneous seven-core fiber. J. Lightwave Technol. 30, 658 (2012). doi:10.1109/JLT.2011.2180509

4. R. Ryf et al., Mode-division multiplexing over 96 km of few-mode fiber using coherent 6x6 MIMO processing. J. Lightwave Technol. 30, 521 (2012). doi:10.1109/JLT.2011.2174336

5. D. Marcuse, Microdeformation losses of single-mode fibers. Appl. Opt. 23, 1082 (1984). doi:10.1364/AO.23.001082 Medline

6. J. Carpenter, B. C. Thomsen, T. D. Wilkinson, Degenerate mode-group division multiplexing, degenerate mode-group division multiplexing. J. Lightwave Technol. 30, 3946 (2012). doi:10.1109/JLT.2012.2206562

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

8. J. Wang et al., Terabit free-space data transmission employing orbital angular momentum multiplexing. Nat. Photonics 6, 488 (2012). doi:10.1038/nphoton.2012.138

9. S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, A. Zeilinger, Experimental quantum cryptography with qutrits. New J. Phys. 8, 75 (2006). doi:10.1088/1367-2630/8/5/075

10. D. McGloin, N. B. Simpson, M. J. Padgett, Transfer of orbital angular momentum from a stressed fiber-optic waveguide to a light beam. Appl. Opt. 37, 469 (1998). doi:10.1364/AO.37.000469 Medline

11. P. Z. Dashti, F. Alhassen, H. P. Lee, Observation of orbital angular momentum transfer between acoustic and optical vortices in optical fiber. Phys. Rev. Lett. 96, 043604 (2006). doi:10.1103/PhysRevLett.96.043604 Medline

12. N. Bozinovic, P. Kristensen, S. Ramachandran, in Frontiers in Optics 2011/Laser Science XXVII, OSA Technical 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, Control of orbital angular momentum of light with optical fibers. Opt. Lett. 37, 2451 (2012). doi:10.1364/OL.37.002451 Medline

14. G. K. L. Wong et al., Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber. Science 337, 446 (2012). doi:10.1126/science.1223824 Medline

15. Materials and methods are available as supplementary materials on Science Online.

16. S. Ramachandran, P. Kristensen, M. F. Yan, Generation and propagation of radially polarized beams in optical fibers. Opt. Lett. 34, 2525 (2009). doi:10.1364/OL.34.002525 Medline

17. H. Sunnerud, C. Xie, M. Karlsson, R. Samuelsson, P. A. Andrekson, A comparison between different PMD compensation techniques. J. Lightwave Technol. 20, 368 (2002). doi:10.1109/50.988985

18. S. Ramachandran, J. W. Nicholson, S. Ghalmi, M. F. Yan, Measurement of multipath interference in the coherent crosstalk regime. IEEE Photon. Technol. Lett. 15, 1171 (2003). doi:10.1109/LPT.2003.814880

19. S. Ramachandran, S. Ghalmi, J. Bromage, S. Chandrasekhar, L. L. Buhl, Evolution and systems impact of coherent distributed multipath interference. IEEE Photon. Technol. Lett. 17, 238 (2005). doi:10.1109/LPT.2004.836902

20. N. Bozinovic et al., in European Conference and Exhibition on 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 of America, Washington, DC, 2013).

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

23. T. Su et al., Demonstration of free space coherent optical communication using integrated silicon photonic orbital angular momentum devices. Opt. Express 20, 9396 (2012). doi:10.1364/OE.20.009396 Medline

24. G. C. Berkhout, M. P. Lavery, J. Courtial, M. W. Beijersbergen, M. J. Padgett, Efficient sorting of orbital angular momentum states of light. Phys. Rev. Lett. 105, 153601 (2010). doi:10.1103/PhysRevLett.105.153601 Medline