Capacity limits of spatially multiplexed free-space communication

  • A Corrigendum to this article was published on 24 December 2015


Increasing the information capacity per unit bandwidth has been a perennial goal of scientists and engineers1. Multiplexing of independent degrees of freedom, such as wavelength, polarization and more recently space, has been a preferred method to increase capacity2,3 in both radiofrequency and optical communication. Orbital angular momentum, a physical property of electromagnetic waves discovered recently4, has been proposed as a new degree of freedom for multiplexing to achieve capacity beyond conventional multiplexing techniques5,6,7,8,9, and has generated widespread and significant interest in the scientific community10,11,12,13,14. However, the capacity of orbital angular momentum multiplexing has not been established or compared to other multiplexing techniques. Here, we show that orbital angular momentum multiplexing is not an optimal technique for realizing the capacity limits of a free-space communication channel15,16,17 and is outperformed by both conventional line-of-sight multi-input multi-output transmission and spatial-mode multiplexing.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Schematic of transmission systems.
Figure 2: Comparison of singular values of the transmission matrix in descending order for different multiplexing/demultiplexing methods.
Figure 3: Spectral efficiencies and effective degrees of freedom (EDOF) for different multiplexing/demultiplexing methods.

Change history

  • 27 November 2015

    In the version of this Letter originally published, in Fig. 3a,b, the x axis labels should have been ‘SNR (dB)’. This has now been corrected in the online versions of the Letter.


  1. 1

    Shannon, C. E. A mathematical theory of communication. Bell Syst. Tech. J. 23, 45 (1948).

    MathSciNet  Google Scholar 

  2. 2

    Ng, S. X., Hanzo, L. L., Keller, T. & Webb, W. Quadrature Amplitude Modulation: From Basics to Adaptive Trellis-Coded, Turbo-Equalised and Space–Time Coded OFDM, CDMA and MC-CDMA Systems (Wiley-IEEE, 2004).

    Google Scholar 

  3. 3

    Evangelides, S. G. Jr, Mollenauer, L. F., Gordon, J. P. & Bergano, N. S. Polarization multiplexing with solitons. J. Lightw. Technol. 10, 28–35 (1992).

    Article  Google Scholar 

  4. 4

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

    ADS  Article  Google Scholar 

  5. 5

    Fabrizio, T. et al. Encoding many channels on the same frequency through radio vorticity: first experimental test. New J. Phys. 14, 033001 (2012).

    Article  Google Scholar 

  6. 6

    Willner, A. E., Wang, J. & Huang, H. A different angle on light communications. Science 337, 655–656 (2012).

    ADS  MathSciNet  Article  Google Scholar 

  7. 7

    Wang, J. et al. Terabit free-space data transmission employing orbital angular momentum multiplexing. Nature Photon. 6, 488–496 (2012).

    ADS  Article  Google Scholar 

  8. 8

    Yan, Y. et al. High-capacity millimetre-wave communications with orbital angular momentum multiplexing. Nature Commun. 5, 4876 (2014).

    ADS  Article  Google Scholar 

  9. 9

    Bozinovic, N. et al. Terabit-scale orbital angular momentum mode division multiplexing in fibers. Science 340, 1545–1548 (2013).

    ADS  Article  Google Scholar 

  10. 10

    Cartiledge, E. Adding a twist to radio technology: spiralling radio waves could revolutionize telecommunications. Nature (2011).

  11. 11

    Edfors, O. & Johansson, A. J. Is orbital angular momentum (OAM) based radio communication an unexploited area? IEEE Trans. Antennas Propag. 60, 1126–1131 (2012).

    ADS  MathSciNet  Article  Google Scholar 

  12. 12

    Michele, T., Christophe, C. & Julien, P.-C. Comment on ‘Reply to Comment on “Encoding many channels on the same frequency through radio vorticity: first experimental test” ’. New J. Phys. 15, 078001 (2013).

    Article  Google Scholar 

  13. 13

    Tamburini, F. et al. Reply to Comment on “Encoding many channels on the same frequency through radio vorticity: first experimental test”. New J. Phys. 14, 118002 (2012).

    ADS  Article  Google Scholar 

  14. 14

    Kish, L. B. & Nevels, R. D. Twisted radio waves and twisted thermodynamics. PLoS ONE 8, e56086 (2013).

    ADS  Article  Google Scholar 

  15. 15

    Mair, A., Vaziri, A., Weihs, G. & Zeilinger, A. Entanglement of the orbital angular momentum states of photons. Nature 412, 313–316 (2001).

    ADS  Article  Google Scholar 

  16. 16

    Molina-Terriza, G., Torres, J. P. & Torner, L. Twisted photons. Nature Phys. 3, 305–310 (2007).

    ADS  Article  Google Scholar 

  17. 17

    Saleh, M. F., Di Giuseppe, G., Saleh, B. E. A. & Teich, M. C. Photonic circuits for generating modal, spectral, and polarization entanglement. IEEE Photon. J. 2, 736–752 (2010).

    Article  Google Scholar 

  18. 18

    Karimi, E. et al. Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface. Light Sci. Appl. 3, e167 (2014).

    MathSciNet  Article  Google Scholar 

  19. 19

    Xinlu, G. et al. Generating, multiplexing/demultiplexing and receiving the orbital angular momentum of radio frequency signals using an optical true time delay unit. J. Opt. 15, 105401 (2013).

    Article  Google Scholar 

  20. 20

    Cai, X. et al. Integrated compact optical vortex beam emitters. Science 338, 363–366 (2012).

    ADS  Article  Google Scholar 

  21. 21

    Strain, M. J. et al. Fast electrical switching of orbital angular momentum modes using ultra-compact integrated vortex emitters. Nature Commun. 5, 4856 (2014).

    ADS  Article  Google Scholar 

  22. 22

    Mirhosseini, M., Malik, M., Shi, Z. & Boyd, R. W. Efficient separation of the orbital angular momentum eigenstates of light. Nature Commun. 4, ( 2013).

  23. 23

    Genevet, P., Lin, J., Kats, M. A. & Capasso, F. Holographic detection of the orbital angular momentum of light with plasmonic photodiodes. Nature Commun. 3, 1278 (2012).

    ADS  Article  Google Scholar 

  24. 24

    Phillips, R. L. & Andrews, L. C. Spot size and divergence for Laguerre Gaussian beams of any order. Appl. Opt. 22, 643–644 (1983).

    ADS  Article  Google Scholar 

  25. 25

    O'Sullivan, M. N., Mirhosseini, M., Malik, M. & Boyd, R. W. Near-perfect sorting of orbital angular momentum and angular position states of light. Opt. Express 20, 24444 (2012).

    ADS  Article  Google Scholar 

  26. 26

    Lavery, M. P. J. et al. The efficient sorting of light's orbital angular momentum for optical communications. Proc. SPIE 8542, 85421R (2012).

    Article  Google Scholar 

  27. 27

    Berkhout, G. C. G., Lavery, M. P. J., Courtial, J., Beijersbergen, M. W. & Padgett, M. J. Efficient sorting of orbital angular momentum states of light. Phys. Rev. Lett. 105, 153601 (2010).

    ADS  Article  Google Scholar 

  28. 28

    Richardson, D. J., Fini, J. M. & Nelson, L. E. Space-division multiplexing in optical fibres. Nature Photon. 7, 354–362 (2013).

    ADS  Article  Google Scholar 

  29. 29

    Foschini, G. J. Layered space–time architecture for wireless communication in a fading environment when using multi-element antennas. Bell Labs Tech. J. 1, 41–59 (1996).

    Article  Google Scholar 

  30. 30

    Goodman, J. W. Introduction to Fourier Optics (McGraw Hill, 1996).

    Google Scholar 

  31. 31

    Wells, D. The Penguin Book of Curious and Interesting Numbers Revised Edition (Penguin, 1986).

    Google Scholar 

  32. 32

    Ren, Y. et al. Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing. Opt. Lett. 38, 4062–4065 (2013).

    ADS  Article  Google Scholar 

  33. 33

    Li, G., Bai, N., Zhao, N. & Xia, C. Space-division multiplexing: the next frontier in optical communication. Adv. Opt. Photon. 6, 413–487 (2014).

    Article  Google Scholar 

  34. 34

    Cover, T. & Thomas, J. A. Elements of Information Theory (Wiley, 2012).

    Google Scholar 

  35. 35

    Shiu, D.-S., Foschini, G. J., Gans, M. J. & Kahn, J. M. Fading correlation and its effect on the capacity of multielement antenna systems. IEEE Trans. Commun. 48, 502–513 (2000).

    Article  Google Scholar 

Download references


This work was supported in part by the National Key Basic Research Program of China (973), project #2014CB340104/3, NSFC projects 61377076, 61307085 and 61431009.

Author information




N.Z., G.L. and J.M.K. conceived and designed the theoretical model. N.Z. and X.L. performed the simulations. N.Z., G.L. and J.M.K. analysed the data. N.Z., G.L. and J.M.K. co-wrote the paper.

Corresponding authors

Correspondence to Guifang Li or Joseph M. Kahn.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 699 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zhao, N., Li, X., Li, G. et al. Capacity limits of spatially multiplexed free-space communication. Nature Photon 9, 822–826 (2015).

Download citation

Further reading


Sign up for the Nature Briefing newsletter for a daily update on COVID-19 science.
Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing