Letter | Published:

Robust wireless power transfer using a nonlinear parity–time-symmetric circuit

Nature volume 546, pages 387390 (15 June 2017) | Download Citation


Considerable progress in wireless power transfer has been made in the realm of non-radiative transfer, which employs magnetic-field coupling in the near field1,2,3,4. A combination of circuit resonance and impedance transformation is often used to help to achieve efficient transfer of power over a predetermined distance of about the size of the resonators3,4. The development of non-radiative wireless power transfer has paved the way towards real-world applications such as wireless powering of implantable medical devices and wireless charging of stationary electric vehicles1,2,5,6,7,8. However, it remains a fundamental challenge to create a wireless power transfer system in which the transfer efficiency is robust against the variation of operating conditions. Here we propose theoretically and demonstrate experimentally that a parity–time-symmetric circuit incorporating a nonlinear gain saturation element provides robust wireless power transfer. Our results show that the transfer efficiency remains near unity over a distance variation of approximately one metre, without the need for any tuning. This is in contrast with conventional methods where high transfer efficiency can only be maintained by constantly tuning the frequency or the internal coupling parameters as the transfer distance or the relative orientation of the source and receiver units is varied. The use of a nonlinear parity–time-symmetric circuit should enable robust wireless power transfer to moving devices or vehicles9,10.

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  1. 1.

    & High-efficiency coupling-insensitive transcutaneous power and data transmission via an inductive link. IEEE Trans. Biomed. Eng. 37, 716–722 (1990)

  2. 2.

    & Closed-loop class E transcutaneous power and data link for microimplants. Med. Biol. Eng. Comput. 39, 589–599 (1992)

  3. 3.

    et al. Wireless power transfer via strongly coupled magnetic resonances. Science 317, 83–86 (2007)

  4. 4.

    et al. Wireless power transfer in the presence of metallic plates: experimental results. AIP Adv. 3, 062102 (2013)

  5. 5.

    RF powering of millimeter- and submillimeter-sized neural prosthetic implants. IEEE Trans. Biomed. Eng. 35, 323–327 (1988)

  6. 6.

    , , & Design of a high frequency inductively coupled power transfer system for electric vehicle battery charge. Appl. Energy 86, 355–363 (2009)

  7. 7.

    , , , & Narrow-width inductive power transfer system for online electrical vehicles. IEEE Trans. Power Electron. 26, 3666–3679 (2011)

  8. 8.

    et al. Wireless power transfer to deep-tissue microimplants. Proc. Natl Acad. Sci. USA 111, 7974–7979 (2014)

  9. 9.

    & Review and Evaluation of Wireless Power Transfer (WPT) for Electric Transit Applications. FTA Report No. 0060, (US Department of Transportation, Federal Transit Administration, 2014)

  10. 10.

    & Wireless power transfer for electric vehicle applications. IEEE J. Emerg. Select. Topics Power Electronics 3, 4–17 (2015)

  11. 11.

    Apparatus for transmitting electrical energy. US patent 1,119,732 (1914)

  12. 12.

    The history of power transmission by radio waves. IEEE Trans. Microw. Theory Tech. 32, 1230–1242 (1984)

  13. 13.

    , & Analysis, experimental results, and range adaptation of magnetically coupled resonators for wireless power transfer. IEEE Trans. Ind. Electron. 58, 544–554 (2011)

  14. 14.

    & Real spectra in non-Hermitian Hamiltonians having PT-symmetry. Phys. Rev. Lett. 80, 5243–5246 (1998)

  15. 15.

    , & Complex extension of quantum mechanics. Phys. Rev. Lett. 89, 270401 (2002)

  16. 16.

    et al. Observation of PT-symmetry breaking in complex optical potentials. Phys. Rev. Lett. 103, 093902 (2009)

  17. 17.

    et al. Observation of parity–time symmetry in optics. Nat. Phys. 6, 192–195 (2010)

  18. 18.

    , , & Beam dynamics in PT symmetric optical lattices. Phys. Rev. Lett. 100, 103904 (2008)

  19. 19.

    et al. Unidirectional invisibility induced by PT-symmetric periodic structures. Phys. Rev. Lett. 106, 213901 (2011)

  20. 20.

    et al. Parity–time-symmetric whispering-gallery microcavities. Nat. Phys. 10, 394 (2014)

  21. 21.

    et al. Pump-induced exceptional points in lasers. Phys. Rev. Lett. 108, 173901 (2012)

  22. 22.

    , , , & Single-mode laser by parity-time symmetry breaking. Science 346, 972–975 (2014)

  23. 23.

    , , , & Parity–time-symmetric microring lasers. Science 346, 975 (2014)

  24. 24.

    et al. Loss-induced suppression and revival of lasing. Science 346, 328–332 (2014)

  25. 25.

    , , , & Nonlinear reversal of the PT-symmetric phase transition in a system of coupled semiconductor microring resonators. Phys. Rev. A 92, 63807 (2015)

  26. 26.

    & Nonlinear modal interactions in parity-time (PT) symmetric lasers. Sci. Rep. 6, 24889 (2016)

  27. 27.

    Waves and Fields in Optoelectronics 197–228 (Prentice Hall, 1984)

  28. 28.

    Lasers 992–996 (University Science Books, 1986)

  29. 29.

    et al. PT-symmetric electronics. J. Phys. A 45, 444029 (2012)

  30. 30.

    et al. Power amplifiers and transmitters for RF and microwave. IEEE Trans. Microw. Theory Tech. 50, 814–826 (2002)

  31. 31.

    & Steady-state ab initio theory of lasers with injected signals. Phys. Rev. A 90, 013840 (2014)

  32. 32.

    & PT symmetry breaking and nonlinear optical isolation in coupled microcavities. Opt. Express 24, 6916 (2016)

  33. 33.

    , , & Adaptive frequency with power-level tracking system for efficient magnetic resonance wireless power transfer. Electron. Lett. 48, 452 (2012)

  34. 34.

    et al. Design and implementation of shaped magnetic-resonance-based wireless power transfer system for roadway-powered moving electric vehicles. IEEE Trans. Ind. Electron. 61, 1179–1192 (2014)

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Part of the work was supported by the TomKat Center for Sustainable Energy at Stanford. S.F. thanks R. Sassoon and A. Cerjan for discussions.

Author information


  1. Department of Electrical Engineering, Ginzton Laboratory, Stanford University, Stanford, California 94305, USA

    • Sid Assawaworrarit
    • , Xiaofang Yu
    •  & Shanhui Fan


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S.A. performed the simulations and experiment. All authors contributed to formulating the analytical model, to analysing the data, and to writing the manuscript. S.F. initiated and supervised the project.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Shanhui Fan.

Reviewer Information Nature thanks Y. Chong and G. Lerosey for their contribution to the peer review of this work.

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Extended data

Supplementary information


  1. 1.

    Demonstration of the PT symmetric scheme in a dynamic wireless power transfer scenario.

    Robust power transfer is achieved by the virtue of PT symmetry in saturation as shown by the constant brightness of the LED bulb when the receiver is moved to and from the source.

  2. 2.

    Demonstration of the conventional scheme in a dynamic wireless power transfer scenario.

    The transferred power level is dependent on the source-to-receiver separation distance as shown by the variation of the LED brightness as the receiver is moved to and from the source.

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