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Broadband passive isolators based on coupled nonlinear resonances

Nature Electronicsvolume 1pages113119 (2018) | Download Citation


Isolators are devices that transmit waves only in one direction, and are widely used to protect sensitive equipment from reflections and interference. These devices inherently require the breaking of Lorentz reciprocity, which can be achieved with an external bias, such as a magnetic field, that breaks time-reversal symmetry. Alternatively, nonlinear effects can be used, which offer a route to fully passive devices that do not require any form of external bias. However, the nonlinear isolators developed so far have limitations in terms of insertion loss, isolation, bandwidth and isolation intensity range. Here, we show that any isolator formed from one nonlinear resonator suffers from these limitations, and that they can be overcome by combining multiple nonlinear resonators with suitable intensity dispersion. We theoretically show, and then experimentally demonstrate using a microwave circuit, that the combination of one Fano and one Lorentzian nonlinear resonator, and a suitable delay line between them, can provide unitary transmission, infinite isolation, broad bandwidth and broad isolation intensity range. We also show that a larger number of resonators can be used to further increase the isolation intensity range without diminishing the other metrics of the device.

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  1. 1.

    Pozar, D. M. Microwave Engineering 3rd edn (John Wiley & Sons, Hoboken, NY, 2005).

  2. 2.

    Potton, R. J. Reciprocity in optics. Rep. Prog. Phys. 67, 717–754 (2004).

  3. 3.

    Kodera, T., Sounas, D. L. & Caloz, C. Magnetless nonreciprocal metamaterial (MNM) technology: application to microwave components. IEEE Trans. Microw. Theory Techn. 61, 1030–1042 (2013).

  4. 4.

    Wang, Z. et al. Gyrotropic response in the absence of a bias field. Proc. Natl Acad. Sci. USA 109, 13194–13197 (2012).

  5. 5.

    Sounas, D. L. & Alù, A. Non-reciprocal photonics based on time modulation. Nat. Photon. 11, 774–783 (2017).

  6. 6.

    Yu, Z. & Fan, S. Complete optical isolation created by indirect interband photonic transitions. Nat. Photon. 3, 91–94 (2009).

  7. 7.

    Lira, H., Yu, Z., Fan, S. & Lipson, M. Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip. Phys. Rev. Lett. 109, 033901 (2012).

  8. 8.

    Wang, D.-W. et al. Optical diode made from a moving photonic crystal. Phys. Rev. Lett. 110, 093901 (2013).

  9. 9.

    Qin, S., Xu, Q. & Wang, Y. E. Nonreciprocal components with distributedly modulated capacitors. IEEE Trans. Microw. Theory Techn. 62, 2260–2272 (2014).

  10. 10.

    Sounas, D. L., Caloz, C. & Alù, A. Giant non-reciprocity at the subwavelength scale using angular momentum-biased metamaterials. Nat. Commun. 4, 2407 (2013).

  11. 11.

    Fleury, R., Sounas, D. L., Sieck, C. F., Haberman, M. R. & Alù, A. Sound isolation and giant linear nonreciprocity in a compact acoustic circulator. Science 343, 516–519 (2014).

  12. 12.

    Sounas, D. L. & Alù, A. Angular-momentum-biased nanorings to realize magnetic-free integrated optical isolation. ACS Photon. 1, 198–204 (2014).

  13. 13.

    Estep, N. A., Sounas, D. L., Soric, J. & Alù, A. Magnetic-free non-reciprocity and isolation based on parametrically modulated coupled-resonator loops. Nat. Phys. 10, 923–927 (2014).

  14. 14.

    Reiskarimian, N. & Krishnaswamy, H. Magnetic-free non-reciprocity based on staggered commutation. Nat. Commun. 7, 11217 (2015).

  15. 15.

    Gallo, K., Assanto, G., Parameswaran, K. R. & Fejer, M. M. All-optical diode in a periodically poled lithium niobate waveguide. Appl. Phys. Lett. 79, 314–316 (2001).

  16. 16.

    Zhou, H. et al. All-optical diodes based on photonic crystal molecules consisting of nonlinear defect pairs. J. Appl. Phys. 99, 123111 (2006).

  17. 17.

    Shadrivov, I. V., Fedotov, V. A., Powell, D. A., Kivshar, Y. S. & Zheludev, N. I. Electromagnetic wave analogue of an electronic diode. New. J. Phys. 13, 033025 (2011).

  18. 18.

    Lepri, S. & Casati, G. Asymmetric wave propagation in nonlinear systems. Phys. Rev. Lett. 106, 164101 (2011).

  19. 19.

    Anand, B. et al. Optical diode action from axially asymmetric nonlinearity in an all-carbon solid-state device. Nano. Lett. 13, 5771–5776 (2013).

  20. 20.

    Peng, B. et al. Parity–time-symmetric whispering-gallery microcavities. Nat. Phys. 10, 394–398 (2014).

  21. 21.

    Lin, X.-S., Yan, J.-H., Wu, L.-J. & Lan, S. High transmission contrast for single resonator based all-optical diodes with pump-assisting. Opt. Express 16, 20949–20954 (2008).

  22. 22.

    Manipatruni, S., Robinson, J. T. & Lipson, M. Optical nonreciprocity in optomechanical structures. Phys. Rev. Lett. 102, 213903 (2009).

  23. 23.

    Miroshnichenko, A. E., Brasselet, E. & Kivshar, Y. S. Reversible optical nonreciprocity in periodic structures with liquid crystals. Appl. Phys. Lett. 96, 063302 (2010).

  24. 24.

    Roy, D. Few-photon optical diode. Phys. Rev. B 81, 155117 (2010).

  25. 25.

    Zhukovsky, S. V. & Smirnov, A. G. All-optical diode action in asymmetric nonlinear photonic multilayers with perfect transmission resonances. Phys. Rev. A 83, 023818 (2011).

  26. 26.

    Aleahmad, P., Khajavikhan, M., Christodoulides, D. & LiKamWa, P. Garnet-free optical circulators monolithically integrated on spatially modified iii–v quantum wells. Preprint at (2016).

  27. 27.

    Fan, L. et al. An all-silicon passive optical diode. Science 335, 447–450 (2012).

  28. 28.

    Fan, L. et al. Silicon optical diode with 40 dB nonreciprocal transmission. Opt. Lett. 38, 1259–1261 (2013).

  29. 29.

    Xu, Y. & Miroshnichenko, A. E. Reconfigurable nonreciprocity with a nonlinear Fano diode. Phys. Rev. B 89, 134306 (2014).

  30. 30.

    Yu, Y. et al. Nonreciprocal transmission in a nonlinear photonic-crystal Fano structure with broken symmetry. Laser Photon. Rev. 9, 241–247 (2015).

  31. 31.

    Mahmoud, A. M., Davoyan, A. R. & Engheta, N. All-passive nonreciprocal metastructure. Nat. Commun. 6, 8359 (2015).

  32. 32.

    Ding, W., Luk’yanchuk, B. & Qiu, C.-W. Ultrahigh-contrast-ratio silicon Fano diode. Phys. Rev. A 85, 025806 (2012).

  33. 33.

    Shi, Y., Yu, Z. & Fan, S. Limitations of nonlinear optical isolators due to dynamic reciprocity. Nat. Photon. 9, 388–392 (2015).

  34. 34.

    Sounas, D. L. & Alù, A. Time-reversal symmetry bounds on the electromagnetic response of asymmetric structures. Phys. Rev. Lett. 118, 154302 (2017).

  35. 35.

    Grigoriev, V. & Biancalana, F. Nonreciprocal switching thresholds in coupled nonlinear microcavities. Opt. Lett. 36, 2131–2133 (2011).

  36. 36.

    Little, B. E., Chu, S. T., Haus, H. A., Foresi, J. & Laine, J.-P. Microring resonator channel dropping filters. J. Lightwave Technol. 15, 998–1005 (1997).

  37. 37.

    Haus, H. A. Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, NJ, 1984).

  38. 38.

    Suh, W., Wang, Z. & Fan, S. Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities. IEEE J. Quantum Electron. 40, 1511 (2004).

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This work was supported by the Air Force Office of Scientific Research with grant No. FA9550-17-1-0002, the Simons Foundation and the National Science Foundation.

Author information


  1. Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, TX, USA

    • Dimitrios L. Sounas
    • , Jason Soric
    •  & Andrea Alù
  2. Advanced Science Research Center, City University of New York, New York, NY, USA

    • Andrea Alù


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All authors contributed equally to this work, including development of the concept, design and execution of the experiment, and manuscript preparation.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Andrea Alù.

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    Supplementary Figure 1 and Supplementary Tables 1–3.

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