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Broadband passive isolators based on coupled nonlinear resonances

Nature Electronics volume 1, pages 113–119 (2018)Cite this article

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Abstract

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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Fig. 1: Nonlinear isolator based on a single nonlinear resonator.
Fig. 2: Nonlinear isolator based on a nonlinear Lorentzian resonator and a nonlinear Fano resonator.
Fig. 3: Nonlinear isolator based on multiple nonlinear resonators.
Fig. 4: Microwave realization of a Lorentzian–Fano nonlinear isolator.

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References

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

    Google Scholar 

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

    Article  Google Scholar 

  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).

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  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).

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

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

    Article  Google Scholar 

  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).

    Article  Google Scholar 

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

    Article  Google Scholar 

  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).

    Article  Google Scholar 

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

    Article  Google Scholar 

  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).

    Article  Google Scholar 

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

    Article  Google Scholar 

  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).

    Article  Google Scholar 

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

    Article  Google Scholar 

  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).

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  26. Aleahmad, P., Khajavikhan, M., Christodoulides, D. & LiKamWa, P. Garnet-free optical circulators monolithically integrated on spatially modified iii–v quantum wells. Preprint at https://arxiv.org/abs/1606.06949 (2016).

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  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).

    Article  Google Scholar 

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

    Google Scholar 

  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).

    Article  Google Scholar 

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Acknowledgements

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.

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Authors and Affiliations

  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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  1. Dimitrios L. Sounas
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  2. Jason Soric
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  3. 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.

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Correspondence to Andrea Alù.

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Supplementary Figure 1 and Supplementary Tables 1–3.

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Sounas, D.L., Soric, J. & Alù, A. Broadband passive isolators based on coupled nonlinear resonances. Nat Electron 1, 113–119 (2018). https://doi.org/10.1038/s41928-018-0025-0

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