Non-reciprocal transmission of microwave acoustic waves in nonlinear parity–time symmetric resonators


Acoustic waves are versatile on-chip information carriers that can be used in applications such as microwave filters and transducers. Nonreciprocal devices, in which the transmission of waves is non-symmetric between two ports, are desirable for the manipulation and routing of phonons, but building acoustic non-reciprocal devices is difficult because acoustic systems typically have a linear response. Here, we report non-reciprocal transmission of microwave surface acoustic waves using a nonlinear parity–time symmetric system based on two coupled acoustic resonators in a lithium niobate platform. Owing to the strong piezoelectricity of lithium niobate, we can tune the gain, loss and nonlinearity of the system using electric circuitry. Our approach can achieve 10 dB of non-reciprocal transmission for surface acoustic waves at a frequency of 200 MHz, and we use it to demonstrate a one-way circulation of acoustic waves in cascading non-reciprocal devices.

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Fig. 1: Non-reciprocal SAW transmission using nonlinear PT-symmetric resonators.
Fig. 2: Characterization of SAW gain and nonlinearity.
Fig. 3: SAW transmission of the nonlinear PT-symmetric resonators.
Fig. 4: One-way circulation of SAWs.

Data availability

Source data are available for the graphs plotted in Figs. 14 and Extended Data Fig. 2. All other data and findings of this study are available from the corresponding author upon reasonable request.


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We thank S. Bogdanovic, M. Yu, M. Zhang, C. Chia, B. Machielse and Y.-F. Xiao for fruitful discussions. This work is supported by the STC Center for Integrated Quantum Materials, NSF grant no. DMR-1231319, NSF CQIS grant no. ECCS-1810233, ONR MURI grant no. N00014-15-1-2761 and AFOSR MURI grant no. FA9550-14-1-0389. N.S. acknowledges support by the Natural Sciences and Engineering Research Council of Canada (NSERC), the AQT Intelligent Quantum Networks and Technologies (INQNET) research programme and the DOE/HEP QuantISED programme grant and QCCFP (Quantum Communication Channels for Fundamental Physics) award no. DE-SC0019219. W.M. acknowledges support from the undergraduate overseas internship programme of Nankai University supported by the National Science Fund for Talent Training in the Basic Sciences, grant no. J1103208. This work was performed in part at the Center for Nanoscale Systems (CNS), Harvard University.

Author information




L.S. conceptualized, designed, fabricated and measured the devices. W.M. and Y.H. analysed the system theoretically, with discussion from other authors. W.M. and L.S. performed numerical simulations. All authors analysed and interpreted the results. L.S. and W.M. prepared the manuscript with contributions from all authors. M.L. and L.Y. supervised the project.

Corresponding authors

Correspondence to Linbo Shao or Marko Lončar.

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Competing interests

M.L. is involved in developing lithium niobate technologies at HyperLight Corporation. The other authors declare no competing interests.

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Extended data

Extended Data Fig. 1 Photo of the printed circuit board (PCB) used for non-reciprocal SAW device measurements.

This PCB supports simultaneous measurements of two devices. Signal from Port 1 to Port 2 is defined as the forward direction.

Extended Data Fig. 2 Measured non-reciprocity of the broken-PT-symmetric SAW resonators versus various input powers.

The non-reciprocity is defined in Equ. (1). Source data

Supplementary information

Supplementary Information

Supplementary Notes 1–5 and Figs. 1–12.

Source data

Source Data Fig. 1

Source data of the plots.

Source Data Fig. 2

Source data of the plots.

Source Data Fig. 3

Source data of the plots.

Source Data Fig. 4

Source data of the plots.

Source Data Extended Data Fig. 2

Source data of the plots.

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Shao, L., Mao, W., Maity, S. et al. Non-reciprocal transmission of microwave acoustic waves in nonlinear parity–time symmetric resonators. Nat Electron 3, 267–272 (2020).

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