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Generalized parity–time symmetry condition for enhanced sensor telemetry

A Publisher Correction to this article was published on 24 May 2018

This article has been updated


Wireless sensors based on micromachined tunable resonators are important in a variety of applications, ranging from medical diagnosis to industrial and environmental monitoring. The sensitivity of these devices is, however, often limited by their low quality (Q) factor. Here, we introduce the concept of isospectral party–time–reciprocal scaling (PTX) symmetry and show that it can be used to build a new family of radiofrequency wireless microsensors exhibiting ultrasensitive responses and ultrahigh resolution, which are well beyond the limitations of conventional passive sensors. We show theoretically, and demonstrate experimentally using microelectromechanical-based wireless pressure sensors, that PTX-symmetric electronic systems share the same eigenfrequencies as their parity–time (PT)-symmetric counterparts, but crucially have different circuit profiles and eigenmodes. This simplifies the electronic circuit design and enables further enhancements to the extrinsic Q-factor of the sensors.

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Fig. 1: Non-Hermitian telemetric sensor system.
Fig. 2: MEMS-based wireless pressure sensor.
Fig. 3: Evolution of eigenfrequencies and reflection spectra as a function of the non-Hermiticity parameter γ and coupling strength κ.
Fig. 4: Pressure-induced spectral changes for conventional and PT-symmetric telemetric sensors.
Fig. 5: Evolution of the eigenfrequencies and reflection spectra for PTX-symmetric telemetric sensors.

Change history

  • 24 May 2018

    In the version of this Article originally published, a division symbol was mistakenly omitted from both of the y axis labels in Fig. 5a. The label in the left panel should have read ‘Re((ω×ω0)/2π) (MHz)’ and the label in the right panel should have read ‘Im((ω×ω0)/2π) (MHz)’. This has now been corrected.


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This work has been supported by the NSF ECCS grant no. 1711409 (to P.-Y.C.), the Air Force Office of Scientific Research, the Welch Foundation with grant no. F-1802 (to A.A.) and the Army Research Office (ARO) grant no. W911NF-17-1-0481 (to R.E.-G.). Device fabrication was carried out in the Nano Fabrication Service Core (nFab) at the Wayne State University.

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Authors and Affiliations



M.S., M.H. and Q.C. designed the PT and PTX circuits and performed experimental measurements. M.S., M.H., Q.C. and M.C. designed and fabricated the MEMS pressure sensor. P.-Y.C., M.S. and M.C. conceived the experimental concepts. P.-Y.C., M.C., R.E.-G. and A.A. developed the concepts. P.-Y.C. and A.A. planned and directed the research. P.-Y.C., R.E.G. and A.A. wrote the manuscript.

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Correspondence to Pai-Yen Chen or Andrea Alù.

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Supplementary Notes 1–3 and Supplementary Figures 1–10

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Chen, PY., Sakhdari, M., Hajizadegan, M. et al. Generalized parity–time symmetry condition for enhanced sensor telemetry. Nat Electron 1, 297–304 (2018).

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