In this article, we report a vector-network-analyzer-free and real-time LC wireless capacitance readout system based on perturbed nonlinear parity-time (PT) symmetry. The system is composed of two inductively coupled reader-sensor parallel RLC resonators with gain and loss, respectively. By searching for the real mode that requires the minimum saturation gain, the steady-state frequency evolution as a function of the sensor capacitance perturbation is analytically deduced. The proposed system can work in different modes by setting different perturbation points. In particular, at the exceptional point of PT symmetry, the system exhibits high sensitivity. Experimental demonstrations revealed the viability of the proposed readout mechanism by measuring the steady-state frequency of the reader resonator in response to the change of trimmer capacitor on the sensor side. Our findings could impact many emerging applications such as implantable medical device for health monitoring, parameter detection in harsh environment, sealed food packages, etc.
References
1.
C. M.
Bender
and S.
Boettcher
, “Real spectra in non-Hermitian Hamiltonians having PT symmetry
,” Phys. Rev. Lett.
80
, 5243
(1998
).2.
C. M.
Bender
, D. C.
Brody
, and H. F.
Jones
, “Complex extension of quantum mechanics
,” Phys. Rev. Lett.
89
, 270401
(2002
).3.
C. M.
Bender
, “Making sense of non-Hermitian Hamiltonians
,” Rep. Prog. Phys.
70
, 947
(2007
).4.
K.
Makris
, R.
El-Ganainy
, D.
Christodoulides
, and Z. H.
Musslimani
, “Beam dynamics in PT symmetric optical lattices
,” Phys. Rev. Lett.
100
, 103904
(2008
).5.
A.
Guo
, G.
Salamo
, D.
Duchesne
, R.
Morandotti
, M.
Volatier-Ravat
, V.
Aimez
, G.
Siviloglou
, and D.
Christodoulides
, “Observation of PT-symmetry breaking in complex optical potentials
,” Phys. Rev. Lett.
103
, 093902
(2009
).6.
C. E.
Rüter
, K. G.
Makris
, R.
El-Ganainy
, D. N.
Christodoulides
, M.
Segev
, and D.
Kip
, “Observation of parity-time symmetry in optics
,” Nat. Phys.
6
, 192
(2010
).7.
X.-Y.
Zhu
, Y.-L.
Xu
, Y.
Zou
, X.-C.
Sun
, C.
He
, M.-H.
Lu
, X.-P.
Liu
, and Y.-F.
Chen
, “Asymmetric diffraction based on a passive parity-time grating
,” Appl. Phys. Lett.
109
, 111101
(2016
).8.
J.
Schindler
, A.
Li
, M. C.
Zheng
, F. M.
Ellis
, and T.
Kottos
, “Experimental study of active LRC circuits with PT symmetries
,” Phys. Rev. A
84
, 040101
(2011
).9.
Z.
Lin
, J.
Schindler
, F. M.
Ellis
, and T.
Kottos
, “Experimental observation of the dual behavior of PT-symmetric scattering
,” Phys. Rev. A
85
, 050101
(2012
).10.
J.
Schindler
, Z.
Lin
, J.
Lee
, H.
Ramezani
, F. M.
Ellis
, and T.
Kottos
, “PT-symmetric electronics
,” J. Phys. A
45
, 444029
(2012
).11.
N.
Bender
, S.
Factor
, J. D.
Bodyfelt
, H.
Ramezani
, D. N.
Christodoulides
, F. M.
Ellis
, and T.
Kottos
, “Observation of asymmetric transport in structures with active nonlinearities
,” Phys. Rev. Lett.
110
, 234101
(2013
).12.
S.
Assawaworrarit
, X.
Yu
, and S.
Fan
, “Robust wireless power transfer using a nonlinear parity–time-symmetric circuit
,” Nature
546
, 387
(2017
).13.
Y.
Choi
, C.
Hahn
, J. W.
Yoon
, and S. H.
Song
, “Observation of an anti-PT-symmetric exceptional point and energy-difference conserving dynamics in electrical circuit resonators
,” Nat. Commun.
9
, 2182
(2018
).14.
P.-Y.
Chen
, M.
Sakhdari
, M.
Hajizadegan
, Q.
Cui
, M. M.-C.
Cheng
, R.
El-Ganainy
, and A.
Alù
, “Generalized parity-time symmetry condition for enhanced sensor telemetry
,” Nat. Electron.
1
, 297
(2018
).15.
M.
Sakhdari
, M.
Hajizadegan
, Y.
Li
, M. M.-C.
Cheng
, J. C.
Hung
, and P.-Y.
Chen
, “Ultrasensitive, parity-time-symmetric wireless reactive and resistive sensors
,” IEEE Sens. J.
18
, 9548
–9555
(2018
).16.
S.
Bittner
, B.
Dietz
, U.
Günther
, H.
Harney
, M.
Miski-Oglu
, A.
Richter
, and F.
Schäfer
, “PT symmetry and spontaneous symmetry breaking in a microwave billiard
,” Phys. Rev. Lett.
108
, 024101
(2012
).17.
Y.
Yu
, W.
Song
, C.
Chen
, T.
Chen
, H.
Ye
, X.
Shen
, Q.
Cheng
, and T.
Li
, “Phase transition of non-Hermitian topological edge states in microwave regime
,” Appl. Phys. Lett.
116
, 211104
(2020
).18.
X.
Zhu
, H.
Ramezani
, C.
Shi
, J.
Zhu
, and X.
Zhang
, “PT-symmetric acoustics
,” Phys. Rev. X
4
, 031042
(2014
).19.
R.
Fleury
, D.
Sounas
, and A.
Alù
, “An invisible acoustic sensor based on parity-time symmetry
,” Nat. Commun.
6
, 5905
(2015
).20.
B.-I.
Popa
and S. A.
Cummer
, “Non-reciprocal and highly nonlinear active acoustic metamaterials
,” Nat. Commun.
5
, 3398
(2014
).21.
Y.
Duan
, Y.
Chang
, J.
Liang
, H.
Zhang
, X.
Duan
, H.
Zhang
, W.
Pang
, and M.
Zhang
, “Wireless gas sensing based on a passive piezoelectric resonant sensor array through near-field induction
,” Appl. Phys. Lett.
109
, 263503
(2016
).22.
C. M.
Boutry
, L.
Beker
, Y.
Kaizawa
, C.
Vassos
, H.
Tran
, A. C.
Hinckley
, R.
Pfattner
, S.
Niu
, J.
Li
, J.
Claverie
et al., “Biodegradable and flexible arterial-pulse sensor for the wireless monitoring of blood flow
,” Nat. Biomed. Eng.
3
, 47
–57
(2019
).23.
Y.
Liang
, M.
Ma
, F.
Zhang
, F.
Liu
, Z.
Liu
, D.
Wang
, and Y.
Li
, “An LC wireless microfluidic sensor based on low temperature co-fired ceramic (LTCC) technology
,” Sensors
19
, 1189
(2019
).24.
X.-X.
Li
and Y.-T.
Fang
, “Sensing gas through coupling effect of quasi-PT-symmetry resonators
,” J. Instrum.
14
, P02010
(2019
).25.
M.
Hajizadegan
, M.
Sakhdari
, S.
Liao
, and P.-Y.
Chen
, “High-sensitivity wireless displacement sensing enabled by PT-symmetric telemetry
,” IEEE Trans. Antennas Propag.
67
, 3445
–3449
(2019
).26.
B. B.
Zhou
, W. J.
Deng
, L. F.
Wang
, L.
Dong
, and Q. A.
Huang
, “Enhancing the remote distance of LC passive wireless sensors by parity-time symmetry breaking
,” Phys. Rev. Appl.
13
, 064022
(2020
).27.
B.-B.
Zhou
, L.-F.
Wang
, L.
Dong
, and Q.-A.
Huang
, “Observation of the perturbed eigenvalues of PT-symmetric LC resonator systems
,” J. Phys. Commun.
5
, 045010
(2021
).28.
M.
Yang
, Z.
Ye
, M.
Farhat
, and P.-Y.
Chen
, “Enhanced radio-frequency sensors based on a self-dual emitter-absorber
,” Phys. Rev. Appl.
15
, 014026
(2021
).29.
M.
Farhat
, M.
Yang
, Z.
Ye
, and P.-Y.
Chen
, “PT-symmetric absorber-laser enables electromagnetic sensors with unprecedented sensitivity
,” ACS Photonics
7
, 2080
–2088
(2020
).30.
M. A.
Carvajal
, P.
Escobedo
, A.
Martinez-Olmos
, and A. J.
Palma
, “Readout circuit with improved sensitivity for contactless LC sensing tags
,” IEEE Sens. J.
20
, 885
–891
(2020
).31.
S.
Niu
, N.
Matsuhisa
, L.
Beker
, J.
Li
, S.
Wang
, J.
Wang
, Y.
Jiang
, X.
Yan
, Y.
Yun
, W.
Burnett
et al., “A wireless body area sensor network based on stretchable passive tags
,” Nat. Electron.
2
, 361
–368
(2019
).32.
Z.
Dong
, Z.
Li
, F.
Yang
, C.-W.
Qiu
, and J. S.
Ho
, “Sensitive readout of implantable microsensors using a wireless system locked to an exceptional point
,” Nat. Electron.
2
, 335
–342
(2019
).33.
S.
Kananian
, G.
Alexopoulos
, and A. S.
Poon
, “Coupling-independent real-time wireless resistive sensing through nonlinear PT symmetry
,” Phys. Rev. Appl.
14
, 064072
(2020
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
2022
Author(s)
You do not currently have access to this content.
