Abstract

A noteworthy challenge in actual wireless sensors is the intrinsic sensing resolution and the sensitivity associated with the response to external perturbation to be measured. To address the issue, we report the realization of enhanced sensitivity in a passive wireless sensing system, consisting of three coupled passive resonators. The input wave is exploited as an effective gain in our open system, thus the ideal parity-time (PT) symmetry can be established, rather than balancing real gain and loss. Then the third-order exceptional points are obtained in ternary PT symmetric systems. With the extrinsic perturbation imposed on any one of resonators, we demonstrate analytically and experimentally that the resonance response of the system follows the cube-root dependence on perturbation. Making use of the effective gain, our results pave a new way, to the best of our knowledge, to realize the ultra-sensitivity of a passive wireless sensing system.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
  3. M. Nabipoor and B. Y. Majlis, “A new passive telemetry LC pressure and temperature sensor optimized for TPMS,” J. Phys.: Conf. Ser. 34, 770–775 (2006).
    [Crossref]
  4. M. A. Fonseca, J. M. English, M. von Arx, and M. G. Allen, “Wireless micromachined ceramic pressure sensor for high-temperature applications,” J. Microelectromech. Syst. 11(4), 337–343 (2002).
    [Crossref]
  5. C. C. Collins, “Miniature passive pressure transensor for implanting in the eye,” IEEE Trans. Biomed. Eng. BME-14(2), 74–83 (1967).
    [Crossref]
  6. L. Y. Chen, B. C.-K. Tee, A. L. Chortos, G. Schwartz, V. Tse, D. J. Lipomi, H.-S. P. Wong, M. V. McConnell, and Z. Bao, “Continuous wireless pressure monitoring and mapping with ultra-small passive sensors for health monitoring and critical care,” Nat. Commun. 5(1), 5028 (2014).
    [Crossref]
  7. S.-Y. Wu and W. Hsu, “Design and characterization of LC strain sensors with novel inductor for sensitivity enhancement,” Smart Mater. Struct. 22(10), 105015 (2013).
    [Crossref]
  8. C. Li, Q. Tan, W. Zhang, C. Xue, and J. Xiong, “An embedded passive resonant sensor using frequency diversity technology for high-temperature wireless measurement,” IEEE Sens. J. 15(2), 1055–1060 (2015).
    [Crossref]
  9. M.-Z. Xie, L.-F. Wang, L. Dong, W.-J. Deng, and Q.-A. Huang, “Low cost paper-based LC wireless humidity sensors and distance-insensitive readout system,” IEEE Sens. J. 19(12), 4717–4725 (2019).
    [Crossref]
  10. S. Bhadra, D. J. Thomson, and G. E. Bridges, “Monitoring acidic and basic volatile concentration using a pH-electrode based wireless passive sensor,” Sens. Actuators, B 209, 803–810 (2015).
    [Crossref]
  11. 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(26), 263503 (2016).
    [Crossref]
  12. 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(5), 297–304 (2018).
    [Crossref]
  13. P.-Y. Chen and R. El-Ganainy, “Exceptional points enhance wireless readout,” Nat. Electron. 2(8), 323–324 (2019).
    [Crossref]
  14. 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(8), 335–342 (2019).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  24. K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100(10), 103904 (2008).
    [Crossref]
  25. S. Klaiman, U. Günther, and N. Moiseyev, “Visualization of branch points in PT-symmetric waveguides,” Phys. Rev. Lett. 101(8), 080402 (2008).
    [Crossref]
  26. 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(3), 192–195 (2010).
    [Crossref]
  27. Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106(21), 213901 (2011).
    [Crossref]
  28. A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488(7410), 167–171 (2012).
    [Crossref]
  29. L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12(2), 108–113 (2013).
    [Crossref]
  30. H. Hodaei, M.-A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Parity-time-symmetric microring lasers,” Science 346(6212), 975–978 (2014).
    [Crossref]
  31. L. Feng, Z. J. Wong, R.-M. Ma, Y. Wang, and X. Zhang, “Single-mode laser by parity-time symmetry breaking,” Science 346(6212), 972–975 (2014).
    [Crossref]
  32. B. Peng, Ş. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346(6207), 328–332 (2014).
    [Crossref]
  33. J. Doppler, A. A. Mailybaev, J. Böhm, U. Kuhl, A. Girschik, F. Libisch, T. J. Milburn, P. Rabl, N. Moiseyev, and S. Rotter, “Dynamically encircling an exceptional point for asymmetric mode switching,” Nature 537(7618), 76–79 (2016).
    [Crossref]
  34. H. Xu, D. Mason, L. Jiang, and J. G. E. Harris, “Topological energy transfer in an optomechanical system with exceptional points,” Nature 537(7618), 80–83 (2016).
    [Crossref]
  35. X. P. Zhou, S. K. Gupta, Z. Huang, Z. D. Yan, P. Zhan, Z. Chen, M. H. Lu, and Z. L. Wang, “Optical lattices with higher-order exceptional points by non-Hermitian coupling,” Appl. Phys. Lett. 113(10), 101108 (2018).
    [Crossref]
  36. Y. Sun, W. Tan, H.-Q. Li, J. Li, and H. Chen, “Experimental demonstration of a coherent perfect absorber with PT phase transition,” Phys. Rev. Lett. 112(14), 143903 (2014).
    [Crossref]
  37. B. Jin, W. Tan, C. Zhang, J. Wu, J. Chen, S. Zhang, and P. Wu, “High-performance terahertz sensing at exceptional points in a bilayer structure,” Adv. Theory Simul. 1(9), 1800070 (2018).
    [Crossref]
  38. A. Kurs, A. Karalis, R. Moffatt, J. D. Joannopoulos, P. Fisher, and M. Soljačić, “Wireless Power Transfer via Strongly Coupled Magnetic Resonances,” Science 317(5834), 83–86 (2007).
    [Crossref]
  39. S. Assawaworrarit, X. Yu, and S. Fan, “Robust wireless power transfer using a nonlinear parity-time-symmetric circuit,” Nature 546(7658), 387–390 (2017).
    [Crossref]
  40. Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent Perfect Absorbers: Time-Reversed Lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
    [Crossref]
  41. S. Longhi, “PT-symmetric laser absorber,” Phys. Rev. A 82(3), 031801 (2010).
    [Crossref]
  42. Y. D. Chong, L. Ge, and A. D. Stone, “PT-Symmetry Breaking and Laser-Absorber Modes in Optical Scattering Systems,” Phys. Rev. Lett. 106(9), 093902 (2011).
    [Crossref]
  43. K. Ding, G. Ma, Z. Q. Zhang, and C. T. Chan, “Experimental Demonstration of an Anisotropic Exceptional Point,” Phys. Rev. Lett. 121(8), 085702 (2018).
    [Crossref]
  44. S. Wang, B. Hou, W. Lu, Y. Chen, Z. Q. Zhang, and C. T. Chan, “Arbitrary order exceptional point induced by photonic spin-orbit interaction in coupled resonators,” Nat. Commun. 10(1), 832 (2019).
    [Crossref]

2019 (5)

M.-Z. Xie, L.-F. Wang, L. Dong, W.-J. Deng, and Q.-A. Huang, “Low cost paper-based LC wireless humidity sensors and distance-insensitive readout system,” IEEE Sens. J. 19(12), 4717–4725 (2019).
[Crossref]

P.-Y. Chen and R. El-Ganainy, “Exceptional points enhance wireless readout,” Nat. Electron. 2(8), 323–324 (2019).
[Crossref]

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(8), 335–342 (2019).
[Crossref]

Ş. K. Özdemir, S. Rotter, F. Nori, and L. Yang, “parity-time symmetry and exceptional points in photonics,” Nat. Mater. 18(8), 783–798 (2019).
[Crossref]

S. Wang, B. Hou, W. Lu, Y. Chen, Z. Q. Zhang, and C. T. Chan, “Arbitrary order exceptional point induced by photonic spin-orbit interaction in coupled resonators,” Nat. Commun. 10(1), 832 (2019).
[Crossref]

2018 (5)

K. Ding, G. Ma, Z. Q. Zhang, and C. T. Chan, “Experimental Demonstration of an Anisotropic Exceptional Point,” Phys. Rev. Lett. 121(8), 085702 (2018).
[Crossref]

B. Jin, W. Tan, C. Zhang, J. Wu, J. Chen, S. Zhang, and P. Wu, “High-performance terahertz sensing at exceptional points in a bilayer structure,” Adv. Theory Simul. 1(9), 1800070 (2018).
[Crossref]

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(5), 297–304 (2018).
[Crossref]

R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, “Non-Hermitian physics and PT symmetry,” Nat. Phys. 14(1), 11–19 (2018).
[Crossref]

X. P. Zhou, S. K. Gupta, Z. Huang, Z. D. Yan, P. Zhan, Z. Chen, M. H. Lu, and Z. L. Wang, “Optical lattices with higher-order exceptional points by non-Hermitian coupling,” Appl. Phys. Lett. 113(10), 101108 (2018).
[Crossref]

2017 (3)

H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Enhanced sensitivity at higher-order exceptional points,” Nature 548(7666), 187–191 (2017).
[Crossref]

W. Chen, ŞK Özdemir, G. Zhao, J. Wiersig, and L. Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature 548(7666), 192–196 (2017).
[Crossref]

S. Assawaworrarit, X. Yu, and S. Fan, “Robust wireless power transfer using a nonlinear parity-time-symmetric circuit,” Nature 546(7658), 387–390 (2017).
[Crossref]

2016 (7)

P.-Y. Chen and J. Jung, “PT-symmetry and singularity-enhanced sensing based on photoexcited graphene metasurfaces,” Phys. Rev. Appl. 5(6), 064018 (2016).
[Crossref]

Z. Lin, A. Pick, M. Lončar, and A. W. Rodriguez, “Enhanced spontaneous emission at third-order Dirac exceptional points in inverse-designed photonic crystals,” Phys. Rev. Lett. 117(10), 107402 (2016).
[Crossref]

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(26), 263503 (2016).
[Crossref]

Q.-A. Huang, L. Dong, and L.-F. Wang, “LC passive wireless sensors toward a wireless sensing platform: status, prospects, and challenges,” J. Microelectromech. Syst. 25(5), 822–841 (2016).
[Crossref]

J. Doppler, A. A. Mailybaev, J. Böhm, U. Kuhl, A. Girschik, F. Libisch, T. J. Milburn, P. Rabl, N. Moiseyev, and S. Rotter, “Dynamically encircling an exceptional point for asymmetric mode switching,” Nature 537(7618), 76–79 (2016).
[Crossref]

H. Xu, D. Mason, L. Jiang, and J. G. E. Harris, “Topological energy transfer in an optomechanical system with exceptional points,” Nature 537(7618), 80–83 (2016).
[Crossref]

K. Ding, G. Ma, M. Xiao, Z. Q. Zhang, and C. T. Chan, “Emergence, Coalescence, and Topological Properties of Multiple Exceptional Points and Their Experimental Realization,” Phys. Rev. X 6(2), 021007 (2016).
[Crossref]

2015 (2)

S. Bhadra, D. J. Thomson, and G. E. Bridges, “Monitoring acidic and basic volatile concentration using a pH-electrode based wireless passive sensor,” Sens. Actuators, B 209, 803–810 (2015).
[Crossref]

C. Li, Q. Tan, W. Zhang, C. Xue, and J. Xiong, “An embedded passive resonant sensor using frequency diversity technology for high-temperature wireless measurement,” IEEE Sens. J. 15(2), 1055–1060 (2015).
[Crossref]

2014 (6)

J. Wiersig, “Enhancing the sensitivity of frequency and energy splitting detection by using exceptional points: application to microcavity sensors for single-particle detection,” Phys. Rev. Lett. 112(20), 203901 (2014).
[Crossref]

L. Y. Chen, B. C.-K. Tee, A. L. Chortos, G. Schwartz, V. Tse, D. J. Lipomi, H.-S. P. Wong, M. V. McConnell, and Z. Bao, “Continuous wireless pressure monitoring and mapping with ultra-small passive sensors for health monitoring and critical care,” Nat. Commun. 5(1), 5028 (2014).
[Crossref]

Y. Sun, W. Tan, H.-Q. Li, J. Li, and H. Chen, “Experimental demonstration of a coherent perfect absorber with PT phase transition,” Phys. Rev. Lett. 112(14), 143903 (2014).
[Crossref]

H. Hodaei, M.-A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Parity-time-symmetric microring lasers,” Science 346(6212), 975–978 (2014).
[Crossref]

L. Feng, Z. J. Wong, R.-M. Ma, Y. Wang, and X. Zhang, “Single-mode laser by parity-time symmetry breaking,” Science 346(6212), 972–975 (2014).
[Crossref]

B. Peng, Ş. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346(6207), 328–332 (2014).
[Crossref]

2013 (2)

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12(2), 108–113 (2013).
[Crossref]

S.-Y. Wu and W. Hsu, “Design and characterization of LC strain sensors with novel inductor for sensitivity enhancement,” Smart Mater. Struct. 22(10), 105015 (2013).
[Crossref]

2012 (1)

A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488(7410), 167–171 (2012).
[Crossref]

2011 (2)

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106(21), 213901 (2011).
[Crossref]

Y. D. Chong, L. Ge, and A. D. Stone, “PT-Symmetry Breaking and Laser-Absorber Modes in Optical Scattering Systems,” Phys. Rev. Lett. 106(9), 093902 (2011).
[Crossref]

2010 (3)

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent Perfect Absorbers: Time-Reversed Lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
[Crossref]

S. Longhi, “PT-symmetric laser absorber,” Phys. Rev. A 82(3), 031801 (2010).
[Crossref]

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(3), 192–195 (2010).
[Crossref]

2009 (1)

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103(9), 093902 (2009).
[Crossref]

2008 (3)

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100(10), 103904 (2008).
[Crossref]

S. Klaiman, U. Günther, and N. Moiseyev, “Visualization of branch points in PT-symmetric waveguides,” Phys. Rev. Lett. 101(8), 080402 (2008).
[Crossref]

P.-J. Chen, D. C. Rodger, S. Saati, M. S. Humayun, and Y.-C. Tai, “Microfabricated implantable parylene-based wireless passive intraocular pressure sensors,” J. Microelectromech. Syst. 17(6), 1342–1351 (2008).
[Crossref]

2007 (1)

A. Kurs, A. Karalis, R. Moffatt, J. D. Joannopoulos, P. Fisher, and M. Soljačić, “Wireless Power Transfer via Strongly Coupled Magnetic Resonances,” Science 317(5834), 83–86 (2007).
[Crossref]

2006 (1)

M. Nabipoor and B. Y. Majlis, “A new passive telemetry LC pressure and temperature sensor optimized for TPMS,” J. Phys.: Conf. Ser. 34, 770–775 (2006).
[Crossref]

2002 (1)

M. A. Fonseca, J. M. English, M. von Arx, and M. G. Allen, “Wireless micromachined ceramic pressure sensor for high-temperature applications,” J. Microelectromech. Syst. 11(4), 337–343 (2002).
[Crossref]

1967 (1)

C. C. Collins, “Miniature passive pressure transensor for implanting in the eye,” IEEE Trans. Biomed. Eng. BME-14(2), 74–83 (1967).
[Crossref]

Aimez, V.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103(9), 093902 (2009).
[Crossref]

Allen, M. G.

M. A. Fonseca, J. M. English, M. von Arx, and M. G. Allen, “Wireless micromachined ceramic pressure sensor for high-temperature applications,” J. Microelectromech. Syst. 11(4), 337–343 (2002).
[Crossref]

Almeida, V. R.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12(2), 108–113 (2013).
[Crossref]

Alù, A.

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(5), 297–304 (2018).
[Crossref]

Assawaworrarit, S.

S. Assawaworrarit, X. Yu, and S. Fan, “Robust wireless power transfer using a nonlinear parity-time-symmetric circuit,” Nature 546(7658), 387–390 (2017).
[Crossref]

Bao, Z.

L. Y. Chen, B. C.-K. Tee, A. L. Chortos, G. Schwartz, V. Tse, D. J. Lipomi, H.-S. P. Wong, M. V. McConnell, and Z. Bao, “Continuous wireless pressure monitoring and mapping with ultra-small passive sensors for health monitoring and critical care,” Nat. Commun. 5(1), 5028 (2014).
[Crossref]

Bender, C. M.

B. Peng, Ş. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346(6207), 328–332 (2014).
[Crossref]

Bersch, C.

A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488(7410), 167–171 (2012).
[Crossref]

Bhadra, S.

S. Bhadra, D. J. Thomson, and G. E. Bridges, “Monitoring acidic and basic volatile concentration using a pH-electrode based wireless passive sensor,” Sens. Actuators, B 209, 803–810 (2015).
[Crossref]

Böhm, J.

J. Doppler, A. A. Mailybaev, J. Böhm, U. Kuhl, A. Girschik, F. Libisch, T. J. Milburn, P. Rabl, N. Moiseyev, and S. Rotter, “Dynamically encircling an exceptional point for asymmetric mode switching,” Nature 537(7618), 76–79 (2016).
[Crossref]

Bridges, G. E.

S. Bhadra, D. J. Thomson, and G. E. Bridges, “Monitoring acidic and basic volatile concentration using a pH-electrode based wireless passive sensor,” Sens. Actuators, B 209, 803–810 (2015).
[Crossref]

Cao, H.

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106(21), 213901 (2011).
[Crossref]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent Perfect Absorbers: Time-Reversed Lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
[Crossref]

Chan, C. T.

S. Wang, B. Hou, W. Lu, Y. Chen, Z. Q. Zhang, and C. T. Chan, “Arbitrary order exceptional point induced by photonic spin-orbit interaction in coupled resonators,” Nat. Commun. 10(1), 832 (2019).
[Crossref]

K. Ding, G. Ma, Z. Q. Zhang, and C. T. Chan, “Experimental Demonstration of an Anisotropic Exceptional Point,” Phys. Rev. Lett. 121(8), 085702 (2018).
[Crossref]

K. Ding, G. Ma, M. Xiao, Z. Q. Zhang, and C. T. Chan, “Emergence, Coalescence, and Topological Properties of Multiple Exceptional Points and Their Experimental Realization,” Phys. Rev. X 6(2), 021007 (2016).
[Crossref]

Chang, Y.

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(26), 263503 (2016).
[Crossref]

Chen, H.

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Figures (5)

Fig. 1.
Fig. 1. (a-b) Schemes and principle illustration of the ternary PT system with extrinsic perturbation $\varepsilon$ imposed on (a) grey and (b) green resonators, respectively. The effective gain, neutral and loss resonators with the same frequency ${\omega _0}$ are shown in red, grey and green spheres, respectively, and $\Gamma $ is the intrinsic loss of each resonator. The green and the red resonators are subjected to the same radiative loss $\gamma$. Coupling strength between the neighboring resonators is denoted by $\kappa$. (c-d) Calculated reflection spectra for the two cases (a) and (b), with different perturbations. Purple, mazarine, skyblue, cyan and claybank lines represent perturbations ${\varepsilon _0} = 0$, ${\varepsilon _0} = 0.001$, ${\varepsilon _0} = 0.01$ and ${\varepsilon _0} = 0.1$, respectively. (e-f) Calculated real (Re) and imaginary (Im) parts of the eigenfrequencies for the two cases (a) and (b) as a function of ${\varepsilon _0}$, respectively. The skyblue, reseda and orange lines in (e)–(f) describe three eigenfrequencies ${\omega _n}$ and ${\omega ^{\prime}_n}$ (n = 1, 2, 3) for the cases of (a)-(b), respectively.
Fig. 2.
Fig. 2. (a) Calculated frequency shifts of reflection dips compared with ${\omega _0}$ as a function of perturbation strength ${\varepsilon _0}$. (b) The results from (a) on a logarithmic coordinate. The blue and green solid lines follow the lines of ${y_1} = {2^{1/3}}\varepsilon _0^{1/3}$ and ${y_2} = \varepsilon _0^{1/3}$, respectively, showing a slope of 1/3. The orange and black solid lines are Re(${\omega _1}$) and Re(${\omega ^{\prime}_1}$) from Figs. 1(e)–(f), respectively. The orange and black marks denote the dip frequency shift due to perturbation operated on the grey and green spheres, respectively.
Fig. 3.
Fig. 3. (a)-(b) Schematics of PT symmetric passive wireless sensing system based on three resonant coils (transmitter, relay and receiver coils), where Γ is the intrinsic loss rate of the resonant coil, and $\varepsilon$ is the extrinsic perturbation imposed on the relay (a) and the receiver (b) coils, respectively. (c) Photograph of our sample.
Fig. 4.
Fig. 4. (a) Reflection spectra of a single passive resonant coil with different perturbations. (b) Resonance frequency shifts of the passive resonant coil compared with f0 as a function of capacitance C1. (c-d) Reflection spectra with different perturbations imposed on (c) relay and (d) receiver coils, respectively. The solid and dashed lines denote experimental data and theoretical results, respectively. (e-f) Calculated real parts of the eigenfrequencies. The skyblue and orange lines in (e) donate describe three eigenfrequencies ${f_n}$ and ${f^{\prime}_n}$ (n = 1, 2, 3) for the cases of Figs. 3(a)–(b), respectively.
Fig. 5.
Fig. 5. (a) Experimental frequency shifts of reflection dips compared with ${f_0}$ of the PT symmetry wireless sensor system as a function of perturbations strength $\varepsilon$. (b) The results from (a) on a logarithmic coordinate. The blue and green solid lines show a slope of 1/3, follow the lines of ${y_3} = {2^{1/3}}{\kappa ^{2/3}}{\varepsilon ^{1/3}}$ and ${y_4} = {2^{1/3}}{\varepsilon ^{1/3}}$, respectively. The orange and black solid lines are Re(${f_1}$) and Re(${f_1}^\prime$) from Figs. 4(e)–(f), respectively. (c) Experimental sensitivity enhancement factor as a function of the strength of perturbations. Orange and black marks denote perturbation imposed on relay and receiver coils, respectively.

Equations (11)

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d a 1 d t = ( i ω 0 γ Γ ) a 1 i κ a 2 + 2 γ s 1 + d a 2 d t = ( i ω 0 Γ ) a 2 i κ a 1 i κ a 3 d a 3 d t = ( i ω 0 γ Γ ) a 3 i κ a 2 ,
s 1 = s 1 + + 2 γ a 1 .
H ( a 1 a 2 a 3 ) = ω ( a 1 a 2 a 3 ) ,
H = ( ω 0 + i γ i Γ κ 0 κ ω 0 i Γ κ 0 κ ω 0 i γ i Γ ) .
Δ ( Δ 2 2 κ 2 + γ 2 ) = 0.
d a 1 d t = ( i ω 0 γ Γ ) a 1 i κ a 2 + 2 γ s 1 + d a 2 d t = ( i ω 0 i ε Γ ) a 2 i κ a 1 i κ a 3 d a 3 d t = ( i ω 0 γ Γ ) a 3 i κ a 2 ,
d a 1 d t = ( i ω 0 γ Γ ) a 1 i κ a 2 + 2 γ s 1 + d a 2 d t = ( i ω 0 Γ ) a 2 i κ a 1 i κ a 3 d a 3 d t = ( i ω 0 γ Γ i ε ) a 3 i κ a 2 ,
H = ( ω 0 + i γ i Γ κ 0 κ ω 0 + ε i Γ κ 0 κ ω 0 i γ i Γ ) ,
H = ( ω 0 + i γ i Γ κ 0 κ ω 0 i Γ κ 0 κ ω 0 + ε i γ i Γ ) ,
R = | s 1 s 1 + | .
f = 1 2 π L ( C 0 + C 1 ) ,

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