Abstract

A rotation sensing mechanism based on higher-order exceptional points in parity-time-symmetric ternary-coupled microresonators is proposed. Due to the properties of third-order exceptional points, rotation-induced frequency splitting is proportional to the cube root of the rotation rate. Moreover, the sensitivity of the proposed rotation sensing mechanism is improved by at least 1 order of magnitude compared with the parity-time-symmetric binary ring rotation sensing mechanism. This kind of sensing mechanism makes on-chip ultrasensitive rotation sensing possible.

© 2019 Optical Society of America

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2019 (1)

H. Zhang, W. Li, P. Han, X. Chang, J. Liu, A. Huang, and Z. Xiao, “Mode broadening induced by rotation rate in an atom assisted microresonator,” J. Appl. Phys. 125, 084502 (2019).
[Crossref]

2018 (2)

M. De Carlo, F. De Leonardis, and V. M. Passaro, “Design rules of a microscale PT-symmetric optical gyroscope using group IV platform,” J. Lightwave Technol. 36, 3261–3268 (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, 11–19 (2018).
[Crossref]

2017 (7)

J. Ren, H. Hodaei, G. Harari, A. U. Hassan, W. Chow, M. Soltani, D. Christodoulides, and M. Khajavikhan, “Ultrasensitive micro-scale parity-time-symmetric ring laser gyroscope,” Opt. Lett. 42, 1556–1559 (2017).
[Crossref]

H. Jing, Ş. K. Özdemir, H. Lü, and F. Nori, “High-order exceptional points in optomechanics,” Sci. Rep. 7, 3386 (2017).
[Crossref]

M. Y. Nada, M. A. K. Othman, and F. Capolino, “Theory of coupled resonator optical waveguides exhibiting high-order exceptional points of degeneracy,” Phys. Rev. B 96, 184304 (2017).
[Crossref]

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, 187–191 (2017).
[Crossref]

S. Sunada, “Large Sagnac frequency splitting in a ring resonator operating at an exceptional point,” Phys. Rev. A 96, 033842 (2017).
[Crossref]

W. Li, H. Zhang, J. Liu, J. Lin, X. Xue, X. Zhang, X. Xu, A. Huang, and Z. Xiao, “On-chip high-sensitivity temperature sensor based on gain-loss coupled microresonators,” J. Opt. Soc. Am. B 34, 1765–1770 (2017).
[Crossref]

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

2016 (5)

C. Ciminelli, D. D’Agostino, G. Carnicella, F. Dell’Olio, D. Conteduca, H. P. M. M. Ambrosius, M. K. Smit, and M. N. Armenise, “A high-Q InP resonant angular velocity sensor for a monolithically integrated optical gyroscope,” IEEE Photon. J. 8, 1–19 (2016).
[Crossref]

H. Zhang, J. Chen, J. Jin, J. Lin, L. Zhao, Z. Bi, A. Huang, and Z. Xiao, “On-chip modulation for rotating sensing of gyroscope based on ring resonator coupled with Mach-Zehnder interferometer,” Sci. Rep. 6, 19024 (2016).
[Crossref]

J. Wiersig, “Sensors operating at exceptional points: general theory,” Phys. Rev. A 93, 033809 (2016).
[Crossref]

Z. P. Liu, J. Zhang, Ş. K. Özdemir, B. Peng, H. Jing, X. Y. Lü, C. W. Li, L. Yang, F. Nori, and Y. X. Liu, “Metrology with PT-symmetric cavities: enhanced sensitivity near the PT-phase transition,” Phys. Rev. Lett. 117, 110802 (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, 107402 (2016).
[Crossref]

2015 (1)

R. Sarma, L. Ge, J. Wiersig, and H. Cao, “Rotating optical microcavities with broken chiral symmetry,” Phys. Rev. Lett. 114, 053903 (2015).
[Crossref]

2014 (4)

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

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

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, 203901 (2014).
[Crossref]

L. Chang, X. Jiang, S. Hua, C. Yang, J. Wen, L. Jiang, G. Li, G. Wang, and M. Xiao, “Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators,” Nat. Photonics. 8, 524–529 (2014).
[Crossref]

2012 (1)

J. W. Ryu, S. Y. Lee, and S. W. Kim, “Analysis of multiple exceptional points related to three interacting eigenmodes in a non-Hermitian Hamiltonian,” Phys. Rev. A 85, 042101 (2012).
[Crossref]

2011 (2)

T. Lu, H. Lee, T. Chen, S. Herchak, J. H. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. USA 108, 5976–5979 (2011).
[Crossref]

L. Jiang, J. Yang, S. Wang, B. Li, and M. Wang, “Fiber Mach–Zehnder interferometer based on microcavities for high-temperature sensing with high sensitivity,” Opt. Lett. 36, 3753–3755 (2011).
[Crossref]

2010 (2)

B. B. Li, Q. Wang, Y. F. Xiao, X. F. Jiang, Y. Li, L. Xiao, and Q. Gong, “On chip, high-sensitivity thermal sensor based on high-Q polydimethylsiloxane-coated microresonator,” Appl. Phys. Lett. 96, 251109 (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, 192–195 (2010).
[Crossref]

2008 (4)

Y. F. Xiao, V. Gaddam, and L. Yang, “Coupled optical microcavities: an enhanced refractometric sensing configuration,” Opt. Express 16, 12538–12543 (2008).
[Crossref]

J. T. Robinson, L. Chen, and M. Lipson, “On-chip gas detection in silicon optical microcavities,” Opt. Express 16, 4296–4301 (2008).
[Crossref]

E. M. Graefe, U. Günther, H. J. Korsch, and A. E. Niederle, “A non-Hermitian symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points,” J. Phys. A Math. Theor. 41, 255206 (2008).
[Crossref]

W. D. Heiss, “Chirality of wavefunctions for three coalescing levels,” J. Phys. A Math. Theor. 41, 244010 (2008).
[Crossref]

2007 (2)

P. Zijlstra, K. L. Van Der Molen, and A. P. Mosk, “Spatial refractive index sensor using whispering gallery modes in an optically trapped microsphere,” Appl. Phys. Lett. 90, 161101 (2007).
[Crossref]

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783–787 (2007).
[Crossref]

2006 (2)

A. Yalcin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Unlu, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron 12, 148–155 (2006).
[Crossref]

J. Scheuer and A. Yariv, “Sagnac effect in coupled-resonator slow-light waveguide structures,” Phys. Rev. Lett. 96, 053901 (2006).
[Crossref]

2005 (1)

C. Ma, X. Yan, Y. Z. Xu, Z. K. Qin, and X. Y. Wang, “Characteristic analysis of bending coupling between two optical waveguides,” Opt. Quantum Electron 37, 1055–1067 (2005).
[Crossref]

2002 (1)

Aldridge, J. C.

A. Yalcin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Unlu, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron 12, 148–155 (2006).
[Crossref]

Ambrosius, H. P. M. M.

C. Ciminelli, D. D’Agostino, G. Carnicella, F. Dell’Olio, D. Conteduca, H. P. M. M. Ambrosius, M. K. Smit, and M. N. Armenise, “A high-Q InP resonant angular velocity sensor for a monolithically integrated optical gyroscope,” IEEE Photon. J. 8, 1–19 (2016).
[Crossref]

Anthes-Washburn, M.

A. Yalcin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Unlu, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron 12, 148–155 (2006).
[Crossref]

Armani, A. M.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783–787 (2007).
[Crossref]

Armenise, M. N.

C. Ciminelli, D. D’Agostino, G. Carnicella, F. Dell’Olio, D. Conteduca, H. P. M. M. Ambrosius, M. K. Smit, and M. N. Armenise, “A high-Q InP resonant angular velocity sensor for a monolithically integrated optical gyroscope,” IEEE Photon. J. 8, 1–19 (2016).
[Crossref]

Bender, C. M.

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Bi, Z.

H. Zhang, J. Chen, J. Jin, J. Lin, L. Zhao, Z. Bi, A. Huang, and Z. Xiao, “On-chip modulation for rotating sensing of gyroscope based on ring resonator coupled with Mach-Zehnder interferometer,” Sci. Rep. 6, 19024 (2016).
[Crossref]

Cao, H.

R. Sarma, L. Ge, J. Wiersig, and H. Cao, “Rotating optical microcavities with broken chiral symmetry,” Phys. Rev. Lett. 114, 053903 (2015).
[Crossref]

Capolino, F.

M. Y. Nada, M. A. K. Othman, and F. Capolino, “Theory of coupled resonator optical waveguides exhibiting high-order exceptional points of degeneracy,” Phys. Rev. B 96, 184304 (2017).
[Crossref]

Carnicella, G.

C. Ciminelli, D. D’Agostino, G. Carnicella, F. Dell’Olio, D. Conteduca, H. P. M. M. Ambrosius, M. K. Smit, and M. N. Armenise, “A high-Q InP resonant angular velocity sensor for a monolithically integrated optical gyroscope,” IEEE Photon. J. 8, 1–19 (2016).
[Crossref]

Chang, L.

L. Chang, X. Jiang, S. Hua, C. Yang, J. Wen, L. Jiang, G. Li, G. Wang, and M. Xiao, “Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators,” Nat. Photonics. 8, 524–529 (2014).
[Crossref]

Chang, X.

H. Zhang, W. Li, P. Han, X. Chang, J. Liu, A. Huang, and Z. Xiao, “Mode broadening induced by rotation rate in an atom assisted microresonator,” J. Appl. Phys. 125, 084502 (2019).
[Crossref]

Chbouki, N.

A. Yalcin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Unlu, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron 12, 148–155 (2006).
[Crossref]

Chen, C.

C. Chen, L. Jin, and R. B. Liu, “Sensitivity of parameter estimation near the exceptional point of a non-Hermitian system,” arXiv:1809.05719v1 (2018).

Chen, J.

H. Zhang, J. Chen, J. Jin, J. Lin, L. Zhao, Z. Bi, A. Huang, and Z. Xiao, “On-chip modulation for rotating sensing of gyroscope based on ring resonator coupled with Mach-Zehnder interferometer,” Sci. Rep. 6, 19024 (2016).
[Crossref]

Chen, L.

Chen, T.

T. Lu, H. Lee, T. Chen, S. Herchak, J. H. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. USA 108, 5976–5979 (2011).
[Crossref]

Chen, W.

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

Chow, W.

Christodoulides, D.

Christodoulides, D. N.

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, 11–19 (2018).
[Crossref]

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, 187–191 (2017).
[Crossref]

H. Hodaei, M. A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Parity-time-symmetric microring lasers,” Science 346, 975–978 (2014).
[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, 192–195 (2010).
[Crossref]

Chu, S.

A. Yalcin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Unlu, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron 12, 148–155 (2006).
[Crossref]

Ciminelli, C.

C. Ciminelli, D. D’Agostino, G. Carnicella, F. Dell’Olio, D. Conteduca, H. P. M. M. Ambrosius, M. K. Smit, and M. N. Armenise, “A high-Q InP resonant angular velocity sensor for a monolithically integrated optical gyroscope,” IEEE Photon. J. 8, 1–19 (2016).
[Crossref]

Conteduca, D.

C. Ciminelli, D. D’Agostino, G. Carnicella, F. Dell’Olio, D. Conteduca, H. P. M. M. Ambrosius, M. K. Smit, and M. N. Armenise, “A high-Q InP resonant angular velocity sensor for a monolithically integrated optical gyroscope,” IEEE Photon. J. 8, 1–19 (2016).
[Crossref]

D’Agostino, D.

C. Ciminelli, D. D’Agostino, G. Carnicella, F. Dell’Olio, D. Conteduca, H. P. M. M. Ambrosius, M. K. Smit, and M. N. Armenise, “A high-Q InP resonant angular velocity sensor for a monolithically integrated optical gyroscope,” IEEE Photon. J. 8, 1–19 (2016).
[Crossref]

De Carlo, M.

De Leonardis, F.

Dell’Olio, F.

C. Ciminelli, D. D’Agostino, G. Carnicella, F. Dell’Olio, D. Conteduca, H. P. M. M. Ambrosius, M. K. Smit, and M. N. Armenise, “A high-Q InP resonant angular velocity sensor for a monolithically integrated optical gyroscope,” IEEE Photon. J. 8, 1–19 (2016).
[Crossref]

Desai, T. A.

A. Yalcin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Unlu, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron 12, 148–155 (2006).
[Crossref]

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C. Ma, X. Yan, Y. Z. Xu, Z. K. Qin, and X. Y. Wang, “Characteristic analysis of bending coupling between two optical waveguides,” Opt. Quantum Electron 37, 1055–1067 (2005).
[Crossref]

Ren, J.

Robinson, J. T.

Rodriguez, A. W.

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, 107402 (2016).
[Crossref]

Rotter, S.

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, 11–19 (2018).
[Crossref]

Rüter, C. E.

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, 192–195 (2010).
[Crossref]

Ryu, J. W.

J. W. Ryu, S. Y. Lee, and S. W. Kim, “Analysis of multiple exceptional points related to three interacting eigenmodes in a non-Hermitian Hamiltonian,” Phys. Rev. A 85, 042101 (2012).
[Crossref]

Sarma, R.

R. Sarma, L. Ge, J. Wiersig, and H. Cao, “Rotating optical microcavities with broken chiral symmetry,” Phys. Rev. Lett. 114, 053903 (2015).
[Crossref]

Scheuer, J.

J. Scheuer and A. Yariv, “Sagnac effect in coupled-resonator slow-light waveguide structures,” Phys. Rev. Lett. 96, 053901 (2006).
[Crossref]

Segev, M.

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, 192–195 (2010).
[Crossref]

Smit, M. K.

C. Ciminelli, D. D’Agostino, G. Carnicella, F. Dell’Olio, D. Conteduca, H. P. M. M. Ambrosius, M. K. Smit, and M. N. Armenise, “A high-Q InP resonant angular velocity sensor for a monolithically integrated optical gyroscope,” IEEE Photon. J. 8, 1–19 (2016).
[Crossref]

Soltani, M.

Sunada, S.

S. Sunada, “Large Sagnac frequency splitting in a ring resonator operating at an exceptional point,” Phys. Rev. A 96, 033842 (2017).
[Crossref]

Unlu, M. S.

A. Yalcin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Unlu, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron 12, 148–155 (2006).
[Crossref]

Vahala, K.

T. Lu, H. Lee, T. Chen, S. Herchak, J. H. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. USA 108, 5976–5979 (2011).
[Crossref]

Vahala, K. J.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783–787 (2007).
[Crossref]

Van, V.

A. Yalcin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Unlu, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron 12, 148–155 (2006).
[Crossref]

Van Der Molen, K. L.

P. Zijlstra, K. L. Van Der Molen, and A. P. Mosk, “Spatial refractive index sensor using whispering gallery modes in an optically trapped microsphere,” Appl. Phys. Lett. 90, 161101 (2007).
[Crossref]

Wang, G.

L. Chang, X. Jiang, S. Hua, C. Yang, J. Wen, L. Jiang, G. Li, G. Wang, and M. Xiao, “Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators,” Nat. Photonics. 8, 524–529 (2014).
[Crossref]

Wang, M.

Wang, Q.

B. B. Li, Q. Wang, Y. F. Xiao, X. F. Jiang, Y. Li, L. Xiao, and Q. Gong, “On chip, high-sensitivity thermal sensor based on high-Q polydimethylsiloxane-coated microresonator,” Appl. Phys. Lett. 96, 251109 (2010).
[Crossref]

Wang, S.

Wang, X. Y.

C. Ma, X. Yan, Y. Z. Xu, Z. K. Qin, and X. Y. Wang, “Characteristic analysis of bending coupling between two optical waveguides,” Opt. Quantum Electron 37, 1055–1067 (2005).
[Crossref]

Wen, J.

L. Chang, X. Jiang, S. Hua, C. Yang, J. Wen, L. Jiang, G. Li, G. Wang, and M. Xiao, “Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators,” Nat. Photonics. 8, 524–529 (2014).
[Crossref]

Wiersig, J.

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

J. Wiersig, “Sensors operating at exceptional points: general theory,” Phys. Rev. A 93, 033809 (2016).
[Crossref]

R. Sarma, L. Ge, J. Wiersig, and H. Cao, “Rotating optical microcavities with broken chiral symmetry,” Phys. Rev. Lett. 114, 053903 (2015).
[Crossref]

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, 203901 (2014).
[Crossref]

Wittek, S.

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, 187–191 (2017).
[Crossref]

Xiao, L.

B. B. Li, Q. Wang, Y. F. Xiao, X. F. Jiang, Y. Li, L. Xiao, and Q. Gong, “On chip, high-sensitivity thermal sensor based on high-Q polydimethylsiloxane-coated microresonator,” Appl. Phys. Lett. 96, 251109 (2010).
[Crossref]

Xiao, M.

L. Chang, X. Jiang, S. Hua, C. Yang, J. Wen, L. Jiang, G. Li, G. Wang, and M. Xiao, “Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators,” Nat. Photonics. 8, 524–529 (2014).
[Crossref]

Xiao, Y. F.

B. B. Li, Q. Wang, Y. F. Xiao, X. F. Jiang, Y. Li, L. Xiao, and Q. Gong, “On chip, high-sensitivity thermal sensor based on high-Q polydimethylsiloxane-coated microresonator,” Appl. Phys. Lett. 96, 251109 (2010).
[Crossref]

Y. F. Xiao, V. Gaddam, and L. Yang, “Coupled optical microcavities: an enhanced refractometric sensing configuration,” Opt. Express 16, 12538–12543 (2008).
[Crossref]

Xiao, Z.

H. Zhang, W. Li, P. Han, X. Chang, J. Liu, A. Huang, and Z. Xiao, “Mode broadening induced by rotation rate in an atom assisted microresonator,” J. Appl. Phys. 125, 084502 (2019).
[Crossref]

W. Li, H. Zhang, J. Liu, J. Lin, X. Xue, X. Zhang, X. Xu, A. Huang, and Z. Xiao, “On-chip high-sensitivity temperature sensor based on gain-loss coupled microresonators,” J. Opt. Soc. Am. B 34, 1765–1770 (2017).
[Crossref]

H. Zhang, J. Chen, J. Jin, J. Lin, L. Zhao, Z. Bi, A. Huang, and Z. Xiao, “On-chip modulation for rotating sensing of gyroscope based on ring resonator coupled with Mach-Zehnder interferometer,” Sci. Rep. 6, 19024 (2016).
[Crossref]

Xu, X.

Xu, Y. Z.

C. Ma, X. Yan, Y. Z. Xu, Z. K. Qin, and X. Y. Wang, “Characteristic analysis of bending coupling between two optical waveguides,” Opt. Quantum Electron 37, 1055–1067 (2005).
[Crossref]

Xue, X.

Yalcin, A.

A. Yalcin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Unlu, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron 12, 148–155 (2006).
[Crossref]

Yan, X.

C. Ma, X. Yan, Y. Z. Xu, Z. K. Qin, and X. Y. Wang, “Characteristic analysis of bending coupling between two optical waveguides,” Opt. Quantum Electron 37, 1055–1067 (2005).
[Crossref]

Yang, C.

L. Chang, X. Jiang, S. Hua, C. Yang, J. Wen, L. Jiang, G. Li, G. Wang, and M. Xiao, “Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators,” Nat. Photonics. 8, 524–529 (2014).
[Crossref]

Yang, J.

Yang, L.

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

Z. P. Liu, J. Zhang, Ş. K. Özdemir, B. Peng, H. Jing, X. Y. Lü, C. W. Li, L. Yang, F. Nori, and Y. X. Liu, “Metrology with PT-symmetric cavities: enhanced sensitivity near the PT-phase transition,” Phys. Rev. Lett. 117, 110802 (2016).
[Crossref]

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Y. F. Xiao, V. Gaddam, and L. Yang, “Coupled optical microcavities: an enhanced refractometric sensing configuration,” Opt. Express 16, 12538–12543 (2008).
[Crossref]

Yariv, A.

J. Scheuer and A. Yariv, “Sagnac effect in coupled-resonator slow-light waveguide structures,” Phys. Rev. Lett. 96, 053901 (2006).
[Crossref]

Zhang, H.

H. Zhang, W. Li, P. Han, X. Chang, J. Liu, A. Huang, and Z. Xiao, “Mode broadening induced by rotation rate in an atom assisted microresonator,” J. Appl. Phys. 125, 084502 (2019).
[Crossref]

W. Li, H. Zhang, J. Liu, J. Lin, X. Xue, X. Zhang, X. Xu, A. Huang, and Z. Xiao, “On-chip high-sensitivity temperature sensor based on gain-loss coupled microresonators,” J. Opt. Soc. Am. B 34, 1765–1770 (2017).
[Crossref]

H. Zhang, J. Chen, J. Jin, J. Lin, L. Zhao, Z. Bi, A. Huang, and Z. Xiao, “On-chip modulation for rotating sensing of gyroscope based on ring resonator coupled with Mach-Zehnder interferometer,” Sci. Rep. 6, 19024 (2016).
[Crossref]

Zhang, J.

Z. P. Liu, J. Zhang, Ş. K. Özdemir, B. Peng, H. Jing, X. Y. Lü, C. W. Li, L. Yang, F. Nori, and Y. X. Liu, “Metrology with PT-symmetric cavities: enhanced sensitivity near the PT-phase transition,” Phys. Rev. Lett. 117, 110802 (2016).
[Crossref]

Zhang, X.

Zhao, G.

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

Zhao, L.

H. Zhang, J. Chen, J. Jin, J. Lin, L. Zhao, Z. Bi, A. Huang, and Z. Xiao, “On-chip modulation for rotating sensing of gyroscope based on ring resonator coupled with Mach-Zehnder interferometer,” Sci. Rep. 6, 19024 (2016).
[Crossref]

Zijlstra, P.

P. Zijlstra, K. L. Van Der Molen, and A. P. Mosk, “Spatial refractive index sensor using whispering gallery modes in an optically trapped microsphere,” Appl. Phys. Lett. 90, 161101 (2007).
[Crossref]

Appl. Phys. Lett. (2)

P. Zijlstra, K. L. Van Der Molen, and A. P. Mosk, “Spatial refractive index sensor using whispering gallery modes in an optically trapped microsphere,” Appl. Phys. Lett. 90, 161101 (2007).
[Crossref]

B. B. Li, Q. Wang, Y. F. Xiao, X. F. Jiang, Y. Li, L. Xiao, and Q. Gong, “On chip, high-sensitivity thermal sensor based on high-Q polydimethylsiloxane-coated microresonator,” Appl. Phys. Lett. 96, 251109 (2010).
[Crossref]

IEEE J. Sel. Top. Quantum Electron (1)

A. Yalcin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Unlu, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron 12, 148–155 (2006).
[Crossref]

IEEE Photon. J. (1)

C. Ciminelli, D. D’Agostino, G. Carnicella, F. Dell’Olio, D. Conteduca, H. P. M. M. Ambrosius, M. K. Smit, and M. N. Armenise, “A high-Q InP resonant angular velocity sensor for a monolithically integrated optical gyroscope,” IEEE Photon. J. 8, 1–19 (2016).
[Crossref]

J. Appl. Phys. (1)

H. Zhang, W. Li, P. Han, X. Chang, J. Liu, A. Huang, and Z. Xiao, “Mode broadening induced by rotation rate in an atom assisted microresonator,” J. Appl. Phys. 125, 084502 (2019).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (1)

J. Phys. A Math. Theor. (2)

E. M. Graefe, U. Günther, H. J. Korsch, and A. E. Niederle, “A non-Hermitian symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points,” J. Phys. A Math. Theor. 41, 255206 (2008).
[Crossref]

W. D. Heiss, “Chirality of wavefunctions for three coalescing levels,” J. Phys. A Math. Theor. 41, 244010 (2008).
[Crossref]

Nat. Photonics. (1)

L. Chang, X. Jiang, S. Hua, C. Yang, J. Wen, L. Jiang, G. Li, G. Wang, and M. Xiao, “Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators,” Nat. Photonics. 8, 524–529 (2014).
[Crossref]

Nat. Phys. (3)

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, 11–19 (2018).
[Crossref]

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[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, 192–195 (2010).
[Crossref]

Nature (2)

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

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, 187–191 (2017).
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

Opt. Quantum Electron (1)

C. Ma, X. Yan, Y. Z. Xu, Z. K. Qin, and X. Y. Wang, “Characteristic analysis of bending coupling between two optical waveguides,” Opt. Quantum Electron 37, 1055–1067 (2005).
[Crossref]

Phys. Rev. A (3)

S. Sunada, “Large Sagnac frequency splitting in a ring resonator operating at an exceptional point,” Phys. Rev. A 96, 033842 (2017).
[Crossref]

J. W. Ryu, S. Y. Lee, and S. W. Kim, “Analysis of multiple exceptional points related to three interacting eigenmodes in a non-Hermitian Hamiltonian,” Phys. Rev. A 85, 042101 (2012).
[Crossref]

J. Wiersig, “Sensors operating at exceptional points: general theory,” Phys. Rev. A 93, 033809 (2016).
[Crossref]

Phys. Rev. B (1)

M. Y. Nada, M. A. K. Othman, and F. Capolino, “Theory of coupled resonator optical waveguides exhibiting high-order exceptional points of degeneracy,” Phys. Rev. B 96, 184304 (2017).
[Crossref]

Phys. Rev. Lett. (5)

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, 107402 (2016).
[Crossref]

Z. P. Liu, J. Zhang, Ş. K. Özdemir, B. Peng, H. Jing, X. Y. Lü, C. W. Li, L. Yang, F. Nori, and Y. X. Liu, “Metrology with PT-symmetric cavities: enhanced sensitivity near the PT-phase transition,” Phys. Rev. Lett. 117, 110802 (2016).
[Crossref]

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, 203901 (2014).
[Crossref]

J. Scheuer and A. Yariv, “Sagnac effect in coupled-resonator slow-light waveguide structures,” Phys. Rev. Lett. 96, 053901 (2006).
[Crossref]

R. Sarma, L. Ge, J. Wiersig, and H. Cao, “Rotating optical microcavities with broken chiral symmetry,” Phys. Rev. Lett. 114, 053903 (2015).
[Crossref]

Proc. Natl. Acad. Sci. USA (1)

T. Lu, H. Lee, T. Chen, S. Herchak, J. H. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. USA 108, 5976–5979 (2011).
[Crossref]

Sci. Rep. (2)

H. Zhang, J. Chen, J. Jin, J. Lin, L. Zhao, Z. Bi, A. Huang, and Z. Xiao, “On-chip modulation for rotating sensing of gyroscope based on ring resonator coupled with Mach-Zehnder interferometer,” Sci. Rep. 6, 19024 (2016).
[Crossref]

H. Jing, Ş. K. Özdemir, H. Lü, and F. Nori, “High-order exceptional points in optomechanics,” Sci. Rep. 7, 3386 (2017).
[Crossref]

Science (2)

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783–787 (2007).
[Crossref]

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

Other (1)

C. Chen, L. Jin, and R. B. Liu, “Sensitivity of parameter estimation near the exceptional point of a non-Hermitian system,” arXiv:1809.05719v1 (2018).

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Figures (9)

Fig. 1.
Fig. 1. Schematic of the rotation sensing mechanism based on higher-order EPs.
Fig. 2.
Fig. 2. Variation curve of the eigenfrequency differences ( ${\omega _{{\rm{EP}}n}} - {\omega _0}$ ) of the three microresonators with the normalized gain/loss contrast ( $g{v_g}/\kappa $ ) in the nonrotating state. (a) Real parts of the eigenfrequency differences. (b) Imaginary parts of the eigenfrequency differences.
Fig. 3.
Fig. 3. Variation curve of the eigenfrequency differences ( ${\omega _{{\rm{EP}}n}} - {\omega _0}$ ) of these three microresonators with increase of the normalized rotational perturbation around EP3. (a) Real parts of the eigenfrequency differences. (b) Imaginary parts of the eigenfrequency differences.
Fig. 4.
Fig. 4. Trajectories of eigenfrequency splitting with increase of the normalized rotational perturbation under the rotating state.
Fig. 5.
Fig. 5. Transmission spectrum of the rotation sensing mechanism under nonrotating state ( $\Omega =100^\circ/{\rm{h}}$ ). (a) and (c) Transmission spectrum of the rotation sensing mechanism in nonrotating state, not at EP3; (b) transmission spectrum of the rotation sensing mechanism at EP3 under the nonrotating state.
Fig. 6.
Fig. 6. Transmission spectrum of the rotation sensing mechanism at EP3 with different rotation rates. (These simulation parameters are $\lambda = 1.55\,\,\unicode{x00B5}{\rm m}$ , $R = 100\,\,\unicode{x00B5}{\rm m}$ , $| {{g_1}} | = | {{g_2}} | = 18.9\,\,{{\rm{m}}^{ - 1}}$ ).
Fig. 7.
Fig. 7. Sensitivity enhancement as a function of the rotational perturbation for the rotation sensing mechanism based on higher-order EPs with different coupling strength levels.
Fig. 8.
Fig. 8. Linewidth of the transmission spectrum. (a) Normalized right-hand linewidth of the transmission spectrum at various rotation rates; (b) HWHM at various rotation rates (the inset shows the results on a logarithmic scale).
Fig. 9.
Fig. 9. Minimum detectable rotation rate $\delta {\Omega _{\min }}$ is plotted as a function of the rotation rate $\Omega $ . When $\lambda =1.55\,\,\unicode{x00B5}{\rm m}$ , $\delta {\lambda _{\min }} = 0.02\,\,{\rm{nm}} $ .

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

d d t a = i ω 0 a + g 1 v g a i κ b i μ s i n ,
d d t b = i ω 0 b i κ a i κ c ,
d d t c = i ω 0 c + g 2 v g c i κ b ,
ω E P 0 = ω 0 ,
ω E P 1 , + 1 = ω 0 ± 2 κ 1 ( g v g 2 κ ) 2 ,
Δ ω = 4 π R Ω λ = 2 Δ ω s ,
ω E P 1 = ω 0 4 1 / 3 e i 4 π / 3 κ 2 / 3 ( Δ ω s ) 1 / 3 ,
ω E P 0 = ω 0 4 1 / 3 κ 2 / 3 ( Δ ω s ) 1 / 3 ,
ω E P + 1 = ω 0 4 1 / 3 e i 4 π / 3 κ 2 / 3 ( Δ ω s ) 1 / 3 .
Δ ω E P 1 , 0 ( 2.381 + 1.375 i ) κ 2 / 3 ( Δ ω s ) 1 / 3 ,
Δ ω E P + 1 , 0 ( 2.381 1.375 i ) κ 2 / 3 ( Δ ω s ) 1 / 3 .
Δ ω E P 3 = Re ( Δ ω E P 1 , 0 ) ,
Δ ω E P 3 = Re ( Δ ω E P + 1 , 0 ) .
s o u t = s i n i μ a .
S o u t S i n = | 1 μ [ U 2 ( i ω i ω 0 + i Δ ω s ) + κ 2 ] U 1 [ U 2 ( i ω i ω 0 + i Δ ω s ) + κ 2 ] + κ 2 U 2 | 2 ,
Δ ω E P 3 Δ ω E P 2 = 1.191 ( 2 κ Δ ω ) 2 3 .
δ Ω min = 1 S F c λ 2 δ λ min ,

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