Abstract

We present a study of single nanoparticle detection using parity-time (PT) symmetric whispering-gallery mode (WGM) resonators. Our theoretical model and numerical simulations show that, with balanced gain and loss, the PT-symmetric WGM nanoparticle sensor, tailored to operate at PT phase transition points (also called exceptional points), exhibits significant enhancement in frequency splitting when compared with a single WGM nanoparticle sensor subject to the same perturbation. The presence of gain in the PT-symmetric system leads to narrower linewidth, which helps to resolve smaller changes in frequency splitting and improve the detection limit of nanoparticle sensing. Furthermore, we also provide a general method for detecting multiple nanoparticles entering the mode volume of a PT-symmetric WGM sensor one by one. Our study shows the feasibility of PT-symmetric WGM resonators for ultrasensitive single nanoparticle and biomolecule sensing.

© 2018 Chinese Laser Press

Full Article  |  PDF Article
OSA Recommended Articles
Whispering gallery mode sensors

Matthew R. Foreman, Jon D. Swaim, and Frank Vollmer
Adv. Opt. Photon. 7(2) 168-240 (2015)

Single virus and nanoparticle size spectrometry by whispering-gallery-mode microcavities

Jiangang Zhu, Şahin Kaya Özdemir, Lina He, Da-Ren Chen, and Lan Yang
Opt. Express 19(17) 16195-16206 (2011)

Hybridizing whispering gallery modes and plasmonic resonances in a photonic metadevice for biosensing applications [Invited]

Carolin Klusmann, Radius N. S. Suryadharma, Jens Oppermann, Carsten Rockstuhl, and Heinz Kalt
J. Opt. Soc. Am. B 34(7) D46-D55 (2017)

References

  • View by:
  • |
  • |
  • |

  1. K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
    [Crossref]
  2. T. J. Kippenberg, S. M. Spillane, D. K. Armani, and K. J. Vahala, “Ultralow-threshold microcavity Raman laser on a microelectronic chip,” Opt. Lett. 29, 1224–1226 (2004).
    [Crossref]
  3. L. Yang, T. Carmon, B. Min, S. M. Spillane, and K. J. Vahala, “Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol-gel process,” Appl. Phys. Lett. 86, 091114 (2005).
    [Crossref]
  4. T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express 15, 17172–17205 (2007).
    [Crossref]
  5. T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
    [Crossref]
  6. F. Monifi, J. Friedlein, Ş. K. Özdemir, and L. Yang, “A robust and tunable add-drop filter using whispering gallery mode microtoroid resonator,” J. Lightwave Technol. 30, 3306–3315 (2012).
    [Crossref]
  7. F. Monifi, Ş. K. Özdemir, and L. Yang, “Tunable add-drop filter using an active whispering gallery mode microcavity,” Appl. Phys. Lett. 103, 181103 (2013).
    [Crossref]
  8. F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
    [Crossref]
  9. J. Zhu, Ş. K. Özdemir, Y. F. Xiao, L. Li, L. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2010).
    [Crossref]
  10. L. He, Ş. K. Özdemir, J. Zhu, and L. Yang, “Ultrasensitive detection of mode splitting in active optical microcavities,” Phys. Rev. A 82, 053810 (2010).
    [Crossref]
  11. L. He, Ş. K. Özdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6, 428–432 (2011).
    [Crossref]
  12. W. Kim, Ş. K. Özdemir, J. Zhu, F. Monifi, C. Coban, and L. Yang, “Detection and size measurement of individual hemozoin nanocrystals in aquatic environment using a whispering gallery mode resonator,” Opt. Express 20, 29426–29446 (2012).
    [Crossref]
  13. F. Vollmer and L. Yang, “Label-free detection with high-Q microcavities: a review of biosensing mechanisms for integrated devices,” Nanophotonics 1, 267–291 (2012).
    [Crossref]
  14. Ş. K. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery Raman microlaser,” Proc. Natl. Acad. Sci. USA 111, E3836–E3844 (2014).
    [Crossref]
  15. B. B. Li, W. R. Clements, X. C. Yu, K. Shi, Q. H. Gong, and Y. F. Xiao, “Single nanoparticle detection using split-mode microcavity Raman lasers,” Proc. Natl. Acad. Sci. USA 111, 14657–14662 (2014).
    [Crossref]
  16. M. R. Foreman, J. D. Swaim, and F. Vollmer, “Whispering gallery mode sensors,” Adv. Opt. Photon. 7, 168–240 (2015).
    [Crossref]
  17. X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620, 8–26 (2008).
    [Crossref]
  18. D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
    [Crossref]
  19. T. Lu, L. Yang, T. Carmon, and B. Min, “A narrow-linewidth on-chip toroid Raman laser,” IEEE J. Quantum Electron. 47, 320–326 (2011).
    [Crossref]
  20. 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]
  21. J. Wiersig, “Structure of whispering-gallery modes in optical microdisks perturbed by nanoparticles,” Phys. Rev. A 84, 063828 (2011).
    [Crossref]
  22. J. Wiersig, “Sensors operating at exceptional points: general theory,” Phys. Rev. A 93, 033809 (2016).
    [Crossref]
  23. 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]
  24. B. Peng, Ş. K. Özdemir, M. Liertzer, W. Chen, J. Kramer, H. Yilmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. USA 113, 6845–6850 (2016).
    [Crossref]
  25. N. Zhang, S. Liu, K. Wang, Z. Gu, M. Li, N. Yi, S. Xiao, and Q. Song, “Single nanoparticle detection using far-field emission of photonic molecule around the exceptional point,” Sci. Rep. 5, 11912 (2015).
    [Crossref]
  26. C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80, 5243–5246 (1998).
    [Crossref]
  27. C. M. Bender, “Making sense of non-Hermitian Hamiltonians,” Rep. Prog. Phys. 70, 947–1018 (2007).
    [Crossref]
  28. 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, 093902 (2009).
    [Crossref]
  29. 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]
  30. A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
    [Crossref]
  31. 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, 108–113 (2013).
    [Crossref]
  32. 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]
  33. L. Feng, Z. J. Wong, R. M. Ma, Y. Wang, and X. Zhang, “Single-mode laser by parity-time symmetry breaking,” Science 346, 972–975 (2014).
    [Crossref]
  34. H. Hodaei, M. A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Parity-time-symmetric microring lasers,” Science 346, 975–978 (2014).
    [Crossref]
  35. B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S. L. Chua, J. D. Joannopoulos, and M. Soljačić, “Spawning rings of exceptional points out of Dirac cones,” Nature 525, 354–358 (2015).
    [Crossref]
  36. M. Wimmer, A. Regensburger, M. A. Miri, C. Bersch, D. N. Christodoulides, and U. Peschel, “Observation of optical solitons in PT-symmetric lattices,” Nat. Commun. 6, 7782 (2015).
    [Crossref]
  37. 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]
  38. 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]
  39. J. Ren, H. Hodaei, G. Harari, A. U. Hassan, W. Chow, M. Soltani, D. N. Christodoulides, and M. Khajavikhan, “Ultrasensitive micro-scale parity-time-symmetric ring laser gyroscope,” Opt. Lett. 42, 1556–1559 (2017).
    [Crossref]
  40. H. Benisty, C. Yan, A. Degiron, and A. T. Lupu, “Healing near-PT-symmetric structures to restore their characteristic singularities: analysis and examples,” J. Lightwave Technol. 30, 2675–2683 (2012).
    [Crossref]
  41. J. Zhu, Ş. K. Özdemir, L. He, and L. Yang, “Controlled manipulation of mode splitting in an optical microcavity by two Rayleigh scatterers,” Opt. Express 18, 23535–23543 (2010).
    [Crossref]
  42. X. Yi, Y. F. Xiao, Y. C. Liu, B. B. Li, Y. L. Chen, Y. Li, and Q. H. Gong, “Multiple-Rayleigh-scatterer-induced mode splitting in a high-Q whispering-gallery-mode microresonator,” Phys. Rev. A 83, 023803 (2011).
    [Crossref]
  43. J. Zhu, Ş. K. Özdemir, L. He, D. R. Chen, and L. Yang, “Single virus and nanoparticle size spectrometry by whispering-gallery-mode microcavities,” Opt. Express 19, 16195–16206 (2011).
    [Crossref]
  44. C. Qiu, J. Shu, Z. Li, X. Zhang, and Q. Xu, “Wavelength tracking with thermally controlled silicon resonators,” Opt. Express 19, 5143–5148 (2011).
    [Crossref]

2017 (3)

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]

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

2016 (3)

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, M. Liertzer, W. Chen, J. Kramer, H. Yilmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. USA 113, 6845–6850 (2016).
[Crossref]

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

2015 (4)

N. Zhang, S. Liu, K. Wang, Z. Gu, M. Li, N. Yi, S. Xiao, and Q. Song, “Single nanoparticle detection using far-field emission of photonic molecule around the exceptional point,” Sci. Rep. 5, 11912 (2015).
[Crossref]

M. R. Foreman, J. D. Swaim, and F. Vollmer, “Whispering gallery mode sensors,” Adv. Opt. Photon. 7, 168–240 (2015).
[Crossref]

B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S. L. Chua, J. D. Joannopoulos, and M. Soljačić, “Spawning rings of exceptional points out of Dirac cones,” Nature 525, 354–358 (2015).
[Crossref]

M. Wimmer, A. Regensburger, M. A. Miri, C. Bersch, D. N. Christodoulides, and U. Peschel, “Observation of optical solitons in PT-symmetric lattices,” Nat. Commun. 6, 7782 (2015).
[Crossref]

2014 (6)

Ş. K. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery Raman microlaser,” Proc. Natl. Acad. Sci. USA 111, E3836–E3844 (2014).
[Crossref]

B. B. Li, W. R. Clements, X. C. Yu, K. Shi, Q. H. Gong, and Y. F. Xiao, “Single nanoparticle detection using split-mode microcavity Raman lasers,” Proc. Natl. Acad. Sci. USA 111, 14657–14662 (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]

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]

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

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, 108–113 (2013).
[Crossref]

F. Monifi, Ş. K. Özdemir, and L. Yang, “Tunable add-drop filter using an active whispering gallery mode microcavity,” Appl. Phys. Lett. 103, 181103 (2013).
[Crossref]

2012 (5)

2011 (6)

X. Yi, Y. F. Xiao, Y. C. Liu, B. B. Li, Y. L. Chen, Y. Li, and Q. H. Gong, “Multiple-Rayleigh-scatterer-induced mode splitting in a high-Q whispering-gallery-mode microresonator,” Phys. Rev. A 83, 023803 (2011).
[Crossref]

J. Zhu, Ş. K. Özdemir, L. He, D. R. Chen, and L. Yang, “Single virus and nanoparticle size spectrometry by whispering-gallery-mode microcavities,” Opt. Express 19, 16195–16206 (2011).
[Crossref]

C. Qiu, J. Shu, Z. Li, X. Zhang, and Q. Xu, “Wavelength tracking with thermally controlled silicon resonators,” Opt. Express 19, 5143–5148 (2011).
[Crossref]

J. Wiersig, “Structure of whispering-gallery modes in optical microdisks perturbed by nanoparticles,” Phys. Rev. A 84, 063828 (2011).
[Crossref]

L. He, Ş. K. Özdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6, 428–432 (2011).
[Crossref]

T. Lu, L. Yang, T. Carmon, and B. Min, “A narrow-linewidth on-chip toroid Raman laser,” IEEE J. Quantum Electron. 47, 320–326 (2011).
[Crossref]

2010 (4)

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]

J. Zhu, Ş. K. Özdemir, Y. F. Xiao, L. Li, L. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2010).
[Crossref]

L. He, Ş. K. Özdemir, J. Zhu, and L. Yang, “Ultrasensitive detection of mode splitting in active optical microcavities,” Phys. Rev. A 82, 053810 (2010).
[Crossref]

J. Zhu, Ş. K. Özdemir, L. He, and L. Yang, “Controlled manipulation of mode splitting in an optical microcavity by two Rayleigh scatterers,” Opt. Express 18, 23535–23543 (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, 093902 (2009).
[Crossref]

2008 (2)

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620, 8–26 (2008).
[Crossref]

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[Crossref]

2007 (2)

T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express 15, 17172–17205 (2007).
[Crossref]

C. M. Bender, “Making sense of non-Hermitian Hamiltonians,” Rep. Prog. Phys. 70, 947–1018 (2007).
[Crossref]

2006 (1)

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref]

2005 (1)

L. Yang, T. Carmon, B. Min, S. M. Spillane, and K. J. Vahala, “Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol-gel process,” Appl. Phys. Lett. 86, 091114 (2005).
[Crossref]

2004 (1)

2003 (2)

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[Crossref]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[Crossref]

1998 (1)

C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80, 5243–5246 (1998).
[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, 093902 (2009).
[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, 108–113 (2013).
[Crossref]

Aoki, T.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref]

Armani, D. K.

T. J. Kippenberg, S. M. Spillane, D. K. Armani, and K. J. Vahala, “Ultralow-threshold microcavity Raman laser on a microelectronic chip,” Opt. Lett. 29, 1224–1226 (2004).
[Crossref]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[Crossref]

Arnold, S.

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[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]

C. M. Bender, “Making sense of non-Hermitian Hamiltonians,” Rep. Prog. Phys. 70, 947–1018 (2007).
[Crossref]

C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80, 5243–5246 (1998).
[Crossref]

Benisty, H.

Bersch, C.

M. Wimmer, A. Regensburger, M. A. Miri, C. Bersch, D. N. Christodoulides, and U. Peschel, “Observation of optical solitons in PT-symmetric lattices,” Nat. Commun. 6, 7782 (2015).
[Crossref]

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

Boettcher, S.

C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80, 5243–5246 (1998).
[Crossref]

Bowen, W. P.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref]

Carmon, T.

T. Lu, L. Yang, T. Carmon, and B. Min, “A narrow-linewidth on-chip toroid Raman laser,” IEEE J. Quantum Electron. 47, 320–326 (2011).
[Crossref]

L. Yang, T. Carmon, B. Min, S. M. Spillane, and K. J. Vahala, “Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol-gel process,” Appl. Phys. Lett. 86, 091114 (2005).
[Crossref]

Chen, D. R.

J. Zhu, Ş. K. Özdemir, L. He, D. R. Chen, and L. Yang, “Single virus and nanoparticle size spectrometry by whispering-gallery-mode microcavities,” Opt. Express 19, 16195–16206 (2011).
[Crossref]

J. Zhu, Ş. K. Özdemir, Y. F. Xiao, L. Li, L. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2010).
[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]

B. Peng, Ş. K. Özdemir, M. Liertzer, W. Chen, J. Kramer, H. Yilmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. USA 113, 6845–6850 (2016).
[Crossref]

Chen, Y. F.

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, 108–113 (2013).
[Crossref]

Chen, Y. L.

X. Yi, Y. F. Xiao, Y. C. Liu, B. B. Li, Y. L. Chen, Y. Li, and Q. H. Gong, “Multiple-Rayleigh-scatterer-induced mode splitting in a high-Q whispering-gallery-mode microresonator,” Phys. Rev. A 83, 023803 (2011).
[Crossref]

Chow, W.

Christodoulides, D. N.

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

M. Wimmer, A. Regensburger, M. A. Miri, C. Bersch, D. N. Christodoulides, and U. Peschel, “Observation of optical solitons in PT-symmetric lattices,” Nat. Commun. 6, 7782 (2015).
[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]

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

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, 093902 (2009).
[Crossref]

Chua, S. L.

B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S. L. Chua, J. D. Joannopoulos, and M. Soljačić, “Spawning rings of exceptional points out of Dirac cones,” Nature 525, 354–358 (2015).
[Crossref]

Clements, W. R.

B. B. Li, W. R. Clements, X. C. Yu, K. Shi, Q. H. Gong, and Y. F. Xiao, “Single nanoparticle detection using split-mode microcavity Raman lasers,” Proc. Natl. Acad. Sci. USA 111, 14657–14662 (2014).
[Crossref]

Coban, C.

Dayan, B.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref]

Degiron, A.

Duchesne, D.

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, 093902 (2009).
[Crossref]

El-Ganainy, R.

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]

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]

Fan, S.

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]

Fan, X.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620, 8–26 (2008).
[Crossref]

Fegadolli, W. S.

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, 108–113 (2013).
[Crossref]

Feng, L.

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

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, 108–113 (2013).
[Crossref]

Foreman, M. R.

Friedlein, J.

Garcia-Gracia, H.

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]

Gianfreda, 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]

Gong, Q. H.

B. B. Li, W. R. Clements, X. C. Yu, K. Shi, Q. H. Gong, and Y. F. Xiao, “Single nanoparticle detection using split-mode microcavity Raman lasers,” Proc. Natl. Acad. Sci. USA 111, 14657–14662 (2014).
[Crossref]

X. Yi, Y. F. Xiao, Y. C. Liu, B. B. Li, Y. L. Chen, Y. Li, and Q. H. Gong, “Multiple-Rayleigh-scatterer-induced mode splitting in a high-Q whispering-gallery-mode microresonator,” Phys. Rev. A 83, 023803 (2011).
[Crossref]

Gu, Z.

N. Zhang, S. Liu, K. Wang, Z. Gu, M. Li, N. Yi, S. Xiao, and Q. Song, “Single nanoparticle detection using far-field emission of photonic molecule around the exceptional point,” Sci. Rep. 5, 11912 (2015).
[Crossref]

Guo, A.

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, 093902 (2009).
[Crossref]

Harari, G.

Hassan, A. U.

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

He, L.

Ş. K. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery Raman microlaser,” Proc. Natl. Acad. Sci. USA 111, E3836–E3844 (2014).
[Crossref]

L. He, Ş. K. Özdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6, 428–432 (2011).
[Crossref]

J. Zhu, Ş. K. Özdemir, L. He, D. R. Chen, and L. Yang, “Single virus and nanoparticle size spectrometry by whispering-gallery-mode microcavities,” Opt. Express 19, 16195–16206 (2011).
[Crossref]

J. Zhu, Ş. K. Özdemir, L. He, and L. Yang, “Controlled manipulation of mode splitting in an optical microcavity by two Rayleigh scatterers,” Opt. Express 18, 23535–23543 (2010).
[Crossref]

L. He, Ş. K. Özdemir, J. Zhu, and L. Yang, “Ultrasensitive detection of mode splitting in active optical microcavities,” Phys. Rev. A 82, 053810 (2010).
[Crossref]

J. Zhu, Ş. K. Özdemir, Y. F. Xiao, L. Li, L. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2010).
[Crossref]

Heinrich, M.

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

Hodaei, H.

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]

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

Hsu, C. W.

B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S. L. Chua, J. D. Joannopoulos, and M. Soljačić, “Spawning rings of exceptional points out of Dirac cones,” Nature 525, 354–358 (2015).
[Crossref]

Huang, S. H.

Ş. K. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery Raman microlaser,” Proc. Natl. Acad. Sci. USA 111, E3836–E3844 (2014).
[Crossref]

Igarashi, Y.

B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S. L. Chua, J. D. Joannopoulos, and M. Soljačić, “Spawning rings of exceptional points out of Dirac cones,” Nature 525, 354–358 (2015).
[Crossref]

Jing, H.

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]

Joannopoulos, J. D.

B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S. L. Chua, J. D. Joannopoulos, and M. Soljačić, “Spawning rings of exceptional points out of Dirac cones,” Nature 525, 354–358 (2015).
[Crossref]

Kaminer, I.

B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S. L. Chua, J. D. Joannopoulos, and M. Soljačić, “Spawning rings of exceptional points out of Dirac cones,” Nature 525, 354–358 (2015).
[Crossref]

Khajavikhan, M.

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]

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

Kim, W.

W. Kim, Ş. K. Özdemir, J. Zhu, F. Monifi, C. Coban, and L. Yang, “Detection and size measurement of individual hemozoin nanocrystals in aquatic environment using a whispering gallery mode resonator,” Opt. Express 20, 29426–29446 (2012).
[Crossref]

L. He, Ş. K. Özdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6, 428–432 (2011).
[Crossref]

Kimble, H. J.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref]

Kip, D.

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]

Kippenberg, T. J.

T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express 15, 17172–17205 (2007).
[Crossref]

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref]

T. J. Kippenberg, S. M. Spillane, D. K. Armani, and K. J. Vahala, “Ultralow-threshold microcavity Raman laser on a microelectronic chip,” Opt. Lett. 29, 1224–1226 (2004).
[Crossref]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[Crossref]

Kramer, J.

B. Peng, Ş. K. Özdemir, M. Liertzer, W. Chen, J. Kramer, H. Yilmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. USA 113, 6845–6850 (2016).
[Crossref]

Lei, F.

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]

Li, B. B.

B. B. Li, W. R. Clements, X. C. Yu, K. Shi, Q. H. Gong, and Y. F. Xiao, “Single nanoparticle detection using split-mode microcavity Raman lasers,” Proc. Natl. Acad. Sci. USA 111, 14657–14662 (2014).
[Crossref]

X. Yi, Y. F. Xiao, Y. C. Liu, B. B. Li, Y. L. Chen, Y. Li, and Q. H. Gong, “Multiple-Rayleigh-scatterer-induced mode splitting in a high-Q whispering-gallery-mode microresonator,” Phys. Rev. A 83, 023803 (2011).
[Crossref]

Li, C. W.

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]

Li, L.

J. Zhu, Ş. K. Özdemir, Y. F. Xiao, L. Li, L. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2010).
[Crossref]

Li, M.

N. Zhang, S. Liu, K. Wang, Z. Gu, M. Li, N. Yi, S. Xiao, and Q. Song, “Single nanoparticle detection using far-field emission of photonic molecule around the exceptional point,” Sci. Rep. 5, 11912 (2015).
[Crossref]

Li, Y.

X. Yi, Y. F. Xiao, Y. C. Liu, B. B. Li, Y. L. Chen, Y. Li, and Q. H. Gong, “Multiple-Rayleigh-scatterer-induced mode splitting in a high-Q whispering-gallery-mode microresonator,” Phys. Rev. A 83, 023803 (2011).
[Crossref]

Li, Z.

Liertzer, M.

B. Peng, Ş. K. Özdemir, M. Liertzer, W. Chen, J. Kramer, H. Yilmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. USA 113, 6845–6850 (2016).
[Crossref]

Liu, S.

N. Zhang, S. Liu, K. Wang, Z. Gu, M. Li, N. Yi, S. Xiao, and Q. Song, “Single nanoparticle detection using far-field emission of photonic molecule around the exceptional point,” Sci. Rep. 5, 11912 (2015).
[Crossref]

Liu, Y. C.

X. Yi, Y. F. Xiao, Y. C. Liu, B. B. Li, Y. L. Chen, Y. Li, and Q. H. Gong, “Multiple-Rayleigh-scatterer-induced mode splitting in a high-Q whispering-gallery-mode microresonator,” Phys. Rev. A 83, 023803 (2011).
[Crossref]

Liu, Y. X.

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]

Liu, Z. P.

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]

Long, G. L.

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]

Ş. K. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery Raman microlaser,” Proc. Natl. Acad. Sci. USA 111, E3836–E3844 (2014).
[Crossref]

Lu, L.

B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S. L. Chua, J. D. Joannopoulos, and M. Soljačić, “Spawning rings of exceptional points out of Dirac cones,” Nature 525, 354–358 (2015).
[Crossref]

Lu, M. H.

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, 108–113 (2013).
[Crossref]

Lu, T.

T. Lu, L. Yang, T. Carmon, and B. Min, “A narrow-linewidth on-chip toroid Raman laser,” IEEE J. Quantum Electron. 47, 320–326 (2011).
[Crossref]

Lü, X. Y.

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]

Lupu, A. T.

Ma, R. M.

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

Makris, K. G.

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]

Min, B.

T. Lu, L. Yang, T. Carmon, and B. Min, “A narrow-linewidth on-chip toroid Raman laser,” IEEE J. Quantum Electron. 47, 320–326 (2011).
[Crossref]

L. Yang, T. Carmon, B. Min, S. M. Spillane, and K. J. Vahala, “Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol-gel process,” Appl. Phys. Lett. 86, 091114 (2005).
[Crossref]

Miri, M. A.

M. Wimmer, A. Regensburger, M. A. Miri, C. Bersch, D. N. Christodoulides, and U. Peschel, “Observation of optical solitons in PT-symmetric lattices,” Nat. Commun. 6, 7782 (2015).
[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]

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

Monifi, F.

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]

Ş. K. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery Raman microlaser,” Proc. Natl. Acad. Sci. USA 111, E3836–E3844 (2014).
[Crossref]

F. Monifi, Ş. K. Özdemir, and L. Yang, “Tunable add-drop filter using an active whispering gallery mode microcavity,” Appl. Phys. Lett. 103, 181103 (2013).
[Crossref]

F. Monifi, J. Friedlein, Ş. K. Özdemir, and L. Yang, “A robust and tunable add-drop filter using whispering gallery mode microtoroid resonator,” J. Lightwave Technol. 30, 3306–3315 (2012).
[Crossref]

W. Kim, Ş. K. Özdemir, J. Zhu, F. Monifi, C. Coban, and L. Yang, “Detection and size measurement of individual hemozoin nanocrystals in aquatic environment using a whispering gallery mode resonator,” Opt. Express 20, 29426–29446 (2012).
[Crossref]

Morandotti, R.

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, 093902 (2009).
[Crossref]

Nori, F.

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]

Oliveira, J. E. B.

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, 108–113 (2013).
[Crossref]

Onishchukov, G.

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

Özdemir, S. K.

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]

B. Peng, Ş. K. Özdemir, M. Liertzer, W. Chen, J. Kramer, H. Yilmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. USA 113, 6845–6850 (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]

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]

Ş. K. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery Raman microlaser,” Proc. Natl. Acad. Sci. USA 111, E3836–E3844 (2014).
[Crossref]

F. Monifi, Ş. K. Özdemir, and L. Yang, “Tunable add-drop filter using an active whispering gallery mode microcavity,” Appl. Phys. Lett. 103, 181103 (2013).
[Crossref]

F. Monifi, J. Friedlein, Ş. K. Özdemir, and L. Yang, “A robust and tunable add-drop filter using whispering gallery mode microtoroid resonator,” J. Lightwave Technol. 30, 3306–3315 (2012).
[Crossref]

W. Kim, Ş. K. Özdemir, J. Zhu, F. Monifi, C. Coban, and L. Yang, “Detection and size measurement of individual hemozoin nanocrystals in aquatic environment using a whispering gallery mode resonator,” Opt. Express 20, 29426–29446 (2012).
[Crossref]

L. He, Ş. K. Özdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6, 428–432 (2011).
[Crossref]

J. Zhu, Ş. K. Özdemir, L. He, D. R. Chen, and L. Yang, “Single virus and nanoparticle size spectrometry by whispering-gallery-mode microcavities,” Opt. Express 19, 16195–16206 (2011).
[Crossref]

J. Zhu, Ş. K. Özdemir, L. He, and L. Yang, “Controlled manipulation of mode splitting in an optical microcavity by two Rayleigh scatterers,” Opt. Express 18, 23535–23543 (2010).
[Crossref]

L. He, Ş. K. Özdemir, J. Zhu, and L. Yang, “Ultrasensitive detection of mode splitting in active optical microcavities,” Phys. Rev. A 82, 053810 (2010).
[Crossref]

J. Zhu, Ş. K. Özdemir, Y. F. Xiao, L. Li, L. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2010).
[Crossref]

Parkins, A. S.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref]

Peng, B.

B. Peng, Ş. K. Özdemir, M. Liertzer, W. Chen, J. Kramer, H. Yilmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. USA 113, 6845–6850 (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]

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]

Ş. K. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery Raman microlaser,” Proc. Natl. Acad. Sci. USA 111, E3836–E3844 (2014).
[Crossref]

Peschel, U.

M. Wimmer, A. Regensburger, M. A. Miri, C. Bersch, D. N. Christodoulides, and U. Peschel, “Observation of optical solitons in PT-symmetric lattices,” Nat. Commun. 6, 7782 (2015).
[Crossref]

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

Pick, A.

B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S. L. Chua, J. D. Joannopoulos, and M. Soljačić, “Spawning rings of exceptional points out of Dirac cones,” Nature 525, 354–358 (2015).
[Crossref]

Qiu, C.

Regensburger, A.

M. Wimmer, A. Regensburger, M. A. Miri, C. Bersch, D. N. Christodoulides, and U. Peschel, “Observation of optical solitons in PT-symmetric lattices,” Nat. Commun. 6, 7782 (2015).
[Crossref]

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

Ren, J.

Rotter, S.

B. Peng, Ş. K. Özdemir, M. Liertzer, W. Chen, J. Kramer, H. Yilmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. USA 113, 6845–6850 (2016).
[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]

Salamo, G. J.

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, 093902 (2009).
[Crossref]

Scherer, A.

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, 108–113 (2013).
[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]

Shi, K.

B. B. Li, W. R. Clements, X. C. Yu, K. Shi, Q. H. Gong, and Y. F. Xiao, “Single nanoparticle detection using split-mode microcavity Raman lasers,” Proc. Natl. Acad. Sci. USA 111, 14657–14662 (2014).
[Crossref]

Shopova, S. I.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620, 8–26 (2008).
[Crossref]

Shu, J.

Siviloglou, G. A.

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, 093902 (2009).
[Crossref]

Soljacic, M.

B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S. L. Chua, J. D. Joannopoulos, and M. Soljačić, “Spawning rings of exceptional points out of Dirac cones,” Nature 525, 354–358 (2015).
[Crossref]

Soltani, M.

Song, Q.

N. Zhang, S. Liu, K. Wang, Z. Gu, M. Li, N. Yi, S. Xiao, and Q. Song, “Single nanoparticle detection using far-field emission of photonic molecule around the exceptional point,” Sci. Rep. 5, 11912 (2015).
[Crossref]

Spillane, S. M.

L. Yang, T. Carmon, B. Min, S. M. Spillane, and K. J. Vahala, “Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol-gel process,” Appl. Phys. Lett. 86, 091114 (2005).
[Crossref]

T. J. Kippenberg, S. M. Spillane, D. K. Armani, and K. J. Vahala, “Ultralow-threshold microcavity Raman laser on a microelectronic chip,” Opt. Lett. 29, 1224–1226 (2004).
[Crossref]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[Crossref]

Sun, Y.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620, 8–26 (2008).
[Crossref]

Suter, J. D.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620, 8–26 (2008).
[Crossref]

Swaim, J. D.

Vahala, K. J.

T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express 15, 17172–17205 (2007).
[Crossref]

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref]

L. Yang, T. Carmon, B. Min, S. M. Spillane, and K. J. Vahala, “Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol-gel process,” Appl. Phys. Lett. 86, 091114 (2005).
[Crossref]

T. J. Kippenberg, S. M. Spillane, D. K. Armani, and K. J. Vahala, “Ultralow-threshold microcavity Raman laser on a microelectronic chip,” Opt. Lett. 29, 1224–1226 (2004).
[Crossref]

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[Crossref]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[Crossref]

Volatier-Ravat, M.

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, 093902 (2009).
[Crossref]

Vollmer, F.

M. R. Foreman, J. D. Swaim, and F. Vollmer, “Whispering gallery mode sensors,” Adv. Opt. Photon. 7, 168–240 (2015).
[Crossref]

F. Vollmer and L. Yang, “Label-free detection with high-Q microcavities: a review of biosensing mechanisms for integrated devices,” Nanophotonics 1, 267–291 (2012).
[Crossref]

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[Crossref]

Wang, K.

N. Zhang, S. Liu, K. Wang, Z. Gu, M. Li, N. Yi, S. Xiao, and Q. Song, “Single nanoparticle detection using far-field emission of photonic molecule around the exceptional point,” Sci. Rep. 5, 11912 (2015).
[Crossref]

Wang, Y.

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

White, I. M.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620, 8–26 (2008).
[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]

B. Peng, Ş. K. Özdemir, M. Liertzer, W. Chen, J. Kramer, H. Yilmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. USA 113, 6845–6850 (2016).
[Crossref]

J. Wiersig, “Sensors operating at exceptional points: general theory,” Phys. Rev. A 93, 033809 (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. Wiersig, “Structure of whispering-gallery modes in optical microdisks perturbed by nanoparticles,” Phys. Rev. A 84, 063828 (2011).
[Crossref]

Wilcut, E.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref]

Wimmer, M.

M. Wimmer, A. Regensburger, M. A. Miri, C. Bersch, D. N. Christodoulides, and U. Peschel, “Observation of optical solitons in PT-symmetric lattices,” Nat. Commun. 6, 7782 (2015).
[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]

Wong, Z. J.

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

Xiao, S.

N. Zhang, S. Liu, K. Wang, Z. Gu, M. Li, N. Yi, S. Xiao, and Q. Song, “Single nanoparticle detection using far-field emission of photonic molecule around the exceptional point,” Sci. Rep. 5, 11912 (2015).
[Crossref]

Xiao, Y. F.

B. B. Li, W. R. Clements, X. C. Yu, K. Shi, Q. H. Gong, and Y. F. Xiao, “Single nanoparticle detection using split-mode microcavity Raman lasers,” Proc. Natl. Acad. Sci. USA 111, 14657–14662 (2014).
[Crossref]

X. Yi, Y. F. Xiao, Y. C. Liu, B. B. Li, Y. L. Chen, Y. Li, and Q. H. Gong, “Multiple-Rayleigh-scatterer-induced mode splitting in a high-Q whispering-gallery-mode microresonator,” Phys. Rev. A 83, 023803 (2011).
[Crossref]

J. Zhu, Ş. K. Özdemir, Y. F. Xiao, L. Li, L. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2010).
[Crossref]

Xu, Q.

Xu, Y. L.

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, 108–113 (2013).
[Crossref]

Yan, C.

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]

B. Peng, Ş. K. Özdemir, M. Liertzer, W. Chen, J. Kramer, H. Yilmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. USA 113, 6845–6850 (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]

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]

Ş. K. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery Raman microlaser,” Proc. Natl. Acad. Sci. USA 111, E3836–E3844 (2014).
[Crossref]

F. Monifi, Ş. K. Özdemir, and L. Yang, “Tunable add-drop filter using an active whispering gallery mode microcavity,” Appl. Phys. Lett. 103, 181103 (2013).
[Crossref]

F. Monifi, J. Friedlein, Ş. K. Özdemir, and L. Yang, “A robust and tunable add-drop filter using whispering gallery mode microtoroid resonator,” J. Lightwave Technol. 30, 3306–3315 (2012).
[Crossref]

F. Vollmer and L. Yang, “Label-free detection with high-Q microcavities: a review of biosensing mechanisms for integrated devices,” Nanophotonics 1, 267–291 (2012).
[Crossref]

W. Kim, Ş. K. Özdemir, J. Zhu, F. Monifi, C. Coban, and L. Yang, “Detection and size measurement of individual hemozoin nanocrystals in aquatic environment using a whispering gallery mode resonator,” Opt. Express 20, 29426–29446 (2012).
[Crossref]

L. He, Ş. K. Özdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6, 428–432 (2011).
[Crossref]

T. Lu, L. Yang, T. Carmon, and B. Min, “A narrow-linewidth on-chip toroid Raman laser,” IEEE J. Quantum Electron. 47, 320–326 (2011).
[Crossref]

J. Zhu, Ş. K. Özdemir, L. He, D. R. Chen, and L. Yang, “Single virus and nanoparticle size spectrometry by whispering-gallery-mode microcavities,” Opt. Express 19, 16195–16206 (2011).
[Crossref]

J. Zhu, Ş. K. Özdemir, L. He, and L. Yang, “Controlled manipulation of mode splitting in an optical microcavity by two Rayleigh scatterers,” Opt. Express 18, 23535–23543 (2010).
[Crossref]

L. He, Ş. K. Özdemir, J. Zhu, and L. Yang, “Ultrasensitive detection of mode splitting in active optical microcavities,” Phys. Rev. A 82, 053810 (2010).
[Crossref]

J. Zhu, Ş. K. Özdemir, Y. F. Xiao, L. Li, L. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2010).
[Crossref]

L. Yang, T. Carmon, B. Min, S. M. Spillane, and K. J. Vahala, “Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol-gel process,” Appl. Phys. Lett. 86, 091114 (2005).
[Crossref]

Yang, X.

Ş. K. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery Raman microlaser,” Proc. Natl. Acad. Sci. USA 111, E3836–E3844 (2014).
[Crossref]

Yi, N.

N. Zhang, S. Liu, K. Wang, Z. Gu, M. Li, N. Yi, S. Xiao, and Q. Song, “Single nanoparticle detection using far-field emission of photonic molecule around the exceptional point,” Sci. Rep. 5, 11912 (2015).
[Crossref]

Yi, X.

X. Yi, Y. F. Xiao, Y. C. Liu, B. B. Li, Y. L. Chen, Y. Li, and Q. H. Gong, “Multiple-Rayleigh-scatterer-induced mode splitting in a high-Q whispering-gallery-mode microresonator,” Phys. Rev. A 83, 023803 (2011).
[Crossref]

Yilmaz, H.

B. Peng, Ş. K. Özdemir, M. Liertzer, W. Chen, J. Kramer, H. Yilmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. USA 113, 6845–6850 (2016).
[Crossref]

Ş. K. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery Raman microlaser,” Proc. Natl. Acad. Sci. USA 111, E3836–E3844 (2014).
[Crossref]

Yu, X. C.

B. B. Li, W. R. Clements, X. C. Yu, K. Shi, Q. H. Gong, and Y. F. Xiao, “Single nanoparticle detection using split-mode microcavity Raman lasers,” Proc. Natl. Acad. Sci. USA 111, 14657–14662 (2014).
[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, N.

N. Zhang, S. Liu, K. Wang, Z. Gu, M. Li, N. Yi, S. Xiao, and Q. Song, “Single nanoparticle detection using far-field emission of photonic molecule around the exceptional point,” Sci. Rep. 5, 11912 (2015).
[Crossref]

Zhang, X.

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

C. Qiu, J. Shu, Z. Li, X. Zhang, and Q. Xu, “Wavelength tracking with thermally controlled silicon resonators,” Opt. Express 19, 5143–5148 (2011).
[Crossref]

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]

Zhen, B.

B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S. L. Chua, J. D. Joannopoulos, and M. Soljačić, “Spawning rings of exceptional points out of Dirac cones,” Nature 525, 354–358 (2015).
[Crossref]

Zhu, H.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620, 8–26 (2008).
[Crossref]

Zhu, J.

Ş. K. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery Raman microlaser,” Proc. Natl. Acad. Sci. USA 111, E3836–E3844 (2014).
[Crossref]

W. Kim, Ş. K. Özdemir, J. Zhu, F. Monifi, C. Coban, and L. Yang, “Detection and size measurement of individual hemozoin nanocrystals in aquatic environment using a whispering gallery mode resonator,” Opt. Express 20, 29426–29446 (2012).
[Crossref]

L. He, Ş. K. Özdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6, 428–432 (2011).
[Crossref]

J. Zhu, Ş. K. Özdemir, L. He, D. R. Chen, and L. Yang, “Single virus and nanoparticle size spectrometry by whispering-gallery-mode microcavities,” Opt. Express 19, 16195–16206 (2011).
[Crossref]

J. Zhu, Ş. K. Özdemir, L. He, and L. Yang, “Controlled manipulation of mode splitting in an optical microcavity by two Rayleigh scatterers,” Opt. Express 18, 23535–23543 (2010).
[Crossref]

L. He, Ş. K. Özdemir, J. Zhu, and L. Yang, “Ultrasensitive detection of mode splitting in active optical microcavities,” Phys. Rev. A 82, 053810 (2010).
[Crossref]

J. Zhu, Ş. K. Özdemir, Y. F. Xiao, L. Li, L. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2010).
[Crossref]

Adv. Opt. Photon. (1)

Anal. Chim. Acta (1)

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620, 8–26 (2008).
[Crossref]

Appl. Phys. Lett. (2)

L. Yang, T. Carmon, B. Min, S. M. Spillane, and K. J. Vahala, “Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol-gel process,” Appl. Phys. Lett. 86, 091114 (2005).
[Crossref]

F. Monifi, Ş. K. Özdemir, and L. Yang, “Tunable add-drop filter using an active whispering gallery mode microcavity,” Appl. Phys. Lett. 103, 181103 (2013).
[Crossref]

IEEE J. Quantum Electron. (1)

T. Lu, L. Yang, T. Carmon, and B. Min, “A narrow-linewidth on-chip toroid Raman laser,” IEEE J. Quantum Electron. 47, 320–326 (2011).
[Crossref]

J. Lightwave Technol. (2)

Nanophotonics (1)

F. Vollmer and L. Yang, “Label-free detection with high-Q microcavities: a review of biosensing mechanisms for integrated devices,” Nanophotonics 1, 267–291 (2012).
[Crossref]

Nat. Commun. (1)

M. Wimmer, A. Regensburger, M. A. Miri, C. Bersch, D. N. Christodoulides, and U. Peschel, “Observation of optical solitons in PT-symmetric lattices,” Nat. Commun. 6, 7782 (2015).
[Crossref]

Nat. Mater. (1)

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, 108–113 (2013).
[Crossref]

Nat. Methods (1)

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[Crossref]

Nat. Nanotechnol. (1)

L. He, Ş. K. Özdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6, 428–432 (2011).
[Crossref]

Nat. Photonics (1)

J. Zhu, Ş. K. Özdemir, Y. F. Xiao, L. Li, L. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2010).
[Crossref]

Nat. Phys. (2)

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 (7)

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

B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S. L. Chua, J. D. Joannopoulos, and M. Soljačić, “Spawning rings of exceptional points out of Dirac cones,” Nature 525, 354–358 (2015).
[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]

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[Crossref]

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[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 (5)

Opt. Lett. (2)

Phys. Rev. A (4)

X. Yi, Y. F. Xiao, Y. C. Liu, B. B. Li, Y. L. Chen, Y. Li, and Q. H. Gong, “Multiple-Rayleigh-scatterer-induced mode splitting in a high-Q whispering-gallery-mode microresonator,” Phys. Rev. A 83, 023803 (2011).
[Crossref]

L. He, Ş. K. Özdemir, J. Zhu, and L. Yang, “Ultrasensitive detection of mode splitting in active optical microcavities,” Phys. Rev. A 82, 053810 (2010).
[Crossref]

J. Wiersig, “Structure of whispering-gallery modes in optical microdisks perturbed by nanoparticles,” Phys. Rev. A 84, 063828 (2011).
[Crossref]

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

Phys. Rev. Lett. (4)

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]

C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80, 5243–5246 (1998).
[Crossref]

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, 093902 (2009).
[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]

Proc. Natl. Acad. Sci. USA (3)

B. Peng, Ş. K. Özdemir, M. Liertzer, W. Chen, J. Kramer, H. Yilmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. USA 113, 6845–6850 (2016).
[Crossref]

Ş. K. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery Raman microlaser,” Proc. Natl. Acad. Sci. USA 111, E3836–E3844 (2014).
[Crossref]

B. B. Li, W. R. Clements, X. C. Yu, K. Shi, Q. H. Gong, and Y. F. Xiao, “Single nanoparticle detection using split-mode microcavity Raman lasers,” Proc. Natl. Acad. Sci. USA 111, 14657–14662 (2014).
[Crossref]

Rep. Prog. Phys. (1)

C. M. Bender, “Making sense of non-Hermitian Hamiltonians,” Rep. Prog. Phys. 70, 947–1018 (2007).
[Crossref]

Sci. Rep. (1)

N. Zhang, S. Liu, K. Wang, Z. Gu, M. Li, N. Yi, S. Xiao, and Q. Song, “Single nanoparticle detection using far-field emission of photonic molecule around the exceptional point,” Sci. Rep. 5, 11912 (2015).
[Crossref]

Science (2)

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

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1. WGM nanoparticle sensors based on (a) the single passive resonator, (b) the single active resonator, and (c) PT-symmetric coupled resonators with balanced gain and loss. The gray-colored small circle denotes a nanoparticle within the mode volume of the resonator. The spectra illustrate sensing mechanisms of the sensors. The dashed red curve shows the spectrum before the nanoparticle binding event; the solid blue curve corresponds to the spectrum after the nanoparticle binding event. The sensors in (a) and (b) exhibit a frequency splitting proportional to ϵ, which is the perturbation strength induced by the nanoparticle. With the assistance of gain, the linewidth of the resonance mode is reduced; thus, the resolvability of mode splitting is improved in (b), compared with the sensor in (a). For the PT-symmetric sensor operating at the phase transition point, the frequency splitting induced by the nanoparticle exhibits a square-root dependence on the perturbation. For a sufficiently small perturbation, the PT-symmetric sensor exhibits much larger frequency splitting. In addition, with balanced gain and loss, the linewidth can be very narrow, which helps to resolve much smaller mode splitting.
Fig. 2.
Fig. 2. Evolution of the (a) real part and (b) imaginary part of eigenfrequencies in PT-symmetric coupled resonators when the coupling strength between two resonators is varied. The PT phase transition point is obtained when the coupling strength κ=κPT=1  GHz. The symbols are the results of numerical simulations, and the color curves are theoretical predictions.
Fig. 3.
Fig. 3. (a) Evolution of the real part of the eigenfrequencies Re(ωω0) in PT-symmetric coupled resonators with single nanoparticle located at resonator μRa when the coupling strength is varied. Two supermodes (blue squares and red circles) are perturbed by the nanoparticle and thus experience frequency shift, whereas the other two supermodes (black squares and circles) are not affected, serving as reference signals. The size and location of the nanoparticle (i.e., perturbation strength) are fixed. (b) Absolute value of the frequency splitting Re(Δω) of two pairs of supermodes in PT-symmetric coupled resonators when changing the coupling strength. The frequency splitting is obtained by calculating the difference between frequencies of the perturbed supermode and its reference. When the coupling strength is zero, it becomes the case of a single WGM sensor: the resonator with the nanoparticle exhibits frequency splitting, whereas the other resonator is not affected at all. At the phase transition point, the PT-symmetric sensor exhibits about twice the frequency splitting compared with the single WGM sensor subject to the same perturbation. The symbols are results from the numerical simulations, and the color curves are the theoretical predictions.
Fig. 4.
Fig. 4. (a) Dependence of sensitivity of a PT-symmetric sensor operating at the phase transition point on the perturbation strength ϵ. Inset shows the log-log plot of the dependence of the sensitivity on the perturbation strength, where a linear slope of 1/2 is clearly seen. (b) Dependences of the sensitivity enhancement on the perturbation strength ϵ (blue squares and dashed curve) and the gain strength γ (red circles and dashed curve). For the former one, the gain (loss) strength γ of the coupled resonators and the coupling strength κ are fixed when changing the perturbation strength ϵ. For the latter, the perturbation strength ϵ of the nanoparticle is fixed when changing the gain (loss) strength γ, and the coupling strength between the resonators is varied to set the system at the phase transition point. The symbols are the results of numerical simulations, and the color curves are theoretical predictions.
Fig. 5.
Fig. 5. (a) Evolution of the imaginary part of the eigenfrequencies Im(ωω0) in PT-symmetric coupled resonators with a single nanoparticle located at resonator μRa when the coupling strength between two resonators is varied. The size and location of the nanoparticle (i.e., perturbation strength) are fixed. (b) Absolute value of the linewidth difference 2Im(Δω) of two pairs of supermodes in PT-symmetric coupled resonators when changing the coupling strength. The linewidth difference is obtained by calculating the difference between the linewidths of the perturbed supermode and its reference. The symbols are results from the numerical simulations, and the color curves are theoretical predictions.
Fig. 6.
Fig. 6. (a) Illustration of the detection of two nanoparticles in a PT-symmetric WGM nanoparticle sensor. The two nanoparticles are placed within the mode volume of the resonator with gain. (b), (c) Variation in frequency splitting as a function of the angular position of the second nanoparticle when (b) the two nanoparticles are identical with the same perturbation strength, and (c) the two nanoparticles are different and hence have different perturbation strengths. The angular position of the first nanoparticle is fixed and set to be zero. Blue squares are numerical simulation results; red solid curves are theoretical predictions. The results are normalized by the frequency splitting induced by the first nanoparticle on a single resonator sensor.
Fig. 7.
Fig. 7. (a) Illustration of the detection of multiple nanoparticles in a PT-symmetric WGM nanoparticle sensor. Ten different nanoparticles (numbered gray circles) are randomly deposited within the mode volume of the resonator with gain one by one. (b) Numerical results of frequency splitting variation for 10 nanoparticles deposited on the PT-symmetric WGM sensor (blue lines and squares) and a single WGM sensor (red lines and circles). The dashed vertical lines are used as eye guides. Results for the single WGM sensor are obtained by removing the lossy resonator in the numerical simulation. Results are normalized by the frequency splitting induced by the first nanoparticle deposited on a single WGM sensor with a value of 73 MHz.

Equations (12)

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

ω1,2=ω0i(γa+γb)/4+κ2(γaγb)2/16,
ω3,4=ω0i(γa+γb)/4κ2(γaγb)2/16,
ω1,2=ω0+κ2κPT2,
ω3,4=ω0κ2κPT2,with  κPT=|γ|/2.
ω1=ω0+ϵ+κ2γ2/4iγϵ+ϵ2,
ω2=ω0+κ2γ2/4,
ω3=ω0+ϵκ2γ2/4iγϵ+ϵ2,
ω4=ω0κ2γ2/4.
η|Re(ΔωPT)Re(Δωsingle)|.
η=|γ/(8ϵ)|,
H1=(ϵ1+ϵ2ϵ1+ϵ2ei2mβ200ϵ1+ϵ2ei2mβ2ϵ1+ϵ20000000000),
H1=i=1NϵiIi,with  Ii=(1ei2mβi00ei2mβi10000000000),

Metrics