Abstract

We report controlled manipulation of mode splitting in an optical microresonator coupled to two nanoprobes. It is demonstrated that, by controlling the positions of the nanoprobes, the split modes can be tuned simultaneously or individually and experience crossing or anti-crossing in frequency and linewidth. A tunable transition between standing wave mode and travelling wave mode is also observed. Underlying physics is discussed by developing a two-scatterer model which can be extended to multiple scatterers. Observed rich dynamics and tunability of split modes in a single microresonator will find immediate applications in optical sensing, opto-mechanics, filters and will provide a platform to study strong light-matter interactions in two-mode cavities.

© 2010 Optical Society of America

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  1. K. J. Vahala, "Optical microcavities," Nature 424, 839-846 (2003).
    [CrossRef] [PubMed]
  2. F. Vollmer, and S. Arnold, "Whispering-gallery-mode biosensing: label-free detection down to single molecules," Nat. Methods 5, 591-596 (2008).
    [CrossRef] [PubMed]
  3. F. Vollmer, S. Arnold, and D. Keng, "Single virus detection from the reactive shift of a whispering-gallery mode," Proc. Natl. Acad. Sci. U.S.A. 105, 20701-20704 (2008).
    [CrossRef] [PubMed]
  4. J. Zhu, S. 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 (2009).
    [CrossRef]
  5. T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, "Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity," Phys. Rev. Lett. 95, 033901 (2005).
    [CrossRef] [PubMed]
  6. T. J. Kippenberg, and K. J. Vahala, "Cavity Opto-Mechanics," Opt. Express 15, 17172-17205 (2007).
    [CrossRef] [PubMed]
  7. S.-B. Lee, J. Yang, S. Moon, S.-Y. Lee, J.-B. Shim, S. W. Kim, J.-H. Lee, and K. An, "Observation of an Exceptional Point in a Chaotic Optical Microcavity," Phys. Rev. Lett. 103, 134101 (2009).
    [CrossRef] [PubMed]
  8. T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, "Static Envelope Patterns in Composite Resonances Generated by Level Crossing in Optical Toroidal Microcavities," Phys. Rev. Lett. 100, 103905 (2008).
    [CrossRef] [PubMed]
  9. D. S. Weiss, V. Sandoghdar, J. Hare, V. Lefvre-Seguin, J.-M. Raimond, and S. Haroche, "Splitting of high-Q Mie modes induced by light backscattering in silica microspheres," Opt. Express 20, 1835-1837 (1995).
  10. T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Modal coupling in traveling-wave resonators," Opt. Lett. 27, 1669 (2002).
    [CrossRef]
  11. A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, "Controlled Coupling of Counterpropagating Whispering-Gallery Modes by a Single Rayleigh Scatterer: A Classical Problem in a Quantum Optical Light," Phys. Rev. Lett. 99, 173603 (2007).
    [CrossRef] [PubMed]
  12. L. Deych, and J. Rubin, "Rayleigh scattering of whispering gallery modes of microspheres due to a single dipole scatterer," Phys. Rev. A 80, 061805 (2009).
    [CrossRef]
  13. L. Chantada, N. I. Nikolaev, A. L. Ivanov, P. Borri, and W. Langbein, "Optical resonances in microcylinders: response to perturbations for biosensing," J. Opt. Soc. Am. B 25, 1312 (2008).
    [CrossRef]
  14. R. G. Knollenberg, "The measurement of latex particle sizes using scattering ratios in the Rayleigh scattering size range," J. Aerosol Sci. 20, 331-345 (1989).
    [CrossRef]

2009 (3)

J. Zhu, S. 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 (2009).
[CrossRef]

S.-B. Lee, J. Yang, S. Moon, S.-Y. Lee, J.-B. Shim, S. W. Kim, J.-H. Lee, and K. An, "Observation of an Exceptional Point in a Chaotic Optical Microcavity," Phys. Rev. Lett. 103, 134101 (2009).
[CrossRef] [PubMed]

L. Deych, and J. Rubin, "Rayleigh scattering of whispering gallery modes of microspheres due to a single dipole scatterer," Phys. Rev. A 80, 061805 (2009).
[CrossRef]

2008 (4)

L. Chantada, N. I. Nikolaev, A. L. Ivanov, P. Borri, and W. Langbein, "Optical resonances in microcylinders: response to perturbations for biosensing," J. Opt. Soc. Am. B 25, 1312 (2008).
[CrossRef]

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, "Static Envelope Patterns in Composite Resonances Generated by Level Crossing in Optical Toroidal Microcavities," Phys. Rev. Lett. 100, 103905 (2008).
[CrossRef] [PubMed]

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

F. Vollmer, S. Arnold, and D. Keng, "Single virus detection from the reactive shift of a whispering-gallery mode," Proc. Natl. Acad. Sci. U.S.A. 105, 20701-20704 (2008).
[CrossRef] [PubMed]

2007 (2)

T. J. Kippenberg, and K. J. Vahala, "Cavity Opto-Mechanics," Opt. Express 15, 17172-17205 (2007).
[CrossRef] [PubMed]

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, "Controlled Coupling of Counterpropagating Whispering-Gallery Modes by a Single Rayleigh Scatterer: A Classical Problem in a Quantum Optical Light," Phys. Rev. Lett. 99, 173603 (2007).
[CrossRef] [PubMed]

2005 (1)

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, "Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity," Phys. Rev. Lett. 95, 033901 (2005).
[CrossRef] [PubMed]

2003 (1)

K. J. Vahala, "Optical microcavities," Nature 424, 839-846 (2003).
[CrossRef] [PubMed]

2002 (1)

1995 (1)

D. S. Weiss, V. Sandoghdar, J. Hare, V. Lefvre-Seguin, J.-M. Raimond, and S. Haroche, "Splitting of high-Q Mie modes induced by light backscattering in silica microspheres," Opt. Express 20, 1835-1837 (1995).

1989 (1)

R. G. Knollenberg, "The measurement of latex particle sizes using scattering ratios in the Rayleigh scattering size range," J. Aerosol Sci. 20, 331-345 (1989).
[CrossRef]

An, K.

S.-B. Lee, J. Yang, S. Moon, S.-Y. Lee, J.-B. Shim, S. W. Kim, J.-H. Lee, and K. An, "Observation of an Exceptional Point in a Chaotic Optical Microcavity," Phys. Rev. Lett. 103, 134101 (2009).
[CrossRef] [PubMed]

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] [PubMed]

F. Vollmer, S. Arnold, and D. Keng, "Single virus detection from the reactive shift of a whispering-gallery mode," Proc. Natl. Acad. Sci. U.S.A. 105, 20701-20704 (2008).
[CrossRef] [PubMed]

Benson, O.

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, "Controlled Coupling of Counterpropagating Whispering-Gallery Modes by a Single Rayleigh Scatterer: A Classical Problem in a Quantum Optical Light," Phys. Rev. Lett. 99, 173603 (2007).
[CrossRef] [PubMed]

Borri, P.

Carmon, T.

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, "Static Envelope Patterns in Composite Resonances Generated by Level Crossing in Optical Toroidal Microcavities," Phys. Rev. Lett. 100, 103905 (2008).
[CrossRef] [PubMed]

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, "Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity," Phys. Rev. Lett. 95, 033901 (2005).
[CrossRef] [PubMed]

Chantada, L.

Chen, D.-R.

J. Zhu, S. 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 (2009).
[CrossRef]

Deych, L.

L. Deych, and J. Rubin, "Rayleigh scattering of whispering gallery modes of microspheres due to a single dipole scatterer," Phys. Rev. A 80, 061805 (2009).
[CrossRef]

Götzinger, S.

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, "Controlled Coupling of Counterpropagating Whispering-Gallery Modes by a Single Rayleigh Scatterer: A Classical Problem in a Quantum Optical Light," Phys. Rev. Lett. 99, 173603 (2007).
[CrossRef] [PubMed]

Hare, J.

D. S. Weiss, V. Sandoghdar, J. Hare, V. Lefvre-Seguin, J.-M. Raimond, and S. Haroche, "Splitting of high-Q Mie modes induced by light backscattering in silica microspheres," Opt. Express 20, 1835-1837 (1995).

Haroche, S.

D. S. Weiss, V. Sandoghdar, J. Hare, V. Lefvre-Seguin, J.-M. Raimond, and S. Haroche, "Splitting of high-Q Mie modes induced by light backscattering in silica microspheres," Opt. Express 20, 1835-1837 (1995).

He, L.

J. Zhu, S. 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 (2009).
[CrossRef]

Ivanov, A. L.

Keng, D.

F. Vollmer, S. Arnold, and D. Keng, "Single virus detection from the reactive shift of a whispering-gallery mode," Proc. Natl. Acad. Sci. U.S.A. 105, 20701-20704 (2008).
[CrossRef] [PubMed]

Kim, S. W.

S.-B. Lee, J. Yang, S. Moon, S.-Y. Lee, J.-B. Shim, S. W. Kim, J.-H. Lee, and K. An, "Observation of an Exceptional Point in a Chaotic Optical Microcavity," Phys. Rev. Lett. 103, 134101 (2009).
[CrossRef] [PubMed]

Kippenberg, T. J.

T. J. Kippenberg, and K. J. Vahala, "Cavity Opto-Mechanics," Opt. Express 15, 17172-17205 (2007).
[CrossRef] [PubMed]

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, "Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity," Phys. Rev. Lett. 95, 033901 (2005).
[CrossRef] [PubMed]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Modal coupling in traveling-wave resonators," Opt. Lett. 27, 1669 (2002).
[CrossRef]

Knollenberg, R. G.

R. G. Knollenberg, "The measurement of latex particle sizes using scattering ratios in the Rayleigh scattering size range," J. Aerosol Sci. 20, 331-345 (1989).
[CrossRef]

Langbein, W.

Lee, J.-H.

S.-B. Lee, J. Yang, S. Moon, S.-Y. Lee, J.-B. Shim, S. W. Kim, J.-H. Lee, and K. An, "Observation of an Exceptional Point in a Chaotic Optical Microcavity," Phys. Rev. Lett. 103, 134101 (2009).
[CrossRef] [PubMed]

Lee, S.-B.

S.-B. Lee, J. Yang, S. Moon, S.-Y. Lee, J.-B. Shim, S. W. Kim, J.-H. Lee, and K. An, "Observation of an Exceptional Point in a Chaotic Optical Microcavity," Phys. Rev. Lett. 103, 134101 (2009).
[CrossRef] [PubMed]

Lee, S.-Y.

S.-B. Lee, J. Yang, S. Moon, S.-Y. Lee, J.-B. Shim, S. W. Kim, J.-H. Lee, and K. An, "Observation of an Exceptional Point in a Chaotic Optical Microcavity," Phys. Rev. Lett. 103, 134101 (2009).
[CrossRef] [PubMed]

Lefvre-Seguin, V.

D. S. Weiss, V. Sandoghdar, J. Hare, V. Lefvre-Seguin, J.-M. Raimond, and S. Haroche, "Splitting of high-Q Mie modes induced by light backscattering in silica microspheres," Opt. Express 20, 1835-1837 (1995).

Li, L.

J. Zhu, S. 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 (2009).
[CrossRef]

Mazzei, A.

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, "Controlled Coupling of Counterpropagating Whispering-Gallery Modes by a Single Rayleigh Scatterer: A Classical Problem in a Quantum Optical Light," Phys. Rev. Lett. 99, 173603 (2007).
[CrossRef] [PubMed]

Menezes, L. de S.

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, "Controlled Coupling of Counterpropagating Whispering-Gallery Modes by a Single Rayleigh Scatterer: A Classical Problem in a Quantum Optical Light," Phys. Rev. Lett. 99, 173603 (2007).
[CrossRef] [PubMed]

Moon, S.

S.-B. Lee, J. Yang, S. Moon, S.-Y. Lee, J.-B. Shim, S. W. Kim, J.-H. Lee, and K. An, "Observation of an Exceptional Point in a Chaotic Optical Microcavity," Phys. Rev. Lett. 103, 134101 (2009).
[CrossRef] [PubMed]

Nikolaev, N. I.

Oxborrow, M.

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, "Static Envelope Patterns in Composite Resonances Generated by Level Crossing in Optical Toroidal Microcavities," Phys. Rev. Lett. 100, 103905 (2008).
[CrossRef] [PubMed]

Özdemir, S. K.

J. Zhu, S. 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 (2009).
[CrossRef]

Raimond, J.-M.

D. S. Weiss, V. Sandoghdar, J. Hare, V. Lefvre-Seguin, J.-M. Raimond, and S. Haroche, "Splitting of high-Q Mie modes induced by light backscattering in silica microspheres," Opt. Express 20, 1835-1837 (1995).

Rokhsari, H.

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, "Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity," Phys. Rev. Lett. 95, 033901 (2005).
[CrossRef] [PubMed]

Rubin, J.

L. Deych, and J. Rubin, "Rayleigh scattering of whispering gallery modes of microspheres due to a single dipole scatterer," Phys. Rev. A 80, 061805 (2009).
[CrossRef]

Sandoghdar, V.

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, "Controlled Coupling of Counterpropagating Whispering-Gallery Modes by a Single Rayleigh Scatterer: A Classical Problem in a Quantum Optical Light," Phys. Rev. Lett. 99, 173603 (2007).
[CrossRef] [PubMed]

D. S. Weiss, V. Sandoghdar, J. Hare, V. Lefvre-Seguin, J.-M. Raimond, and S. Haroche, "Splitting of high-Q Mie modes induced by light backscattering in silica microspheres," Opt. Express 20, 1835-1837 (1995).

Scherer, A.

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, "Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity," Phys. Rev. Lett. 95, 033901 (2005).
[CrossRef] [PubMed]

Schwefel, H. G. L.

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, "Static Envelope Patterns in Composite Resonances Generated by Level Crossing in Optical Toroidal Microcavities," Phys. Rev. Lett. 100, 103905 (2008).
[CrossRef] [PubMed]

Shim, J.-B.

S.-B. Lee, J. Yang, S. Moon, S.-Y. Lee, J.-B. Shim, S. W. Kim, J.-H. Lee, and K. An, "Observation of an Exceptional Point in a Chaotic Optical Microcavity," Phys. Rev. Lett. 103, 134101 (2009).
[CrossRef] [PubMed]

Spillane, S. M.

Stone, A. D.

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, "Static Envelope Patterns in Composite Resonances Generated by Level Crossing in Optical Toroidal Microcavities," Phys. Rev. Lett. 100, 103905 (2008).
[CrossRef] [PubMed]

Vahala, K. J.

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, "Static Envelope Patterns in Composite Resonances Generated by Level Crossing in Optical Toroidal Microcavities," Phys. Rev. Lett. 100, 103905 (2008).
[CrossRef] [PubMed]

T. J. Kippenberg, and K. J. Vahala, "Cavity Opto-Mechanics," Opt. Express 15, 17172-17205 (2007).
[CrossRef] [PubMed]

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, "Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity," Phys. Rev. Lett. 95, 033901 (2005).
[CrossRef] [PubMed]

K. J. Vahala, "Optical microcavities," Nature 424, 839-846 (2003).
[CrossRef] [PubMed]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Modal coupling in traveling-wave resonators," Opt. Lett. 27, 1669 (2002).
[CrossRef]

Vollmer, F.

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

F. Vollmer, S. Arnold, and D. Keng, "Single virus detection from the reactive shift of a whispering-gallery mode," Proc. Natl. Acad. Sci. U.S.A. 105, 20701-20704 (2008).
[CrossRef] [PubMed]

Weiss, D. S.

D. S. Weiss, V. Sandoghdar, J. Hare, V. Lefvre-Seguin, J.-M. Raimond, and S. Haroche, "Splitting of high-Q Mie modes induced by light backscattering in silica microspheres," Opt. Express 20, 1835-1837 (1995).

Xiao, Y.-F.

J. Zhu, S. 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 (2009).
[CrossRef]

Yang, J.

S.-B. Lee, J. Yang, S. Moon, S.-Y. Lee, J.-B. Shim, S. W. Kim, J.-H. Lee, and K. An, "Observation of an Exceptional Point in a Chaotic Optical Microcavity," Phys. Rev. Lett. 103, 134101 (2009).
[CrossRef] [PubMed]

Yang, L.

J. Zhu, S. 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 (2009).
[CrossRef]

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, "Static Envelope Patterns in Composite Resonances Generated by Level Crossing in Optical Toroidal Microcavities," Phys. Rev. Lett. 100, 103905 (2008).
[CrossRef] [PubMed]

Zhu, J.

J. Zhu, S. 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 (2009).
[CrossRef]

Zumofen, G.

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, "Controlled Coupling of Counterpropagating Whispering-Gallery Modes by a Single Rayleigh Scatterer: A Classical Problem in a Quantum Optical Light," Phys. Rev. Lett. 99, 173603 (2007).
[CrossRef] [PubMed]

J. Aerosol Sci. (1)

R. G. Knollenberg, "The measurement of latex particle sizes using scattering ratios in the Rayleigh scattering size range," J. Aerosol Sci. 20, 331-345 (1989).
[CrossRef]

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

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] [PubMed]

Nat. Photonics (1)

J. Zhu, S. 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 (2009).
[CrossRef]

Nature (1)

K. J. Vahala, "Optical microcavities," Nature 424, 839-846 (2003).
[CrossRef] [PubMed]

Opt. Express (2)

T. J. Kippenberg, and K. J. Vahala, "Cavity Opto-Mechanics," Opt. Express 15, 17172-17205 (2007).
[CrossRef] [PubMed]

D. S. Weiss, V. Sandoghdar, J. Hare, V. Lefvre-Seguin, J.-M. Raimond, and S. Haroche, "Splitting of high-Q Mie modes induced by light backscattering in silica microspheres," Opt. Express 20, 1835-1837 (1995).

Opt. Lett. (1)

Phys. Rev. A (1)

L. Deych, and J. Rubin, "Rayleigh scattering of whispering gallery modes of microspheres due to a single dipole scatterer," Phys. Rev. A 80, 061805 (2009).
[CrossRef]

Phys. Rev. Lett. (4)

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, "Controlled Coupling of Counterpropagating Whispering-Gallery Modes by a Single Rayleigh Scatterer: A Classical Problem in a Quantum Optical Light," Phys. Rev. Lett. 99, 173603 (2007).
[CrossRef] [PubMed]

S.-B. Lee, J. Yang, S. Moon, S.-Y. Lee, J.-B. Shim, S. W. Kim, J.-H. Lee, and K. An, "Observation of an Exceptional Point in a Chaotic Optical Microcavity," Phys. Rev. Lett. 103, 134101 (2009).
[CrossRef] [PubMed]

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, "Static Envelope Patterns in Composite Resonances Generated by Level Crossing in Optical Toroidal Microcavities," Phys. Rev. Lett. 100, 103905 (2008).
[CrossRef] [PubMed]

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, "Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity," Phys. Rev. Lett. 95, 033901 (2005).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

F. Vollmer, S. Arnold, and D. Keng, "Single virus detection from the reactive shift of a whispering-gallery mode," Proc. Natl. Acad. Sci. U.S.A. 105, 20701-20704 (2008).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

(a) Schematics of the experiment showing a fiber taper coupled to a microtoroid, and two nano-fiber tips introduced into the mode volume. Transmission spectra are captured by a photo detector (PD). (b) SEM image of a microtoroid. (c) SEM image of a fiber tip. Inset shows the enlarged image of the tip. (d) Cross-section of a microtoroid ring showing the position of a fiber tip in the field of a WGM.

Fig. 2
Fig. 2

(a) Intensity graphs of mode- crossing (top), anti-crossing (middle) and shift (bottom). (b)–(d) Transmission spectra corresponding to the intensity graphs from top to bottom in (a). Increasing time corresponds to increasing size of the second nanotip.

Fig. 3
Fig. 3

(a) Field distribution of a standing wave mode (SWM) obtained from finite-element simulation and the definitions of ϕ and β. Black circles represent the position of two scatterers in the mode. (b) The relation between ϕ and β. Solid curve is calculated from Eq. (3) and * represent the values calculated using finite-element simulations for χ = 0.5 and ξ = 1.

Fig. 4
Fig. 4

Numerical simulations showing three unique patterns of doublet evolution for increasing size of the second nanotip at (a) β = π/2, (b)β = 0, (c)β = 0.44π for ξ = 1, (d) Resonance frequency and linewidth trajectories of the doublets with the exceptional point when ξ, χ and β are varied. Dashed and solid lines correspond to the two SWMs.

Fig. 5
Fig. 5

Calculated frequency shift, linewidth broadening of the doublet and SWM position ϕ as a function of the ratio of second scatterer size over the first one, for (a) β = 0.44π, ξ = 1/4, and (b) β = 0.44π, ξ = 4. Dotted and solid lines correspond to the two SWMs. (c),(d) Experimental observations corresponding to (a) and (b), respectively.

Equations (5)

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Δ ω = 2 g 1 cos 2 ( ϕ ) + 2 g 2 cos 2 ( ϕ β )
Δ γ = 2 Γ 1 cos 2 ( ϕ ) + 2 Γ 2 cos 2 ( ϕ β )
tan ( 2 ϕ ) = g 2 sin ( 2 β ) g 1 + g 2 cos ( 2 β ) = sin ( 2 β ) χ ξ 2 + cos ( 2 β )
δ = 2 | g 1 | χ ξ 2 [ χ 2 ξ 4 + 2 χ ξ 2 cos ( 2 β ) + 1 ] 1 2
ρ = 4 Γ 1 | g 1 | δ χ 3 ξ 4 [ χ 3 ξ 4 + χ ( 1 + χ ) ξ 2 cos ( 2 β ) + 1 ]

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