Abstract

A novel slotted optical microdisk resonator, which significantly enhances light–matter interaction and provides a promising approach for increasing the sensitivity of sensors, is theoretically and numerically investigated. In this slotted resonator, the mode splitting is generated due to reflection of the slot. Remarkably, effects of the slot width and angular position on the mode splitting are mainly studied. The results reveal that the mode splitting is a second function of the slot width, and the maximum mode splitting induced by the slot deformation is achieved with 2.7853×109  Hz/nm. Therefore, the slotted resonator is an excellent candidate for pressure and force sensing. Besides, the influence of the slot angular position on the mode splitting is a cosine curve with the highest sensitivity of 1.23×1011  Hz/deg; thus, the optical characteristic demonstrates that the slotted resonator can be used for inertial measurements.

© 2017 Chinese Laser Press

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References

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2015 (1)

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2015).
[Crossref]

2014 (5)

A. R. Ali, T. Ioppolo, V. Ötügen, M. Christensen, and D. MacFarlane, “Photonic electric field sensor based on polymeric microspheres,” J. Polym. Sci. B 52, 276–279 (2014).
[Crossref]

D. Farnesi, A. Barucci, and G. C. Righini, “Optical frequency conversion in silica-whispering-gallery-mode microspherical resonators,” Phys. Rev. Lett. 112, 093901 (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. B. Li, W. R. Clements, X. C. Yu, K. B. 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]

D. C. Aveline, D. V. Strekalov, and N. Yu, “Micro-slotted whispering gallery mode resonators for optomechanical,” Appl. Phys. Lett. 105, 021111 (2014).
[Crossref]

2013 (2)

S. M. Grist, S. A. Schmidt, and J. Flueckiger, “Silicon photonic micro-disk resonators for label-free biosensing,” Opt. Express 21, 7994–8006 (2013).
[Crossref]

A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering-gallery modes-part I: basics,” IEEE J. Sel. Top. Quantum Electron. 12, 15–32 (2013).

2012 (2)

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

J. Chaste, A. Eichler, J. Moser, G. Ceballos, R. Rurali, and A. Bachtold, “A nanomechanical mass sensor with yoctogram resolution,” Nat. Nanotechnol. 7, 301–304 (2012).
[Crossref]

2011 (2)

C. Junge, S. Nickel, and D. O’Shea, “Bottle microresonator with actively stabilized evanescent coupling,” Opt. Lett. 36, 3488–3490 (2011).
[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, 23803 (2011).
[Crossref]

2010 (5)

T. J. Kippenberg, “Microresonators: particle sizing by mode splitting,” Nat. Photonics 4, 9–10 (2010).
[Crossref]

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

L. He, S. K. Ozdemir, Y. F. Xiao, and L. Yang, “Gain-induced evolution of mode splitting spectra in a high-, active microresonator,” IEEE J. Quantum Electron. 46, 1626–1633 (2010).
[Crossref]

S. Wang, K. Broderick, and H. Smith, “Strong coupling between on chip notched ring resonator and nanoparticle,” Appl. Phys. Lett. 97, 051102 (2010).
[Crossref]

D. O’Shea, A. Rettenmaier, and A. Rauschenbeutel, “Active frequency stabilization of an ultra-high Q whispering-gallery-mode microresonator,” Appl. Phys. B 99, 623–627 (2010).
[Crossref]

2009 (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, 46–49 (2009).
[Crossref]

2007 (2)

A. Mazzei, S. Gotzinger, L. S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled coupling of counter propagating whispering-gallery modes by a single Rayleigh scatterer: a classical problem in a quantum optical light,” Phys. Rev. Lett. 99, 173603 (2007).
[Crossref]

A. M. Armani, R. P. Kulkarni, and S. E. Fraser, “Label-free, single-molecule detection with optical micro-cavities,” Science 317, 783–787 (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]

2004 (2)

H. Rokhsari and K. J. Vahala, “Ultralow loss, high Q, four port resonant couplers for quantum optics and photonics,” Phys. Rev. Lett. 92, 253905 (2004).
[Crossref]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip,” Appl. Phys. Lett. 85, 6113–6115 (2004).
[Crossref]

2003 (1)

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]

2002 (2)

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415, 621–623 (2002).
[Crossref]

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[Crossref]

2000 (1)

1995 (1)

Ali, A. R.

A. R. Ali, T. Ioppolo, V. Ötügen, M. Christensen, and D. MacFarlane, “Photonic electric field sensor based on polymeric microspheres,” J. Polym. Sci. B 52, 276–279 (2014).
[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, A. M.

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

Armani, D. K.

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]

Aveline, D. C.

D. C. Aveline, D. V. Strekalov, and N. Yu, “Micro-slotted whispering gallery mode resonators for optomechanical,” Appl. Phys. Lett. 105, 021111 (2014).
[Crossref]

Bachtold, A.

J. Chaste, A. Eichler, J. Moser, G. Ceballos, R. Rurali, and A. Bachtold, “A nanomechanical mass sensor with yoctogram resolution,” Nat. Nanotechnol. 7, 301–304 (2012).
[Crossref]

Barucci, A.

D. Farnesi, A. Barucci, and G. C. Righini, “Optical frequency conversion in silica-whispering-gallery-mode microspherical resonators,” Phys. Rev. Lett. 112, 093901 (2014).
[Crossref]

Benson, O.

A. Mazzei, S. Gotzinger, L. S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled coupling of counter propagating whispering-gallery modes by a single Rayleigh scatterer: a classical problem in a quantum optical light,” Phys. Rev. Lett. 99, 173603 (2007).
[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]

Broderick, K.

S. Wang, K. Broderick, and H. Smith, “Strong coupling between on chip notched ring resonator and nanoparticle,” Appl. Phys. Lett. 97, 051102 (2010).
[Crossref]

Ceballos, G.

J. Chaste, A. Eichler, J. Moser, G. Ceballos, R. Rurali, and A. Bachtold, “A nanomechanical mass sensor with yoctogram resolution,” Nat. Nanotechnol. 7, 301–304 (2012).
[Crossref]

Chaste, J.

J. Chaste, A. Eichler, J. Moser, G. Ceballos, R. Rurali, and A. Bachtold, “A nanomechanical mass sensor with yoctogram resolution,” Nat. Nanotechnol. 7, 301–304 (2012).
[Crossref]

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, 46–49 (2009).
[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, 23803 (2011).
[Crossref]

Christensen, M.

A. R. Ali, T. Ioppolo, V. Ötügen, M. Christensen, and D. MacFarlane, “Photonic electric field sensor based on polymeric microspheres,” J. Polym. Sci. B 52, 276–279 (2014).
[Crossref]

Clements, W. R.

B. B. Li, W. R. Clements, X. C. Yu, K. B. 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]

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]

Eichler, A.

J. Chaste, A. Eichler, J. Moser, G. Ceballos, R. Rurali, and A. Bachtold, “A nanomechanical mass sensor with yoctogram resolution,” Nat. Nanotechnol. 7, 301–304 (2012).
[Crossref]

Farnesi, D.

D. Farnesi, A. Barucci, and G. C. Righini, “Optical frequency conversion in silica-whispering-gallery-mode microspherical resonators,” Phys. Rev. Lett. 112, 093901 (2014).
[Crossref]

Fink, Y.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[Crossref]

Flueckiger, J.

Fraser, S. E.

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

Gong, Q. H.

B. B. Li, W. R. Clements, X. C. Yu, K. B. 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, 23803 (2011).
[Crossref]

Gorodetsky, M. L.

Gotzinger, S.

A. Mazzei, S. Gotzinger, L. S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled coupling of counter propagating whispering-gallery modes by a single Rayleigh scatterer: a classical problem in a quantum optical light,” Phys. Rev. Lett. 99, 173603 (2007).
[Crossref]

Grist, S. M.

Hare, J.

Haroche, S.

He, L.

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

L. He, S. K. Ozdemir, Y. F. Xiao, and L. Yang, “Gain-induced evolution of mode splitting spectra in a high-, active microresonator,” IEEE J. Quantum Electron. 46, 1626–1633 (2010).
[Crossref]

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, 46–49 (2009).
[Crossref]

Ibanescu, M.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[Crossref]

Ilchenko, V. S.

A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering-gallery modes-part I: basics,” IEEE J. Sel. Top. Quantum Electron. 12, 15–32 (2013).

M. L. Gorodetsky, A. D. Pryamikov, and V. S. Ilchenko, “Rayleigh scattering in high-Q microspheres,” J. Opt. Soc. Am. B 17, 1051–1057 (2000).
[Crossref]

Ioppolo, T.

A. R. Ali, T. Ioppolo, V. Ötügen, M. Christensen, and D. MacFarlane, “Photonic electric field sensor based on polymeric microspheres,” J. Polym. Sci. B 52, 276–279 (2014).
[Crossref]

Joannopoulos, J. D.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[Crossref]

Johnson, S. G.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[Crossref]

Junge, C.

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]

Kippenberg, T. J.

T. J. Kippenberg, “Microresonators: particle sizing by mode splitting,” Nat. Photonics 4, 9–10 (2010).
[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, and K. J. Vahala, “Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip,” Appl. Phys. Lett. 85, 6113–6115 (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]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415, 621–623 (2002).
[Crossref]

Kulkarni, R. P.

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

Lefevre-Seguin, V.

Li, B. B.

B. B. Li, W. R. Clements, X. C. Yu, K. B. 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, 23803 (2011).
[Crossref]

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, 46–49 (2009).
[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, 23803 (2011).
[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, 23803 (2011).
[Crossref]

MacFarlane, D.

A. R. Ali, T. Ioppolo, V. Ötügen, M. Christensen, and D. MacFarlane, “Photonic electric field sensor based on polymeric microspheres,” J. Polym. Sci. B 52, 276–279 (2014).
[Crossref]

Matsko, A. B.

A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering-gallery modes-part I: basics,” IEEE J. Sel. Top. Quantum Electron. 12, 15–32 (2013).

Mazzei, A.

A. Mazzei, S. Gotzinger, L. S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled coupling of counter propagating whispering-gallery modes by a single Rayleigh scatterer: a classical problem in a quantum optical light,” Phys. Rev. Lett. 99, 173603 (2007).
[Crossref]

Menezes, L. S.

A. Mazzei, S. Gotzinger, L. S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled coupling of counter propagating whispering-gallery modes by a single Rayleigh scatterer: a classical problem in a quantum optical light,” Phys. Rev. Lett. 99, 173603 (2007).
[Crossref]

Moser, J.

J. Chaste, A. Eichler, J. Moser, G. Ceballos, R. Rurali, and A. Bachtold, “A nanomechanical mass sensor with yoctogram resolution,” Nat. Nanotechnol. 7, 301–304 (2012).
[Crossref]

Nickel, S.

O’Shea, D.

C. Junge, S. Nickel, and D. O’Shea, “Bottle microresonator with actively stabilized evanescent coupling,” Opt. Lett. 36, 3488–3490 (2011).
[Crossref]

D. O’Shea, A. Rettenmaier, and A. Rauschenbeutel, “Active frequency stabilization of an ultra-high Q whispering-gallery-mode microresonator,” Appl. Phys. B 99, 623–627 (2010).
[Crossref]

Ötügen, V.

A. R. Ali, T. Ioppolo, V. Ötügen, M. Christensen, and D. MacFarlane, “Photonic electric field sensor based on polymeric microspheres,” J. Polym. Sci. B 52, 276–279 (2014).
[Crossref]

Ozdemir, S. K.

L. He, S. K. Ozdemir, Y. F. Xiao, and L. Yang, “Gain-induced evolution of mode splitting spectra in a high-, active microresonator,” IEEE J. Quantum Electron. 46, 1626–1633 (2010).
[Crossref]

Özdemir, S. K.

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

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, 46–49 (2009).
[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]

Pryamikov, A. D.

Raimond, J. M.

Rauschenbeutel, A.

D. O’Shea, A. Rettenmaier, and A. Rauschenbeutel, “Active frequency stabilization of an ultra-high Q whispering-gallery-mode microresonator,” Appl. Phys. B 99, 623–627 (2010).
[Crossref]

Rettenmaier, A.

D. O’Shea, A. Rettenmaier, and A. Rauschenbeutel, “Active frequency stabilization of an ultra-high Q whispering-gallery-mode microresonator,” Appl. Phys. B 99, 623–627 (2010).
[Crossref]

Righini, G. C.

D. Farnesi, A. Barucci, and G. C. Righini, “Optical frequency conversion in silica-whispering-gallery-mode microspherical resonators,” Phys. Rev. Lett. 112, 093901 (2014).
[Crossref]

Rokhsari, H.

H. Rokhsari and K. J. Vahala, “Ultralow loss, high Q, four port resonant couplers for quantum optics and photonics,” Phys. Rev. Lett. 92, 253905 (2004).
[Crossref]

Rurali, R.

J. Chaste, A. Eichler, J. Moser, G. Ceballos, R. Rurali, and A. Bachtold, “A nanomechanical mass sensor with yoctogram resolution,” Nat. Nanotechnol. 7, 301–304 (2012).
[Crossref]

Sandoghdar, V.

A. Mazzei, S. Gotzinger, L. S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled coupling of counter propagating whispering-gallery modes by a single Rayleigh scatterer: a classical problem in a quantum optical light,” Phys. Rev. Lett. 99, 173603 (2007).
[Crossref]

D. S. Weiss, V. Sandoghdar, J. Hare, V. Lefevre-Seguin, J. M. Raimond, and S. Haroche, “Splitting of high-Q Mie modes induced by light backscattering in silica microspheres,” Opt. Lett. 20, 1835–1837 (1995).
[Crossref]

Schmidt, S. A.

Shi, K. B.

B. B. Li, W. R. Clements, X. C. Yu, K. B. 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]

Skorobogatiy, M. A.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[Crossref]

Smith, H.

S. Wang, K. Broderick, and H. Smith, “Strong coupling between on chip notched ring resonator and nanoparticle,” Appl. Phys. Lett. 97, 051102 (2010).
[Crossref]

Spillane, S. M.

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip,” Appl. Phys. Lett. 85, 6113–6115 (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]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415, 621–623 (2002).
[Crossref]

Strekalov, D. V.

D. C. Aveline, D. V. Strekalov, and N. Yu, “Micro-slotted whispering gallery mode resonators for optomechanical,” Appl. Phys. Lett. 105, 021111 (2014).
[Crossref]

Vahala, K. J.

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2015).
[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]

H. Rokhsari and K. J. Vahala, “Ultralow loss, high Q, four port resonant couplers for quantum optics and photonics,” Phys. Rev. Lett. 92, 253905 (2004).
[Crossref]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip,” Appl. Phys. Lett. 85, 6113–6115 (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]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415, 621–623 (2002).
[Crossref]

Vollmer, F.

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

Wang, S.

S. Wang, K. Broderick, and H. Smith, “Strong coupling between on chip notched ring resonator and nanoparticle,” Appl. Phys. Lett. 97, 051102 (2010).
[Crossref]

Weisberg, O.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[Crossref]

Weiss, D. S.

Wiersig, J.

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]

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]

Xiao, Y. F.

B. B. Li, W. R. Clements, X. C. Yu, K. B. 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, 23803 (2011).
[Crossref]

L. He, S. K. Ozdemir, Y. F. Xiao, and L. Yang, “Gain-induced evolution of mode splitting spectra in a high-, active microresonator,” IEEE J. Quantum Electron. 46, 1626–1633 (2010).
[Crossref]

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, 46–49 (2009).
[Crossref]

Yang, L.

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

L. He, S. K. Ozdemir, Y. F. Xiao, and L. Yang, “Gain-induced evolution of mode splitting spectra in a high-, active microresonator,” IEEE J. Quantum Electron. 46, 1626–1633 (2010).
[Crossref]

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

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, 46–49 (2009).
[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, 23803 (2011).
[Crossref]

Yu, N.

D. C. Aveline, D. V. Strekalov, and N. Yu, “Micro-slotted whispering gallery mode resonators for optomechanical,” Appl. Phys. Lett. 105, 021111 (2014).
[Crossref]

Yu, X. C.

B. B. Li, W. R. Clements, X. C. Yu, K. B. 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]

Zhu, J.

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

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, 46–49 (2009).
[Crossref]

Zumofen, G.

A. Mazzei, S. Gotzinger, L. S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled coupling of counter propagating whispering-gallery modes by a single Rayleigh scatterer: a classical problem in a quantum optical light,” Phys. Rev. Lett. 99, 173603 (2007).
[Crossref]

Appl. Phys. B (1)

D. O’Shea, A. Rettenmaier, and A. Rauschenbeutel, “Active frequency stabilization of an ultra-high Q whispering-gallery-mode microresonator,” Appl. Phys. B 99, 623–627 (2010).
[Crossref]

Appl. Phys. Lett. (3)

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip,” Appl. Phys. Lett. 85, 6113–6115 (2004).
[Crossref]

D. C. Aveline, D. V. Strekalov, and N. Yu, “Micro-slotted whispering gallery mode resonators for optomechanical,” Appl. Phys. Lett. 105, 021111 (2014).
[Crossref]

S. Wang, K. Broderick, and H. Smith, “Strong coupling between on chip notched ring resonator and nanoparticle,” Appl. Phys. Lett. 97, 051102 (2010).
[Crossref]

IEEE J. Quantum Electron. (1)

L. He, S. K. Ozdemir, Y. F. Xiao, and L. Yang, “Gain-induced evolution of mode splitting spectra in a high-, active microresonator,” IEEE J. Quantum Electron. 46, 1626–1633 (2010).
[Crossref]

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

A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering-gallery modes-part I: basics,” IEEE J. Sel. Top. Quantum Electron. 12, 15–32 (2013).

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

J. Polym. Sci. B (1)

A. R. Ali, T. Ioppolo, V. Ötügen, M. Christensen, and D. MacFarlane, “Photonic electric field sensor based on polymeric microspheres,” J. Polym. Sci. B 52, 276–279 (2014).
[Crossref]

Nanophotonics (1)

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

Nat. Nanotechnol. (1)

J. Chaste, A. Eichler, J. Moser, G. Ceballos, R. Rurali, and A. Bachtold, “A nanomechanical mass sensor with yoctogram resolution,” Nat. Nanotechnol. 7, 301–304 (2012).
[Crossref]

Nat. Photonics (2)

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, 46–49 (2009).
[Crossref]

T. J. Kippenberg, “Microresonators: particle sizing by mode splitting,” Nat. Photonics 4, 9–10 (2010).
[Crossref]

Nature (4)

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]

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]

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2015).
[Crossref]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415, 621–623 (2002).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (2)

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, 23803 (2011).
[Crossref]

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

Phys. Rev. E (1)

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[Crossref]

Phys. Rev. Lett. (4)

A. Mazzei, S. Gotzinger, L. S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled coupling of counter propagating whispering-gallery modes by a single Rayleigh scatterer: a classical problem in a quantum optical light,” Phys. Rev. Lett. 99, 173603 (2007).
[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]

D. Farnesi, A. Barucci, and G. C. Righini, “Optical frequency conversion in silica-whispering-gallery-mode microspherical resonators,” Phys. Rev. Lett. 112, 093901 (2014).
[Crossref]

H. Rokhsari and K. J. Vahala, “Ultralow loss, high Q, four port resonant couplers for quantum optics and photonics,” Phys. Rev. Lett. 92, 253905 (2004).
[Crossref]

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

B. B. Li, W. R. Clements, X. C. Yu, K. B. 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]

Science (1)

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

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Figures (8)

Fig. 1.
Fig. 1. (a) Electric field distribution of resonator. (b) Electric field distribution of the slotted resonator.
Fig. 2.
Fig. 2. Schematic of the optical WGM microdisk resonator with a single slot. ain, the amplitude of input light; aCWout, output amplitude of CW; aCCWout, output amplitude of CCW.
Fig. 3.
Fig. 3. Schematic representation of Δr(φ), φ, and θ are the polar angle and the angular position of slot, respectively.
Fig. 4.
Fig. 4. Normalized transmission of the theory model (red solid line) and FEM simulation (blue dash–dot line) with the slot width of 220 nm and the slot angular position of 0°. The close agreement between the theoretical and simulation result is obtained with κ0=1.211×1011  Hz, Γ=1.65κ0, κex=1.78  κ0, γ=2.215κ0, and γc=8.4κ0.
Fig. 5.
Fig. 5. Simulation results of the normalized transmission without single slot (corresponding parameter in the theoretical model: κ0=1.211×1011  Hz, κex=1.78κ0) and under the difference slot width of 50 nm (corresponding parameters in the theoretical model: κ0=1.211×1011  Hz, Γ=0.4κ0, κex=1.78κ0, γ=1.59κ0 and γc=1.4κ0), 100 nm (corresponding parameters in the theoretical model: κ0=1.211×1011  Hz, Γ=0.7κ0, κex=1.78κ0, γ=1.74κ0 and γc=3.9κ0) and 200 nm (corresponding parameters in the theoretical model: κ0=1.211×1011  Hz, Γ=1.4κ0, κex=1.78κ0, γ=2.09κ0 and γc=7.9κ0).
Fig. 6.
Fig. 6. (a) Normalized detuning frequency as a function of the slot width; the blue solid curve presents the theoretical results, and the red dash curve depicts the simulation results. (b) Normalized linewidth broadening induced by the slot and Q factor of the slotted resonator with different slot widths.
Fig. 7.
Fig. 7. (a) Normalized transmission in a slotted resonator with the slot width of 150 nm and the slot angular position of 0° (corresponding parameters in the theoretical model: κ0=1.211×1011  Hz, Γ=κ0, κex=1.78κ0, γ=1.89κ0, and γc=6.1κ0), 60° (corresponding parameters in the theoretical model: κ0=1.211×1011  Hz, Γ=0.85κ0, κex=1.78κ0, γ=1.815κ0, and γc=5.8κ0) and 160° (corresponding parameters in the theoretical model: κ0=1.211×1011  Hz, Γ=0.6κ0, κex=2κ0, γ=1.8κ0, and γc=3.3κ0). (b) Relationship between slot width and normalized detuning frequency with the slot angular position of 0° (green dash line), 60° (blue dash–dot line), and 160° (red solid line).
Fig. 8.
Fig. 8. Normalized detuning frequency as a function of the slot angular position in a slotted resonator with the slot width of 150 nm. Blue line presents the theory analysis results; red line depicts the FEM simulation results for the case of azimuthal number m=41.

Equations (10)

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T=|aCWout|2/|ain|2=|1κex(iΔw+iγc+Γ+κ0+κex2)(iΔw+iγc+Γ+κ0+κex2)2(iγc+Γ2)2|2,
R=n1n+1[14ne2ika(n+1)2e2ika(n1)2],
γc=|R|τ0γ,
Γ=Γsτ0=δSn2(r)|E(r)|2drτ0n2(r)|E0(r)|2dr,
{Eρ=jw2μ0ϵiβ2(βdEzdφjmwμ0ρHz)Eφ=jw2μ0ϵiβ2(jmβρEz+wμ0dHzdρ)Hρ=jw2μ0ϵiβ2(βdHzdφ+jmwϵiρEz)Hφ=jw2μ0ϵiβ2(jmβρHzwϵidEzdρ),
Ψ(ρ)={AmJm(k0neffρ),ρR0BmHm(1)(k0ρ),ρ>R0,
γc=|n1τ0(n+1)[14ne2ika(n+1)2e2ika(n1)2]|[κ0+κex+δSn2(r)|E(r)|2drn2(r)|E(r)|2dr]/2.
Δfθ=f02ECW|Δϵ|ECCWE0|ϵ0|E0+(Γ+κex+κ0)/4π,
Δfθ=f0Δϵ(r)ECW(r)ECCW*(r)dr2ϵ0(r)|E0(r)|2dr+(Γ+κex+κ0)/4π.
κex=k4ϵ0μ0δn2(r)E0(r)Efiber(r)dr,

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