Abstract

Optical whispering gallery microcavities with high-quality factors have shown great potential toward achieveing ultrahigh-sensitivity sensing up to a single molecule or nanoparticle, which raises a huge demand on a deep theoretical insight into the crucial phenomena such as the mode shift, mode splitting, and mode broadening in sensing experiments. Here we propose an intuitive model to analyze these phenomena from the viewpoint of the nanoparticle-induced multiple scattering of the azimuthally propagating mode (APM). The model unveils explicit relations between these phenomena and the phase change and energy loss of the APM when scattered at the nanoparticle; the model also explains the observed polarization-dependent preservation of one resonance and the particle-dependent redshift or blueshift. The model indicates that the particle-induced coupling between the pair of unperturbed degenerate whispering gallery modes (WGMs) and the coupling between the WGMs and the free-space radiation modes, which are widely adopted in current theoretical formalisms, are realized via the reflection and scattering-induced free-space radiation of the APM, respectively, and additionally exhibits the contribution of cross coupling between the unperturbed WGMs and other different WGMs to forming the splitting resonant modes, especially for large particles.

© 2017 Chinese Laser Press

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References

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2016 (4)

J. Su, A. F. G. Goldberg, and B. M. Stoltz, “Label-free detection of single nanoparticles and biological molecules using microtoroid optical resonators,” Light Sci. Appl. 5, e16001 (2016).
[Crossref]

B. Q. Shen, X. C. Yu, Y. Y. Zhi, L. Wang, D. H. Kim, Q. H. Gong, and Y. F. Xiao, “Detection of single nanoparticles using the dissipative interaction in a high-Q microcavity,” Phys. Rev. Appl. 5, 024011 (2016).
[Crossref]

W. Y. Yu, W. C. Jiang, Q. Lin, and T. Lu, “Cavity optomechanical spring sensing of single molecules,” Nat. Commun. 7, 12311 (2016).
[Crossref]

P. Miao, Z. F. Zhang, J. B. Sun, W. Walasik, S. Longhi, N. M. Litchinitser, and L. Feng, “Orbital angular momentum microlaser,” Science 353, 464–467 (2016).
[Crossref]

2015 (1)

L. Deych and V. Shuvayev, “Theory of nanoparticle-induced frequency shifts of whispering-gallery-mode resonances in spheroidal optical resonators,” Phys. Rev. A 92, 013842 (2015).
[Crossref]

2014 (7)

Y. W. Hu, L. B. Shao, S. Arnold, Y. C. Liu, C. Y. Ma, and Y. F. Xiao, “Mode broadening induced by nanoparticles in an optical whispering-gallery microcavity,” Phys. Rev. A 90, 043847 (2014).
[Crossref]

S. K. Ozdemir, J. G. 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]

M. D. Baaske, M. R. Foreman, and F. Vollmer, “Single-molecule nucleic acid interactions monitored on a label-free microcavity biosensor platform,” Nat. Nanotechnol. 9, 933–939 (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]

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]

S. Longhi and L. Feng, “PT-symmetric microring laser-absorber,” Opt. Lett. 39, 5026–5029 (2014).
[Crossref]

Y. Li, H. Liu, H. Jia, F. Bo, G. Zhang, and J. Xu, “Fully-vectorial modeling of cylindrical microresonators with aperiodic Fourier modal method,” J. Opt. Soc. Am. A 31, 2459–2466 (2014).
[Crossref]

2013 (6)

X. Du, S. Vincent, and T. Lu, “Full-vectorial whispering-gallery-mode cavity analysis,” Opt. Express 21, 22012–22022 (2013).
[Crossref]

H. Liu, “Coherent-form energy conservation relation for the elastic scattering of a guided mode in a symmetric scattering system,” Opt. Express 21, 24093–24098 (2013).
[Crossref]

Q. Li, A. A. Eftekhar, Z. X. Xia, and A. Adibi, “Unified approach to mode splitting and scattering loss in high-Q whispering-gallery-mode microresonators,” Phys. Rev. A 88, 033816 (2013).
[Crossref]

M. R. Foreman and F. Vollmer, “Theory of resonance shifts of whispering gallery modes by arbitrary plasmonic nanoparticles,” New J. Phys. 15, 083006 (2013).
[Crossref]

V. R. Dantham, S. Holler, C. Barbre, D. Keng, V. Kolchenko, and S. Arnold, “Label-free detection of single protein using a nanoplasmonic-photonic hybrid microcavity,” Nano Lett. 13, 3347–3351 (2013).
[Crossref]

L. B. Shao, X. F. Jiang, X. C. Yu, B. B. Li, W. R. Clements, F. Vollmer, W. Wang, Y. F. Xiao, and Q. H. Gong, “Detection of single nanoparticles and lentiviruses using microcavity resonance broadening,” Adv. Mater. 25, 5616–5620 (2013).
[Crossref]

2012 (3)

Y. C. Shen and J. T. Shen, “Nanoparticle sensing using whispering-gallery-mode resonators: plasmonic and Rayleigh scatterers,” Phys. Rev. A 85, 013801 (2012).
[Crossref]

X. L. Cai, J. W. Wang, M. J. Strain, B. Johnson-Morris, J. B. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. T. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (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]

2011 (5)

J. Wiersig, “Structure of whispering-gallery modes in optical microdisks perturbed by nanoparticles,” Phys. Rev. A 84, 063828 (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, 023803 (2011).
[Crossref]

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

L. Deych, M. Ostrowski, and Y. Yi, “Defect-induced whispering-gallery-mode resonances in optical microdisk resonators,” Opt. Lett. 36, 3154–3156 (2011).
[Crossref]

W. Kim, S. K. Ozdemir, J. G. Zhu, and L. Yang, “Observation and characterization of mode splitting in microsphere resonators in aquatic environment,” Appl. Phys. Lett. 98, 141106 (2011).
[Crossref]

2010 (6)

H. Liu, “Symmetry in the elementary scattering of surface plasmon polaritons and a generalized symmetry principle,” Opt. Lett. 35, 2876–2878 (2010).
[Crossref]

S. Lee, S. C. Eom, J. S. Chang, C. Huh, G. Y. Sung, and J. H. Shin, “Label-free optical biosensing using a horizontal air-slot SiNx microdisk resonator,” Opt. Express 18, 20638–20644 (2010).
[Crossref]

M. Hammer, “HCMT models of optical microring-resonator circuits,” J. Opt. Soc. Am. B 27, 2237–2246 (2010).
[Crossref]

J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. 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]

J. T. Rubin and L. Deych, “Ab initio theory of defect scattering in spherical whispering-gallery-mode resonators,” Phys. Rev. A 81, 053827 (2010).
[Crossref]

D. Bucci, B. Martin, and A. Morand, “Study of propagation modes of bent waveguides and micro-ring resonators by means of the aperiodic fourier modal method,” Proc. SPIE 7597, 75970U (2010).
[Crossref]

2009 (2)

J. T. Shen and S. H. Fan, “Theory of single-photon transport in a single-mode waveguide. II. Coupling to a whispering-gallery resonator containing a two-level atom,” Phys. Rev. A 79, 023838 (2009).
[Crossref]

I. Teraoka and S. Arnold, “Resonance shifts of counterpropagating whispering-gallery modes: degenerate perturbation theory and application to resonator sensors with axial symmetry,” J. Opt. Soc. Am. B 26, 1321–1329 (2009).
[Crossref]

2008 (3)

K. R. Hiremath and V. N. Astratov, “Perturbations of whispering gallery modes by nanoparticles embedded in microcavities,” Opt. Express 16, 5421–5426 (2008).
[Crossref]

S. Arnold, R. Ramjit, D. Keng, V. Kolchenko, and I. Teraoka, “MicroParticle photophysics illuminates viral bio-sensing,” Faraday Discuss. 137, 65–83 (2008).
[Crossref]

F. Vollmer, S. Arnold, and D. Keng, “Single virus detection from the reactive shift of a whispering-gallery mode,” Proc. Natl. Acad. Sci. USA 105, 20701–20704 (2008).
[Crossref]

2007 (3)

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

K. Srinivasan and O. Painter, “Mode coupling and cavity-quantum-dot interactions in a fiber-coupled microdisk cavity,” Phys. Rev. A 75, 023814 (2007).
[Crossref]

A. Mazzei, S. Goetzinger, L. D. 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]

2006 (1)

J. Ctyroky, I. Richter, and M. Sinor, “Dual resonance in a waveguide-coupled ring microresonator,” Opt. Quantum Electron. 38, 781–797 (2006).
[Crossref]

2005 (2)

2003 (2)

S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28, 272–274 (2003).
[Crossref]

L. Li, “Fourier modal method for crossed anisotropic gratings with arbitrary permittivity and permeability tensors,” J. Opt. A 5, 345–355 (2003).
[Crossref]

2001 (1)

2000 (2)

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]

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36, 321–322 (2000).
[Crossref]

1996 (1)

1995 (1)

Adibi, A.

Q. Li, A. A. Eftekhar, Z. X. Xia, and A. Adibi, “Unified approach to mode splitting and scattering loss in high-Q whispering-gallery-mode microresonators,” Phys. Rev. A 88, 033816 (2013).
[Crossref]

Armani, A. M.

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

Arnold, S.

Y. W. Hu, L. B. Shao, S. Arnold, Y. C. Liu, C. Y. Ma, and Y. F. Xiao, “Mode broadening induced by nanoparticles in an optical whispering-gallery microcavity,” Phys. Rev. A 90, 043847 (2014).
[Crossref]

V. R. Dantham, S. Holler, C. Barbre, D. Keng, V. Kolchenko, and S. Arnold, “Label-free detection of single protein using a nanoplasmonic-photonic hybrid microcavity,” Nano Lett. 13, 3347–3351 (2013).
[Crossref]

I. Teraoka and S. Arnold, “Resonance shifts of counterpropagating whispering-gallery modes: degenerate perturbation theory and application to resonator sensors with axial symmetry,” J. Opt. Soc. Am. B 26, 1321–1329 (2009).
[Crossref]

F. Vollmer, S. Arnold, and D. Keng, “Single virus detection from the reactive shift of a whispering-gallery mode,” Proc. Natl. Acad. Sci. USA 105, 20701–20704 (2008).
[Crossref]

S. Arnold, R. Ramjit, D. Keng, V. Kolchenko, and I. Teraoka, “MicroParticle photophysics illuminates viral bio-sensing,” Faraday Discuss. 137, 65–83 (2008).
[Crossref]

S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28, 272–274 (2003).
[Crossref]

Astratov, V. N.

Baaske, M. D.

M. D. Baaske, M. R. Foreman, and F. Vollmer, “Single-molecule nucleic acid interactions monitored on a label-free microcavity biosensor platform,” Nat. Nanotechnol. 9, 933–939 (2014).
[Crossref]

Barbre, C.

V. R. Dantham, S. Holler, C. Barbre, D. Keng, V. Kolchenko, and S. Arnold, “Label-free detection of single protein using a nanoplasmonic-photonic hybrid microcavity,” Nano Lett. 13, 3347–3351 (2013).
[Crossref]

Benson, O.

A. Mazzei, S. Goetzinger, L. D. 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]

Bo, F.

Borselli, M.

Boyd, R. W.

Bucci, D.

D. Bucci, B. Martin, and A. Morand, “Study of propagation modes of bent waveguides and micro-ring resonators by means of the aperiodic fourier modal method,” Proc. SPIE 7597, 75970U (2010).
[Crossref]

Cai, X. L.

X. L. Cai, J. W. Wang, M. J. Strain, B. Johnson-Morris, J. B. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. T. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
[Crossref]

Chang, J. S.

Chen, D. R.

J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. 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]

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L. B. Shao, X. F. Jiang, X. C. Yu, B. B. Li, W. R. Clements, F. Vollmer, W. Wang, Y. F. Xiao, and Q. H. Gong, “Detection of single nanoparticles and lentiviruses using microcavity resonance broadening,” Adv. Mater. 25, 5616–5620 (2013).
[Crossref]

M. R. Foreman and F. Vollmer, “Theory of resonance shifts of whispering gallery modes by arbitrary plasmonic nanoparticles,” New J. Phys. 15, 083006 (2013).
[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, S. Arnold, and D. Keng, “Single virus detection from the reactive shift of a whispering-gallery mode,” Proc. Natl. Acad. Sci. USA 105, 20701–20704 (2008).
[Crossref]

S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28, 272–274 (2003).
[Crossref]

Walasik, W.

P. Miao, Z. F. Zhang, J. B. Sun, W. Walasik, S. Longhi, N. M. Litchinitser, and L. Feng, “Orbital angular momentum microlaser,” Science 353, 464–467 (2016).
[Crossref]

Wang, J. W.

X. L. Cai, J. W. Wang, M. J. Strain, B. Johnson-Morris, J. B. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. T. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
[Crossref]

Wang, L.

B. Q. Shen, X. C. Yu, Y. Y. Zhi, L. Wang, D. H. Kim, Q. H. Gong, and Y. F. Xiao, “Detection of single nanoparticles using the dissipative interaction in a high-Q microcavity,” Phys. Rev. Appl. 5, 024011 (2016).
[Crossref]

Wang, W.

L. B. Shao, X. F. Jiang, X. C. Yu, B. B. Li, W. R. Clements, F. Vollmer, W. Wang, Y. F. Xiao, and Q. H. Gong, “Detection of single nanoparticles and lentiviruses using microcavity resonance broadening,” Adv. Mater. 25, 5616–5620 (2013).
[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]

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

Xia, Z. X.

Q. Li, A. A. Eftekhar, Z. X. Xia, and A. Adibi, “Unified approach to mode splitting and scattering loss in high-Q whispering-gallery-mode microresonators,” Phys. Rev. A 88, 033816 (2013).
[Crossref]

Xiao, Y. F.

B. Q. Shen, X. C. Yu, Y. Y. Zhi, L. Wang, D. H. Kim, Q. H. Gong, and Y. F. Xiao, “Detection of single nanoparticles using the dissipative interaction in a high-Q microcavity,” Phys. Rev. Appl. 5, 024011 (2016).
[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]

Y. W. Hu, L. B. Shao, S. Arnold, Y. C. Liu, C. Y. Ma, and Y. F. Xiao, “Mode broadening induced by nanoparticles in an optical whispering-gallery microcavity,” Phys. Rev. A 90, 043847 (2014).
[Crossref]

L. B. Shao, X. F. Jiang, X. C. Yu, B. B. Li, W. R. Clements, F. Vollmer, W. Wang, Y. F. Xiao, and Q. H. Gong, “Detection of single nanoparticles and lentiviruses using microcavity resonance broadening,” Adv. Mater. 25, 5616–5620 (2013).
[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. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. 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, J.

Yang, L.

S. K. Ozdemir, J. G. 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. 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, S. K. Ozdemir, J. G. Zhu, and L. Yang, “Observation and characterization of mode splitting in microsphere resonators in aquatic environment,” Appl. Phys. Lett. 98, 141106 (2011).
[Crossref]

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

J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. 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]

Yang, X.

S. K. Ozdemir, J. G. 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]

Yariv, A.

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36, 321–322 (2000).
[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]

Yi, Y.

Yilmaz, H.

S. K. Ozdemir, J. G. 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, S. T.

X. L. Cai, J. W. Wang, M. J. Strain, B. Johnson-Morris, J. B. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. T. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
[Crossref]

Yu, W. Y.

W. Y. Yu, W. C. Jiang, Q. Lin, and T. Lu, “Cavity optomechanical spring sensing of single molecules,” Nat. Commun. 7, 12311 (2016).
[Crossref]

Yu, X. C.

B. Q. Shen, X. C. Yu, Y. Y. Zhi, L. Wang, D. H. Kim, Q. H. Gong, and Y. F. Xiao, “Detection of single nanoparticles using the dissipative interaction in a high-Q microcavity,” Phys. Rev. Appl. 5, 024011 (2016).
[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]

L. B. Shao, X. F. Jiang, X. C. Yu, B. B. Li, W. R. Clements, F. Vollmer, W. Wang, Y. F. Xiao, and Q. H. Gong, “Detection of single nanoparticles and lentiviruses using microcavity resonance broadening,” Adv. Mater. 25, 5616–5620 (2013).
[Crossref]

Zhang, G.

Zhang, Z. F.

P. Miao, Z. F. Zhang, J. B. Sun, W. Walasik, S. Longhi, N. M. Litchinitser, and L. Feng, “Orbital angular momentum microlaser,” Science 353, 464–467 (2016).
[Crossref]

Zhi, Y. Y.

B. Q. Shen, X. C. Yu, Y. Y. Zhi, L. Wang, D. H. Kim, Q. H. Gong, and Y. F. Xiao, “Detection of single nanoparticles using the dissipative interaction in a high-Q microcavity,” Phys. Rev. Appl. 5, 024011 (2016).
[Crossref]

Zhu, J. B.

X. L. Cai, J. W. Wang, M. J. Strain, B. Johnson-Morris, J. B. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. T. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
[Crossref]

Zhu, J. G.

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

W. Kim, S. K. Ozdemir, J. G. Zhu, and L. Yang, “Observation and characterization of mode splitting in microsphere resonators in aquatic environment,” Appl. Phys. Lett. 98, 141106 (2011).
[Crossref]

J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. 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]

Zumofen, G.

A. Mazzei, S. Goetzinger, L. D. 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]

Adv. Mater. (1)

L. B. Shao, X. F. Jiang, X. C. Yu, B. B. Li, W. R. Clements, F. Vollmer, W. Wang, Y. F. Xiao, and Q. H. Gong, “Detection of single nanoparticles and lentiviruses using microcavity resonance broadening,” Adv. Mater. 25, 5616–5620 (2013).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

W. Kim, S. K. Ozdemir, J. G. Zhu, and L. Yang, “Observation and characterization of mode splitting in microsphere resonators in aquatic environment,” Appl. Phys. Lett. 98, 141106 (2011).
[Crossref]

Electron. Lett. (1)

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36, 321–322 (2000).
[Crossref]

Faraday Discuss. (1)

S. Arnold, R. Ramjit, D. Keng, V. Kolchenko, and I. Teraoka, “MicroParticle photophysics illuminates viral bio-sensing,” Faraday Discuss. 137, 65–83 (2008).
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L. Li, “Fourier modal method for crossed anisotropic gratings with arbitrary permittivity and permeability tensors,” J. Opt. A 5, 345–355 (2003).
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J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (3)

Light Sci. Appl. (1)

J. Su, A. F. G. Goldberg, and B. M. Stoltz, “Label-free detection of single nanoparticles and biological molecules using microtoroid optical resonators,” Light Sci. Appl. 5, e16001 (2016).
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Nano Lett. (1)

V. R. Dantham, S. Holler, C. Barbre, D. Keng, V. Kolchenko, and S. Arnold, “Label-free detection of single protein using a nanoplasmonic-photonic hybrid microcavity,” Nano Lett. 13, 3347–3351 (2013).
[Crossref]

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)

W. Y. Yu, W. C. Jiang, Q. Lin, and T. Lu, “Cavity optomechanical spring sensing of single molecules,” Nat. Commun. 7, 12311 (2016).
[Crossref]

Nat. Nanotechnol. (2)

M. D. Baaske, M. R. Foreman, and F. Vollmer, “Single-molecule nucleic acid interactions monitored on a label-free microcavity biosensor platform,” Nat. Nanotechnol. 9, 933–939 (2014).
[Crossref]

L. N. He, K. Ozdemir, J. G. 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. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. 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]

New J. Phys. (1)

M. R. Foreman and F. Vollmer, “Theory of resonance shifts of whispering gallery modes by arbitrary plasmonic nanoparticles,” New J. Phys. 15, 083006 (2013).
[Crossref]

Opt. Express (5)

Opt. Lett. (5)

Opt. Quantum Electron. (1)

J. Ctyroky, I. Richter, and M. Sinor, “Dual resonance in a waveguide-coupled ring microresonator,” Opt. Quantum Electron. 38, 781–797 (2006).
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Phys. Rev. A (9)

J. T. Shen and S. H. Fan, “Theory of single-photon transport in a single-mode waveguide. II. Coupling to a whispering-gallery resonator containing a two-level atom,” Phys. Rev. A 79, 023838 (2009).
[Crossref]

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

J. T. Rubin and L. Deych, “Ab initio theory of defect scattering in spherical whispering-gallery-mode resonators,” Phys. Rev. A 81, 053827 (2010).
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L. Deych and V. Shuvayev, “Theory of nanoparticle-induced frequency shifts of whispering-gallery-mode resonances in spheroidal optical resonators,” Phys. Rev. A 92, 013842 (2015).
[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]

Y. W. Hu, L. B. Shao, S. Arnold, Y. C. Liu, C. Y. Ma, and Y. F. Xiao, “Mode broadening induced by nanoparticles in an optical whispering-gallery microcavity,” Phys. Rev. A 90, 043847 (2014).
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K. Srinivasan and O. Painter, “Mode coupling and cavity-quantum-dot interactions in a fiber-coupled microdisk cavity,” Phys. Rev. A 75, 023814 (2007).
[Crossref]

Y. C. Shen and J. T. Shen, “Nanoparticle sensing using whispering-gallery-mode resonators: plasmonic and Rayleigh scatterers,” Phys. Rev. A 85, 013801 (2012).
[Crossref]

Q. Li, A. A. Eftekhar, Z. X. Xia, and A. Adibi, “Unified approach to mode splitting and scattering loss in high-Q whispering-gallery-mode microresonators,” Phys. Rev. A 88, 033816 (2013).
[Crossref]

Phys. Rev. Appl. (1)

B. Q. Shen, X. C. Yu, Y. Y. Zhi, L. Wang, D. H. Kim, Q. H. Gong, and Y. F. Xiao, “Detection of single nanoparticles using the dissipative interaction in a high-Q microcavity,” Phys. Rev. Appl. 5, 024011 (2016).
[Crossref]

Phys. Rev. Lett. (2)

A. Mazzei, S. Goetzinger, L. D. 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]

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]

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

F. Vollmer, S. Arnold, and D. Keng, “Single virus detection from the reactive shift of a whispering-gallery mode,” Proc. Natl. Acad. Sci. USA 105, 20701–20704 (2008).
[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]

S. K. Ozdemir, J. G. 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]

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Science (3)

X. L. Cai, J. W. Wang, M. J. Strain, B. Johnson-Morris, J. B. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. T. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
[Crossref]

P. Miao, Z. F. Zhang, J. B. Sun, W. Walasik, S. Longhi, N. M. Litchinitser, and L. Feng, “Orbital angular momentum microlaser,” Science 353, 464–467 (2016).
[Crossref]

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783–787 (2007).
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Figures (8)

Fig. 1.
Fig. 1.

(a) Schematic of a z-invariant cylindrical microcavity with a nanoparticle (blue sector) adsorbed on its surface. a and b denote the complex amplitude coefficients of the two counterpropagating APMs matched to the resonant mode. (b) Scattering coefficients ρ and τ characterizing the reflection and transmission of the APM at the nanoparticle.

Fig. 2.
Fig. 2.

(a) Frequency shift δ [relative to the unperturbed TM1,42 WGM with resonance frequency Re(νc,0)=1.969550×1014  Hz] and (b) Q-factor of S-mode (blue) and AS-mode (red) as a function of nanoparticle size D. Inset in (b) shows 1/Qprop (dotted curves) and 1/Qscat (dashed–dot curves). (c)–(e) arg(τ±ρ), |τ±ρ|, and neff of the resonant modes solved for different D (the solid and dashed curves corresponding to left and right axes, respectively, the blue and red curves corresponding to the S-mode and the AS-mode, respectively). (f) Δw (characterizing the resolvability of mode splitting) for different D. The inset shows details for small particle sizes. In (a), (b), and (f), the solid curves, dashed curves (completely superimposed by the solid curves), and circles represent the predictions of the original model, the simplified model, and the FEM numerical results, respectively.

Fig. 3.
Fig. 3.

Same as Fig. 2 but for the resonant modes corresponding to the unperturbed TE1,42 WGM [with resonance frequency Re(νc,0)=1.941902×1014  Hz].

Fig. 4.
Fig. 4.

Electric-field intensities (a) |EAPM|2 and (b) |Eres|2 of the APM field and of the residual field for the TM S-mode (already shown in Fig. 2) with particle size D=100  nm. The APM field is artificially extended into the deep subwavelength ϕ range of the nanoparticle where the APM has no definition. (c) and (d) The same as (a) and (b) but for a larger D=500  nm. Here the electric radial-components of the two matched counterpropagating APMs are normalized to have Er=1 at r=7.95  μm and ϕ=0 for the two particle sizes, so that a direct comparison of their corresponding residual fields can reflect the weight of the residual field relative to the matched APM field (or to the total field).

Fig. 5.
Fig. 5.

(a) Diagram of the cylindrical microcavity with adsorption of a nanoparticle under the Cartesian coordinate system (x,y,z). a and b are the complex amplitude coefficients of the two counterpropagating APMs matched to the resonant mode considered in the model. (b) The system is mapped to be an equivalent straight waveguide with adsorption of a periodic array of nanoparticles along the ϕ direction under the extended cylindrical coordinate system (r,z,ϕ). (c) Scattering problem for defining the reflection and transmission coefficients ρ and τ of the matched APM at the nanoparticle. (d) Artificial periodic structure for applying the a-FMM to model the scattering problem shown in (c).

Fig. 6.
Fig. 6.

(a)–(b) Iteration process of solving the complex eigenfrequency of the resonant mode (blue and red curves for S-mode and AS-mode, respectively) in Fig. 2 in the main text, with adsorbed nanoparticle size D=100  nm. N represents the number of iteration, and the initial value of iteration is ν0=1.9986×1014  Hz (corresponding to wavelength 1.5 μm). The inset in (a) is a magnified view of the iteration curves. (c)–(f) |ρ|, |τ|, Re(neff), and Im(neff) plotted as a function of frequency ν (the shown frequency range corresponding to a wavelength range 1.3–1.7 μm).

Fig. 7.
Fig. 7.

(a)–(f) The same as Fig. 2 in the main text but for the resonant mode corresponding to the unperturbed TM1,59 WGM [with resonance frequency Re(νc,0)=1.964712×1014  Hz] supported by the microcavity with radius R=11  μm. (g)–(h) The same as Figs. 2(a)2(b) in the main text but corresponding to TE3,100 WGM with Re(νc,0)=1.974072×1014  Hz and R=20  μm.

Fig. 8.
Fig. 8.

Blueshift (δ>0) relative to the unperturbed TM1,42 (a) and TE1,42 (c) WGMs plotted as a function of nanoparticle size D. The results are obtained for a refractive index 0.59 of the adsorbed particle that is lower than the refractive index of the particle’s surrounding medium of air. All other parameters are the same as those in Fig. 2 of the main text. (b) and (d) show the negative values of arg(τ±ρ) for different D corresponding to (a) and (c), respectively. The blue and red curves show the results of the S-mode and the AS-mode, respectively.

Equations (21)

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

a=auτ+buρ,
b=buτ+auρ,
u(τ±ρ)=1.
ν=c4π2neff[arg(τ±ρ)+2πm+iln|τ±ρ|]c4π2pRe(neff){1+i[qpIm(neff)Re(neff)]},
δRe(νc,0)arg(τ±ρ)2πm,
1Q2Im(neff)Re(neff)ln|τ±ρ|πm,
ΔRe(νc,0)12πm|arg(τ+ρ)arg(τρ)|,
wRe(νc,0)2Im(neff)Re(neff)12πm(ln|τ+ρ|+ln|τρ|).
x=rcosϕ,y=rsinϕ,z=z,
gij=[10001000r2],
Er(r,ϕ)=n=MMSn(ϕ)exp(inKr),
Sn(ϕ)=p=1Pwn,p{cp+exp(iβpϕ)+cpexp[iβp(ϕϕ)]}.
Er=p=1Pcp+Ep,r++p=1PcpEp,r,
Ep,r+=[n=MMwn,pexp(inKr)]exp(iβpϕ),
Ep,r=[n=MMwn,pexp(inKr)]exp[iβp(ϕϕ)],
ν=c4π2p+iqRe(neff)+iIm(neff)=c4π2pRe(neff)1+iqp1+iIm(neff)Re(neff)=c4π2pRe(neff)(1+iqp){1iIm(neff)Re(neff)+o[Im(neff)Re(neff)]}c4π2pRe(neff)(1+iqp)[1iIm(neff)Re(neff)]=c4π2pRe(neff){[1+qpIm(neff)Re(neff)]+i[qpIm(neff)Re(neff)]}c4π2pRe(neff){1+i[qpIm(neff)Re(neff)]},
Ψ(r,ϕ)=n=1[cnΨn(r,ϕ)+cnΨn(r,ϕ)],
Ψm(r,ϕ)|Ψn(r,ϕ)=Ψn(r,ϕ)|Ψn(r,ϕ)δm,n,Ψm(r,ϕ)|Ψn(r,ϕ)=0,Ψm(r,ϕ)|Ψn(r,ϕ)=0,
ΨA(r,ϕ)|ΨB(r,ϕ)=0+{[E1,B(r,ϕ)H2,A(r,ϕ)E2,B(r,ϕ)H1,A(r,ϕ)][E1,A(r,ϕ)H2,B(r,ϕ)E2,A(r,ϕ)H1,B(r,ϕ)]}dr,
E=(e1,e2,e3)[E1E2E3]=(r,z,ϕ)[ErEzEϕ],
cm=Ψm(r,ϕ)|Ψ(r,ϕ)Ψm(r,ϕ)|Ψm(r,ϕ),cm=Ψm(r,ϕ)|Ψ(r,ϕ)Ψm(r,ϕ)|Ψm(r,ϕ).

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