Abstract

We present a rigorous numerical study of a Rayleigh nanoparticle sensing scheme using a whispering-gallery-mode resonator and compare the results to a recent theoretical analysis. Our calculations confirm that the number of adsorbed nanoparticles is accurately proportional to the central spectral shift of the transmission spectrum. Moreover, our results show that when two particles are in proximity, so that each particle experiences the polarization field from the other, the induced secondary spectral shift remains small. Our calculations provide a basis for extending the sensing scheme to large particle influx regimes for real-world applications, such as the determination of the concentration of ultra-fine particles in arc welding, ambient atmosphere, combustion, or on-road aerosol due to traffic exhaust emissions.

© 2012 Optical Society of America

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References

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  1. A. Gupta and M. Gupta, “Synthesis and surface engineering of iron oxide nanoparticles for biomedical applications,” Biomaterials 26, 3995–4021 (2005).
    [CrossRef]
  2. W. Haiss, N. Thanh, J. Aveyard, and D. G. Fernig, “Determination of size and concentration of gold nanoparticles from UV-vis spectra,” Anal. Chem. 79, 4215–4221 (2007).
    [CrossRef]
  3. J. P. Shi, D. E. Evans, A. A. Khan, and R. M. Harrison, “Sources and concentration of nanoparticles (<10  nm diameter) in the urban atmosphere,” Atmos. Environ. 35, 1193–1202 (2001).
    [CrossRef]
  4. A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering-gallery modes-part I: basics,” IEEE J. Sel. Top. Quantum Electron. 12, 3–14 (2006).
    [CrossRef]
  5. M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
    [CrossRef]
  6. Y. Shen and J.-T. Shen, “Nanoparticle sensing using whispering-gallery-mode resonators: plasmonic and Rayleigh scatterers,” Phys. Rev. A 85, 013801 (2012).
    [CrossRef]
  7. L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
    [CrossRef]
  8. K. Vahala, ed., Optical Microcavities, Advanced Series in Applied Physics (World Scientific, 2004).
  9. A. Mazzei, S. Gotzinger, L. D. 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, 173603–4 (2007).
    [CrossRef]
  10. J. Zhu, S. K. Ozdemir, 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]
  11. http://www.comsol.com (version 4.3).
  12. S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
    [CrossRef]
  13. S. A. Dyer, ed., Survey of Instrumentation and Measurement (Wiley, 2001).
  14. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, 1995).
  15. D. J. Griffiths, Introduction to Electrodynamics (Prentice Hall, 1999).
  16. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  17. X. Yi, Y.-F. Xiao, Y.-C. Liu, B.-B. Li, Y.-L. Chen, Y. Li, and Q. Gong, “Multiple-Rayleigh-scatterer-induced mode splitting in a high-Q whispering-gallery-mode microresonator,” Phys. Rev. A 83, 023803 (2011).
    [CrossRef]

2012 (1)

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

2011 (1)

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

2010 (1)

J. Zhu, S. K. Ozdemir, 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]

2007 (2)

A. Mazzei, S. Gotzinger, L. D. 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, 173603–4 (2007).
[CrossRef]

W. Haiss, N. Thanh, J. Aveyard, and D. G. Fernig, “Determination of size and concentration of gold nanoparticles from UV-vis spectra,” Anal. Chem. 79, 4215–4221 (2007).
[CrossRef]

2006 (1)

A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering-gallery modes-part I: basics,” IEEE J. Sel. Top. Quantum Electron. 12, 3–14 (2006).
[CrossRef]

2005 (1)

A. Gupta and M. Gupta, “Synthesis and surface engineering of iron oxide nanoparticles for biomedical applications,” Biomaterials 26, 3995–4021 (2005).
[CrossRef]

2003 (1)

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

2001 (1)

J. P. Shi, D. E. Evans, A. A. Khan, and R. M. Harrison, “Sources and concentration of nanoparticles (<10  nm diameter) in the urban atmosphere,” Atmos. Environ. 35, 1193–1202 (2001).
[CrossRef]

2000 (1)

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[CrossRef]

1993 (1)

L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[CrossRef]

Aveyard, J.

W. Haiss, N. Thanh, J. Aveyard, and D. G. Fernig, “Determination of size and concentration of gold nanoparticles from UV-vis spectra,” Anal. Chem. 79, 4215–4221 (2007).
[CrossRef]

Benson, O.

A. Mazzei, S. Gotzinger, L. D. 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, 173603–4 (2007).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Brune, M.

L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[CrossRef]

Cai, M.

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[CrossRef]

Chen, D.-R.

J. Zhu, S. K. Ozdemir, 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, Y.-L.

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

Collot, L.

L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[CrossRef]

Evans, D. E.

J. P. Shi, D. E. Evans, A. A. Khan, and R. M. Harrison, “Sources and concentration of nanoparticles (<10  nm diameter) in the urban atmosphere,” Atmos. Environ. 35, 1193–1202 (2001).
[CrossRef]

Fernig, D. G.

W. Haiss, N. Thanh, J. Aveyard, and D. G. Fernig, “Determination of size and concentration of gold nanoparticles from UV-vis spectra,” Anal. Chem. 79, 4215–4221 (2007).
[CrossRef]

Gong, Q.

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

Gotzinger, S.

A. Mazzei, S. Gotzinger, L. D. 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, 173603–4 (2007).
[CrossRef]

Griffiths, D. J.

D. J. Griffiths, Introduction to Electrodynamics (Prentice Hall, 1999).

Gupta, A.

A. Gupta and M. Gupta, “Synthesis and surface engineering of iron oxide nanoparticles for biomedical applications,” Biomaterials 26, 3995–4021 (2005).
[CrossRef]

Gupta, M.

A. Gupta and M. Gupta, “Synthesis and surface engineering of iron oxide nanoparticles for biomedical applications,” Biomaterials 26, 3995–4021 (2005).
[CrossRef]

Haiss, W.

W. Haiss, N. Thanh, J. Aveyard, and D. G. Fernig, “Determination of size and concentration of gold nanoparticles from UV-vis spectra,” Anal. Chem. 79, 4215–4221 (2007).
[CrossRef]

Haroche, S.

L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[CrossRef]

Harrison, R. M.

J. P. Shi, D. E. Evans, A. A. Khan, and R. M. Harrison, “Sources and concentration of nanoparticles (<10  nm diameter) in the urban atmosphere,” Atmos. Environ. 35, 1193–1202 (2001).
[CrossRef]

He, L.

J. Zhu, S. K. Ozdemir, 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]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

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, 3–14 (2006).
[CrossRef]

Joannopoulos, J. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, 1995).

Khan, A. A.

J. P. Shi, D. E. Evans, A. A. Khan, and R. M. Harrison, “Sources and concentration of nanoparticles (<10  nm diameter) in the urban atmosphere,” Atmos. Environ. 35, 1193–1202 (2001).
[CrossRef]

Kippenberg, T. J.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

Lefèvre-Seguin, V.

L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[CrossRef]

Li, B.-B.

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

Li, L.

J. Zhu, S. K. Ozdemir, 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, Y.

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

Liu, Y.-C.

X. Yi, Y.-F. Xiao, Y.-C. Liu, B.-B. Li, Y.-L. Chen, Y. Li, and Q. Gong, “Multiple-Rayleigh-scatterer-induced mode splitting in a high-Q whispering-gallery-mode microresonator,” Phys. Rev. A 83, 023803 (2011).
[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, 3–14 (2006).
[CrossRef]

Mazzei, A.

A. Mazzei, S. Gotzinger, L. D. 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, 173603–4 (2007).
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, 1995).

Menezes, L. D. S.

A. Mazzei, S. Gotzinger, L. D. 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, 173603–4 (2007).
[CrossRef]

Ozdemir, S. K.

J. Zhu, S. K. Ozdemir, 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]

Painter, O.

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[CrossRef]

Painter, O. J.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

Raimond, J. M.

L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[CrossRef]

Sandoghdar, V.

A. Mazzei, S. Gotzinger, L. D. 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, 173603–4 (2007).
[CrossRef]

Shen, J.-T.

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

Shen, Y.

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

Shi, J. P.

J. P. Shi, D. E. Evans, A. A. Khan, and R. M. Harrison, “Sources and concentration of nanoparticles (<10  nm diameter) in the urban atmosphere,” Atmos. Environ. 35, 1193–1202 (2001).
[CrossRef]

Spillane, S. M.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

Thanh, N.

W. Haiss, N. Thanh, J. Aveyard, and D. G. Fernig, “Determination of size and concentration of gold nanoparticles from UV-vis spectra,” Anal. Chem. 79, 4215–4221 (2007).
[CrossRef]

Vahala, K. J.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, 1995).

Xiao, Y.-F.

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

J. Zhu, S. K. Ozdemir, 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]

Yang, L.

J. Zhu, S. K. Ozdemir, 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]

Yi, X.

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

Zhu, J.

J. Zhu, S. K. Ozdemir, 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]

Zumofen, G.

A. Mazzei, S. Gotzinger, L. D. 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, 173603–4 (2007).
[CrossRef]

Anal. Chem. (1)

W. Haiss, N. Thanh, J. Aveyard, and D. G. Fernig, “Determination of size and concentration of gold nanoparticles from UV-vis spectra,” Anal. Chem. 79, 4215–4221 (2007).
[CrossRef]

Atmos. Environ. (1)

J. P. Shi, D. E. Evans, A. A. Khan, and R. M. Harrison, “Sources and concentration of nanoparticles (<10  nm diameter) in the urban atmosphere,” Atmos. Environ. 35, 1193–1202 (2001).
[CrossRef]

Biomaterials (1)

A. Gupta and M. Gupta, “Synthesis and surface engineering of iron oxide nanoparticles for biomedical applications,” Biomaterials 26, 3995–4021 (2005).
[CrossRef]

Europhys. Lett. (1)

L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[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, 3–14 (2006).
[CrossRef]

Nat. Photonics (1)

J. Zhu, S. K. Ozdemir, 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]

Phys. Rev. A (2)

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

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

Phys. Rev. Lett. (3)

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[CrossRef]

A. Mazzei, S. Gotzinger, L. D. 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, 173603–4 (2007).
[CrossRef]

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

Other (6)

S. A. Dyer, ed., Survey of Instrumentation and Measurement (Wiley, 2001).

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, 1995).

D. J. Griffiths, Introduction to Electrodynamics (Prentice Hall, 1999).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

http://www.comsol.com (version 4.3).

K. Vahala, ed., Optical Microcavities, Advanced Series in Applied Physics (World Scientific, 2004).

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Figures (2)

Fig. 1.
Fig. 1.

(a) Angular positions of five consecutive particles (radius a = 30 nm , index n = 1.57 ) adsorbed onto the resonator. The last two configurations both have five adsorbed particles, but with different angular positions. (b) Transmission spectra versus number of adsorbed particles N . The center of each spectrum is indicated by arrows of the same color. (c) Central spectral shift S ( N ) (black squares) and frequency splitting Δ ( N ) (gray dots) versus N . The brown dot (single light gray in print) indicates the value for the last five-particle configuration in (a). Least square fitting yields the following: TM mode, S ( N ) = 0.7887 N GHz ; TE mode, S ( N ) = 1.058 N GHz .

Fig. 2.
Fig. 2.

S ( 2 ) / 2 S ( 1 ) as a function of d / a . S ( 2 ) is the central spectral shift including the proximity effect. S ( 1 ) is the central spectral shift due to a single particle. The direction of the electric field of the WGM resonator is denoted by the light blue arrows.

Equations (1)

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

H / = H 0 / + j = 1 N H I / = [ ω c 2 α 1 N ( E ρ 2 + E θ 2 + E z 2 ) i γ ] ( a a + b b ) 2 α ( E ρ 2 E θ 2 + E z 2 ) j = 1 N ( e 2 i m θ j b a + e 2 i m θ j a b ) .

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