Abstract

The effect of a dielectric substrate on whispering-gallery-mode (WGM)-based devices is experimentally investigated and theoretically quantified for spherical dielectric microresonators with 5μm diameter. The interaction with a dielectric substrate yields a homogeneous broadening with a threshold-like behavior versus the azimuthal quantum number, which is accompanied by an energy renormalization of about 20% of the broadening. The WGM orbital planes of narrowest spectral linewidth (close to the Mie value) in the presence of a substrate are identified, and the consequences for the scattering spectrum analysis of microsphere devices relying on high-Q factors are discussed.

© 2006 Optical Society of America

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  1. R. K. Chang and A. J. Campillo, Optical Processes in Microcavities (World Scientific, 1996).
    [CrossRef]
  2. M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, "Fiber-coupled microsphere laser," Opt. Lett. 25, 1430-1432 (2000).
    [CrossRef]
  3. A. Yu. Smirnov, S. N. Rashkeev, and A. M. Zagoskin, "Polarization switching in optical microsphere resonator," Appl. Phys. Lett. 80, 3503-3505 (2002).
    [CrossRef]
  4. B. E. Little, S. T. Chu, and H. A. Haus, "Track changing by use of the phase response of microspheres and resonators," Opt. Lett. 23, 894-896 (1998).
    [CrossRef]
  5. 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] [PubMed]
  6. M. Noto, F. Vollmer, D. Keng, I. Teraoka, and S. Arnold, "Nanolayer characterization through wavelength multiplexing of microsphere resonator," Opt. Lett. 30, 510-512 (2003).
    [CrossRef]
  7. U. Woggon, R. Wannemacher, M. V. Artemyev, B. Möller, N. Le Thomas, V. Anikeyev, and O. Schöps, "Dot-in-a-dot: electronic and photonic confinement in all three dimensions," Appl. Phys. B 77, 469-484 (2003).
    [CrossRef]
  8. J. R. Buck and H. J. Kimble, "Optimal sizes of dielectric microspheres for cavity QED with strong coupling," Phys. Rev. A 67, 033806 (2003).
    [CrossRef]
  9. D. W. Vernooy, V. S. Ilchenko, H. Mabuchi, E. W. Streed, and H. J. Kimble, "High-Q measurements of fused-silica microspheres in the near infrared," Opt. Lett. 23, 247-249 (1998).
    [CrossRef]
  10. W. von Klitzing, R. Long, V. S. Ilchenko, J. Hare, and V. Lefvre-Seguin, "Frequency tuning of the whispering-gallery modes of silica microspheres for cavity quantum electrodynamics and spectroscopy," Opt. Lett. 26, 166-168 (2001).
    [CrossRef]
  11. 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] [PubMed]
  12. Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, "Heavy photon states in photonic chains of resonantly coupled cavities with supermonodispersive microspheres," Phys. Rev. Lett. 94, 203905 (2005).
    [CrossRef] [PubMed]
  13. H. Ishikawa, H. Tamaru, and K. Miyano, "Observation of a modulation effect caused by a microsphere resonator strongly coupled to a dielectric substrate," Opt. Lett. 24, 643-645 (1999).
    [CrossRef]
  14. H. Ishikawa, H. Tamaru, and K. Miyano, "Microsphere resonators strongly coupled to a plane dielectric substrate: coupling via the optical near field," J. Opt. Soc. Am. B 17, 802-813 (2000).
    [CrossRef]
  15. E. Fucile, P. Denti, F. Borghese, R. Saija, and O. I. Sindoni, "Optical properties of a sphere in the vicinity of a plane surface," J. Opt. Soc. Am. A 14, 1505-1514 (1997).
    [CrossRef]
  16. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).
  17. G. Chen, R. K. Chang, S. C. Hill, and P. W. Barber, "Frequency splitting of degenerate spherical cavity modes: stimulated Raman scattering spectrum of deformed droplets," Opt. Lett. 16, 1269-1271 (1991).
    [CrossRef] [PubMed]
  18. H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, "Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets," Phys. Rev. A 41, 5187-5198 (1990).
    [CrossRef] [PubMed]
  19. H. M. Lai, C. C. Lam, P. T. Leung, and K. Young, "Effect of perturbations on the widths of narrow morphology-dependent resonances in Mie scattering," J. Opt. Soc. Am. B 8, 1962-1973 (1991).
    [CrossRef]
  20. P. A. Bobbert and J. Vlieger, "Light scattering by a sphere on a substrate," Physica A 137, 209-242 (1986).
    [CrossRef]
  21. P. A. Bobbert, J. Vlieger, and R. Greef, "Light reflection from a substrate sparsely seeded with spheres-comparison with an ellipsometric experiment," Physica A 137, 243-257 (1986).
    [CrossRef]

2005

Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, "Heavy photon states in photonic chains of resonantly coupled cavities with supermonodispersive microspheres," Phys. Rev. Lett. 94, 203905 (2005).
[CrossRef] [PubMed]

2003

U. Woggon, R. Wannemacher, M. V. Artemyev, B. Möller, N. Le Thomas, V. Anikeyev, and O. Schöps, "Dot-in-a-dot: electronic and photonic confinement in all three dimensions," Appl. Phys. B 77, 469-484 (2003).
[CrossRef]

J. R. Buck and H. J. Kimble, "Optimal sizes of dielectric microspheres for cavity QED with strong coupling," Phys. Rev. A 67, 033806 (2003).
[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] [PubMed]

M. Noto, F. Vollmer, D. Keng, I. Teraoka, and S. Arnold, "Nanolayer characterization through wavelength multiplexing of microsphere resonator," Opt. Lett. 30, 510-512 (2003).
[CrossRef]

2002

A. Yu. Smirnov, S. N. Rashkeev, and A. M. Zagoskin, "Polarization switching in optical microsphere resonator," Appl. Phys. Lett. 80, 3503-3505 (2002).
[CrossRef]

2001

2000

M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, "Fiber-coupled microsphere laser," Opt. Lett. 25, 1430-1432 (2000).
[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] [PubMed]

H. Ishikawa, H. Tamaru, and K. Miyano, "Microsphere resonators strongly coupled to a plane dielectric substrate: coupling via the optical near field," J. Opt. Soc. Am. B 17, 802-813 (2000).
[CrossRef]

1999

1998

1997

1991

1990

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, "Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets," Phys. Rev. A 41, 5187-5198 (1990).
[CrossRef] [PubMed]

1986

P. A. Bobbert and J. Vlieger, "Light scattering by a sphere on a substrate," Physica A 137, 209-242 (1986).
[CrossRef]

P. A. Bobbert, J. Vlieger, and R. Greef, "Light reflection from a substrate sparsely seeded with spheres-comparison with an ellipsometric experiment," Physica A 137, 243-257 (1986).
[CrossRef]

Anikeyev, V.

U. Woggon, R. Wannemacher, M. V. Artemyev, B. Möller, N. Le Thomas, V. Anikeyev, and O. Schöps, "Dot-in-a-dot: electronic and photonic confinement in all three dimensions," Appl. Phys. B 77, 469-484 (2003).
[CrossRef]

Arnold, S.

Artemyev, M. V.

U. Woggon, R. Wannemacher, M. V. Artemyev, B. Möller, N. Le Thomas, V. Anikeyev, and O. Schöps, "Dot-in-a-dot: electronic and photonic confinement in all three dimensions," Appl. Phys. B 77, 469-484 (2003).
[CrossRef]

Barber, P. W.

G. Chen, R. K. Chang, S. C. Hill, and P. W. Barber, "Frequency splitting of degenerate spherical cavity modes: stimulated Raman scattering spectrum of deformed droplets," Opt. Lett. 16, 1269-1271 (1991).
[CrossRef] [PubMed]

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, "Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets," Phys. Rev. A 41, 5187-5198 (1990).
[CrossRef] [PubMed]

Bobbert, P. A.

P. A. Bobbert and J. Vlieger, "Light scattering by a sphere on a substrate," Physica A 137, 209-242 (1986).
[CrossRef]

P. A. Bobbert, J. Vlieger, and R. Greef, "Light reflection from a substrate sparsely seeded with spheres-comparison with an ellipsometric experiment," Physica A 137, 243-257 (1986).
[CrossRef]

Borghese, F.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

Buck, J. R.

J. R. Buck and H. J. Kimble, "Optimal sizes of dielectric microspheres for cavity QED with strong coupling," Phys. Rev. A 67, 033806 (2003).
[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] [PubMed]

M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, "Fiber-coupled microsphere laser," Opt. Lett. 25, 1430-1432 (2000).
[CrossRef]

Campillo, A. J.

R. K. Chang and A. J. Campillo, Optical Processes in Microcavities (World Scientific, 1996).
[CrossRef]

Chang, R. K.

Chen, G.

Chu, S. T.

Denti, P.

Fucile, E.

Greef, R.

P. A. Bobbert, J. Vlieger, and R. Greef, "Light reflection from a substrate sparsely seeded with spheres-comparison with an ellipsometric experiment," Physica A 137, 243-257 (1986).
[CrossRef]

Hara, Y.

Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, "Heavy photon states in photonic chains of resonantly coupled cavities with supermonodispersive microspheres," Phys. Rev. Lett. 94, 203905 (2005).
[CrossRef] [PubMed]

Hare, J.

Haus, H. A.

Hill, S. C.

G. Chen, R. K. Chang, S. C. Hill, and P. W. Barber, "Frequency splitting of degenerate spherical cavity modes: stimulated Raman scattering spectrum of deformed droplets," Opt. Lett. 16, 1269-1271 (1991).
[CrossRef] [PubMed]

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, "Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets," Phys. Rev. A 41, 5187-5198 (1990).
[CrossRef] [PubMed]

Holler, S.

Ilchenko, V. S.

Ishikawa, H.

H. Ishikawa, H. Tamaru, and K. Miyano, "Microsphere resonators strongly coupled to a plane dielectric substrate: coupling via the optical near field," J. Opt. Soc. Am. B 17, 802-813 (2000).
[CrossRef]

H. Ishikawa, H. Tamaru, and K. Miyano, "Observation of a modulation effect caused by a microsphere resonator strongly coupled to a dielectric substrate," Opt. Lett. 24, 643-645 (1999).
[CrossRef]

Keng, D.

Khoshsima, M.

Kimble, H. J.

J. R. Buck and H. J. Kimble, "Optimal sizes of dielectric microspheres for cavity QED with strong coupling," Phys. Rev. A 67, 033806 (2003).
[CrossRef]

D. W. Vernooy, V. S. Ilchenko, H. Mabuchi, E. W. Streed, and H. J. Kimble, "High-Q measurements of fused-silica microspheres in the near infrared," Opt. Lett. 23, 247-249 (1998).
[CrossRef]

Kuwata-Gonokami, M.

Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, "Heavy photon states in photonic chains of resonantly coupled cavities with supermonodispersive microspheres," Phys. Rev. Lett. 94, 203905 (2005).
[CrossRef] [PubMed]

Lai, H. M.

H. M. Lai, C. C. Lam, P. T. Leung, and K. Young, "Effect of perturbations on the widths of narrow morphology-dependent resonances in Mie scattering," J. Opt. Soc. Am. B 8, 1962-1973 (1991).
[CrossRef]

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, "Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets," Phys. Rev. A 41, 5187-5198 (1990).
[CrossRef] [PubMed]

Lam, C. C.

Le Thomas, N.

U. Woggon, R. Wannemacher, M. V. Artemyev, B. Möller, N. Le Thomas, V. Anikeyev, and O. Schöps, "Dot-in-a-dot: electronic and photonic confinement in all three dimensions," Appl. Phys. B 77, 469-484 (2003).
[CrossRef]

Lefvre-Seguin, V.

Leung, P. T.

H. M. Lai, C. C. Lam, P. T. Leung, and K. Young, "Effect of perturbations on the widths of narrow morphology-dependent resonances in Mie scattering," J. Opt. Soc. Am. B 8, 1962-1973 (1991).
[CrossRef]

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, "Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets," Phys. Rev. A 41, 5187-5198 (1990).
[CrossRef] [PubMed]

Little, B. E.

Long, R.

Mabuchi, H.

Miyano, K.

H. Ishikawa, H. Tamaru, and K. Miyano, "Microsphere resonators strongly coupled to a plane dielectric substrate: coupling via the optical near field," J. Opt. Soc. Am. B 17, 802-813 (2000).
[CrossRef]

H. Ishikawa, H. Tamaru, and K. Miyano, "Observation of a modulation effect caused by a microsphere resonator strongly coupled to a dielectric substrate," Opt. Lett. 24, 643-645 (1999).
[CrossRef]

Möller, B.

U. Woggon, R. Wannemacher, M. V. Artemyev, B. Möller, N. Le Thomas, V. Anikeyev, and O. Schöps, "Dot-in-a-dot: electronic and photonic confinement in all three dimensions," Appl. Phys. B 77, 469-484 (2003).
[CrossRef]

Mukaiyama, T.

Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, "Heavy photon states in photonic chains of resonantly coupled cavities with supermonodispersive microspheres," Phys. Rev. Lett. 94, 203905 (2005).
[CrossRef] [PubMed]

Noto, M.

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] [PubMed]

M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, "Fiber-coupled microsphere laser," Opt. Lett. 25, 1430-1432 (2000).
[CrossRef]

Rashkeev, S. N.

A. Yu. Smirnov, S. N. Rashkeev, and A. M. Zagoskin, "Polarization switching in optical microsphere resonator," Appl. Phys. Lett. 80, 3503-3505 (2002).
[CrossRef]

Saija, R.

Schöps, O.

U. Woggon, R. Wannemacher, M. V. Artemyev, B. Möller, N. Le Thomas, V. Anikeyev, and O. Schöps, "Dot-in-a-dot: electronic and photonic confinement in all three dimensions," Appl. Phys. B 77, 469-484 (2003).
[CrossRef]

Sercel, P. C.

Sindoni, O. I.

Smirnov, A. Yu.

A. Yu. Smirnov, S. N. Rashkeev, and A. M. Zagoskin, "Polarization switching in optical microsphere resonator," Appl. Phys. Lett. 80, 3503-3505 (2002).
[CrossRef]

Streed, E. W.

Takeda, K.

Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, "Heavy photon states in photonic chains of resonantly coupled cavities with supermonodispersive microspheres," Phys. Rev. Lett. 94, 203905 (2005).
[CrossRef] [PubMed]

Tamaru, H.

H. Ishikawa, H. Tamaru, and K. Miyano, "Microsphere resonators strongly coupled to a plane dielectric substrate: coupling via the optical near field," J. Opt. Soc. Am. B 17, 802-813 (2000).
[CrossRef]

H. Ishikawa, H. Tamaru, and K. Miyano, "Observation of a modulation effect caused by a microsphere resonator strongly coupled to a dielectric substrate," Opt. Lett. 24, 643-645 (1999).
[CrossRef]

Teraoka, I.

Vahala, K. J.

M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, "Fiber-coupled microsphere laser," Opt. Lett. 25, 1430-1432 (2000).
[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] [PubMed]

Vernooy, D. W.

Vlieger, J.

P. A. Bobbert, J. Vlieger, and R. Greef, "Light reflection from a substrate sparsely seeded with spheres-comparison with an ellipsometric experiment," Physica A 137, 243-257 (1986).
[CrossRef]

P. A. Bobbert and J. Vlieger, "Light scattering by a sphere on a substrate," Physica A 137, 209-242 (1986).
[CrossRef]

Vollmer, F.

von Klitzing, W.

Wannemacher, R.

U. Woggon, R. Wannemacher, M. V. Artemyev, B. Möller, N. Le Thomas, V. Anikeyev, and O. Schöps, "Dot-in-a-dot: electronic and photonic confinement in all three dimensions," Appl. Phys. B 77, 469-484 (2003).
[CrossRef]

Woggon, U.

U. Woggon, R. Wannemacher, M. V. Artemyev, B. Möller, N. Le Thomas, V. Anikeyev, and O. Schöps, "Dot-in-a-dot: electronic and photonic confinement in all three dimensions," Appl. Phys. B 77, 469-484 (2003).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

Young, K.

H. M. Lai, C. C. Lam, P. T. Leung, and K. Young, "Effect of perturbations on the widths of narrow morphology-dependent resonances in Mie scattering," J. Opt. Soc. Am. B 8, 1962-1973 (1991).
[CrossRef]

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, "Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets," Phys. Rev. A 41, 5187-5198 (1990).
[CrossRef] [PubMed]

Zagoskin, A. M.

A. Yu. Smirnov, S. N. Rashkeev, and A. M. Zagoskin, "Polarization switching in optical microsphere resonator," Appl. Phys. Lett. 80, 3503-3505 (2002).
[CrossRef]

Appl. Phys. B

U. Woggon, R. Wannemacher, M. V. Artemyev, B. Möller, N. Le Thomas, V. Anikeyev, and O. Schöps, "Dot-in-a-dot: electronic and photonic confinement in all three dimensions," Appl. Phys. B 77, 469-484 (2003).
[CrossRef]

Appl. Phys. Lett.

A. Yu. Smirnov, S. N. Rashkeev, and A. M. Zagoskin, "Polarization switching in optical microsphere resonator," Appl. Phys. Lett. 80, 3503-3505 (2002).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

H. M. Lai, C. C. Lam, P. T. Leung, and K. Young, "Effect of perturbations on the widths of narrow morphology-dependent resonances in Mie scattering," J. Opt. Soc. Am. B 8, 1962-1973 (1991).
[CrossRef]

H. Ishikawa, H. Tamaru, and K. Miyano, "Microsphere resonators strongly coupled to a plane dielectric substrate: coupling via the optical near field," J. Opt. Soc. Am. B 17, 802-813 (2000).
[CrossRef]

Opt. Lett.

G. Chen, R. K. Chang, S. C. Hill, and P. W. Barber, "Frequency splitting of degenerate spherical cavity modes: stimulated Raman scattering spectrum of deformed droplets," Opt. Lett. 16, 1269-1271 (1991).
[CrossRef] [PubMed]

D. W. Vernooy, V. S. Ilchenko, H. Mabuchi, E. W. Streed, and H. J. Kimble, "High-Q measurements of fused-silica microspheres in the near infrared," Opt. Lett. 23, 247-249 (1998).
[CrossRef]

B. E. Little, S. T. Chu, and H. A. Haus, "Track changing by use of the phase response of microspheres and resonators," Opt. Lett. 23, 894-896 (1998).
[CrossRef]

M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, "Fiber-coupled microsphere laser," Opt. Lett. 25, 1430-1432 (2000).
[CrossRef]

W. von Klitzing, R. Long, V. S. Ilchenko, J. Hare, and V. Lefvre-Seguin, "Frequency tuning of the whispering-gallery modes of silica microspheres for cavity quantum electrodynamics and spectroscopy," Opt. Lett. 26, 166-168 (2001).
[CrossRef]

H. Ishikawa, H. Tamaru, and K. Miyano, "Observation of a modulation effect caused by a microsphere resonator strongly coupled to a dielectric substrate," Opt. Lett. 24, 643-645 (1999).
[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] [PubMed]

M. Noto, F. Vollmer, D. Keng, I. Teraoka, and S. Arnold, "Nanolayer characterization through wavelength multiplexing of microsphere resonator," Opt. Lett. 30, 510-512 (2003).
[CrossRef]

Phys. Rev. A

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, "Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets," Phys. Rev. A 41, 5187-5198 (1990).
[CrossRef] [PubMed]

J. R. Buck and H. J. Kimble, "Optimal sizes of dielectric microspheres for cavity QED with strong coupling," Phys. Rev. A 67, 033806 (2003).
[CrossRef]

Phys. Rev. Lett.

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] [PubMed]

Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, "Heavy photon states in photonic chains of resonantly coupled cavities with supermonodispersive microspheres," Phys. Rev. Lett. 94, 203905 (2005).
[CrossRef] [PubMed]

Physica A

P. A. Bobbert and J. Vlieger, "Light scattering by a sphere on a substrate," Physica A 137, 209-242 (1986).
[CrossRef]

P. A. Bobbert, J. Vlieger, and R. Greef, "Light reflection from a substrate sparsely seeded with spheres-comparison with an ellipsometric experiment," Physica A 137, 243-257 (1986).
[CrossRef]

Other

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

R. K. Chang and A. J. Campillo, Optical Processes in Microcavities (World Scientific, 1996).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

(a) Experimental scattering spectrum of a d = 6 μ m microsphere on a quartz substrate (left scale, upper curve) and a corresponding spectrum calculated by Mie theory (right scale, lower curve). (b) Zoom of (a) around the TE 1 42 and the TE 2 37 WGMs. (c) Scheme of the sphere–substrate geometry.

Fig. 2
Fig. 2

(a) Spectrally and spatially resolved scattering intensity of a sphere of d = 4.47 μ m around the TE 1 30 mode, on a linear grey scale from zero (white) to black. The image is taken from a 300 nm wide center section of the sphere equatorial plane, as shown in the inset. (b) Spectrum averaged over the position. In the inset the linewidths for the modes are plotted versus their energy and compared with the Mie value (dotted line).

Fig. 3
Fig. 3

(a) Spectrally and spatially resolved scattering intensity of a sphere of d = 4.51 μ m around the TE 1 30 mode, on a linear grey scale from zero (white) to black. The image is taken from a 300 nm wide center section of the sphere equatorial plane, as shown in the inset. (b) Spectrum averaged over a selected area of the position. In the inset the linewidths for the modes are plotted versus their energy and compared to the Mie value (dotted line).

Fig. 4
Fig. 4

Modeling of the TE 1 30 WGM for a polystyrene sphere with a diameter d = 4.5 μ m . (a) Linewidth variation versus the azimuthal quantum number m for different index of refraction n s of the substrate. (b) Spectrum resulting from a shape deformation of ϵ 1 % in absence of the substrate. (c) Normalized spectrum of even m modes and ϵ = 0 in presence of the substrate.

Fig. 5
Fig. 5

(a) Microsphere line width of a TE 1 30 m WGM versus the shape perturbation amplitude for a polystyrene sphere with a diameter d = 4.5 μ m . The azimuthal quantum number m along the shape deformation symmetry axis is taken equal to zero. (b) Linewidth versus m for μ = 0.01 and different angular momenta L of the shape deformation. The drawings represent the rim of the sphere in a plane, including the symmetry axis (dashed arrow) for the different L.

Equations (4)

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

1 Q = 1 Q 0 + μ 2 c 2 + O ( μ 3 ) ,
c 2 = n r 2 1 2 π x 0 2 L + 1 2 l + 1 l = l L and l l l + L ( 2 l + 1 ) C ( l L l , 000 ) 2 × C ( l L l , m 0 m ) 2 j l ( 1 ) ( n r x 0 ) W l ( x 0 ) 2 ,
Ψ p ( r ) = l = 1 m = l l v l m p Ψ l m ( r ) , with Ψ l m ( r ) = j l ( 1 ) ( k r ) Y l m ( θ , ϕ ) ,
Π p ( r ) = l = 1 m = l l w l m p Π l m ( r ) , with Π l m ( r ) = h l ( 1 ) ( k r ) Y l m ( θ , ϕ ) ,

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