Abstract

Optical coupling between a spherical microresonator and a plane dielectric substrate is investigated for a small sphere whose diameter is only a few ten times as large as the optical wavelength. A unique characteristic of small microresonators, relaxation of the phase-matching requirement that is due to the small size, is demonstrated on the basis of experimental results and model numerical calculations. The difference between the frequency and the propagation constant as parameters to describe the resonances of microresonators is clarified. Based on the numerical results, intrinsic restriction on a distance between the resonator and the coupler is also suggested.

© 2001 Optical Society of America

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  1. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
    [CrossRef]
  2. D. Rafizadeh, J. P. Zhang, S. C. Hagness, A. Taflove, K. A. Stair, S. T. Ho, and R. C. Tiberio, “Waveguide-coupled AlGaAs/GaAs microcavity ring and disk resonators with high finesse and 21.6-nm free spectral range,” Opt. Lett. 22, 1244–1246 (1997).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  5. A. Shinya and M. Fukui, “Finite-difference time-domain analysis of the interaction of Gaussian evanescent light with a single dielectric sphere or ordered dielectric spheres,” Opt. Rev. 6, 215–223 (1999).
    [CrossRef]
  6. T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, “Tight-binding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999).
    [CrossRef]
  7. 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]
  8. F. C. Blom, D. R. van Dijk, H. J. W. M. Hoekstra, A. Driessen, and Th. J. A. Popma, “Experimental study of integrated-optics microcavity resonators: toward an all-optical switching device,” Appl. Phys. Lett. 71, 747–749 (1997).
    [CrossRef]
  9. B. E. Little, J. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10, 549–551 (1998).
    [CrossRef]
  10. F. C. Blom, H. Keldman, H. J. W. M. Hoekstra, A. Driessen, Th. J. A. Popma, S. T. Chu, and B. E. Little, “A single channel dropping filter based on a cylindrical microresonator,” Opt. Commun. 167, 77–82 (1999).
    [CrossRef]
  11. S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15, 2154–2165 (1997).
    [CrossRef]
  12. S. C. Hagness, J. P. Zhang, R. C. Tiberio, and S. T. Ho, “Propagation loss measurement in semiconductor microcavity ring and disk resonators,” J. Lightwave Technol. 16, 1308–1314 (1998).
    [CrossRef]
  13. M. K. Chin and S. T. Ho, “Design and modeling of waveguide-coupled single-mode microring resonators,” J. Lightwave Technol. 16, 1433–1446 (1998).
    [CrossRef]
  14. M. K. Chin, C. Youtsey, W. Zhao, T. Pierson, Z. Ren, S. L. Wu, L. Wang, Y. G. Zhao, and S. T. Ho, “GaAs microcavity channel-dropping filter based on a race-track resonator,” IEEE Photon. Technol. Lett. 11, 1620–1622 (1999).
    [CrossRef]
  15. M. L. M. Balistreri, D. J. W. Klunder, F. C. Blom, A. Driessen, H. W. J. M. Hoekstra, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Visualizing the whispering gallery modes in a cylindrical optical microcavity,” Opt. Lett. 24, 1829–1831 (1999).
    [CrossRef]
  16. M. Cai and K. Vahala, “Highly efficient optical power transfer to whispering-gallery modes by use of a symmetrical dual-coupling configuration,” Opt. Lett. 25, 260–262 (2000).
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  18. S. Schiller, I. I. Yu, M. M. Fejer, and R. L. Byer, “Fused silica monolithic total-internal-reflection resonator,” Opt. Lett. 17, 378–380 (1992).
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    [CrossRef] [PubMed]
  21. D. R. Rowland and J. D. Love, “Evanescent wave coupling of whispering gallery modes of a dielectric cylinder,” IEE Proc. J 140, 177–188 (1993).
  22. In the case of an add–drop filter, light is coupled out only from the secondary output port (secondary waveguide). Output intensity at the primary waveguide disappears because of the destructive interference between the incident and the output beams.
  23. J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, “Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper,” Opt. Lett. 22, 1129–1131 (1997).
    [CrossRef] [PubMed]
  24. This can be estimated by one plotting the electric field of the corresponding resonant mode (whispering-gallery-mode) at a surface of interest [see Figs. 6(a) and 6(b) of Ref. 28]. When a curved substrate or waveguide is used as a coupler, Δz can be larger than this value.
  25. For a larger glass spherical resonator in contact with a waveguide and hence in the overcoupled condition, QT in the range of 105–106 has been reported. The quality factor of a small resonator is expected to be lower.
  26. M. L. Gorodetsky and V. S. Ilchenko, “Optical microsphere resonator: optimal coupling to high-Q whispering-gallery modes,” J. Opt. Soc. Am. B 16, 147–154 (1999).
    [CrossRef]
  27. 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]
  28. 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. A 17, 802–813 (2000).
    [CrossRef]
  29. We label the mode number (i.e., total angular momentum of the mode) by l, the azimuthal mode number (z component of angular momentum) by m, and the order number (number of the intensity maximum in the radial direction) by s. The quantization axis of the angular momentum is taken parallel to the substrate and perpendicular to the incidence plane.
  30. The position of the observation plane (z in the caption of Fig. 4) is determined from the lateral position of the totally reflected part of the beam. Then the phase difference between the reflected beam and the coupled-out beam is fixed by the model
  31. G. Roll, T. Kaiser, S. Lange, and G. Schweiger, “Ray interpretation of multipole fields in spherical dielectric cavities,” J. Opt. Soc. Am. A 15, 2879–2891 (1998).
    [CrossRef]

2000 (2)

1999 (7)

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]

M. L. M. Balistreri, D. J. W. Klunder, F. C. Blom, A. Driessen, H. W. J. M. Hoekstra, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Visualizing the whispering gallery modes in a cylindrical optical microcavity,” Opt. Lett. 24, 1829–1831 (1999).
[CrossRef]

M. L. Gorodetsky and V. S. Ilchenko, “Optical microsphere resonator: optimal coupling to high-Q whispering-gallery modes,” J. Opt. Soc. Am. B 16, 147–154 (1999).
[CrossRef]

A. Shinya and M. Fukui, “Finite-difference time-domain analysis of the interaction of Gaussian evanescent light with a single dielectric sphere or ordered dielectric spheres,” Opt. Rev. 6, 215–223 (1999).
[CrossRef]

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, “Tight-binding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999).
[CrossRef]

F. C. Blom, H. Keldman, H. J. W. M. Hoekstra, A. Driessen, Th. J. A. Popma, S. T. Chu, and B. E. Little, “A single channel dropping filter based on a cylindrical microresonator,” Opt. Commun. 167, 77–82 (1999).
[CrossRef]

M. K. Chin, C. Youtsey, W. Zhao, T. Pierson, Z. Ren, S. L. Wu, L. Wang, Y. G. Zhao, and S. T. Ho, “GaAs microcavity channel-dropping filter based on a race-track resonator,” IEEE Photon. Technol. Lett. 11, 1620–1622 (1999).
[CrossRef]

1998 (5)

1997 (5)

J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, “Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper,” Opt. Lett. 22, 1129–1131 (1997).
[CrossRef] [PubMed]

D. Rafizadeh, J. P. Zhang, S. C. Hagness, A. Taflove, K. A. Stair, S. T. Ho, and R. C. Tiberio, “Waveguide-coupled AlGaAs/GaAs microcavity ring and disk resonators with high finesse and 21.6-nm free spectral range,” Opt. Lett. 22, 1244–1246 (1997).
[CrossRef] [PubMed]

F. C. Blom, D. R. van Dijk, H. J. W. M. Hoekstra, A. Driessen, and Th. J. A. Popma, “Experimental study of integrated-optics microcavity resonators: toward an all-optical switching device,” Appl. Phys. Lett. 71, 747–749 (1997).
[CrossRef]

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15, 2154–2165 (1997).
[CrossRef]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

1996 (1)

1995 (1)

1993 (1)

D. R. Rowland and J. D. Love, “Evanescent wave coupling of whispering gallery modes of a dielectric cylinder,” IEE Proc. J 140, 177–188 (1993).

1992 (1)

1989 (1)

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[CrossRef]

1982 (1)

1969 (1)

E. A. J. Marcatili, “Bends in optical dielectric guides,” Bell Syst. Tech. J. 48, 2103–2132 (1969).
[CrossRef]

Arnold, S.

Balistreri, M. L. M.

Birks, T. A.

Blom, F. C.

M. L. M. Balistreri, D. J. W. Klunder, F. C. Blom, A. Driessen, H. W. J. M. Hoekstra, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Visualizing the whispering gallery modes in a cylindrical optical microcavity,” Opt. Lett. 24, 1829–1831 (1999).
[CrossRef]

F. C. Blom, H. Keldman, H. J. W. M. Hoekstra, A. Driessen, Th. J. A. Popma, S. T. Chu, and B. E. Little, “A single channel dropping filter based on a cylindrical microresonator,” Opt. Commun. 167, 77–82 (1999).
[CrossRef]

F. C. Blom, D. R. van Dijk, H. J. W. M. Hoekstra, A. Driessen, and Th. J. A. Popma, “Experimental study of integrated-optics microcavity resonators: toward an all-optical switching device,” Appl. Phys. Lett. 71, 747–749 (1997).
[CrossRef]

Braginsky, V. B.

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[CrossRef]

Byer, R. L.

Cai, M.

Cheung, G.

Chin, M. K.

M. K. Chin, C. Youtsey, W. Zhao, T. Pierson, Z. Ren, S. L. Wu, L. Wang, Y. G. Zhao, and S. T. Ho, “GaAs microcavity channel-dropping filter based on a race-track resonator,” IEEE Photon. Technol. Lett. 11, 1620–1622 (1999).
[CrossRef]

M. K. Chin and S. T. Ho, “Design and modeling of waveguide-coupled single-mode microring resonators,” J. Lightwave Technol. 16, 1433–1446 (1998).
[CrossRef]

Chodorow, M.

Chu, S. T.

F. C. Blom, H. Keldman, H. J. W. M. Hoekstra, A. Driessen, Th. J. A. Popma, S. T. Chu, and B. E. Little, “A single channel dropping filter based on a cylindrical microresonator,” Opt. Commun. 167, 77–82 (1999).
[CrossRef]

B. E. Little, J. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10, 549–551 (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]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

Connolly, J.

Driessen, A.

M. L. M. Balistreri, D. J. W. Klunder, F. C. Blom, A. Driessen, H. W. J. M. Hoekstra, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Visualizing the whispering gallery modes in a cylindrical optical microcavity,” Opt. Lett. 24, 1829–1831 (1999).
[CrossRef]

F. C. Blom, H. Keldman, H. J. W. M. Hoekstra, A. Driessen, Th. J. A. Popma, S. T. Chu, and B. E. Little, “A single channel dropping filter based on a cylindrical microresonator,” Opt. Commun. 167, 77–82 (1999).
[CrossRef]

F. C. Blom, D. R. van Dijk, H. J. W. M. Hoekstra, A. Driessen, and Th. J. A. Popma, “Experimental study of integrated-optics microcavity resonators: toward an all-optical switching device,” Appl. Phys. Lett. 71, 747–749 (1997).
[CrossRef]

Fejer, M. M.

Foresi, J.

B. E. Little, J. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10, 549–551 (1998).
[CrossRef]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

Fukui, M.

A. Shinya and M. Fukui, “Finite-difference time-domain analysis of the interaction of Gaussian evanescent light with a single dielectric sphere or ordered dielectric spheres,” Opt. Rev. 6, 215–223 (1999).
[CrossRef]

Gorodetsky, M. L.

M. L. Gorodetsky and V. S. Ilchenko, “Optical microsphere resonator: optimal coupling to high-Q whispering-gallery modes,” J. Opt. Soc. Am. B 16, 147–154 (1999).
[CrossRef]

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[CrossRef]

Greene, W.

B. E. Little, J. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10, 549–551 (1998).
[CrossRef]

Griffel, G.

Hagness, S. C.

Haus, H. A.

B. E. Little, J. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10, 549–551 (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]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

Ho, S. T.

M. K. Chin, C. Youtsey, W. Zhao, T. Pierson, Z. Ren, S. L. Wu, L. Wang, Y. G. Zhao, and S. T. Ho, “GaAs microcavity channel-dropping filter based on a race-track resonator,” IEEE Photon. Technol. Lett. 11, 1620–1622 (1999).
[CrossRef]

M. K. Chin and S. T. Ho, “Design and modeling of waveguide-coupled single-mode microring resonators,” J. Lightwave Technol. 16, 1433–1446 (1998).
[CrossRef]

S. C. Hagness, J. P. Zhang, R. C. Tiberio, and S. T. Ho, “Propagation loss measurement in semiconductor microcavity ring and disk resonators,” J. Lightwave Technol. 16, 1308–1314 (1998).
[CrossRef]

D. Rafizadeh, J. P. Zhang, S. C. Hagness, A. Taflove, K. A. Stair, S. T. Ho, and R. C. Tiberio, “Waveguide-coupled AlGaAs/GaAs microcavity ring and disk resonators with high finesse and 21.6-nm free spectral range,” Opt. Lett. 22, 1244–1246 (1997).
[CrossRef] [PubMed]

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15, 2154–2165 (1997).
[CrossRef]

Hoekstra, H. J. W. M.

F. C. Blom, H. Keldman, H. J. W. M. Hoekstra, A. Driessen, Th. J. A. Popma, S. T. Chu, and B. E. Little, “A single channel dropping filter based on a cylindrical microresonator,” Opt. Commun. 167, 77–82 (1999).
[CrossRef]

F. C. Blom, D. R. van Dijk, H. J. W. M. Hoekstra, A. Driessen, and Th. J. A. Popma, “Experimental study of integrated-optics microcavity resonators: toward an all-optical switching device,” Appl. Phys. Lett. 71, 747–749 (1997).
[CrossRef]

Hoekstra, H. W. J. M.

Ilchenko, V. S.

M. L. Gorodetsky and V. S. Ilchenko, “Optical microsphere resonator: optimal coupling to high-Q whispering-gallery modes,” J. Opt. Soc. Am. B 16, 147–154 (1999).
[CrossRef]

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[CrossRef]

Ippen, E. P.

B. E. Little, J. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10, 549–551 (1998).
[CrossRef]

Ishikawa, H.

Jacques, F.

Jimba, Y.

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, “Tight-binding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999).
[CrossRef]

Kaiser, T.

Keldman, H.

F. C. Blom, H. Keldman, H. J. W. M. Hoekstra, A. Driessen, Th. J. A. Popma, S. T. Chu, and B. E. Little, “A single channel dropping filter based on a cylindrical microresonator,” Opt. Commun. 167, 77–82 (1999).
[CrossRef]

Kimerling, L. C.

B. E. Little, J. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10, 549–551 (1998).
[CrossRef]

Klunder, D. J. W.

Knight, J. C.

Korterik, J. P.

Kuipers, L.

Kuwata-Gonokami, M.

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, “Tight-binding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999).
[CrossRef]

Laine, J.-P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

Lange, S.

Little, B. E.

F. C. Blom, H. Keldman, H. J. W. M. Hoekstra, A. Driessen, Th. J. A. Popma, S. T. Chu, and B. E. Little, “A single channel dropping filter based on a cylindrical microresonator,” Opt. Commun. 167, 77–82 (1999).
[CrossRef]

B. E. Little, J. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10, 549–551 (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]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

Love, J. D.

D. R. Rowland and J. D. Love, “Evanescent wave coupling of whispering gallery modes of a dielectric cylinder,” IEE Proc. J 140, 177–188 (1993).

Marcatili, E. A. J.

E. A. J. Marcatili, “Bends in optical dielectric guides,” Bell Syst. Tech. J. 48, 2103–2132 (1969).
[CrossRef]

Miyano, K.

Miyazaki, H.

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, “Tight-binding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999).
[CrossRef]

Morris, N.

Mukaiyama, T.

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, “Tight-binding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999).
[CrossRef]

Pierson, T.

M. K. Chin, C. Youtsey, W. Zhao, T. Pierson, Z. Ren, S. L. Wu, L. Wang, Y. G. Zhao, and S. T. Ho, “GaAs microcavity channel-dropping filter based on a race-track resonator,” IEEE Photon. Technol. Lett. 11, 1620–1622 (1999).
[CrossRef]

Popma, Th. J. A.

F. C. Blom, H. Keldman, H. J. W. M. Hoekstra, A. Driessen, Th. J. A. Popma, S. T. Chu, and B. E. Little, “A single channel dropping filter based on a cylindrical microresonator,” Opt. Commun. 167, 77–82 (1999).
[CrossRef]

F. C. Blom, D. R. van Dijk, H. J. W. M. Hoekstra, A. Driessen, and Th. J. A. Popma, “Experimental study of integrated-optics microcavity resonators: toward an all-optical switching device,” Appl. Phys. Lett. 71, 747–749 (1997).
[CrossRef]

Rafizadeh, D.

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15, 2154–2165 (1997).
[CrossRef]

D. Rafizadeh, J. P. Zhang, S. C. Hagness, A. Taflove, K. A. Stair, S. T. Ho, and R. C. Tiberio, “Waveguide-coupled AlGaAs/GaAs microcavity ring and disk resonators with high finesse and 21.6-nm free spectral range,” Opt. Lett. 22, 1244–1246 (1997).
[CrossRef] [PubMed]

Ren, Z.

M. K. Chin, C. Youtsey, W. Zhao, T. Pierson, Z. Ren, S. L. Wu, L. Wang, Y. G. Zhao, and S. T. Ho, “GaAs microcavity channel-dropping filter based on a race-track resonator,” IEEE Photon. Technol. Lett. 11, 1620–1622 (1999).
[CrossRef]

Roll, G.

Rowland, D. R.

D. R. Rowland and J. D. Love, “Evanescent wave coupling of whispering gallery modes of a dielectric cylinder,” IEE Proc. J 140, 177–188 (1993).

Schiller, S.

Schweiger, G.

Serpengüzel, A.

Shaw, H. J.

Shinya, A.

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M. K. Chin, C. Youtsey, W. Zhao, T. Pierson, Z. Ren, S. L. Wu, L. Wang, Y. G. Zhao, and S. T. Ho, “GaAs microcavity channel-dropping filter based on a race-track resonator,” IEEE Photon. Technol. Lett. 11, 1620–1622 (1999).
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[CrossRef]

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F. C. Blom, D. R. van Dijk, H. J. W. M. Hoekstra, A. Driessen, and Th. J. A. Popma, “Experimental study of integrated-optics microcavity resonators: toward an all-optical switching device,” Appl. Phys. Lett. 71, 747–749 (1997).
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[CrossRef]

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[CrossRef]

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[CrossRef]

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A. Shinya and M. Fukui, “Finite-difference time-domain analysis of the interaction of Gaussian evanescent light with a single dielectric sphere or ordered dielectric spheres,” Opt. Rev. 6, 215–223 (1999).
[CrossRef]

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[CrossRef]

Other (5)

In the case of an add–drop filter, light is coupled out only from the secondary output port (secondary waveguide). Output intensity at the primary waveguide disappears because of the destructive interference between the incident and the output beams.

We label the mode number (i.e., total angular momentum of the mode) by l, the azimuthal mode number (z component of angular momentum) by m, and the order number (number of the intensity maximum in the radial direction) by s. The quantization axis of the angular momentum is taken parallel to the substrate and perpendicular to the incidence plane.

The position of the observation plane (z in the caption of Fig. 4) is determined from the lateral position of the totally reflected part of the beam. Then the phase difference between the reflected beam and the coupled-out beam is fixed by the model

This can be estimated by one plotting the electric field of the corresponding resonant mode (whispering-gallery-mode) at a surface of interest [see Figs. 6(a) and 6(b) of Ref. 28]. When a curved substrate or waveguide is used as a coupler, Δz can be larger than this value.

For a larger glass spherical resonator in contact with a waveguide and hence in the overcoupled condition, QT in the range of 105–106 has been reported. The quality factor of a small resonator is expected to be lower.

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Figures (9)

Fig. 1
Fig. 1

Schematics of the experimental setup. o, observation plane; t, transform plane; PD, photodetector.

Fig. 2
Fig. 2

Experimental results: (a) transmission microscope image of a 5-µm resonator and (b)–(d) TIRM images of a 5-µm resonator at the TM34,1 resonance wavelength (λ=579.58 nm). Observation planes are located at (b) z1 µm, (c) z2.5 µm, and (d) z4 µm below the substrate surface. The incidence angle is set at 50°, and the incident and the detected beams are both p polarized.

Fig. 3
Fig. 3

Experimental results: (a) transmission microscope image of a 9-µm resonator and (b)–(d) TIRM images of a 9-µm resonator at the resonance wavelength. Observation planes are located at (b) z1 µm, (c) z2.5 µm, and (d) z4 µm. The incidence angle and the polarization are the same as in Fig. 2.

Fig. 4
Fig. 4

Calculated results: (a) position and size of the spherical microresonator. The diameter and the refractive index of the sphere are chosen as 2a=4.864 µm, nres=1.52, respectively. The wavelength is set to coincide with TM34,1=579.58 nm. (b)–(d) Calculated TIRM images corresponding to Fig. 2. Locations of the observation plane are varied as (b) z1 µm, (c)z2.5 µm, and (d) z4 µm. A totally reflected Gaussian beam and two WGMs [(l,m)=(34,34) and (l,m)=(34,32)] are superposed (see Fig. 5). The relative amplitude and phase of the two WGMs are chosen as A34=A32 and ϕ34-ϕ32=2π/3 in (b)–(d).

Fig. 5
Fig. 5

Shape of the individual beams used to plot Fig. 4 (cross section at z=1 µm): (a) totally reflected Gaussian beam, (b) WGM of (l,m)=(34,34), (c) WGM of (l,m)=(34,32). The relative amplitude is the same as in Fig. 4.

Fig. 6
Fig. 6

Calculated results: (a) intensity distribution of the p-polarized component of the WGM of (l,m)=(34,34) in the k plane. Inner and outer dotted circles, respectively, represent the boundary between the propagating wave and the evanescent wave in air and in the substrate. (b) Angular intensity distribution of the WGM of (l,m)=(34,34), which corresponds to the intensity distribution along ky=0 in (a). The resonator and the substrate are in contact as in Figs. 4 and 5.

Fig. 7
Fig. 7

Calculated results: (a) intensity distribution of the p-polarized component of the WGM of (l,m)=(34,34) in the k plane when the resonator–substrate distance is d=rc,e-a=0.70 µm. (b) Angular intensity distribution of the WGM of (l,m)=(34,34) (solid curve). The result for d=(rc,e-a)×0.5=0.35 µm is also shown (dotted curve).

Fig. 8
Fig. 8

Wave front of the outgoing spherical wave in the presence of a dielectric sphere. log{[Re(Debye potential)]2} of (l,m)=(34,34) at the first-order resonant wavelength is plotted within the equator plane. The size of the plot is 10 µm×10 µm and is plotted only outside of the sphere. The diameter of the sphere and the mode number l are 4.864 µm and 34, respectively. The location of the external caustic is indicated by a white dotted circle.

Fig. 9
Fig. 9

Experimental results showing excitation of a WGM by plane waves with considerably different incidence angles. A glass spherical microresonator of 5 µm in diameter is used, and the incident and the detected beams are both p polarized. The observation plane is located approximately 1 µm below the substrate surface. The third row corresponds to the case of the excitation below the critical angle of the substrate (41°).

Equations (3)

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βl=nres sin θlcωl,
Δβl1Δzl,
Δβlβl=Δωlnres sin θlcβlΔωlnres sin θlc+ωlnresΔ(sin θl)cβl=Δωlωl+Δ(sin θl)sin θl,

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