Abstract

We have numerically studied a taper-microsphere coupling system with coupled-mode theory by introducing a mode-coupling mechanism. Transmission and reflection coefficients have been obtained directly through numerical calculation for a spherical silica microcavity. In the presence of the modal coupling mechanism, the optimal condition for transferring the light energy into the microsphere is no longer the critical coupling point. Instead, it should be in the under-coupling regime and can be reached by optimizing the size of the fiber taper and the taper-microsphere gap.

© 2008 Optical Society of America

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  1. M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, “Ultimate Q of microsphere resonator,” Opt. Lett. 21, 453-455 (1996).
    [CrossRef] [PubMed]
  2. V. Sandoghdar, F. Treussart, J. Hare, V. Lefevre-Seguin, J.-M. Raimond, and S. Haroche, “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, 1777-1780 (2006).
    [CrossRef]
  3. M. Cai, O. Painter, and K. J. Vahala, “Fiber-coupled microsphere laser,” Opt. Lett. 25, 1430-1432 (2000).
    [CrossRef]
  4. F. Lissillour, D. Messager, G. Stéphan, and P. Féron, “Whispering-gallery-mode laser at 1.56 μm excited by a fiber taper,” Opt. Lett. 26, 1051-1053 (2001).
    [CrossRef]
  5. S. I. Shopova, G. Farca, A. T. Rosenberger, W. M. Wickramanayake, and N. A. Kotov, “Microsphere whispering-gallery-mode laser using HgTe quantum dots,” Appl. Phys. Lett. 85, 6101-6103 (2004).
    [CrossRef]
  6. P. Bianucci, C. R. Fietz, J. W. Robertson, G. Shvets, and C.-K. Shih, “Whispering gallery resonators as polarization converters,” Opt. Lett. 32, 2224-2226 (2007).
    [CrossRef] [PubMed]
  7. D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyod, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).
    [CrossRef]
  8. Y. F. Xiao, X. B. Zou, W. Jiang, Y. L. Chen, and G. C. Guo, “Analog to multiple electromagnetically induced transparency in all-optical drop-filter systems,” Phys. Rev. A 75, 063833 (2007).
    [CrossRef]
  9. D. Braunstein, A. M. Khazanov, G. A. Koganov, and R. Shuker, “Lowering of threshold conditions for nonlinear effects in a microsphere,” Phys. Rev. A 53, 3565-3572 (1996).
    [CrossRef] [PubMed]
  10. S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415, 621-623 (2002).
    [CrossRef] [PubMed]
  11. Y. S. Park, A. K. Cook, and H. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Lett. 6, 2075-2079 (2006).
    [CrossRef] [PubMed]
  12. Y. F. Xiao, X. M. Lin, J. Gao, Z. F. Han, and G. C. Guo, “Realizing quantum controlled phase flip through cavity QED,” Phys. Rev. A 70, 042314 (2004).
    [CrossRef]
  13. 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]
  14. M. L. Gorodetsky and V. S. Ilchenko, “High-Q optical whispering-gallery microresonators: precession approach for spherical mode analysis and emission patterns with prism couplers,” Opt. Commun. 113, 133-143 (1994).
    [CrossRef]
  15. V. S. Ilchenko, X. S. Yao, and L. Maleki, “Pigtailing the high-Q microsphere cavity: a simple fiber coupler for optical whispering-gallery modes,” Opt. Lett. 24, 723-725 (1999).
    [CrossRef]
  16. 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]
  17. M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Opt. Lett. 85, 74-77 (2000).
  18. T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Modal coupling in traveling-wave resonators,” Opt. Lett. 27, 1669-1671 (2002).
    [CrossRef]
  19. M. L. Gorodetsky, A. D. Pryamikov, and V. S. Ilchenko, “Rayleigh scattering in high-Q microsphere,” J. Opt. Soc. Am. B 17, 1051-1057 (2000).
    [CrossRef]
  20. 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]
  21. Z. Guo, H. Quan, and S. Pau, “Near-field gap effects on small microcavity whispering-gallery mode resonator,” J. Phys. D 39, 5133-5136 (2006).
    [CrossRef]
  22. M. J. Humphrey, E. Dale, A. T. Rosenberger, and D. K. Bandy, “Calculation of optimal fiber radius and whispering-gallery mode spectra for a fiber-coupled microsphere,” Opt. Commun. 271, 124-131 (2007).
    [CrossRef]
  23. H. A. Haus and W. Huang, “Coupled-mode theory,” in Proc. IEEE 79, 1505-1518 (1991).
    [CrossRef]
  24. D. R. Rowland and J. D. Love, “Evanescent wave coupling of whispering gallery modes of a dielectric cylinder,” IEE Proc.-J: Optoelectron. 140, 177-188 (1993).
    [CrossRef]
  25. B. E. Little, J. -P. Laine, and H. A. Haus, “Analytic theory of coupling from tapered fibers and half-blocks into microsphere resonators,” J. Lightwave Technol. 17, 704-715 (1999).
    [CrossRef]
  26. M. L. Gorodetsky and V. S. Ilchenko, “Optical microsphere resonators: optimal coupling to high-Q whispering-gallery modes,” J. Opt. Soc. Am. B 16, 147-154 (1999).
    [CrossRef]
  27. Y. Lu, J. Wang, X. Xu, S. Pan, and C. Zhang, “Optimal conditions of coupling between the propagating mode in a tapered fiber and the given WG mode in a high-Q microsphere,” Optik (Stuttgart) 112, 109-113 (2001).
    [CrossRef]

2007 (4)

P. Bianucci, C. R. Fietz, J. W. Robertson, G. Shvets, and C.-K. Shih, “Whispering gallery resonators as polarization converters,” Opt. Lett. 32, 2224-2226 (2007).
[CrossRef] [PubMed]

Y. F. Xiao, X. B. Zou, W. Jiang, Y. L. Chen, and G. C. Guo, “Analog to multiple electromagnetically induced transparency in all-optical drop-filter systems,” Phys. Rev. A 75, 063833 (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]

M. J. Humphrey, E. Dale, A. T. Rosenberger, and D. K. Bandy, “Calculation of optimal fiber radius and whispering-gallery mode spectra for a fiber-coupled microsphere,” Opt. Commun. 271, 124-131 (2007).
[CrossRef]

2006 (3)

Z. Guo, H. Quan, and S. Pau, “Near-field gap effects on small microcavity whispering-gallery mode resonator,” J. Phys. D 39, 5133-5136 (2006).
[CrossRef]

V. Sandoghdar, F. Treussart, J. Hare, V. Lefevre-Seguin, J.-M. Raimond, and S. Haroche, “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, 1777-1780 (2006).
[CrossRef]

Y. S. Park, A. K. Cook, and H. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Lett. 6, 2075-2079 (2006).
[CrossRef] [PubMed]

2004 (3)

Y. F. Xiao, X. M. Lin, J. Gao, Z. F. Han, and G. C. Guo, “Realizing quantum controlled phase flip through cavity QED,” Phys. Rev. A 70, 042314 (2004).
[CrossRef]

S. I. Shopova, G. Farca, A. T. Rosenberger, W. M. Wickramanayake, and N. A. Kotov, “Microsphere whispering-gallery-mode laser using HgTe quantum dots,” Appl. Phys. Lett. 85, 6101-6103 (2004).
[CrossRef]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyod, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).
[CrossRef]

2003 (1)

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]

2002 (2)

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

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Modal coupling in traveling-wave resonators,” Opt. Lett. 27, 1669-1671 (2002).
[CrossRef]

2001 (2)

Y. Lu, J. Wang, X. Xu, S. Pan, and C. Zhang, “Optimal conditions of coupling between the propagating mode in a tapered fiber and the given WG mode in a high-Q microsphere,” Optik (Stuttgart) 112, 109-113 (2001).
[CrossRef]

F. Lissillour, D. Messager, G. Stéphan, and P. Féron, “Whispering-gallery-mode laser at 1.56 μm excited by a fiber taper,” Opt. Lett. 26, 1051-1053 (2001).
[CrossRef]

2000 (3)

1999 (3)

1997 (1)

1996 (2)

M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, “Ultimate Q of microsphere resonator,” Opt. Lett. 21, 453-455 (1996).
[CrossRef] [PubMed]

D. Braunstein, A. M. Khazanov, G. A. Koganov, and R. Shuker, “Lowering of threshold conditions for nonlinear effects in a microsphere,” Phys. Rev. A 53, 3565-3572 (1996).
[CrossRef] [PubMed]

1994 (1)

M. L. Gorodetsky and V. S. Ilchenko, “High-Q optical whispering-gallery microresonators: precession approach for spherical mode analysis and emission patterns with prism couplers,” Opt. Commun. 113, 133-143 (1994).
[CrossRef]

1993 (1)

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

1991 (1)

H. A. Haus and W. Huang, “Coupled-mode theory,” in Proc. IEEE 79, 1505-1518 (1991).
[CrossRef]

Bandy, D. K.

M. J. Humphrey, E. Dale, A. T. Rosenberger, and D. K. Bandy, “Calculation of optimal fiber radius and whispering-gallery mode spectra for a fiber-coupled microsphere,” Opt. Commun. 271, 124-131 (2007).
[CrossRef]

Bianucci, P.

Birks, T. A.

Boyod, R. W.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyod, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Braunstein, D.

D. Braunstein, A. M. Khazanov, G. A. Koganov, and R. Shuker, “Lowering of threshold conditions for nonlinear effects in a microsphere,” Phys. Rev. A 53, 3565-3572 (1996).
[CrossRef] [PubMed]

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,” Opt. Lett. 85, 74-77 (2000).

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

Chang, H.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyod, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Chen, Y. L.

Y. F. Xiao, X. B. Zou, W. Jiang, Y. L. Chen, and G. C. Guo, “Analog to multiple electromagnetically induced transparency in all-optical drop-filter systems,” Phys. Rev. A 75, 063833 (2007).
[CrossRef]

Cheung, G.

Cook, A. K.

Y. S. Park, A. K. Cook, and H. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Lett. 6, 2075-2079 (2006).
[CrossRef] [PubMed]

Dale, E.

M. J. Humphrey, E. Dale, A. T. Rosenberger, and D. K. Bandy, “Calculation of optimal fiber radius and whispering-gallery mode spectra for a fiber-coupled microsphere,” Opt. Commun. 271, 124-131 (2007).
[CrossRef]

Farca, G.

S. I. Shopova, G. Farca, A. T. Rosenberger, W. M. Wickramanayake, and N. A. Kotov, “Microsphere whispering-gallery-mode laser using HgTe quantum dots,” Appl. Phys. Lett. 85, 6101-6103 (2004).
[CrossRef]

Féron, P.

Fietz, C. R.

Fuller, K. A.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyod, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Gao, J.

Y. F. Xiao, X. M. Lin, J. Gao, Z. F. Han, and G. C. Guo, “Realizing quantum controlled phase flip through cavity QED,” Phys. Rev. A 70, 042314 (2004).
[CrossRef]

Gorodetsky, M. L.

Guo, G. C.

Y. F. Xiao, X. B. Zou, W. Jiang, Y. L. Chen, and G. C. Guo, “Analog to multiple electromagnetically induced transparency in all-optical drop-filter systems,” Phys. Rev. A 75, 063833 (2007).
[CrossRef]

Y. F. Xiao, X. M. Lin, J. Gao, Z. F. Han, and G. C. Guo, “Realizing quantum controlled phase flip through cavity QED,” Phys. Rev. A 70, 042314 (2004).
[CrossRef]

Guo, Z.

Z. Guo, H. Quan, and S. Pau, “Near-field gap effects on small microcavity whispering-gallery mode resonator,” J. Phys. D 39, 5133-5136 (2006).
[CrossRef]

Han, Z. F.

Y. F. Xiao, X. M. Lin, J. Gao, Z. F. Han, and G. C. Guo, “Realizing quantum controlled phase flip through cavity QED,” Phys. Rev. A 70, 042314 (2004).
[CrossRef]

Hare, J.

V. Sandoghdar, F. Treussart, J. Hare, V. Lefevre-Seguin, J.-M. Raimond, and S. Haroche, “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, 1777-1780 (2006).
[CrossRef]

Haroche, S.

V. Sandoghdar, F. Treussart, J. Hare, V. Lefevre-Seguin, J.-M. Raimond, and S. Haroche, “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, 1777-1780 (2006).
[CrossRef]

Haus, H. A.

Huang, W.

H. A. Haus and W. Huang, “Coupled-mode theory,” in Proc. IEEE 79, 1505-1518 (1991).
[CrossRef]

Humphrey, M. J.

M. J. Humphrey, E. Dale, A. T. Rosenberger, and D. K. Bandy, “Calculation of optimal fiber radius and whispering-gallery mode spectra for a fiber-coupled microsphere,” Opt. Commun. 271, 124-131 (2007).
[CrossRef]

Ilchenko, V. S.

Jacques, F.

Jiang, W.

Y. F. Xiao, X. B. Zou, W. Jiang, Y. L. Chen, and G. C. Guo, “Analog to multiple electromagnetically induced transparency in all-optical drop-filter systems,” Phys. Rev. A 75, 063833 (2007).
[CrossRef]

Khazanov, A. M.

D. Braunstein, A. M. Khazanov, G. A. Koganov, and R. Shuker, “Lowering of threshold conditions for nonlinear effects in a microsphere,” Phys. Rev. A 53, 3565-3572 (1996).
[CrossRef] [PubMed]

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]

Kippenberg, T. J.

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

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Modal coupling in traveling-wave resonators,” Opt. Lett. 27, 1669-1671 (2002).
[CrossRef]

Knight, J. C.

Koganov, G. A.

D. Braunstein, A. M. Khazanov, G. A. Koganov, and R. Shuker, “Lowering of threshold conditions for nonlinear effects in a microsphere,” Phys. Rev. A 53, 3565-3572 (1996).
[CrossRef] [PubMed]

Kotov, N. A.

S. I. Shopova, G. Farca, A. T. Rosenberger, W. M. Wickramanayake, and N. A. Kotov, “Microsphere whispering-gallery-mode laser using HgTe quantum dots,” Appl. Phys. Lett. 85, 6101-6103 (2004).
[CrossRef]

Laine, J. -P.

Lefevre-Seguin, V.

V. Sandoghdar, F. Treussart, J. Hare, V. Lefevre-Seguin, J.-M. Raimond, and S. Haroche, “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, 1777-1780 (2006).
[CrossRef]

Lin, X. M.

Y. F. Xiao, X. M. Lin, J. Gao, Z. F. Han, and G. C. Guo, “Realizing quantum controlled phase flip through cavity QED,” Phys. Rev. A 70, 042314 (2004).
[CrossRef]

Lissillour, F.

Little, B. E.

Love, J. D.

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

Lu, Y.

Y. Lu, J. Wang, X. Xu, S. Pan, and C. Zhang, “Optimal conditions of coupling between the propagating mode in a tapered fiber and the given WG mode in a high-Q microsphere,” Optik (Stuttgart) 112, 109-113 (2001).
[CrossRef]

Maleki, L.

Messager, D.

Painter, O.

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]

M. Cai, O. Painter, and K. J. Vahala, “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,” Opt. Lett. 85, 74-77 (2000).

Pan, S.

Y. Lu, J. Wang, X. Xu, S. Pan, and C. Zhang, “Optimal conditions of coupling between the propagating mode in a tapered fiber and the given WG mode in a high-Q microsphere,” Optik (Stuttgart) 112, 109-113 (2001).
[CrossRef]

Park, Y. S.

Y. S. Park, A. K. Cook, and H. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Lett. 6, 2075-2079 (2006).
[CrossRef] [PubMed]

Pau, S.

Z. Guo, H. Quan, and S. Pau, “Near-field gap effects on small microcavity whispering-gallery mode resonator,” J. Phys. D 39, 5133-5136 (2006).
[CrossRef]

Pryamikov, A. D.

Quan, H.

Z. Guo, H. Quan, and S. Pau, “Near-field gap effects on small microcavity whispering-gallery mode resonator,” J. Phys. D 39, 5133-5136 (2006).
[CrossRef]

Raimond, J.-M.

V. Sandoghdar, F. Treussart, J. Hare, V. Lefevre-Seguin, J.-M. Raimond, and S. Haroche, “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, 1777-1780 (2006).
[CrossRef]

Robertson, J. W.

Rosenberger, A. T.

M. J. Humphrey, E. Dale, A. T. Rosenberger, and D. K. Bandy, “Calculation of optimal fiber radius and whispering-gallery mode spectra for a fiber-coupled microsphere,” Opt. Commun. 271, 124-131 (2007).
[CrossRef]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyod, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).
[CrossRef]

S. I. Shopova, G. Farca, A. T. Rosenberger, W. M. Wickramanayake, and N. A. Kotov, “Microsphere whispering-gallery-mode laser using HgTe quantum dots,” Appl. Phys. Lett. 85, 6101-6103 (2004).
[CrossRef]

Rowland, D. R.

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

Sandoghdar, V.

V. Sandoghdar, F. Treussart, J. Hare, V. Lefevre-Seguin, J.-M. Raimond, and S. Haroche, “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, 1777-1780 (2006).
[CrossRef]

Savchenkov, A. A.

Shih, C.-K.

Shopova, S. I.

S. I. Shopova, G. Farca, A. T. Rosenberger, W. M. Wickramanayake, and N. A. Kotov, “Microsphere whispering-gallery-mode laser using HgTe quantum dots,” Appl. Phys. Lett. 85, 6101-6103 (2004).
[CrossRef]

Shuker, R.

D. Braunstein, A. M. Khazanov, G. A. Koganov, and R. Shuker, “Lowering of threshold conditions for nonlinear effects in a microsphere,” Phys. Rev. A 53, 3565-3572 (1996).
[CrossRef] [PubMed]

Shvets, G.

Smith, D. D.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyod, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Spillane, S. M.

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

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Modal coupling in traveling-wave resonators,” Opt. Lett. 27, 1669-1671 (2002).
[CrossRef]

Srinivasan, K.

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]

Stéphan, G.

Treussart, F.

V. Sandoghdar, F. Treussart, J. Hare, V. Lefevre-Seguin, J.-M. Raimond, and S. Haroche, “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, 1777-1780 (2006).
[CrossRef]

Vahala, K. J.

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Modal coupling in traveling-wave resonators,” Opt. Lett. 27, 1669-1671 (2002).
[CrossRef]

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

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

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

Wang, H.

Y. S. Park, A. K. Cook, and H. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Lett. 6, 2075-2079 (2006).
[CrossRef] [PubMed]

Wang, J.

Y. Lu, J. Wang, X. Xu, S. Pan, and C. Zhang, “Optimal conditions of coupling between the propagating mode in a tapered fiber and the given WG mode in a high-Q microsphere,” Optik (Stuttgart) 112, 109-113 (2001).
[CrossRef]

Wickramanayake, W. M.

S. I. Shopova, G. Farca, A. T. Rosenberger, W. M. Wickramanayake, and N. A. Kotov, “Microsphere whispering-gallery-mode laser using HgTe quantum dots,” Appl. Phys. Lett. 85, 6101-6103 (2004).
[CrossRef]

Xiao, Y. F.

Y. F. Xiao, X. B. Zou, W. Jiang, Y. L. Chen, and G. C. Guo, “Analog to multiple electromagnetically induced transparency in all-optical drop-filter systems,” Phys. Rev. A 75, 063833 (2007).
[CrossRef]

Y. F. Xiao, X. M. Lin, J. Gao, Z. F. Han, and G. C. Guo, “Realizing quantum controlled phase flip through cavity QED,” Phys. Rev. A 70, 042314 (2004).
[CrossRef]

Xu, X.

Y. Lu, J. Wang, X. Xu, S. Pan, and C. Zhang, “Optimal conditions of coupling between the propagating mode in a tapered fiber and the given WG mode in a high-Q microsphere,” Optik (Stuttgart) 112, 109-113 (2001).
[CrossRef]

Yao, X. S.

Zhang, C.

Y. Lu, J. Wang, X. Xu, S. Pan, and C. Zhang, “Optimal conditions of coupling between the propagating mode in a tapered fiber and the given WG mode in a high-Q microsphere,” Optik (Stuttgart) 112, 109-113 (2001).
[CrossRef]

Zou, X. B.

Y. F. Xiao, X. B. Zou, W. Jiang, Y. L. Chen, and G. C. Guo, “Analog to multiple electromagnetically induced transparency in all-optical drop-filter systems,” Phys. Rev. A 75, 063833 (2007).
[CrossRef]

Appl. Phys. Lett. (1)

S. I. Shopova, G. Farca, A. T. Rosenberger, W. M. Wickramanayake, and N. A. Kotov, “Microsphere whispering-gallery-mode laser using HgTe quantum dots,” Appl. Phys. Lett. 85, 6101-6103 (2004).
[CrossRef]

IEE Proc.-J: Optoelectron. (1)

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

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (2)

J. Phys. D (1)

Z. Guo, H. Quan, and S. Pau, “Near-field gap effects on small microcavity whispering-gallery mode resonator,” J. Phys. D 39, 5133-5136 (2006).
[CrossRef]

Nano Lett. (1)

Y. S. Park, A. K. Cook, and H. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Lett. 6, 2075-2079 (2006).
[CrossRef] [PubMed]

Nature (1)

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

Opt. Commun. (2)

M. J. Humphrey, E. Dale, A. T. Rosenberger, and D. K. Bandy, “Calculation of optimal fiber radius and whispering-gallery mode spectra for a fiber-coupled microsphere,” Opt. Commun. 271, 124-131 (2007).
[CrossRef]

M. L. Gorodetsky and V. S. Ilchenko, “High-Q optical whispering-gallery microresonators: precession approach for spherical mode analysis and emission patterns with prism couplers,” Opt. Commun. 113, 133-143 (1994).
[CrossRef]

Opt. Lett. (8)

Optik (Stuttgart) (1)

Y. Lu, J. Wang, X. Xu, S. Pan, and C. Zhang, “Optimal conditions of coupling between the propagating mode in a tapered fiber and the given WG mode in a high-Q microsphere,” Optik (Stuttgart) 112, 109-113 (2001).
[CrossRef]

Phys. Rev. A (7)

V. Sandoghdar, F. Treussart, J. Hare, V. Lefevre-Seguin, J.-M. Raimond, and S. Haroche, “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, 1777-1780 (2006).
[CrossRef]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyod, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Y. F. Xiao, X. B. Zou, W. Jiang, Y. L. Chen, and G. C. Guo, “Analog to multiple electromagnetically induced transparency in all-optical drop-filter systems,” Phys. Rev. A 75, 063833 (2007).
[CrossRef]

D. Braunstein, A. M. Khazanov, G. A. Koganov, and R. Shuker, “Lowering of threshold conditions for nonlinear effects in a microsphere,” Phys. Rev. A 53, 3565-3572 (1996).
[CrossRef] [PubMed]

Y. F. Xiao, X. M. Lin, J. Gao, Z. F. Han, and G. C. Guo, “Realizing quantum controlled phase flip through cavity QED,” Phys. Rev. A 70, 042314 (2004).
[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]

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]

Proc. IEEE (1)

H. A. Haus and W. Huang, “Coupled-mode theory,” in Proc. IEEE 79, 1505-1518 (1991).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic of a microsphere coupled to a fiber taper. At the coupling region, an adiabatically stretched fiber taper is simplified as a cylinder. E i is the input electrical field into the coupling region, E cw , and E ccw are the clockwise and counterclockwise WGM fields, which are distributed near the surface of the microsphere and E r , and E t are the reflected and transmitted fields after coupling. η is the coupling strength between the cavity and fiber taper modes.

Fig. 2
Fig. 2

Energy transport properties of the fiber taper. The brightness represents transmission rate; (a), (c), (e), and (g) are transmission with different fiber tapers, radius, and gaps in microsphere; (b) is reflection; (d), (f), and (h) are ratio of energy coupled into the microsphere. Modal coupling coefficients are: (a), g = 0 ; (c) and (d), g = 0.1 κ 0 ; (e) and (f), g = κ 0 ; (c), (g), and (h), g = 10 κ 0 . Other parameters are: microsphere diameter D = 35 μ m , working wavelength λ = 780 nm , Q 0 = 10 7 .

Fig. 3
Fig. 3

Normalized energy transmission (solid curve), reflection (dashed curve), and transferring into microsphere (dotted curve) versus the fiber taper radius when microspheres are in contact with taper with modal coupling strength β = 10 κ 0 . The inflection is due to the mode splitting disappearing. Other parameters are the same as in Fig. 2.

Equations (8)

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η s f = η f s * = ω Δ ϵ 4 V s E f E s * exp ( i Δ β z ) d v ,
Δ E s E s = 1 η f s 2 e ω τ 2 Q 0 ,
d E ccw d t = ( κ 0 + κ 1 + i Δ ω ) E ccw + i g E cw + i η s f τ E in ,
d E cw d t = ( κ 0 + κ 1 + i Δ ω ) E cw + i g E ccw ,
E r = i η f s E cw ,
E t = 1 η s f 2 E in + i η f s E ccw ,
T = E t E in 2 = 1 η s f 2 2 κ 1 ( κ 0 + κ 1 + i Δ ω ) ( κ 0 + κ 1 + i Δ ω ) 2 + g 2 2 ,
R = E r E in 2 = 2 κ 1 g g 2 + ( κ 0 + κ 1 + i Δ ω ) 2 2 .

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