Abstract

We have experimentally demonstrated the existence of optical whispering-gallery-modes (WGMs) with quality factors in excess of 108 in elliptical cavities fabricated with LiNbO3. The efficiency of evanescent coupling to the modes through a diamond prism was as high as 97.3%. This is the best value ever achieved for evanescent coupling to a WGM resonator using a prism. The free spectral ranges of the WGMs are successfully modeled using an eikonal approximation.

© 2007 Optical Society of America

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  3. V. S. Ilchenko, X. S. Yao, and L. Maleki, Opt. Lett. 24, 723 (1999).
    [CrossRef]
  4. D. K. Armani, T. Kippenberg, S. M. Spillane and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature,  421, 925 (2003).
    [CrossRef] [PubMed]
  5. A. C. R. Pipino, J. W. Hudgens, and R. E. Huie, "Evanescent wave cavity ring-down spectroscopy with a total-internal-reflection minicavity," Rev. Sci. Instrum. 68, 2978, (1997).
    [CrossRef]
  6. C. Manolatou, M. J. Khan, S. H. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, "Coupling of modes analysis of resonant channel add-drop filters," IEEE J. Quantum Electron. 35, 1322 (1999).
    [CrossRef]
  7. A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, "Low threshold optical oscillations in a whispering gallery mode CaF2 resonator," Phys. Rev. Lett. 93, 243905 (2004).
    [CrossRef]
  8. T. J. Kippenberg, M. Spillane, and K. J. Vahala, "Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity," Phys. Rev. Lett. 93, 083904 (2004).
    [CrossRef] [PubMed]
  9. S. Spillane, T. Kippenberg, and K. Vahala, "Ultralow-threshold Raman laser using a spherical dielectric microcavity," Nature 415, 621 (2002).
    [CrossRef] [PubMed]
  10. A. A. Savchenkov, A. B. Matsko, M. Mohageg, and L. Maleki, "Ringdown spectroscopy of stimulated Raman scattering in a whispering gallery mode resonator," Opt. Lett. 32, 497 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
  12. A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, "Tunable filter based on whispering gallery modes," Electron. Lett. 39, 389 (2003).
    [CrossRef]
  13. M. Mohageg, A. A. Savchenkov, D. Strekalov, A. B. Matsko, V.S. Ilchenko and L. Maleki, "Reconfigurable optical filter," Electron. Lett. 41, 356 (2005).
    [CrossRef]
  14. V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, "Sub-MicroWatt photonic microwave receiver," IEEE Photon. Technol. Lett. 14, 1602 (2002).
    [CrossRef]
  15. A. B. Matsko, L. Maleki, A. A. Savchenkov, and V. S. Ilchenko, "Whispering gallery mode based optoelectronic microwave oscillator," J. Mod. Opt. 50, 2523 (2003).
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  18. For instance, N. Bohr, "The spectra of helium and hydrogen," Nature 92, 231 (1914) and the following series.
    [CrossRef]
  19. A. A. Savchenkov, I. S. Grudinin, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, "Morphology-dependent photonic circuit elements," Opt. Lett. 31, 1313 (2006).
    [CrossRef] [PubMed]
  20. S. Ancey, A. Folacci, and P. Gabrielli, "Whispering-gallery modes and resonances of an elliptic cavity," J. Phys. A: Math. Gen. 34, 1341 (2001).
    [CrossRef]
  21. S. M. Spillane, T. J. Kippenberg, O. J. Painter, K. J. Vahala, "Ideality in a fiber-taper-coupled microresonator system for application to Cavity Quanum Electrodynamics," Phys. Rev. Lett. 91,043902 (2003).
    [CrossRef] [PubMed]
  22. M. Mohageg, D. Strekalov, A. Savchenkov, A. Matsko, V. Ilchenko, and L. Maleki, "Calligraphic poling of Lithium Niobate," Opt. Express 13, 3408 (2005).
    [CrossRef] [PubMed]

2007

2006

2005

M. Mohageg, A. A. Savchenkov, D. Strekalov, A. B. Matsko, V.S. Ilchenko and L. Maleki, "Reconfigurable optical filter," Electron. Lett. 41, 356 (2005).
[CrossRef]

M. Mohageg, D. Strekalov, A. Savchenkov, A. Matsko, V. Ilchenko, and L. Maleki, "Calligraphic poling of Lithium Niobate," Opt. Express 13, 3408 (2005).
[CrossRef] [PubMed]

2004

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, "Low threshold optical oscillations in a whispering gallery mode CaF2 resonator," Phys. Rev. Lett. 93, 243905 (2004).
[CrossRef]

T. J. Kippenberg, M. Spillane, and K. J. Vahala, "Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity," Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef] [PubMed]

2003

V. S. Ilchenko, A. B. Matsko, A. A. Savchenkov, and L. Maleki, "Low-threshold parametric nonlinear optics with quasi-phase-matched whispering-gallery modes," J. Opt. Soc. Am. B 20, 1304 (2003).
[CrossRef]

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, "Tunable filter based on whispering gallery modes," Electron. Lett. 39, 389 (2003).
[CrossRef]

D. K. Armani, T. Kippenberg, S. M. Spillane and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature,  421, 925 (2003).
[CrossRef] [PubMed]

A. B. Matsko, L. Maleki, A. A. Savchenkov, and V. S. Ilchenko, "Whispering gallery mode based optoelectronic microwave oscillator," J. Mod. Opt. 50, 2523 (2003).

S. M. Spillane, T. J. Kippenberg, O. J. Painter, K. J. Vahala, "Ideality in a fiber-taper-coupled microresonator system for application to Cavity Quanum Electrodynamics," Phys. Rev. Lett. 91,043902 (2003).
[CrossRef] [PubMed]

2002

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, "Sub-MicroWatt photonic microwave receiver," IEEE Photon. Technol. Lett. 14, 1602 (2002).
[CrossRef]

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

2001

S. Ancey, A. Folacci, and P. Gabrielli, "Whispering-gallery modes and resonances of an elliptic cavity," J. Phys. A: Math. Gen. 34, 1341 (2001).
[CrossRef]

1999

C. Manolatou, M. J. Khan, S. H. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, "Coupling of modes analysis of resonant channel add-drop filters," IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

V. S. Ilchenko, X. S. Yao, and L. Maleki, Opt. Lett. 24, 723 (1999).
[CrossRef]

1997

A. C. R. Pipino, J. W. Hudgens, and R. E. Huie, "Evanescent wave cavity ring-down spectroscopy with a total-internal-reflection minicavity," Rev. Sci. Instrum. 68, 2978, (1997).
[CrossRef]

1960

J. B. Keller and S. I. Rubinow, "Asymptotic solution of eigenvalue problems," Ann. Phys. 9, 24 (1960).
[CrossRef]

1914

For instance, N. Bohr, "The spectra of helium and hydrogen," Nature 92, 231 (1914) and the following series.
[CrossRef]

Ancey, S.

S. Ancey, A. Folacci, and P. Gabrielli, "Whispering-gallery modes and resonances of an elliptic cavity," J. Phys. A: Math. Gen. 34, 1341 (2001).
[CrossRef]

Armani, D. K.

D. K. Armani, T. Kippenberg, S. M. Spillane and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature,  421, 925 (2003).
[CrossRef] [PubMed]

Bohr, N.

For instance, N. Bohr, "The spectra of helium and hydrogen," Nature 92, 231 (1914) and the following series.
[CrossRef]

Fan, S. H.

C. Manolatou, M. J. Khan, S. H. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, "Coupling of modes analysis of resonant channel add-drop filters," IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

Folacci, A.

S. Ancey, A. Folacci, and P. Gabrielli, "Whispering-gallery modes and resonances of an elliptic cavity," J. Phys. A: Math. Gen. 34, 1341 (2001).
[CrossRef]

Gabrielli, P.

S. Ancey, A. Folacci, and P. Gabrielli, "Whispering-gallery modes and resonances of an elliptic cavity," J. Phys. A: Math. Gen. 34, 1341 (2001).
[CrossRef]

Grudinin, I. S.

Haus, H. A.

C. Manolatou, M. J. Khan, S. H. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, "Coupling of modes analysis of resonant channel add-drop filters," IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

Hudgens, J. W.

A. C. R. Pipino, J. W. Hudgens, and R. E. Huie, "Evanescent wave cavity ring-down spectroscopy with a total-internal-reflection minicavity," Rev. Sci. Instrum. 68, 2978, (1997).
[CrossRef]

Huie, R. E.

A. C. R. Pipino, J. W. Hudgens, and R. E. Huie, "Evanescent wave cavity ring-down spectroscopy with a total-internal-reflection minicavity," Rev. Sci. Instrum. 68, 2978, (1997).
[CrossRef]

Ilchenko, V.

Ilchenko, V. S.

A. A. Savchenkov, I. S. Grudinin, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, "Morphology-dependent photonic circuit elements," Opt. Lett. 31, 1313 (2006).
[CrossRef] [PubMed]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, "Low threshold optical oscillations in a whispering gallery mode CaF2 resonator," Phys. Rev. Lett. 93, 243905 (2004).
[CrossRef]

V. S. Ilchenko, A. B. Matsko, A. A. Savchenkov, and L. Maleki, "Low-threshold parametric nonlinear optics with quasi-phase-matched whispering-gallery modes," J. Opt. Soc. Am. B 20, 1304 (2003).
[CrossRef]

A. B. Matsko, L. Maleki, A. A. Savchenkov, and V. S. Ilchenko, "Whispering gallery mode based optoelectronic microwave oscillator," J. Mod. Opt. 50, 2523 (2003).

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, "Tunable filter based on whispering gallery modes," Electron. Lett. 39, 389 (2003).
[CrossRef]

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, "Sub-MicroWatt photonic microwave receiver," IEEE Photon. Technol. Lett. 14, 1602 (2002).
[CrossRef]

V. S. Ilchenko, X. S. Yao, and L. Maleki, Opt. Lett. 24, 723 (1999).
[CrossRef]

Ilchenko, V.S.

M. Mohageg, A. A. Savchenkov, D. Strekalov, A. B. Matsko, V.S. Ilchenko and L. Maleki, "Reconfigurable optical filter," Electron. Lett. 41, 356 (2005).
[CrossRef]

Joannopoulos, J. D.

C. Manolatou, M. J. Khan, S. H. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, "Coupling of modes analysis of resonant channel add-drop filters," IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

Keller, J. B.

J. B. Keller and S. I. Rubinow, "Asymptotic solution of eigenvalue problems," Ann. Phys. 9, 24 (1960).
[CrossRef]

Khan, M. J.

C. Manolatou, M. J. Khan, S. H. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, "Coupling of modes analysis of resonant channel add-drop filters," IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

Kippenberg, T.

D. K. Armani, T. Kippenberg, S. M. Spillane and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature,  421, 925 (2003).
[CrossRef] [PubMed]

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

Kippenberg, T. J.

T. J. Kippenberg, M. Spillane, and K. J. Vahala, "Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity," Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, O. J. Painter, K. J. Vahala, "Ideality in a fiber-taper-coupled microresonator system for application to Cavity Quanum Electrodynamics," Phys. Rev. Lett. 91,043902 (2003).
[CrossRef] [PubMed]

Maleki, L.

A. A. Savchenkov, A. B. Matsko, M. Mohageg, and L. Maleki, "Ringdown spectroscopy of stimulated Raman scattering in a whispering gallery mode resonator," Opt. Lett. 32, 497 (2007).
[CrossRef] [PubMed]

A. A. Savchenkov, I. S. Grudinin, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, "Morphology-dependent photonic circuit elements," Opt. Lett. 31, 1313 (2006).
[CrossRef] [PubMed]

M. Mohageg, A. A. Savchenkov, D. Strekalov, A. B. Matsko, V.S. Ilchenko and L. Maleki, "Reconfigurable optical filter," Electron. Lett. 41, 356 (2005).
[CrossRef]

M. Mohageg, D. Strekalov, A. Savchenkov, A. Matsko, V. Ilchenko, and L. Maleki, "Calligraphic poling of Lithium Niobate," Opt. Express 13, 3408 (2005).
[CrossRef] [PubMed]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, "Low threshold optical oscillations in a whispering gallery mode CaF2 resonator," Phys. Rev. Lett. 93, 243905 (2004).
[CrossRef]

V. S. Ilchenko, A. B. Matsko, A. A. Savchenkov, and L. Maleki, "Low-threshold parametric nonlinear optics with quasi-phase-matched whispering-gallery modes," J. Opt. Soc. Am. B 20, 1304 (2003).
[CrossRef]

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, "Tunable filter based on whispering gallery modes," Electron. Lett. 39, 389 (2003).
[CrossRef]

A. B. Matsko, L. Maleki, A. A. Savchenkov, and V. S. Ilchenko, "Whispering gallery mode based optoelectronic microwave oscillator," J. Mod. Opt. 50, 2523 (2003).

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, "Sub-MicroWatt photonic microwave receiver," IEEE Photon. Technol. Lett. 14, 1602 (2002).
[CrossRef]

V. S. Ilchenko, X. S. Yao, and L. Maleki, Opt. Lett. 24, 723 (1999).
[CrossRef]

Manolatou, C.

C. Manolatou, M. J. Khan, S. H. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, "Coupling of modes analysis of resonant channel add-drop filters," IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

Matsko, A.

Matsko, A. B.

A. A. Savchenkov, A. B. Matsko, M. Mohageg, and L. Maleki, "Ringdown spectroscopy of stimulated Raman scattering in a whispering gallery mode resonator," Opt. Lett. 32, 497 (2007).
[CrossRef] [PubMed]

A. A. Savchenkov, I. S. Grudinin, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, "Morphology-dependent photonic circuit elements," Opt. Lett. 31, 1313 (2006).
[CrossRef] [PubMed]

M. Mohageg, A. A. Savchenkov, D. Strekalov, A. B. Matsko, V.S. Ilchenko and L. Maleki, "Reconfigurable optical filter," Electron. Lett. 41, 356 (2005).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, "Low threshold optical oscillations in a whispering gallery mode CaF2 resonator," Phys. Rev. Lett. 93, 243905 (2004).
[CrossRef]

V. S. Ilchenko, A. B. Matsko, A. A. Savchenkov, and L. Maleki, "Low-threshold parametric nonlinear optics with quasi-phase-matched whispering-gallery modes," J. Opt. Soc. Am. B 20, 1304 (2003).
[CrossRef]

A. B. Matsko, L. Maleki, A. A. Savchenkov, and V. S. Ilchenko, "Whispering gallery mode based optoelectronic microwave oscillator," J. Mod. Opt. 50, 2523 (2003).

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, "Tunable filter based on whispering gallery modes," Electron. Lett. 39, 389 (2003).
[CrossRef]

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, "Sub-MicroWatt photonic microwave receiver," IEEE Photon. Technol. Lett. 14, 1602 (2002).
[CrossRef]

Mohageg, M.

Painter, O. J.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, K. J. Vahala, "Ideality in a fiber-taper-coupled microresonator system for application to Cavity Quanum Electrodynamics," Phys. Rev. Lett. 91,043902 (2003).
[CrossRef] [PubMed]

Pipino, A. C. R.

A. C. R. Pipino, J. W. Hudgens, and R. E. Huie, "Evanescent wave cavity ring-down spectroscopy with a total-internal-reflection minicavity," Rev. Sci. Instrum. 68, 2978, (1997).
[CrossRef]

Rubinow, S. I.

J. B. Keller and S. I. Rubinow, "Asymptotic solution of eigenvalue problems," Ann. Phys. 9, 24 (1960).
[CrossRef]

Savchenkov, A.

Savchenkov, A. A.

A. A. Savchenkov, A. B. Matsko, M. Mohageg, and L. Maleki, "Ringdown spectroscopy of stimulated Raman scattering in a whispering gallery mode resonator," Opt. Lett. 32, 497 (2007).
[CrossRef] [PubMed]

A. A. Savchenkov, I. S. Grudinin, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, "Morphology-dependent photonic circuit elements," Opt. Lett. 31, 1313 (2006).
[CrossRef] [PubMed]

M. Mohageg, A. A. Savchenkov, D. Strekalov, A. B. Matsko, V.S. Ilchenko and L. Maleki, "Reconfigurable optical filter," Electron. Lett. 41, 356 (2005).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, "Low threshold optical oscillations in a whispering gallery mode CaF2 resonator," Phys. Rev. Lett. 93, 243905 (2004).
[CrossRef]

V. S. Ilchenko, A. B. Matsko, A. A. Savchenkov, and L. Maleki, "Low-threshold parametric nonlinear optics with quasi-phase-matched whispering-gallery modes," J. Opt. Soc. Am. B 20, 1304 (2003).
[CrossRef]

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, "Tunable filter based on whispering gallery modes," Electron. Lett. 39, 389 (2003).
[CrossRef]

A. B. Matsko, L. Maleki, A. A. Savchenkov, and V. S. Ilchenko, "Whispering gallery mode based optoelectronic microwave oscillator," J. Mod. Opt. 50, 2523 (2003).

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, "Sub-MicroWatt photonic microwave receiver," IEEE Photon. Technol. Lett. 14, 1602 (2002).
[CrossRef]

Spillane, M.

T. J. Kippenberg, M. Spillane, and K. J. Vahala, "Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity," Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef] [PubMed]

Spillane, S.

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

Spillane, S. M.

D. K. Armani, T. Kippenberg, S. M. Spillane and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature,  421, 925 (2003).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, O. J. Painter, K. J. Vahala, "Ideality in a fiber-taper-coupled microresonator system for application to Cavity Quanum Electrodynamics," Phys. Rev. Lett. 91,043902 (2003).
[CrossRef] [PubMed]

Strekalov, D.

A. A. Savchenkov, I. S. Grudinin, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, "Morphology-dependent photonic circuit elements," Opt. Lett. 31, 1313 (2006).
[CrossRef] [PubMed]

M. Mohageg, A. A. Savchenkov, D. Strekalov, A. B. Matsko, V.S. Ilchenko and L. Maleki, "Reconfigurable optical filter," Electron. Lett. 41, 356 (2005).
[CrossRef]

M. Mohageg, D. Strekalov, A. Savchenkov, A. Matsko, V. Ilchenko, and L. Maleki, "Calligraphic poling of Lithium Niobate," Opt. Express 13, 3408 (2005).
[CrossRef] [PubMed]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, "Low threshold optical oscillations in a whispering gallery mode CaF2 resonator," Phys. Rev. Lett. 93, 243905 (2004).
[CrossRef]

Vahala, K.

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

Vahala, K. J.

T. J. Kippenberg, M. Spillane, and K. J. Vahala, "Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity," Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef] [PubMed]

D. K. Armani, T. Kippenberg, S. M. Spillane and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature,  421, 925 (2003).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, O. J. Painter, K. J. Vahala, "Ideality in a fiber-taper-coupled microresonator system for application to Cavity Quanum Electrodynamics," Phys. Rev. Lett. 91,043902 (2003).
[CrossRef] [PubMed]

Villeneuve, P. R.

C. Manolatou, M. J. Khan, S. H. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, "Coupling of modes analysis of resonant channel add-drop filters," IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

Yao, X. S.

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Figures (4)

Fig. 2.
Fig. 2.

The three elliptical LiNbO3 resonators referred to in this paper.

Fig. 3.
Fig. 3.

Our experimental setup. CW Laser light scanned over several dozen GHz is evanescently coupled to the elliptical resonators through a diamond prism. The S11 element of the scattering matrix is collected by a 3mm diameter light pipe and sent to an InGaAs photodiode. Some of the laser light is sent through a Fabry-Perot etalon of known separation to form a relative frequency reference.

Fig. 4.
Fig. 4.

As the position of the coupling prism is shifted around the perimeter of the resonator, the same spectrum is recovered at all points. This confirms the fundamental assumption in the development of the eikonal model—which in turn validates our application of Bohr-Sommerfeld quantization.

Fig. 5.
Fig. 5.

We achieved a coupling efficiency of 97.3% into an elliptical WGM. The inset shows a Lorentzian fit (continuous red curve) to the measured data (blue dots) in the vicinity of optimal coupling. The best fit curve has a linewidth of 1.3 MHz, which corresponds to a quality factor of approximately 1.5 ∙ 108. The amplitude of the fit corresponds to a maximum coupling efficiency of 99.5%.

Tables (1)

Tables Icon

Table 1. Comparison of predictions from eikonal model to measured FSRs. Ceff stands for the coupling efficiency of the most efficiently coupled mode.

Equations (5)

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

( 2 + k 2 ) ψ = 0
ψ = j = 1 N A j exp ( ik S j )
k P S d σ ̅ = 2 π q q = 2,3,4
2 ka E ( 1 , ε ) = πq
Δ v = c 4 naE ( 1 , ε )

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