Abstract

The optical loss of whispering gallery modes of resonantly excited microresonator spheres is determined by optical lifetime measurements. The phase-shift cavity ring-down technique is used to extract ring-down times and optical loss from the difference in amplitude modulation phase between the light entering the microresonator and light scattered from the microresonator. In addition, the phase lag of the light exiting the waveguide, which was used to couple light into the resonator, was measured. The intensity and phase measurements were fully described by a model that assumed interference of the cavity modes with the light propagating in the waveguide.

© 2008 Optical Society of America

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  1. A. M. Armani, D. K. Armani, B. Min, K. J. Vahala, and S. M. Spillane, "Ultra-high-Q microcavity operation in H2O and D2O," Appl. Phys. Lett. 87, 151118 (2005).
    [CrossRef]
  2. R. W. Boyd and J. E. Heebner, "Sensitive disk resonator photonic biosensor," Appl. Opt. 40, 5742 (2001).
    [CrossRef]
  3. C. Chao and L. J. Guo, "Polymer microring resonators fabricated by nanoimprint technique," J. Vac. Sci. Technol. B 20, 2862 (2002).
    [CrossRef]
  4. E. Krioukov, D. J. W. Klunder, A. Driessen, J. Greve, and C. Otto, "Integrated optical microcavities for enhanced evanescent-wave spectroscopy," Opt. Lett. 27, 1504 (2002).
    [CrossRef]
  5. T. Ling and L. J. Guo, "A unique resonance mode observed in a prism-coupled micro-tube resonator sensor with superior index sensitivity," Opt. Express 15, 17424 (2007).
    [CrossRef] [PubMed]
  6. 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 (1998).
    [CrossRef]
  7. I. M. White, H. Oveys, and X. Fan, "Liquid-core optical ring-resonator sensors," Opt. Lett. 31, 1319 (2008).
    [CrossRef]
  8. T. J. Kippenberg, S. M. Spillane, D. K. Armani, and K. J. Vahala, "Ultralow-threshold microcavity Raman laser on a microelectronic chip," Opt. Lett. 29, 1224 (2004).
    [CrossRef] [PubMed]
  9. S. I. Shopova, G. Farca, A. T. Rosenberger, W. M. S. Wickramanayake, and N. A. Kotov, "Microsphere whispering-gallery-mode laser using HgTe quantum dots," Appl. Phys. Lett. 85, 6101 (2004).
    [CrossRef]
  10. M. Cai, G. Hunziker, and K. Vahala, "Fiber-Optic Add-Drop Device Based on a Silica Microsphere Whispering Gallery Mode System," IEEE Photon. Technol. Lett 11, 686 (1999).
    [CrossRef]
  11. 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 (2003).
    [CrossRef] [PubMed]
  12. G. Farca, S. I. Shopova, and A. T. Rosenberger, "Cavity-enhanced laser absorption spectroscopy using microresonator whispering-gallery modes," Opt. Express 15, 17443 (2007).
    [CrossRef] [PubMed]
  13. A. M. Armani and K. J. Vahala, "Heavy water detection using ultra-high-Q microcavities," Opt. Lett. 31, 1896 (2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  16. G. Berden, R. Peeters, and G. Meijer, "Cavity ring-down spectroscopy: Experimental schemes and applications," Int. Rev. Phys. Chem. 19, 565 (2000).
    [CrossRef]
  17. A. C. R. Pipino, "Ultrasensitive surface spectroscopy with a miniature optical resonator," Phys. Rev. Lett. 83, 3093 (1999).
    [CrossRef]
  18. R. S. Brown, I. Kozin, Z. Tong, R. D. Oleschuk, and H.-P. Loock, "Fiber-loop ring-down spectroscopy," J. Chem. Phys. 117, 10444 (2002).
    [CrossRef]
  19. D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 42, 925 (2003).
    [CrossRef]
  20. R. Engeln, G. von Helden, G. Berden, and G. Meijer, "Phase shift cavity ring down absorption spectroscopy," Chem. Phys. Lett. 262, 105 (1996).
    [CrossRef]
  21. Z. Tong, A. Wright, T. McCormick, R. Li, R. D. Oleschuk, and H.-P. Loock, "Phase-Shift Fiber-Loop Ring-Down Spectroscopy," Anal. Chem. 76, 6594 (2004).
    [CrossRef] [PubMed]
  22. M. C. Chan and S. H. Yeung, "High-resolution cavity enhanced absorption spectroscopy using phase-sensitive detection," Chem. Phys. Lett. 373, 100 (2003).
    [CrossRef]
  23. J. Rezac, "Properties and applications of whispering-gallery mode resonances in fused silica microspheres," Ph.D. (Oklahoma State University, 2002).
  24. 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]
  25. T. J. Kippenberg, "Nonlinear Optics in Ultra-high-Q Whispering-Gallery Optical Microcavities," Ph.D. (California Institute of Technology, 2004).

2008

2007

2006

2005

A. M. Armani, D. K. Armani, B. Min, K. J. Vahala, and S. M. Spillane, "Ultra-high-Q microcavity operation in H2O and D2O," Appl. Phys. Lett. 87, 151118 (2005).
[CrossRef]

2004

T. J. Kippenberg, S. M. Spillane, D. K. Armani, and K. J. Vahala, "Ultralow-threshold microcavity Raman laser on a microelectronic chip," Opt. Lett. 29, 1224 (2004).
[CrossRef] [PubMed]

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

Z. Tong, A. Wright, T. McCormick, R. Li, R. D. Oleschuk, and H.-P. Loock, "Phase-Shift Fiber-Loop Ring-Down Spectroscopy," Anal. Chem. 76, 6594 (2004).
[CrossRef] [PubMed]

2003

M. C. Chan and S. H. Yeung, "High-resolution cavity enhanced absorption spectroscopy using phase-sensitive detection," Chem. Phys. Lett. 373, 100 (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 (2003).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 42, 925 (2003).
[CrossRef]

K. J. Vahala, "Optical microcavities," Nature 424, 839 (2003).
[CrossRef] [PubMed]

2002

C. Chao and L. J. Guo, "Polymer microring resonators fabricated by nanoimprint technique," J. Vac. Sci. Technol. B 20, 2862 (2002).
[CrossRef]

E. Krioukov, D. J. W. Klunder, A. Driessen, J. Greve, and C. Otto, "Integrated optical microcavities for enhanced evanescent-wave spectroscopy," Opt. Lett. 27, 1504 (2002).
[CrossRef]

R. S. Brown, I. Kozin, Z. Tong, R. D. Oleschuk, and H.-P. Loock, "Fiber-loop ring-down spectroscopy," J. Chem. Phys. 117, 10444 (2002).
[CrossRef]

2001

2000

G. Berden, R. Peeters, and G. Meijer, "Cavity ring-down spectroscopy: Experimental schemes and applications," Int. Rev. Phys. Chem. 19, 565 (2000).
[CrossRef]

1999

A. C. R. Pipino, "Ultrasensitive surface spectroscopy with a miniature optical resonator," Phys. Rev. Lett. 83, 3093 (1999).
[CrossRef]

M. Cai, G. Hunziker, and K. Vahala, "Fiber-Optic Add-Drop Device Based on a Silica Microsphere Whispering Gallery Mode System," IEEE Photon. Technol. Lett 11, 686 (1999).
[CrossRef]

1998

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]

1996

R. Engeln, G. von Helden, G. Berden, and G. Meijer, "Phase shift cavity ring down absorption spectroscopy," Chem. Phys. Lett. 262, 105 (1996).
[CrossRef]

Armani, A. M.

A. M. Armani and K. J. Vahala, "Heavy water detection using ultra-high-Q microcavities," Opt. Lett. 31, 1896 (2006).
[CrossRef] [PubMed]

A. M. Armani, D. K. Armani, B. Min, K. J. Vahala, and S. M. Spillane, "Ultra-high-Q microcavity operation in H2O and D2O," Appl. Phys. Lett. 87, 151118 (2005).
[CrossRef]

Armani, D. K.

A. M. Armani, D. K. Armani, B. Min, K. J. Vahala, and S. M. Spillane, "Ultra-high-Q microcavity operation in H2O and D2O," Appl. Phys. Lett. 87, 151118 (2005).
[CrossRef]

T. J. Kippenberg, S. M. Spillane, D. K. Armani, and K. J. Vahala, "Ultralow-threshold microcavity Raman laser on a microelectronic chip," Opt. Lett. 29, 1224 (2004).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 42, 925 (2003).
[CrossRef]

Arnold, S.

Berden, G.

G. Berden, R. Peeters, and G. Meijer, "Cavity ring-down spectroscopy: Experimental schemes and applications," Int. Rev. Phys. Chem. 19, 565 (2000).
[CrossRef]

R. Engeln, G. von Helden, G. Berden, and G. Meijer, "Phase shift cavity ring down absorption spectroscopy," Chem. Phys. Lett. 262, 105 (1996).
[CrossRef]

Boyd, R. W.

Brown, R. S.

R. S. Brown, I. Kozin, Z. Tong, R. D. Oleschuk, and H.-P. Loock, "Fiber-loop ring-down spectroscopy," J. Chem. Phys. 117, 10444 (2002).
[CrossRef]

Cai, M.

M. Cai, G. Hunziker, and K. Vahala, "Fiber-Optic Add-Drop Device Based on a Silica Microsphere Whispering Gallery Mode System," IEEE Photon. Technol. Lett 11, 686 (1999).
[CrossRef]

Chan, M. C.

M. C. Chan and S. H. Yeung, "High-resolution cavity enhanced absorption spectroscopy using phase-sensitive detection," Chem. Phys. Lett. 373, 100 (2003).
[CrossRef]

Chao, C.

C. Chao and L. J. Guo, "Polymer microring resonators fabricated by nanoimprint technique," J. Vac. Sci. Technol. B 20, 2862 (2002).
[CrossRef]

Driessen, A.

Engeln, R.

R. Engeln, G. von Helden, G. Berden, and G. Meijer, "Phase shift cavity ring down absorption spectroscopy," Chem. Phys. Lett. 262, 105 (1996).
[CrossRef]

Fan, X.

Farca, G.

G. Farca, S. I. Shopova, and A. T. Rosenberger, "Cavity-enhanced laser absorption spectroscopy using microresonator whispering-gallery modes," Opt. Express 15, 17443 (2007).
[CrossRef] [PubMed]

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

Greve, J.

Guo, L. J.

T. Ling and L. J. Guo, "A unique resonance mode observed in a prism-coupled micro-tube resonator sensor with superior index sensitivity," Opt. Express 15, 17424 (2007).
[CrossRef] [PubMed]

C. Chao and L. J. Guo, "Polymer microring resonators fabricated by nanoimprint technique," J. Vac. Sci. Technol. B 20, 2862 (2002).
[CrossRef]

Heebner, J. E.

Holler, S.

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]

Hunziker, G.

M. Cai, G. Hunziker, and K. Vahala, "Fiber-Optic Add-Drop Device Based on a Silica Microsphere Whispering Gallery Mode System," IEEE Photon. Technol. Lett 11, 686 (1999).
[CrossRef]

Ilchenko, V. S.

Khoshsima, M.

Kimble, H. J.

Kippenberg, T. J.

T. J. Kippenberg, S. M. Spillane, D. K. Armani, and K. J. Vahala, "Ultralow-threshold microcavity Raman laser on a microelectronic chip," Opt. Lett. 29, 1224 (2004).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 42, 925 (2003).
[CrossRef]

Klunder, D. J. W.

Kotov, N. A.

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

Kozin, I.

R. S. Brown, I. Kozin, Z. Tong, R. D. Oleschuk, and H.-P. Loock, "Fiber-loop ring-down spectroscopy," J. Chem. Phys. 117, 10444 (2002).
[CrossRef]

Krioukov, E.

Li, R.

Z. Tong, A. Wright, T. McCormick, R. Li, R. D. Oleschuk, and H.-P. Loock, "Phase-Shift Fiber-Loop Ring-Down Spectroscopy," Anal. Chem. 76, 6594 (2004).
[CrossRef] [PubMed]

Ling, T.

Loock, H.-P.

Z. Tong, A. Wright, T. McCormick, R. Li, R. D. Oleschuk, and H.-P. Loock, "Phase-Shift Fiber-Loop Ring-Down Spectroscopy," Anal. Chem. 76, 6594 (2004).
[CrossRef] [PubMed]

R. S. Brown, I. Kozin, Z. Tong, R. D. Oleschuk, and H.-P. Loock, "Fiber-loop ring-down spectroscopy," J. Chem. Phys. 117, 10444 (2002).
[CrossRef]

Mabuchi, H.

McCormick, T.

Z. Tong, A. Wright, T. McCormick, R. Li, R. D. Oleschuk, and H.-P. Loock, "Phase-Shift Fiber-Loop Ring-Down Spectroscopy," Anal. Chem. 76, 6594 (2004).
[CrossRef] [PubMed]

Meijer, G.

G. Berden, R. Peeters, and G. Meijer, "Cavity ring-down spectroscopy: Experimental schemes and applications," Int. Rev. Phys. Chem. 19, 565 (2000).
[CrossRef]

R. Engeln, G. von Helden, G. Berden, and G. Meijer, "Phase shift cavity ring down absorption spectroscopy," Chem. Phys. Lett. 262, 105 (1996).
[CrossRef]

Min, B.

A. M. Armani, D. K. Armani, B. Min, K. J. Vahala, and S. M. Spillane, "Ultra-high-Q microcavity operation in H2O and D2O," Appl. Phys. Lett. 87, 151118 (2005).
[CrossRef]

Oleschuk, R. D.

Z. Tong, A. Wright, T. McCormick, R. Li, R. D. Oleschuk, and H.-P. Loock, "Phase-Shift Fiber-Loop Ring-Down Spectroscopy," Anal. Chem. 76, 6594 (2004).
[CrossRef] [PubMed]

R. S. Brown, I. Kozin, Z. Tong, R. D. Oleschuk, and H.-P. Loock, "Fiber-loop ring-down spectroscopy," J. Chem. Phys. 117, 10444 (2002).
[CrossRef]

Otto, C.

Oveys, H.

Peeters, R.

G. Berden, R. Peeters, and G. Meijer, "Cavity ring-down spectroscopy: Experimental schemes and applications," Int. Rev. Phys. Chem. 19, 565 (2000).
[CrossRef]

Pipino, A. C. R.

A. C. R. Pipino, "Ultrasensitive surface spectroscopy with a miniature optical resonator," Phys. Rev. Lett. 83, 3093 (1999).
[CrossRef]

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]

Rosenberger, A. T.

Shopova, S. I.

G. Farca, S. I. Shopova, and A. T. Rosenberger, "Cavity-enhanced laser absorption spectroscopy using microresonator whispering-gallery modes," Opt. Express 15, 17443 (2007).
[CrossRef] [PubMed]

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

Spillane, S. M.

A. M. Armani, D. K. Armani, B. Min, K. J. Vahala, and S. M. Spillane, "Ultra-high-Q microcavity operation in H2O and D2O," Appl. Phys. Lett. 87, 151118 (2005).
[CrossRef]

T. J. Kippenberg, S. M. Spillane, D. K. Armani, and K. J. Vahala, "Ultralow-threshold microcavity Raman laser on a microelectronic chip," Opt. Lett. 29, 1224 (2004).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 42, 925 (2003).
[CrossRef]

Streed, E. W.

Teraoka, I.

Tong, Z.

Z. Tong, A. Wright, T. McCormick, R. Li, R. D. Oleschuk, and H.-P. Loock, "Phase-Shift Fiber-Loop Ring-Down Spectroscopy," Anal. Chem. 76, 6594 (2004).
[CrossRef] [PubMed]

R. S. Brown, I. Kozin, Z. Tong, R. D. Oleschuk, and H.-P. Loock, "Fiber-loop ring-down spectroscopy," J. Chem. Phys. 117, 10444 (2002).
[CrossRef]

Vahala, K.

M. Cai, G. Hunziker, and K. Vahala, "Fiber-Optic Add-Drop Device Based on a Silica Microsphere Whispering Gallery Mode System," IEEE Photon. Technol. Lett 11, 686 (1999).
[CrossRef]

Vahala, K. J.

A. M. Armani and K. J. Vahala, "Heavy water detection using ultra-high-Q microcavities," Opt. Lett. 31, 1896 (2006).
[CrossRef] [PubMed]

A. M. Armani, D. K. Armani, B. Min, K. J. Vahala, and S. M. Spillane, "Ultra-high-Q microcavity operation in H2O and D2O," Appl. Phys. Lett. 87, 151118 (2005).
[CrossRef]

T. J. Kippenberg, S. M. Spillane, D. K. Armani, and K. J. Vahala, "Ultralow-threshold microcavity Raman laser on a microelectronic chip," Opt. Lett. 29, 1224 (2004).
[CrossRef] [PubMed]

K. J. Vahala, "Optical microcavities," Nature 424, 839 (2003).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 42, 925 (2003).
[CrossRef]

Vernooy, D. W.

Vollmer, F.

von Helden, G.

R. Engeln, G. von Helden, G. Berden, and G. Meijer, "Phase shift cavity ring down absorption spectroscopy," Chem. Phys. Lett. 262, 105 (1996).
[CrossRef]

White, I. M.

Wickramanayake, W. M. S.

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

Wright, A.

Z. Tong, A. Wright, T. McCormick, R. Li, R. D. Oleschuk, and H.-P. Loock, "Phase-Shift Fiber-Loop Ring-Down Spectroscopy," Anal. Chem. 76, 6594 (2004).
[CrossRef] [PubMed]

Yeung, S. H.

M. C. Chan and S. H. Yeung, "High-resolution cavity enhanced absorption spectroscopy using phase-sensitive detection," Chem. Phys. Lett. 373, 100 (2003).
[CrossRef]

Anal. Chem.

Z. Tong, A. Wright, T. McCormick, R. Li, R. D. Oleschuk, and H.-P. Loock, "Phase-Shift Fiber-Loop Ring-Down Spectroscopy," Anal. Chem. 76, 6594 (2004).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. Lett.

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

A. M. Armani, D. K. Armani, B. Min, K. J. Vahala, and S. M. Spillane, "Ultra-high-Q microcavity operation in H2O and D2O," Appl. Phys. Lett. 87, 151118 (2005).
[CrossRef]

Chem. Phys. Lett.

M. C. Chan and S. H. Yeung, "High-resolution cavity enhanced absorption spectroscopy using phase-sensitive detection," Chem. Phys. Lett. 373, 100 (2003).
[CrossRef]

R. Engeln, G. von Helden, G. Berden, and G. Meijer, "Phase shift cavity ring down absorption spectroscopy," Chem. Phys. Lett. 262, 105 (1996).
[CrossRef]

IEEE Photon. Technol. Lett

M. Cai, G. Hunziker, and K. Vahala, "Fiber-Optic Add-Drop Device Based on a Silica Microsphere Whispering Gallery Mode System," IEEE Photon. Technol. Lett 11, 686 (1999).
[CrossRef]

Int. Rev. Phys. Chem.

G. Berden, R. Peeters, and G. Meijer, "Cavity ring-down spectroscopy: Experimental schemes and applications," Int. Rev. Phys. Chem. 19, 565 (2000).
[CrossRef]

J. Chem. Phys.

R. S. Brown, I. Kozin, Z. Tong, R. D. Oleschuk, and H.-P. Loock, "Fiber-loop ring-down spectroscopy," J. Chem. Phys. 117, 10444 (2002).
[CrossRef]

J. Vac. Sci. Technol. B

C. Chao and L. J. Guo, "Polymer microring resonators fabricated by nanoimprint technique," J. Vac. Sci. Technol. B 20, 2862 (2002).
[CrossRef]

Nature

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 42, 925 (2003).
[CrossRef]

K. J. Vahala, "Optical microcavities," Nature 424, 839 (2003).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

A. C. R. Pipino, "Ultrasensitive surface spectroscopy with a miniature optical resonator," Phys. Rev. Lett. 83, 3093 (1999).
[CrossRef]

Rev Sci Instrum

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]

Other

T. J. Kippenberg, "Nonlinear Optics in Ultra-high-Q Whispering-Gallery Optical Microcavities," Ph.D. (California Institute of Technology, 2004).

J. Rezac, "Properties and applications of whispering-gallery mode resonances in fused silica microspheres," Ph.D. (Oklahoma State University, 2002).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Intensity of the transmission through the waveguide near a resonance (Eq. (5)). (b) the phase near that resonance calculated from Eq. (7) (c) The corresponding phase-shift spectrum from Eq. (8). For all calculations the absorption coefficient α was varied in 10 increments between 0.1–1.9 m-1critical=1 m-1) and the following set of parameters was used: coupling parameter Γ=0.9995, neff =1.45; L=1 mm; ω=2 1014 s-1.

Fig. 2.
Fig. 2.

Whispering-gallery mode spectrum of a 300 micron diameter silica microsphere in contact with a 3 micron diameter tapered fiber. Spectra are recorded in transmission (top) and in scattering mode (bottom).

Fig. 3.
Fig. 3.

Phase-shift spectrum and intensity spectra of a 300 µm diameter microsphere. (a) The measurement was conducted by detecting the light transmitted through the fiber taper. (b) Scattered light was collected above the microsphere. The modulation frequency is 1.6 MHz.

Fig. 4.
Fig. 4.

Transmitted light (upper trace) and phase angle WGM spectrum of the microsphere. The phase-shift CRD spectra show that some of the WGMs are overcoupled (positive going peaks) whereas others are undercoupled (negative).

Fig. 5.
Fig. 5.

Modulation frequency dependent phase-shift for the four peaks shown in the transmission spectrum (solid lines and symbols, see Fig. 3(a)) and the three peaks shown in the scattering spectrum (dashed, empty symbols, Fig. 3(b) From the former the slopes of the linear fits can be used to calculate the parameter 2lnΓ/[(2lnΓ)2-(αL/2)2] as 757, 829, 962, 1039, respectively (see Eq. (10)). Ring-down times of 5.6, 7.5 and 4.6 ns are obtained directly from the slope of linear fits of the modulation frequency dependent phase-shift for peaks A, B and C in the scattering spectrum.

Equations (20)

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E inc = E 0 e i ω t ( 1 β + i 2 β cos Ω t )
= E 0 1 β e i ω t + E 0 β 2 ( e i ( ω + Ω ) t + π 2 + e i ( ω Ω ) t + π 2 )
E trans = E ω 1 β e i ( ω t + Φ ) + E ω + Ω β 2 e i [ ( ω + Ω ) t + Φ + + π 2 ] + E ω Ω β 2 e i [ ( ω Ω ) t + Φ + π 2 ]
I trans = n eff ε 0 c 2
[ ( 1 β ) E ω 2 + β 2 ( E ω + Ω 2 + E ω + Ω 2 ) + E ω E ω + Ω 2 β ( 1 β ) sin ( Ω t + Φ Φ + ) + E ω E ω Ω 2 β ( 1 β ) sin ( Ω t + Φ Φ ) + β E ω + Ω E ω Ω cos ( 2 Ω t + Φ + Φ ) ]
E = E ref E inc = Γ e α L 2 e i L k 1 Γ e α L 2 e i L k
I = Γ 2 2 Γ e α L 2 cos ( L k ) + e α L 1 2 Γ e α L 2 cos ( L k ) + Γ 2 e α L
E = Γ ( Γ 2 + 1 ) e α L 2 cos ( L k ) + Γ e α L + i ( Γ 2 1 ) e α L 2 sin ( L k ) 1 2 Γ e α L 2 cos ( L k ) + Γ 2 e α L
tan ϕ = Im ( E ) Re ( E )
= ( Γ 2 1 ) e α L 2 sin ( L k ) Γ ( Γ 2 + 1 ) e α L 2 cos ( L k ) + Γ e α L
( Φ + Φ ) = 2 Ω n eff L c Φ L k
Δ Φ = Φ + Φ 2 Ω n eff L c x ( 1 Γ 2 ) Γ ( 1 + x 2 ) x ( 1 + Γ 2 )
Δ Φ = Φ + Φ 2 Ω n eff L c 2 ln ( Γ ) ( ln Γ ) 2 ( α L 2 ) 2
τ = n eff L c ( ln Γ 2 + α L )
I ( ω , t ) = E 0 2 ( ω ) ( 1 + β cos ( 2 Ω t ) )
I ( ω , t ) = 1 τ t E 0 2 ( ω ) ( 1 + β cos ( 2 Ω t ) ) exp [ ( t t ) τ ] d t
= E 0 2 ( ω ) ( 1 + β 1 + 4 Ω 2 τ 2 cos ( 2 Ω t tan 1 ( 2 Ω τ ) ) )
Δ Φ = tan 1 ( 2 Ω τ )
2 Ω τ
2 Ω n eff L c 1 2 ln Γ + α L

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