Abstract

A theoretical analysis of the operation of a chemical sensor based on cavity-enhanced optical absorption is given for a system in which the cavity is a dielectric whispering-gallery microresonator. Continuous-wave input is assumed, and the detection sensitivity is characterized in terms of an effective absorption path length. In the case of tunable single-frequency input, it is shown that monitoring analyte-induced changes in the throughput dip depth enables detection with relative sensitivity greater than that of frequency-shift and cavity-ringdown methods. In addition, for the case of broadband input and drop-port output, an analysis applicable to microcavity-enhanced absorbance spectroscopy experiments is given.

© 2007 Optical Society of America

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References

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  1. A. B. Matsko and V. S. Ilchenko, "Optical Resonators with Whispering-Gallery Modes - Part I: Basics," IEEE J. Sel. Top. Quantum Electron. 12, 3-14 (2006).
    [CrossRef]
  2. V. S. Ilchenko and A. B. Matsko, "Optical Resonators with Whispering-Gallery Modes - Part II: Applications," IEEE J. Sel. Top. Quantum Electron. 12, 15-32 (2006).
    [CrossRef]
  3. I. Teraoka, S. Arnold, and F. Vollmer, "Perturbation approach to resonance shifts of whispering-gallery modes in a dielectric microsphere as a probe of a surrounding medium," J. Opt. Soc. Am. B 20, 1937-1946 (2003).
    [CrossRef]
  4. N. M. Hanumegowda, C. J. Stica, B. C. Patel, I. White and X. Fan, "Refractometric sensors based on microsphere resonators," Appl. Phys. Lett. 87, 201107 (2005).
    [CrossRef]
  5. A. M. Armani and K. J. Vahala, "Heavy water detection using ultra-high-Q microcavities," Opt. Lett. 31, 1896-1898 (2006).
    [CrossRef] [PubMed]
  6. 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, 497-499 (2007).
    [CrossRef] [PubMed]
  7. R. W. Boyd and J. E. Heebner, "Sensitive disk resonator photonic biosensor," Appl. Opt. 40, 5742-5747 (2001).
    [CrossRef]
  8. 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]
  9. 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]
  10. M. Cai, O. Painter, and K. J. Vahala, "Observation of Critical Coupling in a Fiber Taper to a Silica-Microsphere Whispering-Gallery Mode System," Phys. Rev. Lett. 85, 74-77 (2000).
    [CrossRef] [PubMed]
  11. G. Farca, S. I. Shopova, and A. T. Rosenberger are preparing a manuscript to be called "Cavity-enhanced laser absorption spectroscopy using microresonator whispering-gallery modes."
  12. 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]
  13. J. Zhang, B. N. Strecker, R. K. Shelton, S.-J. Ja, J. V. Hryniewicz, and A. T. Rosenberger are preparing a manuscript to be called "A broadband whispering-gallery mode microsphere absorbance spectrometer."
  14. S. L. Westcott, J. Zhang, R. K. Shelton, N. M. K. Bruce, S. Gupta, S. L. Keen, J. W. Tillman, L. B. Wald, B. N. Strecker, A. T. Rosenberger, R. R. Davidson, W. Chen, K. G. Donovan, and J. V. Hryniewicz are preparing a manuscript to be called "Broadband optical absorbance spectroscopy using a whispering gallery mode microsphere resonator."

2007 (2)

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, 497-499 (2007).
[CrossRef] [PubMed]

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)

A. B. Matsko and V. S. Ilchenko, "Optical Resonators with Whispering-Gallery Modes - Part I: Basics," IEEE J. Sel. Top. Quantum Electron. 12, 3-14 (2006).
[CrossRef]

V. S. Ilchenko and A. B. Matsko, "Optical Resonators with Whispering-Gallery Modes - Part II: Applications," IEEE J. Sel. Top. Quantum Electron. 12, 15-32 (2006).
[CrossRef]

A. M. Armani and K. J. Vahala, "Heavy water detection using ultra-high-Q microcavities," Opt. Lett. 31, 1896-1898 (2006).
[CrossRef] [PubMed]

2005 (1)

N. M. Hanumegowda, C. J. Stica, B. C. Patel, I. White and X. Fan, "Refractometric sensors based on microsphere resonators," Appl. Phys. Lett. 87, 201107 (2005).
[CrossRef]

2003 (1)

2001 (1)

2000 (1)

M. Cai, O. Painter, and K. J. Vahala, "Observation of Critical Coupling in a Fiber Taper to a Silica-Microsphere Whispering-Gallery Mode System," Phys. Rev. Lett. 85, 74-77 (2000).
[CrossRef] [PubMed]

1999 (1)

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]

Armani, A. M.

Arnold, S.

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]

Boyd, R. W.

Cai, M.

M. Cai, O. Painter, and K. J. Vahala, "Observation of Critical Coupling in a Fiber Taper to a Silica-Microsphere Whispering-Gallery Mode System," Phys. Rev. Lett. 85, 74-77 (2000).
[CrossRef] [PubMed]

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]

Fan, X.

N. M. Hanumegowda, C. J. Stica, B. C. Patel, I. White and X. Fan, "Refractometric sensors based on microsphere resonators," Appl. Phys. Lett. 87, 201107 (2005).
[CrossRef]

Gorodetsky, M. L.

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]

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]

Hanumegowda, N. M.

N. M. Hanumegowda, C. J. Stica, B. C. Patel, I. White and X. Fan, "Refractometric sensors based on microsphere resonators," Appl. Phys. Lett. 87, 201107 (2005).
[CrossRef]

Heebner, J. E.

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.

A. B. Matsko and V. S. Ilchenko, "Optical Resonators with Whispering-Gallery Modes - Part I: Basics," IEEE J. Sel. Top. Quantum Electron. 12, 3-14 (2006).
[CrossRef]

V. S. Ilchenko and A. B. Matsko, "Optical Resonators with Whispering-Gallery Modes - Part II: Applications," IEEE J. Sel. Top. Quantum Electron. 12, 15-32 (2006).
[CrossRef]

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]

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]

Maleki, L.

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, 497-499 (2007).
[CrossRef] [PubMed]

A. B. Matsko and V. S. Ilchenko, "Optical Resonators with Whispering-Gallery Modes - Part I: Basics," IEEE J. Sel. Top. Quantum Electron. 12, 3-14 (2006).
[CrossRef]

V. S. Ilchenko and A. B. Matsko, "Optical Resonators with Whispering-Gallery Modes - Part II: Applications," IEEE J. Sel. Top. Quantum Electron. 12, 15-32 (2006).
[CrossRef]

Mohageg, M.

Painter, O.

M. Cai, O. Painter, and K. J. Vahala, "Observation of Critical Coupling in a Fiber Taper to a Silica-Microsphere Whispering-Gallery Mode System," Phys. Rev. Lett. 85, 74-77 (2000).
[CrossRef] [PubMed]

Patel, B. C.

N. M. Hanumegowda, C. J. Stica, B. C. Patel, I. White and X. Fan, "Refractometric sensors based on microsphere resonators," Appl. Phys. Lett. 87, 201107 (2005).
[CrossRef]

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]

Savchenkov, A. A.

Stica, C. J.

N. M. Hanumegowda, C. J. Stica, B. C. Patel, I. White and X. Fan, "Refractometric sensors based on microsphere resonators," Appl. Phys. Lett. 87, 201107 (2005).
[CrossRef]

Teraoka, I.

Vahala, K. J.

A. M. Armani and K. J. Vahala, "Heavy water detection using ultra-high-Q microcavities," Opt. Lett. 31, 1896-1898 (2006).
[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," Phys. Rev. Lett. 85, 74-77 (2000).
[CrossRef] [PubMed]

Vollmer, F.

White, I.

N. M. Hanumegowda, C. J. Stica, B. C. Patel, I. White and X. Fan, "Refractometric sensors based on microsphere resonators," Appl. Phys. Lett. 87, 201107 (2005).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

N. M. Hanumegowda, C. J. Stica, B. C. Patel, I. White and X. Fan, "Refractometric sensors based on microsphere resonators," Appl. Phys. Lett. 87, 201107 (2005).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

A. B. Matsko and V. S. Ilchenko, "Optical Resonators with Whispering-Gallery Modes - Part I: Basics," IEEE J. Sel. Top. Quantum Electron. 12, 3-14 (2006).
[CrossRef]

V. S. Ilchenko and A. B. Matsko, "Optical Resonators with Whispering-Gallery Modes - Part II: Applications," IEEE J. Sel. Top. Quantum Electron. 12, 15-32 (2006).
[CrossRef]

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

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. (2)

Phys. Rev. Lett. (1)

M. Cai, O. Painter, and K. J. Vahala, "Observation of Critical Coupling in a Fiber Taper to a Silica-Microsphere Whispering-Gallery Mode System," Phys. Rev. Lett. 85, 74-77 (2000).
[CrossRef] [PubMed]

Other (3)

G. Farca, S. I. Shopova, and A. T. Rosenberger are preparing a manuscript to be called "Cavity-enhanced laser absorption spectroscopy using microresonator whispering-gallery modes."

J. Zhang, B. N. Strecker, R. K. Shelton, S.-J. Ja, J. V. Hryniewicz, and A. T. Rosenberger are preparing a manuscript to be called "A broadband whispering-gallery mode microsphere absorbance spectrometer."

S. L. Westcott, J. Zhang, R. K. Shelton, N. M. K. Bruce, S. Gupta, S. L. Keen, J. W. Tillman, L. B. Wald, B. N. Strecker, A. T. Rosenberger, R. R. Davidson, W. Chen, K. G. Donovan, and J. V. Hryniewicz are preparing a manuscript to be called "Broadband optical absorbance spectroscopy using a whispering gallery mode microsphere resonator."

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Figures (2)

Fig. 1.
Fig. 1.

Four-mirror ring cavity model. Left, microcavity and tapered fiber in contact. Light can couple from the fiber into the resonator and vice versa. Right, the four-mirror ring cavity equivalent. The top mirror is partially transmitting; all others have 100% reflectivity.

Fig. 2.
Fig. 2.

Hemispherical prism coupling scheme. The microsphere is in a V-groove channel for the solvent and analyte. Left, polar view showing input and output coupling. Right, equatorial view illustrating how precessed light is collected at the drop port.

Equations (9)

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

R δ = r e α L 2 e 1 r e α L 2 e , 2
M δ = 1 R δ = TαL 1 4 ( T + αL ) 2 + 4 sin 2 1 2 δ TαL 1 4 ( T + αL ) 2 + δ 2 .
M 0 = 4 x ( 1 + x ) 2 .
d M 0 M 0 ( 1 x 1 + x ) f α i + f α s d α a L eff t d α a .
L eff t = ( 1 x 1 + x ) f α i .
L eff e = 1 α a ln M 0 M 0 + Δ M 0 .
D δ = T e α L 4 e 2 1 r 2 e α L 2 e 2 = T 2 ( T + 1 2 α L ) 2 + 4 sin 2 1 2 δ = D 0 ( 1 2 Δ δ ) 2 ( 1 2 Δ δ ) 2 + ( 2 sin 1 2 δ ) 2 .
D I = D 0 1 + ( 4 Δ δ ) 2 { D 0 = 4 T 2 ( Δ δ ) 2 for Δ δ 1 D 0 Δ δ 4 = T 2 Δ δ for Δ δ 1 .
D 0 a = 4 T 2 ( 2 T + α i L + f α a L ) 2 = D 0 ( 1 + 1 2 α a L eff ) 2 , where L eff = 2 f L 2 T + α i L .

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