Abstract

We examine the resonance spectrum change after turning on the light to feed the fiber taper evanescently coupled to a silica whispering gallery mode (WGM) resonator surrounded by different gases at different pressures. The resonance shifted to a longer wavelength, indicating a temperature rise, before reaching a steady state. The increment was proportional to the power of the light and approximately reciprocally proportional to the thermal conductivity of the surrounding gas, whereas the rate of the shift was approximately proportional to the thermal conductivity. The temperature rise, caused by absorption of intense WGM in silica, was significant even when the wavelength scan range contained only a few tall resonance peaks. We then estimated the power of heat generation and the mean power of WGM during the wavelength scan.

© 2013 Optical Society of America

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References

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  1. A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Review of applications of whispering-gallery mode resonators in photonics and nonlinear optics,” Progr. Rep. 42-162 (IPN, 2005), p. 1.
  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 and S. Arnold, “Theory on resonance shifts in TE and TM whispering gallery modes by non-radial perturbations for sensing applications,” J. Opt. Soc. Am. B 23, 1381–1389 (2006).
    [CrossRef]
  4. G. Schweiger and M. Horn, “Effect of changes in size and index of refraction on the resonance wavelength of microspheres,” J. Opt. Soc. Am. A 23, 212–217 (2006).
    [CrossRef]
  5. E. Krioukov, D. J. W. Klunder, A. Driessen, J. Greve, and C. Otto, “Sensor based on an integrated optical microcavity,” Opt. Lett. 27, 512–514 (2002).
    [CrossRef]
  6. M. Noto, D. Keng, I. Teraoka, and S. Arnold, “Detection of protein orientation on silica surface using transverse electric/transverse magnetic whispering gallery modes,” Biophys. J. 92, 4466–4472 (2007).
    [CrossRef]
  7. 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]
  8. F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80, 4057–4059(2002).
    [CrossRef]
  9. H. Zhu, J. D. Suter, and X. Fan, “Label-free optical ring resonator bio/chemical sensors,” in Optical Guided-Wave Chemical and Biosensors II, M. Zourob and A. Lakhtakia, eds. (Springer, 2010).
  10. S. Soria, S. Berneschi, M. Brenci, F. Cosi, G. Nunzi Conti, S. Pelli, and G. C. Righini, “Optical microspherical resonators for biomedical sensing,” Sensors 11, 785–805 (2011).
    [CrossRef]
  11. 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 (1989).
    [CrossRef]
  12. T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express 12, 4742–4750 (2004).
    [CrossRef]
  13. C. Schmidt, A. Chipouline, T. Pertsch, A. Tünnermann, O. Egorov, F. Lederer, and L. Deych, “Nonlinear thermal effects in optical microspheres at different wavelength sweeping speeds,” Opt. Express 16, 6285–6301 (2008).
    [CrossRef]
  14. A. T. Rosenberger, E. B. Dale, D. Ganta, and J. P. Rezac, “Investigating properties of surfaces and thin films using microsphere whispering-gallery modes,” Proc. SPIE 6872, 68720U (2008).
    [CrossRef]
  15. D. Ganta, E. B. Dale, J. P. Rezac, and A. T. Rosenberger, “Optical method for measuring thermal accommodation coefficients using a whispering-gallery microresonator,” J. Chem. Phys. 135, 084313 (2011).
    [CrossRef]
  16. M. Han and A. Wang, “Temperature compensation of optical microresonators using a surface layer with negative thermo-optic coefficient,” Opt. Lett. 32, 1800–1802 (2007).
    [CrossRef]
  17. J. H. Lienhard and J. H. Lienhard, A Heat Transfer Textbook, 4th ed. (Prentice-Hall, 1981).
  18. P. Atkins and J. de Paula, Elements of Physical Chemistry, 5th ed. (Oxford, 2009).
  19. D. Keng, “Surface interaction, polarization and molecular weight effects for a whispering gallery mode sensor,” Ph.D. thesis (Polytechnic Institute of NYU, 2009).
  20. E. A. Mason and S. C. Saxena, “Approximate formula for the thermal conductivity of gas mixtures,” Phys. Fluids 1, 361–369 (1958).
    [CrossRef]
  21. M. Agarwal and I. Teraoka, “Mode latching and self tuning of whispering gallery modes in a stand-alone silica microsphere,” Appl. Phys. Lett. 101, 251105 (2012).
    [CrossRef]
  22. Corning SMF-28 Optical Fiber Product Information (2002).
  23. From the chart in http://www.invocom.et.put.poznan.pl/~invocom/C/P1-9/swiatlowody_en/p1-1_2_2.htm .
  24. The estimates of the scattering component and absorption component vary from report to report. The value we use here is an example.

2012

M. Agarwal and I. Teraoka, “Mode latching and self tuning of whispering gallery modes in a stand-alone silica microsphere,” Appl. Phys. Lett. 101, 251105 (2012).
[CrossRef]

2011

D. Ganta, E. B. Dale, J. P. Rezac, and A. T. Rosenberger, “Optical method for measuring thermal accommodation coefficients using a whispering-gallery microresonator,” J. Chem. Phys. 135, 084313 (2011).
[CrossRef]

S. Soria, S. Berneschi, M. Brenci, F. Cosi, G. Nunzi Conti, S. Pelli, and G. C. Righini, “Optical microspherical resonators for biomedical sensing,” Sensors 11, 785–805 (2011).
[CrossRef]

2008

C. Schmidt, A. Chipouline, T. Pertsch, A. Tünnermann, O. Egorov, F. Lederer, and L. Deych, “Nonlinear thermal effects in optical microspheres at different wavelength sweeping speeds,” Opt. Express 16, 6285–6301 (2008).
[CrossRef]

A. T. Rosenberger, E. B. Dale, D. Ganta, and J. P. Rezac, “Investigating properties of surfaces and thin films using microsphere whispering-gallery modes,” Proc. SPIE 6872, 68720U (2008).
[CrossRef]

2007

M. Han and A. Wang, “Temperature compensation of optical microresonators using a surface layer with negative thermo-optic coefficient,” Opt. Lett. 32, 1800–1802 (2007).
[CrossRef]

M. Noto, D. Keng, I. Teraoka, and S. Arnold, “Detection of protein orientation on silica surface using transverse electric/transverse magnetic whispering gallery modes,” Biophys. J. 92, 4466–4472 (2007).
[CrossRef]

2006

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]

I. Teraoka and S. Arnold, “Theory on resonance shifts in TE and TM whispering gallery modes by non-radial perturbations for sensing applications,” J. Opt. Soc. Am. B 23, 1381–1389 (2006).
[CrossRef]

G. Schweiger and M. Horn, “Effect of changes in size and index of refraction on the resonance wavelength of microspheres,” J. Opt. Soc. Am. A 23, 212–217 (2006).
[CrossRef]

2005

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]

2004

2002

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80, 4057–4059(2002).
[CrossRef]

E. Krioukov, D. J. W. Klunder, A. Driessen, J. Greve, and C. Otto, “Sensor based on an integrated optical microcavity,” Opt. Lett. 27, 512–514 (2002).
[CrossRef]

1989

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 (1989).
[CrossRef]

1958

E. A. Mason and S. C. Saxena, “Approximate formula for the thermal conductivity of gas mixtures,” Phys. Fluids 1, 361–369 (1958).
[CrossRef]

Agarwal, M.

M. Agarwal and I. Teraoka, “Mode latching and self tuning of whispering gallery modes in a stand-alone silica microsphere,” Appl. Phys. Lett. 101, 251105 (2012).
[CrossRef]

Arnold, S.

M. Noto, D. Keng, I. Teraoka, and S. Arnold, “Detection of protein orientation on silica surface using transverse electric/transverse magnetic whispering gallery modes,” Biophys. J. 92, 4466–4472 (2007).
[CrossRef]

I. Teraoka and S. Arnold, “Theory on resonance shifts in TE and TM whispering gallery modes by non-radial perturbations for sensing applications,” J. Opt. Soc. Am. B 23, 1381–1389 (2006).
[CrossRef]

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80, 4057–4059(2002).
[CrossRef]

Atkins, P.

P. Atkins and J. de Paula, Elements of Physical Chemistry, 5th ed. (Oxford, 2009).

Berneschi, S.

S. Soria, S. Berneschi, M. Brenci, F. Cosi, G. Nunzi Conti, S. Pelli, and G. C. Righini, “Optical microspherical resonators for biomedical sensing,” Sensors 11, 785–805 (2011).
[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 (1989).
[CrossRef]

Braun, D.

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80, 4057–4059(2002).
[CrossRef]

Brenci, M.

S. Soria, S. Berneschi, M. Brenci, F. Cosi, G. Nunzi Conti, S. Pelli, and G. C. Righini, “Optical microspherical resonators for biomedical sensing,” Sensors 11, 785–805 (2011).
[CrossRef]

Carmon, T.

Chipouline, A.

Cosi, F.

S. Soria, S. Berneschi, M. Brenci, F. Cosi, G. Nunzi Conti, S. Pelli, and G. C. Righini, “Optical microspherical resonators for biomedical sensing,” Sensors 11, 785–805 (2011).
[CrossRef]

Dale, E. B.

D. Ganta, E. B. Dale, J. P. Rezac, and A. T. Rosenberger, “Optical method for measuring thermal accommodation coefficients using a whispering-gallery microresonator,” J. Chem. Phys. 135, 084313 (2011).
[CrossRef]

A. T. Rosenberger, E. B. Dale, D. Ganta, and J. P. Rezac, “Investigating properties of surfaces and thin films using microsphere whispering-gallery modes,” Proc. SPIE 6872, 68720U (2008).
[CrossRef]

de Paula, J.

P. Atkins and J. de Paula, Elements of Physical Chemistry, 5th ed. (Oxford, 2009).

Deych, L.

Driessen, A.

Egorov, O.

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]

H. Zhu, J. D. Suter, and X. Fan, “Label-free optical ring resonator bio/chemical sensors,” in Optical Guided-Wave Chemical and Biosensors II, M. Zourob and A. Lakhtakia, eds. (Springer, 2010).

Ganta, D.

D. Ganta, E. B. Dale, J. P. Rezac, and A. T. Rosenberger, “Optical method for measuring thermal accommodation coefficients using a whispering-gallery microresonator,” J. Chem. Phys. 135, 084313 (2011).
[CrossRef]

A. T. Rosenberger, E. B. Dale, D. Ganta, and J. P. Rezac, “Investigating properties of surfaces and thin films using microsphere whispering-gallery modes,” Proc. SPIE 6872, 68720U (2008).
[CrossRef]

Gorodetsky, M. L.

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 (1989).
[CrossRef]

Greve, J.

Han, M.

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]

Horn, M.

G. Schweiger and M. Horn, “Effect of changes in size and index of refraction on the resonance wavelength of microspheres,” J. Opt. Soc. Am. A 23, 212–217 (2006).
[CrossRef]

Ilchenko, V. S.

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]

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 (1989).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Review of applications of whispering-gallery mode resonators in photonics and nonlinear optics,” Progr. Rep. 42-162 (IPN, 2005), p. 1.

Keng, D.

M. Noto, D. Keng, I. Teraoka, and S. Arnold, “Detection of protein orientation on silica surface using transverse electric/transverse magnetic whispering gallery modes,” Biophys. J. 92, 4466–4472 (2007).
[CrossRef]

D. Keng, “Surface interaction, polarization and molecular weight effects for a whispering gallery mode sensor,” Ph.D. thesis (Polytechnic Institute of NYU, 2009).

Khoshsima, M.

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80, 4057–4059(2002).
[CrossRef]

Klunder, D. J. W.

Krioukov, E.

Lederer, F.

Libchaber, A.

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80, 4057–4059(2002).
[CrossRef]

Lienhard, J. H.

J. H. Lienhard and J. H. Lienhard, A Heat Transfer Textbook, 4th ed. (Prentice-Hall, 1981).

J. H. Lienhard and J. H. Lienhard, A Heat Transfer Textbook, 4th ed. (Prentice-Hall, 1981).

Maleki, L.

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Review of applications of whispering-gallery mode resonators in photonics and nonlinear optics,” Progr. Rep. 42-162 (IPN, 2005), p. 1.

Mason, E. A.

E. A. Mason and S. C. Saxena, “Approximate formula for the thermal conductivity of gas mixtures,” Phys. Fluids 1, 361–369 (1958).
[CrossRef]

Matsko, A. B.

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. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Review of applications of whispering-gallery mode resonators in photonics and nonlinear optics,” Progr. Rep. 42-162 (IPN, 2005), p. 1.

Noto, M.

M. Noto, D. Keng, I. Teraoka, and S. Arnold, “Detection of protein orientation on silica surface using transverse electric/transverse magnetic whispering gallery modes,” Biophys. J. 92, 4466–4472 (2007).
[CrossRef]

Nunzi Conti, G.

S. Soria, S. Berneschi, M. Brenci, F. Cosi, G. Nunzi Conti, S. Pelli, and G. C. Righini, “Optical microspherical resonators for biomedical sensing,” Sensors 11, 785–805 (2011).
[CrossRef]

Otto, C.

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]

Pelli, S.

S. Soria, S. Berneschi, M. Brenci, F. Cosi, G. Nunzi Conti, S. Pelli, and G. C. Righini, “Optical microspherical resonators for biomedical sensing,” Sensors 11, 785–805 (2011).
[CrossRef]

Pertsch, T.

Rezac, J. P.

D. Ganta, E. B. Dale, J. P. Rezac, and A. T. Rosenberger, “Optical method for measuring thermal accommodation coefficients using a whispering-gallery microresonator,” J. Chem. Phys. 135, 084313 (2011).
[CrossRef]

A. T. Rosenberger, E. B. Dale, D. Ganta, and J. P. Rezac, “Investigating properties of surfaces and thin films using microsphere whispering-gallery modes,” Proc. SPIE 6872, 68720U (2008).
[CrossRef]

Righini, G. C.

S. Soria, S. Berneschi, M. Brenci, F. Cosi, G. Nunzi Conti, S. Pelli, and G. C. Righini, “Optical microspherical resonators for biomedical sensing,” Sensors 11, 785–805 (2011).
[CrossRef]

Rosenberger, A. T.

D. Ganta, E. B. Dale, J. P. Rezac, and A. T. Rosenberger, “Optical method for measuring thermal accommodation coefficients using a whispering-gallery microresonator,” J. Chem. Phys. 135, 084313 (2011).
[CrossRef]

A. T. Rosenberger, E. B. Dale, D. Ganta, and J. P. Rezac, “Investigating properties of surfaces and thin films using microsphere whispering-gallery modes,” Proc. SPIE 6872, 68720U (2008).
[CrossRef]

Savchenkov, A. A.

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Review of applications of whispering-gallery mode resonators in photonics and nonlinear optics,” Progr. Rep. 42-162 (IPN, 2005), p. 1.

Saxena, S. C.

E. A. Mason and S. C. Saxena, “Approximate formula for the thermal conductivity of gas mixtures,” Phys. Fluids 1, 361–369 (1958).
[CrossRef]

Schmidt, C.

Schweiger, G.

G. Schweiger and M. Horn, “Effect of changes in size and index of refraction on the resonance wavelength of microspheres,” J. Opt. Soc. Am. A 23, 212–217 (2006).
[CrossRef]

Soria, S.

S. Soria, S. Berneschi, M. Brenci, F. Cosi, G. Nunzi Conti, S. Pelli, and G. C. Righini, “Optical microspherical resonators for biomedical sensing,” Sensors 11, 785–805 (2011).
[CrossRef]

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]

Strekalov, D.

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Review of applications of whispering-gallery mode resonators in photonics and nonlinear optics,” Progr. Rep. 42-162 (IPN, 2005), p. 1.

Suter, J. D.

H. Zhu, J. D. Suter, and X. Fan, “Label-free optical ring resonator bio/chemical sensors,” in Optical Guided-Wave Chemical and Biosensors II, M. Zourob and A. Lakhtakia, eds. (Springer, 2010).

Teraoka, I.

M. Agarwal and I. Teraoka, “Mode latching and self tuning of whispering gallery modes in a stand-alone silica microsphere,” Appl. Phys. Lett. 101, 251105 (2012).
[CrossRef]

M. Noto, D. Keng, I. Teraoka, and S. Arnold, “Detection of protein orientation on silica surface using transverse electric/transverse magnetic whispering gallery modes,” Biophys. J. 92, 4466–4472 (2007).
[CrossRef]

I. Teraoka and S. Arnold, “Theory on resonance shifts in TE and TM whispering gallery modes by non-radial perturbations for sensing applications,” J. Opt. Soc. Am. B 23, 1381–1389 (2006).
[CrossRef]

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80, 4057–4059(2002).
[CrossRef]

Tünnermann, A.

Vahala, K. J.

Vollmer, F.

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80, 4057–4059(2002).
[CrossRef]

Wang, A.

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]

Yang, L.

Zhu, H.

H. Zhu, J. D. Suter, and X. Fan, “Label-free optical ring resonator bio/chemical sensors,” in Optical Guided-Wave Chemical and Biosensors II, M. Zourob and A. Lakhtakia, eds. (Springer, 2010).

Appl. Phys. Lett.

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]

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80, 4057–4059(2002).
[CrossRef]

M. Agarwal and I. Teraoka, “Mode latching and self tuning of whispering gallery modes in a stand-alone silica microsphere,” Appl. Phys. Lett. 101, 251105 (2012).
[CrossRef]

Biophys. J.

M. Noto, D. Keng, I. Teraoka, and S. Arnold, “Detection of protein orientation on silica surface using transverse electric/transverse magnetic whispering gallery modes,” Biophys. J. 92, 4466–4472 (2007).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

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. Chem. Phys.

D. Ganta, E. B. Dale, J. P. Rezac, and A. T. Rosenberger, “Optical method for measuring thermal accommodation coefficients using a whispering-gallery microresonator,” J. Chem. Phys. 135, 084313 (2011).
[CrossRef]

J. Opt. Soc. Am. A

G. Schweiger and M. Horn, “Effect of changes in size and index of refraction on the resonance wavelength of microspheres,” J. Opt. Soc. Am. A 23, 212–217 (2006).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Phys. Fluids

E. A. Mason and S. C. Saxena, “Approximate formula for the thermal conductivity of gas mixtures,” Phys. Fluids 1, 361–369 (1958).
[CrossRef]

Phys. Lett. A

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 (1989).
[CrossRef]

Proc. SPIE

A. T. Rosenberger, E. B. Dale, D. Ganta, and J. P. Rezac, “Investigating properties of surfaces and thin films using microsphere whispering-gallery modes,” Proc. SPIE 6872, 68720U (2008).
[CrossRef]

Sensors

S. Soria, S. Berneschi, M. Brenci, F. Cosi, G. Nunzi Conti, S. Pelli, and G. C. Righini, “Optical microspherical resonators for biomedical sensing,” Sensors 11, 785–805 (2011).
[CrossRef]

Other

J. H. Lienhard and J. H. Lienhard, A Heat Transfer Textbook, 4th ed. (Prentice-Hall, 1981).

P. Atkins and J. de Paula, Elements of Physical Chemistry, 5th ed. (Oxford, 2009).

D. Keng, “Surface interaction, polarization and molecular weight effects for a whispering gallery mode sensor,” Ph.D. thesis (Polytechnic Institute of NYU, 2009).

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Review of applications of whispering-gallery mode resonators in photonics and nonlinear optics,” Progr. Rep. 42-162 (IPN, 2005), p. 1.

H. Zhu, J. D. Suter, and X. Fan, “Label-free optical ring resonator bio/chemical sensors,” in Optical Guided-Wave Chemical and Biosensors II, M. Zourob and A. Lakhtakia, eds. (Springer, 2010).

Corning SMF-28 Optical Fiber Product Information (2002).

From the chart in http://www.invocom.et.put.poznan.pl/~invocom/C/P1-9/swiatlowody_en/p1-1_2_2.htm .

The estimates of the scattering component and absorption component vary from report to report. The value we use here is an example.

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Figures (7)

Fig. 1.
Fig. 1.

Measurement system for WGMs in different atmospheres. A microsphere resonator sits on top of the gap between a head-on pair of tapers. Light from a laser is fed to one of the tapers, and the other taper collects the light from the resonator. The dashed line represents a vacuum chamber. A micrograph of the microsphere resonator is included.

Fig. 2.
Fig. 2.

Resonance spectra of a sphere (161.0 μm radius) in 2HgN2 in a 5 mA down scan (1302.8989–1302.9320 nm) of the wavelength of a laser (5dB), shown as a function of the channel number (1–1025). The spectra were collected from right to left. The light was turned on in the 18th scan (a). Spectra of the 19th (b), 20th (c), and 1100th (d) scans are horizontally displaced to align the corresponding peaks along the dashed line. (e) and (f) zoom parts of (a) and (b). Each nearly vertical line connects the peaks that belong to the same mode.

Fig. 3.
Fig. 3.

Channel shift rate dc/dt, plotted as a function of time t since the light was brought into a sphere of radius 161.0 μm in ambient air. Plots are shown for different levels of attenuation in the feed light, indicated adjacent to the plots. For each attenuation, results compiled from three experiments are shown. (Inset) The total shift in channels versus relative power of the feed light (1=0dB).

Fig. 4.
Fig. 4.

Decay rate Γ of dc/dt (a) and the total shift (b), plotted as a function of gauge pressure of air. The sphere radius was 161.0 μm. A shift of +100 translates into a temperature increase of 0.255 K.

Fig. 5.
Fig. 5.

Channel shift rate dc/dt, plotted as a function of time t since the light was brought into a sphere of radius 161.0 μm in He, N2, O2, and CO2, each at 10Hg. For each gas, results compiled from three experiments are shown. The N2, O2, and CO2 data are multiplied by 3, 9, and 27, respectively, to avoid overlap.

Fig. 6.
Fig. 6.

Decay rate Γ of dc/dt, plotted as a function of thermal conductivity of gas, κ. The data are shown for pressures of He, N2, O2, and CO2 at 20, 10, and 2Hg and for pressures of mixtures between 10 and 0Hg. The dashed–dotted and solid lines are theoretical estimates assuming an isolated sphere and a sphere on a 125 μm stem, respectively. The dashed line is a linear fit to the data of pure gases.

Fig. 7.
Fig. 7.

Temperature rise ΔT, plotted as a function of the decay rate Γ. The pressures are identical to those in Fig. 6. The straight line has a slope of 1.

Tables (1)

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Table 1. Thermal Conductivity κ and Collisional Cross Section σ at 300 K, Mean Free Path (MFP) at 300 K, 1 atm, and the Pressure pc that Makes MFP Equal to the Sphere Radius 161.0 μm

Equations (6)

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ΔT=Pheat/(4πκa)
Γ=4πκa/Csp,
Δλ/λ=9.739ppm×ΔT/K.
MFP=kBT2σp,
pc=kBT2σa.
Pheat=2πaαabsPWGM,

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