Abstract

We propose a highly sensitive chemical sensor by functionally coating a zeolite film on the external surface of an optical microsphere. Using the perturbation theory, a model is developed to calculate sensor sensitivity and analyze the impact of the zeolite film thickness. The quality factor and detection limit are also investigated by using an approximate model. Simulations show that a zeolite coating can effectively increase sensitivity. The results provide physical insights for the design and optimization of various parameters for desired sensor performance.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. N. M. Hanumegowda, C. J. Stica, B. C. Patel, I. M. White, and X. Fan, “Refractometric sensors based on microsphere resonators,” Appl. Phys. Lett. 87, 201107 (2005).
    [CrossRef]
  4. H. Y. Zhu, J. D. Suter, I. M. White, and X. D. Fan, “Aptamer based microsphere biosensor for thrombin detection,” Sensors 6, 785–795 (2006).
    [CrossRef]
  5. 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]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  12. J. Zhang, X. Tang, J. Dong, T. Wei, and H. Xiao, “Zeolite thin film-coated long period fiber grating sensor for measuring trace chemical,” Opt. Express 16, 8317–8323 (2008).
    [CrossRef] [PubMed]
  13. J. Zhang, M. Luo, H. Xiao, and J. Dong, “Interferometric study on the adsorption-dependent refractive index of silicalite thin films grown on optical fibers,” Chem. Mater. 18, 4–6 (2006).
    [CrossRef]
  14. I. Braun, G. Ihlein, F. Laeri, J. U. Nöckel, G. Schulz-Ekloff, F. Schüth, U. Vietze, Ö. Weiss, and D. Wöhrle, “Hexagonal microlasers based on organic dyes in nanoporous crystals,” Appl. Phys. B 70, 335–343 (2000).
    [CrossRef]
  15. Y. Yang, Y. F. Xiao, C. H. Dong, J. M. Cui, Z. F. Han, G. D. Li, and G. C. Guo, “Fiber-taper-coupled zeolite cylindrical microcavity with hexagonal cross section,” Appl. Opt. 46, 7590–7593(2007).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  23. 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]
  24. V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality factor and nonlinear properties of optical whispering gallery modes,” Phys. Lett. A 137, 393–397 (1989).
    [CrossRef]
  25. C. H. Dong, F. W. Sun, C. L. Zou, X. F. Ren, G. C. Guo, and Z. F. Han, “High-Q silica microsphere by poly (methyl methacrylate) coating and modifying,” Appl. Phys. Lett. 96, 061106(2010).
    [CrossRef]
  26. L. He, Y. F. Xiao, C. Dong, J. Zhu, V. Gaddam, and L. Yang, “Compensation of thermal refraction effect in high-Q toroidal microresonator by polydimethylsiloxane coating,” Appl. Phys. Lett. 93, 201102 (2008).
    [CrossRef]
  27. 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]
  28. S. Schiller and R. L. Byer, “High-resolution spectroscopy of whispering gallery modes in large dielectric spheres,” Opt. Lett. 16, 1138–1140 (1991).
    [CrossRef] [PubMed]

2010

C. H. Dong, F. W. Sun, C. L. Zou, X. F. Ren, G. C. Guo, and Z. F. Han, “High-Q silica microsphere by poly (methyl methacrylate) coating and modifying,” Appl. Phys. Lett. 96, 061106(2010).
[CrossRef]

2008

L. He, Y. F. Xiao, C. Dong, J. Zhu, V. Gaddam, and L. Yang, “Compensation of thermal refraction effect in high-Q toroidal microresonator by polydimethylsiloxane coating,” Appl. Phys. Lett. 93, 201102 (2008).
[CrossRef]

F. Vollmer and S. Arnord, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Meth. 5, 591–596 (2008).
[CrossRef]

J. Zhang, X. Tang, J. Dong, T. Wei, and H. Xiao, “Zeolite thin film-coated long period fiber grating sensor for measuring trace chemical,” Opt. Express 16, 8317–8323 (2008).
[CrossRef] [PubMed]

2007

2006

C. Y. Chao and L. J. Guo, “Design and optimization of microring resonators in biochemical sensing applications,” J. Lightwave Technol. 24, 1395–1402 (2006).
[CrossRef]

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

I. Teraoka and S. Arnold, “Enhancing the sensitivity of a whispering-gallery mode microsphere sensor by a high-refractive-index surface layer,” J. Opt. Soc. Am. B 23, 1434–1442 (2006).
[CrossRef]

N. M. Hanumegowda, I. M. White, and X. Fan, “Aqueous mercuric ion detection with microsphere optical ring resonator sensors,” Sens. Actuators B 120, 207–212 (2006).
[CrossRef]

H. Y. Zhu, J. D. Suter, I. M. White, and X. D. Fan, “Aptamer based microsphere biosensor for thrombin detection,” Sensors 6, 785–795 (2006).
[CrossRef]

J. Zhang, M. Luo, H. Xiao, and J. Dong, “Interferometric study on the adsorption-dependent refractive index of silicalite thin films grown on optical fibers,” Chem. Mater. 18, 4–6 (2006).
[CrossRef]

A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering-gallery modes—part I: basics,” IEEE J. Quantum Electron. 12, 3–14 (2006).
[CrossRef]

2005

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

H. Xiao, J. Zhang, J. Dong, M. Luo, R. Lee, and V. Romero, “Synthesis of MFI zeolite films on optical fibers for detection of chemical vapors,” Opt. Lett. 30, 1270–1272 (2005).
[CrossRef] [PubMed]

2003

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]

M. E. Davis, “Ordered porous materials for emerging applications,” Nature 417, 813–821 (2002).
[CrossRef] [PubMed]

2000

I. Braun, G. Ihlein, F. Laeri, J. U. Nöckel, G. Schulz-Ekloff, F. Schüth, U. Vietze, Ö. Weiss, and D. Wöhrle, “Hexagonal microlasers based on organic dyes in nanoporous crystals,” Appl. Phys. B 70, 335–343 (2000).
[CrossRef]

1999

1997

C. Striebel, K. Hoffmann, and F. Marlow, “The microcrystal prism method for refractive index measurements on zeolite-based nanocomposites,” Micro. Mater. 9, 43–50 (1997).
[CrossRef]

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]

1996

T. Bein, “Synthesis and applications of molecular sieve layers and membranes,” Chem. Mat. 8, 1636–1653 (1996).
[CrossRef]

1991

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, 393–397 (1989).
[CrossRef]

1988

Arnold, S.

Arnord, S.

F. Vollmer and S. Arnord, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Meth. 5, 591–596 (2008).
[CrossRef]

Bein, T.

T. Bein, “Synthesis and applications of molecular sieve layers and membranes,” Chem. Mat. 8, 1636–1653 (1996).
[CrossRef]

Birks, T. A.

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, 393–397 (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]

Braun, I.

I. Braun, G. Ihlein, F. Laeri, J. U. Nöckel, G. Schulz-Ekloff, F. Schüth, U. Vietze, Ö. Weiss, and D. Wöhrle, “Hexagonal microlasers based on organic dyes in nanoporous crystals,” Appl. Phys. B 70, 335–343 (2000).
[CrossRef]

Byer, R. L.

Chao, C. Y.

Cheung, G.

Cui, J. M.

Davis, M. E.

M. E. Davis, “Ordered porous materials for emerging applications,” Nature 417, 813–821 (2002).
[CrossRef] [PubMed]

Dong, C.

L. He, Y. F. Xiao, C. Dong, J. Zhu, V. Gaddam, and L. Yang, “Compensation of thermal refraction effect in high-Q toroidal microresonator by polydimethylsiloxane coating,” Appl. Phys. Lett. 93, 201102 (2008).
[CrossRef]

Dong, C. H.

C. H. Dong, F. W. Sun, C. L. Zou, X. F. Ren, G. C. Guo, and Z. F. Han, “High-Q silica microsphere by poly (methyl methacrylate) coating and modifying,” Appl. Phys. Lett. 96, 061106(2010).
[CrossRef]

Y. Yang, Y. F. Xiao, C. H. Dong, J. M. Cui, Z. F. Han, G. D. Li, and G. C. Guo, “Fiber-taper-coupled zeolite cylindrical microcavity with hexagonal cross section,” Appl. Opt. 46, 7590–7593(2007).
[CrossRef] [PubMed]

Dong, J.

Fan, X.

N. M. Hanumegowda, I. M. White, and X. Fan, “Aqueous mercuric ion detection with microsphere optical ring resonator sensors,” Sens. Actuators B 120, 207–212 (2006).
[CrossRef]

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

Fan, X. D.

H. Y. Zhu, J. D. Suter, I. M. White, and X. D. Fan, “Aptamer based microsphere biosensor for thrombin detection,” Sensors 6, 785–795 (2006).
[CrossRef]

Gaddam, V.

L. He, Y. F. Xiao, C. Dong, J. Zhu, V. Gaddam, and L. Yang, “Compensation of thermal refraction effect in high-Q toroidal microresonator by polydimethylsiloxane coating,” Appl. Phys. Lett. 93, 201102 (2008).
[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]

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality factor and nonlinear properties of optical whispering gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[CrossRef]

Guo, G. C.

C. H. Dong, F. W. Sun, C. L. Zou, X. F. Ren, G. C. Guo, and Z. F. Han, “High-Q silica microsphere by poly (methyl methacrylate) coating and modifying,” Appl. Phys. Lett. 96, 061106(2010).
[CrossRef]

Y. Yang, Y. F. Xiao, C. H. Dong, J. M. Cui, Z. F. Han, G. D. Li, and G. C. Guo, “Fiber-taper-coupled zeolite cylindrical microcavity with hexagonal cross section,” Appl. Opt. 46, 7590–7593(2007).
[CrossRef] [PubMed]

Guo, L. J.

Han, Z. F.

C. H. Dong, F. W. Sun, C. L. Zou, X. F. Ren, G. C. Guo, and Z. F. Han, “High-Q silica microsphere by poly (methyl methacrylate) coating and modifying,” Appl. Phys. Lett. 96, 061106(2010).
[CrossRef]

Y. Yang, Y. F. Xiao, C. H. Dong, J. M. Cui, Z. F. Han, G. D. Li, and G. C. Guo, “Fiber-taper-coupled zeolite cylindrical microcavity with hexagonal cross section,” Appl. Opt. 46, 7590–7593(2007).
[CrossRef] [PubMed]

Hanumegowda, N. M.

N. M. Hanumegowda, I. M. White, and X. Fan, “Aqueous mercuric ion detection with microsphere optical ring resonator sensors,” Sens. Actuators B 120, 207–212 (2006).
[CrossRef]

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

Haus, H. A.

He, L.

L. He, Y. F. Xiao, C. Dong, J. Zhu, V. Gaddam, and L. Yang, “Compensation of thermal refraction effect in high-Q toroidal microresonator by polydimethylsiloxane coating,” Appl. Phys. Lett. 93, 201102 (2008).
[CrossRef]

Hightower, R. L.

Hoffmann, K.

C. Striebel, K. Hoffmann, and F. Marlow, “The microcrystal prism method for refractive index measurements on zeolite-based nanocomposites,” Micro. Mater. 9, 43–50 (1997).
[CrossRef]

Holler, S.

Ihlein, G.

I. Braun, G. Ihlein, F. Laeri, J. U. Nöckel, G. Schulz-Ekloff, F. Schüth, U. Vietze, Ö. Weiss, and D. Wöhrle, “Hexagonal microlasers based on organic dyes in nanoporous crystals,” Appl. Phys. B 70, 335–343 (2000).
[CrossRef]

Ilchenko, V. S.

A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering-gallery modes—part I: basics,” IEEE J. Quantum Electron. 12, 3–14 (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]

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality factor and nonlinear properties of optical whispering gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[CrossRef]

Jacques, F.

Khoshsima, M.

S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28, 272–274 (2003).
[CrossRef] [PubMed]

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]

Knight, J. C.

Laeri, F.

I. Braun, G. Ihlein, F. Laeri, J. U. Nöckel, G. Schulz-Ekloff, F. Schüth, U. Vietze, Ö. Weiss, and D. Wöhrle, “Hexagonal microlasers based on organic dyes in nanoporous crystals,” Appl. Phys. B 70, 335–343 (2000).
[CrossRef]

Laine, J. P.

Lee, R.

Li, G. D.

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]

Little, B. E.

Luo, M.

J. Zhang, M. Luo, H. Xiao, and J. Dong, “Interferometric study on the adsorption-dependent refractive index of silicalite thin films grown on optical fibers,” Chem. Mater. 18, 4–6 (2006).
[CrossRef]

H. Xiao, J. Zhang, J. Dong, M. Luo, R. Lee, and V. Romero, “Synthesis of MFI zeolite films on optical fibers for detection of chemical vapors,” Opt. Lett. 30, 1270–1272 (2005).
[CrossRef] [PubMed]

Marlow, F.

C. Striebel, K. Hoffmann, and F. Marlow, “The microcrystal prism method for refractive index measurements on zeolite-based nanocomposites,” Micro. Mater. 9, 43–50 (1997).
[CrossRef]

Matsko, A. B.

A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering-gallery modes—part I: basics,” IEEE J. Quantum Electron. 12, 3–14 (2006).
[CrossRef]

Nöckel, J. U.

I. Braun, G. Ihlein, F. Laeri, J. U. Nöckel, G. Schulz-Ekloff, F. Schüth, U. Vietze, Ö. Weiss, and D. Wöhrle, “Hexagonal microlasers based on organic dyes in nanoporous crystals,” Appl. Phys. B 70, 335–343 (2000).
[CrossRef]

Patel, B. C.

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

Ren, X. F.

C. H. Dong, F. W. Sun, C. L. Zou, X. F. Ren, G. C. Guo, and Z. F. Han, “High-Q silica microsphere by poly (methyl methacrylate) coating and modifying,” Appl. Phys. Lett. 96, 061106(2010).
[CrossRef]

Richardson, C. B.

Romero, V.

Schiller, S.

Schulz-Ekloff, G.

I. Braun, G. Ihlein, F. Laeri, J. U. Nöckel, G. Schulz-Ekloff, F. Schüth, U. Vietze, Ö. Weiss, and D. Wöhrle, “Hexagonal microlasers based on organic dyes in nanoporous crystals,” Appl. Phys. B 70, 335–343 (2000).
[CrossRef]

Schüth, F.

I. Braun, G. Ihlein, F. Laeri, J. U. Nöckel, G. Schulz-Ekloff, F. Schüth, U. Vietze, Ö. Weiss, and D. Wöhrle, “Hexagonal microlasers based on organic dyes in nanoporous crystals,” Appl. Phys. B 70, 335–343 (2000).
[CrossRef]

Stica, C. J.

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

Striebel, C.

C. Striebel, K. Hoffmann, and F. Marlow, “The microcrystal prism method for refractive index measurements on zeolite-based nanocomposites,” Micro. Mater. 9, 43–50 (1997).
[CrossRef]

Sun, F. W.

C. H. Dong, F. W. Sun, C. L. Zou, X. F. Ren, G. C. Guo, and Z. F. Han, “High-Q silica microsphere by poly (methyl methacrylate) coating and modifying,” Appl. Phys. Lett. 96, 061106(2010).
[CrossRef]

Suter, J. D.

H. Y. Zhu, J. D. Suter, I. M. White, and X. D. Fan, “Aptamer based microsphere biosensor for thrombin detection,” Sensors 6, 785–795 (2006).
[CrossRef]

Tang, X.

Teraoka, I.

Vietze, U.

I. Braun, G. Ihlein, F. Laeri, J. U. Nöckel, G. Schulz-Ekloff, F. Schüth, U. Vietze, Ö. Weiss, and D. Wöhrle, “Hexagonal microlasers based on organic dyes in nanoporous crystals,” Appl. Phys. B 70, 335–343 (2000).
[CrossRef]

Vollmer, F.

F. Vollmer and S. Arnord, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Meth. 5, 591–596 (2008).
[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, 272–274 (2003).
[CrossRef] [PubMed]

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]

Wei, T.

Weiss, Ö.

I. Braun, G. Ihlein, F. Laeri, J. U. Nöckel, G. Schulz-Ekloff, F. Schüth, U. Vietze, Ö. Weiss, and D. Wöhrle, “Hexagonal microlasers based on organic dyes in nanoporous crystals,” Appl. Phys. B 70, 335–343 (2000).
[CrossRef]

White, I. M.

H. Y. Zhu, J. D. Suter, I. M. White, and X. D. Fan, “Aptamer based microsphere biosensor for thrombin detection,” Sensors 6, 785–795 (2006).
[CrossRef]

N. M. Hanumegowda, I. M. White, and X. Fan, “Aqueous mercuric ion detection with microsphere optical ring resonator sensors,” Sens. Actuators B 120, 207–212 (2006).
[CrossRef]

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

Wöhrle, D.

I. Braun, G. Ihlein, F. Laeri, J. U. Nöckel, G. Schulz-Ekloff, F. Schüth, U. Vietze, Ö. Weiss, and D. Wöhrle, “Hexagonal microlasers based on organic dyes in nanoporous crystals,” Appl. Phys. B 70, 335–343 (2000).
[CrossRef]

Xiao, H.

Xiao, Y. F.

L. He, Y. F. Xiao, C. Dong, J. Zhu, V. Gaddam, and L. Yang, “Compensation of thermal refraction effect in high-Q toroidal microresonator by polydimethylsiloxane coating,” Appl. Phys. Lett. 93, 201102 (2008).
[CrossRef]

Y. Yang, Y. F. Xiao, C. H. Dong, J. M. Cui, Z. F. Han, G. D. Li, and G. C. Guo, “Fiber-taper-coupled zeolite cylindrical microcavity with hexagonal cross section,” Appl. Opt. 46, 7590–7593(2007).
[CrossRef] [PubMed]

Yang, L.

L. He, Y. F. Xiao, C. Dong, J. Zhu, V. Gaddam, and L. Yang, “Compensation of thermal refraction effect in high-Q toroidal microresonator by polydimethylsiloxane coating,” Appl. Phys. Lett. 93, 201102 (2008).
[CrossRef]

Yang, Y.

Zhang, J.

Zhu, H. Y.

H. Y. Zhu, J. D. Suter, I. M. White, and X. D. Fan, “Aptamer based microsphere biosensor for thrombin detection,” Sensors 6, 785–795 (2006).
[CrossRef]

Zhu, J.

L. He, Y. F. Xiao, C. Dong, J. Zhu, V. Gaddam, and L. Yang, “Compensation of thermal refraction effect in high-Q toroidal microresonator by polydimethylsiloxane coating,” Appl. Phys. Lett. 93, 201102 (2008).
[CrossRef]

Zou, C. L.

C. H. Dong, F. W. Sun, C. L. Zou, X. F. Ren, G. C. Guo, and Z. F. Han, “High-Q silica microsphere by poly (methyl methacrylate) coating and modifying,” Appl. Phys. Lett. 96, 061106(2010).
[CrossRef]

Appl. Opt.

Appl. Phys. B

I. Braun, G. Ihlein, F. Laeri, J. U. Nöckel, G. Schulz-Ekloff, F. Schüth, U. Vietze, Ö. Weiss, and D. Wöhrle, “Hexagonal microlasers based on organic dyes in nanoporous crystals,” Appl. Phys. B 70, 335–343 (2000).
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IEEE J. Quantum Electron.

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Figures (8)

Fig. 1
Fig. 1

Proposed zeolite-coated microsphere sensor.

Fig. 2
Fig. 2

Sensitivity of TE modes (solid curves) and TM modes (dashed curves) of two orders ( v = 1 , 2) as a function of the zeolite film thickness.

Fig. 3
Fig. 3

Sensitivity for TE modes of v = 1 in microspheres of different radii as a function of the zeolite film thickness.

Fig. 4
Fig. 4

Electric field distribution along the radial direction for TE modes in the microsphere of a 0 = 25 μm coated with zeolite films of various thicknesses. Modes of the (a) first order ( v = 1 ) and (b) second order ( v = 2 ). The dashed and solid curves represent the internal field in the microsphere and the zeolite film, and the dashed-dotted curves represent the evanescent field in the surrounding medium.

Fig. 5
Fig. 5

δ λ R as a function of δ n for TE modes of v = 1 at a 0 = 25 μm with various coating thicknesses. The lines represent δ λ R = δ n × S . The discrete spots represent the actual values of δ λ R calculated by Eqs. (1, 2).

Fig. 6
Fig. 6

Electric field distribution along the radial direction for TE modes of v = 1 before (solid curves) and after (dashed curves) a refractive index change of δ n = 0.06 .

Fig. 7
Fig. 7

Q in for the WGMs of (a) v = 1 and (b) v = 2 as a function of h at λ R 1550 nm . The solid and dashed curves represent the quality factors for the TE and TM modes, respectively.

Fig. 8
Fig. 8

S × Q tot for the WGMs of (a) v = 1 and (b) v = 2 as a function of h at λ R 1550 nm . The solid and dashed curves represent the values for the TE and TM modes, respectively.

Equations (22)

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η s χ l ( n 0 k a 0 ) χ l ( n 0 k a 0 ) = ψ l ( n s k a 0 ) ψ l ( n s k a 0 ) ,
η 0 χ l ( n 0 k a 1 ) χ l ( n 0 k a 1 ) = B l ψ l ( n c l k a 1 ) + χ l ( n c l k a 1 ) B l ψ l ( n c l k a 1 ) + χ l ( n c l k a 1 ) ,
B l = η c l ψ l ( n s k a 0 ) χ l ( n c l k a 0 ) ψ l ( n s k a 0 ) χ l ( n c l k a 0 ) ψ l ( n c l k a 0 ) ψ l ( n s k a 0 ) η c l ψ l ( n c l k a 0 ) ψ l ( n s k a 0 ) , η c l = { n s / n c l , TE modes n c l / n s , TM modes .
S = δ λ R δ n = λ R δ n · δ k k 0 ,
( δ k k 0 ) TE = δ ( n 0 2 ) 0 T 0 2 ( r ) d r 2 0 [ n ( r ) T 0 ( r ) ] 2 d r , TE modes ,
( δ k k 0 ) TM = δ ( n 0 2 ) [ T 0 ( a 0 ) T 0 ( a 0 + ) + n 0 2 k 0 2 0 T 0 2 d r ] 2 n 0 4 k 0 2 0 T 0 2 ( r ) d r , TM modes ,
T ( r ) = { ψ l ( n s k r ) r < a 0 D l χ l ( n 0 k r ) r > a 0 ,
( S 0 ) TE = n 0 λ R I 0 n s 2 I s + n 0 2 I 0 ,
( S 0 ) TM = λ R 2 [ n 0 k 0 I 0 D l 2 χ l ( n 0 k 0 a 0 ) χ l ( n 0 k 0 a 0 ) ] 2 π n 0 2 ( I s + I 0 ) ,
I s = 0 a 0 [ ψ l ( n s k 0 r ) ] 2 d r , I 0 = a 0 [ D l χ l ( n 0 k 0 r ) ] 2 d r .
( δ k k 0 ) TE = δ ( n c l 2 ) a 0 a 1 T 0 2 ( r ) d r 2 0 [ n ( r ) T 0 ( r ) ] 2 d r , TE modes ,
( δ k k 0 ) TM = δ ( n c l 2 ) [ T 0 ( a 1 ) T 0 ( a 1 ) T 0 ( a 0 + ) T 0 ( a 0 ) + n c l 2 k 0 2 a 0 a 1 T 0 2 d r ] 2 n c l 4 k 0 2 0 T 0 2 ( r ) d r , TM modes ,
T ( r ) = { A l ψ l ( n s k r ) r < a 0 B l ψ l ( n c l k r ) + χ l ( n c l k r ) a 0 < r < a 1 C l χ l ( n 0 k r ) r > a 1 ,
A l = B l ψ l ( n c l k a 0 ) + χ l ( n c l k a 0 ) ψ l ( n s k a 0 ) , C l = B l ψ l ( n c l k a 1 ) + χ l ( n c l k a 1 ) χ l ( n 0 k a 1 ) .
S TE = n c l λ R I c l n s 2 I s + n c l 2 I c l + n 0 2 I 0 ,
S TM = λ R 2 [ n s n 0 k 0 I c l + n s C l 2 χ l ( n 0 k 0 a 1 ) χ l ( n 0 k 0 a 1 ) n 0 A l 2 ψ l ( n s k 0 a 0 ) ψ l ( n s k 0 a 0 ) ] 2 π n s n 0 n c l ( I s + I c l + I 0 ) ,
I s = 0 a 0 [ A l ψ l ( n s k 0 r ) ] 2 d r , I 0 = a 1 [ C l χ l ( n 0 k 0 r ) ] 2 d r ,
I c l = a 0 a 1 [ B l ψ l ( n c l k 0 r ) + χ l ( n c l k 0 r ) ] 2 d r .
1 Q tot = 1 Q in + 1 Q ex ,
1 Q in η 1 1 ( Q in ) h = 0 + η 2 1 ( Q in ) h h 0 ,
η 1 = n s 2 I s n s 2 I s + n c l 2 I c l + n 0 2 I 0 , η 2 = n c l 2 I c l n s 2 I s + n c l 2 I c l + n 0 2 I 0 ( TE modes ) ,
η 1 = I s I s + I c l + I 0 , η 2 = I c l I s + I c l + I 0 ( TM modes ) .

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