Abstract

We present a theoretical study of the sensing properties of silica microtube resonator sensors. By solving the Maxwell’s equations to obtain the electric field distribution in a cylindrical coordinate system and by using the perturbation method, we have analyzed in detail the sensing properties of silica microtube resonator sensors, which include the bulk refractive index, surface, and absorption sensing sensitivities with different radial order resonant modes. We found that a type of resonant mode, different from the evanescent modes commonly employed in previous investigations, is very promising for sensing changes of the refractive index. Furthermore, the resonant mode with high electric field at the inner boundary of the microtube is ideal for surface sensing applications. The high Q factor resonant mode is useful for the absorption sensing application. These sensing properties analyzed by using the perturbation method match very well with the results from the Mie scattering method. Finally, the limitation of the perturbation method is discussed.

© 2009 Optical Society of America

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  1. I. M. White, H. Oveys, and X. D. Fan, “Liquid-core optical ring-resonator sensors,” Opt. Lett. 31, 1319-1321 (2006).
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    [CrossRef] [PubMed]
  3. H. Y. Zhu, I. M. White, J. D. Suter, M. Zourob, and X. D. Fan, “Opto-fluidic micro-ring resonator for sensitive label-free viral detection,” Analyst (Cambridge, U.K.) 133, 356-360 (2008).
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  5. I. M. White, J. D. Suter, H. Oveys, and X. D. Fan, “Universal coupling between metal-clad waveguide and optical ring resonators,” Opt. Express 15, 646-651 (2007).
    [CrossRef] [PubMed]
  6. 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, 17424-17432 (2007).
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  7. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
    [CrossRef]
  8. 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, 1434-1441 (2006).
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  9. P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, 1990).
    [CrossRef]
  10. H. J. Moon and K. An, “Interferential coupling effect on the whispering-gallery mode lasing in a double-layered microcylinder,” Appl. Phys. Lett. 80, 3250-3252 (2002).
    [CrossRef]
  11. 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]
  12. X. D. Fan, I. M. White, H. Y. Zhou, J. D. Suter, and H. Oveys, “Overview of novel integrated optical ring resonator bio/chemical sensors,” Proc. SPIE 6452, 64520M (2007).
    [CrossRef]

2008 (1)

H. Y. Zhu, I. M. White, J. D. Suter, M. Zourob, and X. D. Fan, “Opto-fluidic micro-ring resonator for sensitive label-free viral detection,” Analyst (Cambridge, U.K.) 133, 356-360 (2008).
[CrossRef]

2007 (4)

2006 (3)

2002 (1)

H. J. Moon and K. An, “Interferential coupling effect on the whispering-gallery mode lasing in a double-layered microcylinder,” Appl. Phys. Lett. 80, 3250-3252 (2002).
[CrossRef]

2001 (1)

An, K.

H. J. Moon and K. An, “Interferential coupling effect on the whispering-gallery mode lasing in a double-layered microcylinder,” Appl. Phys. Lett. 80, 3250-3252 (2002).
[CrossRef]

Arnold, S.

Barber, P. W.

P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, 1990).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
[CrossRef]

Boyd, R. W.

Fan, X. D.

H. Y. Zhu, I. M. White, J. D. Suter, M. Zourob, and X. D. Fan, “Opto-fluidic micro-ring resonator for sensitive label-free viral detection,” Analyst (Cambridge, U.K.) 133, 356-360 (2008).
[CrossRef]

I. M. White, J. D. Suter, H. Oveys, and X. D. Fan, “Universal coupling between metal-clad waveguide and optical ring resonators,” Opt. Express 15, 646-651 (2007).
[CrossRef] [PubMed]

I. M. White, J. Gohring, and X. D. Fan, “SERS-based detection in an optofluidic ring resonator platform,” Opt. Express 15, 17433-17442 (2007).
[CrossRef] [PubMed]

X. D. Fan, I. M. White, H. Y. Zhou, J. D. Suter, and H. Oveys, “Overview of novel integrated optical ring resonator bio/chemical sensors,” Proc. SPIE 6452, 64520M (2007).
[CrossRef]

I. M. White, H. Oveys, and X. D. Fan, “Liquid-core optical ring-resonator sensors,” Opt. Lett. 31, 1319-1321 (2006).
[CrossRef] [PubMed]

Gohring, J.

Guo, L. J.

Heebner, J. E.

Hill, S. C.

P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, 1990).
[CrossRef]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
[CrossRef]

Ling, T.

Moon, H. J.

H. J. Moon and K. An, “Interferential coupling effect on the whispering-gallery mode lasing in a double-layered microcylinder,” Appl. Phys. Lett. 80, 3250-3252 (2002).
[CrossRef]

Oveys, H.

Suter, J. D.

H. Y. Zhu, I. M. White, J. D. Suter, M. Zourob, and X. D. Fan, “Opto-fluidic micro-ring resonator for sensitive label-free viral detection,” Analyst (Cambridge, U.K.) 133, 356-360 (2008).
[CrossRef]

I. M. White, J. D. Suter, H. Oveys, and X. D. Fan, “Universal coupling between metal-clad waveguide and optical ring resonators,” Opt. Express 15, 646-651 (2007).
[CrossRef] [PubMed]

X. D. Fan, I. M. White, H. Y. Zhou, J. D. Suter, and H. Oveys, “Overview of novel integrated optical ring resonator bio/chemical sensors,” Proc. SPIE 6452, 64520M (2007).
[CrossRef]

Teraoka, I.

White, I. M.

H. Y. Zhu, I. M. White, J. D. Suter, M. Zourob, and X. D. Fan, “Opto-fluidic micro-ring resonator for sensitive label-free viral detection,” Analyst (Cambridge, U.K.) 133, 356-360 (2008).
[CrossRef]

I. M. White, J. Gohring, and X. D. Fan, “SERS-based detection in an optofluidic ring resonator platform,” Opt. Express 15, 17433-17442 (2007).
[CrossRef] [PubMed]

I. M. White, J. D. Suter, H. Oveys, and X. D. Fan, “Universal coupling between metal-clad waveguide and optical ring resonators,” Opt. Express 15, 646-651 (2007).
[CrossRef] [PubMed]

X. D. Fan, I. M. White, H. Y. Zhou, J. D. Suter, and H. Oveys, “Overview of novel integrated optical ring resonator bio/chemical sensors,” Proc. SPIE 6452, 64520M (2007).
[CrossRef]

I. M. White, H. Oveys, and X. D. Fan, “Liquid-core optical ring-resonator sensors,” Opt. Lett. 31, 1319-1321 (2006).
[CrossRef] [PubMed]

Zhou, H. Y.

X. D. Fan, I. M. White, H. Y. Zhou, J. D. Suter, and H. Oveys, “Overview of novel integrated optical ring resonator bio/chemical sensors,” Proc. SPIE 6452, 64520M (2007).
[CrossRef]

Zhu, H. Y.

H. Y. Zhu, I. M. White, J. D. Suter, M. Zourob, and X. D. Fan, “Opto-fluidic micro-ring resonator for sensitive label-free viral detection,” Analyst (Cambridge, U.K.) 133, 356-360 (2008).
[CrossRef]

Zourob, M.

H. Y. Zhu, I. M. White, J. D. Suter, M. Zourob, and X. D. Fan, “Opto-fluidic micro-ring resonator for sensitive label-free viral detection,” Analyst (Cambridge, U.K.) 133, 356-360 (2008).
[CrossRef]

Analyst (Cambridge, U.K.) (1)

H. Y. Zhu, I. M. White, J. D. Suter, M. Zourob, and X. D. Fan, “Opto-fluidic micro-ring resonator for sensitive label-free viral detection,” Analyst (Cambridge, U.K.) 133, 356-360 (2008).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

H. J. Moon and K. An, “Interferential coupling effect on the whispering-gallery mode lasing in a double-layered microcylinder,” Appl. Phys. Lett. 80, 3250-3252 (2002).
[CrossRef]

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

Opt. Express (3)

Opt. Lett. (1)

Proc. SPIE (1)

X. D. Fan, I. M. White, H. Y. Zhou, J. D. Suter, and H. Oveys, “Overview of novel integrated optical ring resonator bio/chemical sensors,” Proc. SPIE 6452, 64520M (2007).
[CrossRef]

Other (2)

P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, 1990).
[CrossRef]

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Schematic of the silica microtube resonator. n 1 , n 2 , and n 3 are the refractive indices of the liquid, the silica wall, and the air, and R 1 and R 2 are the inner and outer radius of the microtube, respectively.

Fig. 2
Fig. 2

Typical evanescent mode ( E 700 35 ) and nonevanescent mode ( E 700 37 ) field distribution in the silica microtube resonator.

Fig. 3
Fig. 3

Simulated bulk refractive index sensing sensitivity of different radial order modes with the same azimuthal number M = 700 by the perturbation and Mie scattering methods.

Fig. 4
Fig. 4

Simulated surface sensing sensitivity of different radial order modes with the same azimuthal number M = 700 by the perturbation and Mie scattering methods. The biofilm’s refractive index is assumed to be 1.46.

Fig. 5
Fig. 5

Simulated absorption sensing sensitivity of different radial order modes with same azimuthal number M = 700 by the perturbation and Mie scattering methods. The absorption coefficient of liquid is assumed to be α = 0.327 cm 1 .

Fig. 6
Fig. 6

Simulation showing the difference in resonance peak shift between the Mie scattering method and the perturbation method as a function of bulk refractive index change for evanescent modes E 700 32 , E 700 33 , E 700 34 , E 700 35 .

Equations (33)

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E z = { B 1 J m ( k 0 n 1 r ) exp [ i ( m θ ω t ) ] 0 r < R 1 B 2 J m ( k 0 n 2 r ) + [ B 3 N m ( k 0 n 2 r ) ] exp [ i ( m θ ω t ) ] R 1 r < R 2 B 4 H m ( 1 ) ( k 0 n 3 r ) exp [ i ( m θ ω t ) ] R 2 r < + } ,
E z 1 ( R 1 ) = E z 2 ( R 1 ) ,
E z 1 r r = R 1 = E z 2 r r = R 1 .
B 1 J m ( k 0 n 1 R 1 ) = B 2 J m ( k 0 n 2 R 1 ) + B 3 N m ( k 0 n 2 R 1 ) ,
B 1 n 1 J m ( k 0 n 1 R 1 ) = B 2 n 2 J m ( k 0 n 2 R 1 ) + B 3 n 2 N m ( k 0 n 2 R 1 ) .
E z 2 ( R 2 ) = E z 3 ( R 2 ) ,
E z 2 r r = R 2 = E z 3 r r = R 2 .
B 4 H m ( 1 ) ( k 0 n 3 R 2 ) = B 2 J m ( k 0 n 2 R 2 ) + B 3 N m ( k 0 n 2 R 2 ) ,
B 4 n 3 H m ( 1 ) ( k 0 n 3 R 2 ) = B 2 n 2 J m ( k 0 n 2 R 2 ) + B 3 n 2 N m ( k 0 n 2 R 2 ) .
J m ( k 0 n 1 R 1 ) n 1 J m ( k 0 n 1 R 1 ) = ( B 2 B 3 ) J m ( k 0 n 2 R 1 ) + N m ( k 0 n 2 R 1 ) ( B 2 B 3 ) n 2 J m ( k 0 n 2 R 1 ) + n 2 N m ( k 0 n 2 R 1 ) ,
H m ( 1 ) ( k 0 n 1 R 2 ) n 3 H m ( 1 ) ( k 0 n 1 R 2 ) = ( B 2 B 3 ) J m ( k 0 n 2 R 2 ) + N m ( k 0 n 2 R 2 ) ( B 2 B 3 ) n 2 J m ( k 0 n 2 R 2 ) + n 2 N m ( k 0 n 2 R 2 ) .
B 2 B 3 = n 2 H m ( 1 ) ( k 0 n 1 R 2 ) N m ( k 0 n 2 R 2 ) n 3 H m ( 1 ) ( k 0 n 1 R 2 ) N m ( k 0 n 2 R 2 ) n 3 H m ( 1 ) ( k 0 n 1 R 2 ) J m ( k 0 n 2 R 2 ) n 2 H m ( 1 ) ( k 0 n 1 R 2 ) J m ( k 0 n 2 R 2 ) .
B 1 = B 3 ( C J m ( k 0 n 2 R 1 ) + N m ( k 0 n 2 R 1 ) J m ( k 0 n 1 R 1 ) ) = B 3 A m 1 ,
B 4 = B 3 ( C J m ( k 0 n 2 R 2 ) + N m ( k 0 n 2 R 2 ) H m ( 1 ) ( k 0 n 3 R 2 ) ) = B 3 A m 3 .
E z = { B 3 { A m 1 J m ( k 0 n 1 r ) exp [ i ( m θ ω t ) ] } 0 r < R 1 B 3 { [ C J m ( k 0 n 2 r ) + N m ( k 0 n 2 r ) ] exp [ i ( m θ ω t ) ] } R 1 r < R 2 B 3 { A m 3 H m ( 1 ) ( k 0 n 3 r ) exp [ i ( m θ ω t ) ] } R 2 r < + } ,
A m 1 = C J m ( k 0 n 2 R 1 ) + N m ( k 0 n 2 R 1 ) J m ( k 0 n 1 R 1 ) ,
A m 3 = C J m ( k 0 n 2 R 2 ) + N m ( k 0 n 2 R 2 ) H m ( 1 ) ( k 0 n 3 R 2 ) .
S bulk = δ λ δ n = λ n 1 v 1 E z 2 d r v n 2 E z 2 d r ,
× × E 0 = k 0 2 ε E 0 ,
× × E 1 = k 1 2 ε 1 E 1 ,
v E 0 * × × E 1 d r = k 1 2 v E 0 * ε E 1 d r + k 1 2 v 1 E 0 * ( ε film ε liquid ) E 1 d r ,
v E 0 * × × E 1 d r = v E 1 × × E 0 * d r = k 0 2 v E 1 ε E 0 * d r ,
( k 0 2 k 1 2 ) v E 1 ε E 0 * d r = k 1 2 v 1 E 0 * ( ε film ε liquid ) E 1 d r .
δ λ λ = v 1 E 0 * ( ε film ε liquid ) E 1 d r 2 v E 1 ε E 0 * d r E R 1 2 ( ε film ε liquid ) π R 1 T 0 2 π ( 0 + E 0 ε E 0 * r d r ) d θ ,
S surface = δ λ T = λ E R 1 2 ( ε film ε liquid ) π R 1 0 2 π ( 0 + E 0 ε E 0 * r d r ) d θ .
× × E 2 = ( k 2 i k 2 ) 2 ε 2 E 2 ,
× × E 3 = ( k 2 i k 3 ) 2 ε 3 E 3 ,
( k 2 i k 2 ) 2 ε 2 E 2 E 2 * d r = ( k 2 i k 3 ) 2 ε 3 E 3 E 3 * d r .
k 3 k 2 k 2 = n 2 v 1 E 2 E 2 * d r v ε 2 E 2 E 2 * d r ( κ 3 κ 2 ) ,
k 2 κ 3 = k 3 κ 2 .
Γ = 2 n 2 v 1 E 2 E 2 * d r v ε 2 E 2 E 2 * d r .
Q = 1 κ Γ = 4 π λ α Γ ,
S abs = δ Q δ α = 4 π λ α 2 Γ = Q α .

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