Abstract

This study performs a detailed theoretical analysis of refractive index (RI) sensors based on whispering gallery modes (WGMs) in liquid core optical ring resonators (LCORRs). Both TE- and TM-polarized WGMs of various orders are considered. The analysis shows that WGMs of higher orders need thicker walls to achieve a near-zero thermal drift, but WGMs of different orders exhibit a similar RI sensing performance at the thermostable wall thicknesses. The RI detection limit is very low at the thermo stable thickness. The theoretical predications should provide a general guidance in the development of LCORR-based thermostable RI sensors.

© 2011 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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2010 (2)

H. Li, Y. Guo, Y. Sun, K. Reddy, and X. Fan, “Analysis of single nanoparticle detection by using 3-dimensionally confined optofluidic ring resonators,” Opt. Express 18, 25081–25088(2010).
[CrossRef] [PubMed]

B. B. Li, Q. Y. Wang, Y. F. Xiao, X. F. Jiang, Y. Li, L. X. Xiao, and Q. H. Cong, “On chip, high-sensitivity thermal sensor based on high-Q polydimethylsiloxane-coated microresonator,” Appl. Phys. Lett. 96, 251109 (2010).
[CrossRef]

2009 (1)

2008 (3)

2007 (6)

2006 (4)

2005 (1)

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]

1998 (1)

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

1996 (1)

1973 (1)

Andrés, M. V.

Arnold, S.

Arnord, S.

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

Bohren, C. F.

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

Chao, C. Y.

Cong, Q. H.

B. B. Li, Q. Y. Wang, Y. F. Xiao, X. F. Jiang, Y. Li, L. X. Xiao, and Q. H. Cong, “On chip, high-sensitivity thermal sensor based on high-Q polydimethylsiloxane-coated microresonator,” Appl. Phys. Lett. 96, 251109 (2010).
[CrossRef]

Corodetsky, M. L.

Dale, P. S.

Díez, A.

Fan, X.

H. Li, Y. Guo, Y. Sun, K. Reddy, and X. Fan, “Analysis of single nanoparticle detection by using 3-dimensionally confined optofluidic ring resonators,” Opt. Express 18, 25081–25088(2010).
[CrossRef] [PubMed]

I. M. White and X. Fan, “On the performance quantification of resonant refractive index sensors,” Opt. Express 16, 1020–1028 (2008).
[CrossRef] [PubMed]

Y. Sun and X. Fan, “Analysis of ring resonators for chemical vapor sensor development,” Opt. Express 16, 10254–10268(2008).
[CrossRef] [PubMed]

H. Zhu, I. M. White, J. D. Suter, P. S. Dale, and X. Fan, “Analysis of biomolecule detection with optofluidic ring resonator sensors,” Opt. Express 15, 9139–9146 (2007).
[CrossRef] [PubMed]

J. D. Suter, I. M. White, H. Zhu, and X. Fan, “Thermal characterization of liquid core optical ring resonator sensors,” Appl. Opt. 46, 389–396 (2007).
[CrossRef] [PubMed]

I. M. White, H. Zhu, J. D. Suter, N. M. Hanumegowda, H. Oveys, M. Zourob, and X. Fan, “Refractometric sensors for lab-on-a-chip based on optical ring resonators,” IEEE Sens. J. 7, 28–35 (2007).
[CrossRef]

I. M. White, H. Oveys, X. Fan, T. L. Smith, and J. Zhang, “Integrated multiplexed biosensors based on liquid core optical ring resonators and antiresonant reflecting optical waveguides,” Appl. Phys. Lett. 89, 191106 (2006).
[CrossRef]

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

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]

Gimeno, B.

Guo, L. J.

Guo, Y.

Hale, G. M.

Hanumegowda, N. M.

I. M. White, H. Zhu, J. D. Suter, N. M. Hanumegowda, H. Oveys, M. Zourob, and X. Fan, “Refractometric sensors for lab-on-a-chip based on optical ring resonators,” IEEE Sens. J. 7, 28–35 (2007).
[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]

Huffman, D. R.

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

Ilchenko, V. S.

Jiang, X. F.

B. B. Li, Q. Y. Wang, Y. F. Xiao, X. F. Jiang, Y. Li, L. X. Xiao, and Q. H. Cong, “On chip, high-sensitivity thermal sensor based on high-Q polydimethylsiloxane-coated microresonator,” Appl. Phys. Lett. 96, 251109 (2010).
[CrossRef]

Li, B. B.

B. B. Li, Q. Y. Wang, Y. F. Xiao, X. F. Jiang, Y. Li, L. X. Xiao, and Q. H. Cong, “On chip, high-sensitivity thermal sensor based on high-Q polydimethylsiloxane-coated microresonator,” Appl. Phys. Lett. 96, 251109 (2010).
[CrossRef]

Li, H.

Li, Y.

B. B. Li, Q. Y. Wang, Y. F. Xiao, X. F. Jiang, Y. Li, L. X. Xiao, and Q. H. Cong, “On chip, high-sensitivity thermal sensor based on high-Q polydimethylsiloxane-coated microresonator,” Appl. Phys. Lett. 96, 251109 (2010).
[CrossRef]

Ling, T.

Oveys, H.

I. M. White, H. Zhu, J. D. Suter, N. M. Hanumegowda, H. Oveys, M. Zourob, and X. Fan, “Refractometric sensors for lab-on-a-chip based on optical ring resonators,” IEEE Sens. J. 7, 28–35 (2007).
[CrossRef]

I. M. White, H. Oveys, X. Fan, T. L. Smith, and J. Zhang, “Integrated multiplexed biosensors based on liquid core optical ring resonators and antiresonant reflecting optical waveguides,” Appl. Phys. Lett. 89, 191106 (2006).
[CrossRef]

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

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]

Querry, M. R.

Reddy, K.

Savchenkov, A. A.

Smith, T. L.

I. M. White, H. Oveys, X. Fan, T. L. Smith, and J. Zhang, “Integrated multiplexed biosensors based on liquid core optical ring resonators and antiresonant reflecting optical waveguides,” Appl. Phys. Lett. 89, 191106 (2006).
[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]

Sun, Y.

Suter, J. D.

Teraoka, I.

Vollmer, F.

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

Wang, Q. Y.

B. B. Li, Q. Y. Wang, Y. F. Xiao, X. F. Jiang, Y. Li, L. X. Xiao, and Q. H. Cong, “On chip, high-sensitivity thermal sensor based on high-Q polydimethylsiloxane-coated microresonator,” Appl. Phys. Lett. 96, 251109 (2010).
[CrossRef]

White, I. M.

I. M. White and X. Fan, “On the performance quantification of resonant refractive index sensors,” Opt. Express 16, 1020–1028 (2008).
[CrossRef] [PubMed]

H. Zhu, I. M. White, J. D. Suter, P. S. Dale, and X. Fan, “Analysis of biomolecule detection with optofluidic ring resonator sensors,” Opt. Express 15, 9139–9146 (2007).
[CrossRef] [PubMed]

J. D. Suter, I. M. White, H. Zhu, and X. Fan, “Thermal characterization of liquid core optical ring resonator sensors,” Appl. Opt. 46, 389–396 (2007).
[CrossRef] [PubMed]

I. M. White, H. Zhu, J. D. Suter, N. M. Hanumegowda, H. Oveys, M. Zourob, and X. Fan, “Refractometric sensors for lab-on-a-chip based on optical ring resonators,” IEEE Sens. J. 7, 28–35 (2007).
[CrossRef]

I. M. White, H. Oveys, X. Fan, T. L. Smith, and J. Zhang, “Integrated multiplexed biosensors based on liquid core optical ring resonators and antiresonant reflecting optical waveguides,” Appl. Phys. Lett. 89, 191106 (2006).
[CrossRef]

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

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]

Xiao, L. X.

B. B. Li, Q. Y. Wang, Y. F. Xiao, X. F. Jiang, Y. Li, L. X. Xiao, and Q. H. Cong, “On chip, high-sensitivity thermal sensor based on high-Q polydimethylsiloxane-coated microresonator,” Appl. Phys. Lett. 96, 251109 (2010).
[CrossRef]

Xiao, Y. F.

B. B. Li, Q. Y. Wang, Y. F. Xiao, X. F. Jiang, Y. Li, L. X. Xiao, and Q. H. Cong, “On chip, high-sensitivity thermal sensor based on high-Q polydimethylsiloxane-coated microresonator,” Appl. Phys. Lett. 96, 251109 (2010).
[CrossRef]

Zamora, V.

Zhang, J.

I. M. White, H. Oveys, X. Fan, T. L. Smith, and J. Zhang, “Integrated multiplexed biosensors based on liquid core optical ring resonators and antiresonant reflecting optical waveguides,” Appl. Phys. Lett. 89, 191106 (2006).
[CrossRef]

Zhu, H.

Zourob, M.

I. M. White, H. Zhu, J. D. Suter, N. M. Hanumegowda, H. Oveys, M. Zourob, and X. Fan, “Refractometric sensors for lab-on-a-chip based on optical ring resonators,” IEEE Sens. J. 7, 28–35 (2007).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (3)

B. B. Li, Q. Y. Wang, Y. F. Xiao, X. F. Jiang, Y. Li, L. X. Xiao, and Q. H. Cong, “On chip, high-sensitivity thermal sensor based on high-Q polydimethylsiloxane-coated microresonator,” Appl. Phys. Lett. 96, 251109 (2010).
[CrossRef]

I. M. White, H. Oveys, X. Fan, T. L. Smith, and J. Zhang, “Integrated multiplexed biosensors based on liquid core optical ring resonators and antiresonant reflecting optical waveguides,” Appl. Phys. Lett. 89, 191106 (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]

IEEE Sens. J. (1)

I. M. White, H. Zhu, J. D. Suter, N. M. Hanumegowda, H. Oveys, M. Zourob, and X. Fan, “Refractometric sensors for lab-on-a-chip based on optical ring resonators,” IEEE Sens. J. 7, 28–35 (2007).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (3)

Nat. Methods (1)

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

Opt. Express (6)

Opt. Lett. (2)

Other (1)

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

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Figures (9)

Fig. 1
Fig. 1

Schematic structure of an LCORR with an inner radius of R 1 and outer radius of R 2 . n 1 , n 2 , and n 3 are the refractive indices of the liquid core, ring wall, and surrounding medium, respectively.

Fig. 2
Fig. 2

δ λ R / δ T for TM modes (solid curves) and TE modes (dashed curves) of the first three orders as a function of the LCORR wall thickness h 0 . The symbols denote δ λ R / δ T = 0 for the TM l = 1 (filled cirlces), TE l = 1 (open circles), TM l = 2 (filled diamonds), TE l = 2 (open diamonds), TM l = 3 (filled stars), and TE l = 3 (open stars) modes, respectively.

Fig. 3
Fig. 3

Resonant wavelength shift δ λ R as a function of the temperature change δ T for the TM l = 1 mode at various LCORR wall thicknesses.

Fig. 4
Fig. 4

RI sensitivity S for TM modes (solid curves) and TE modes (dashed curves) of the first three orders as a function of the LCORR wall thickness h 0 . The symbols denote δ λ R / δ T = 0 for the TM l = 1 (filled circles), TE l = 1 (open circles), TM l = 2 (filled diamonds), TE l = 2 (open diamonds), TM l = 3 (filled stars), and TE l = 3 (open stars) modes, respectively.

Fig. 5
Fig. 5

Resonant wavelength shift δ λ R as a function of the RI change δ n 1 for the TM l = 1 mode at various LCORR wall thicknesses.

Fig. 6
Fig. 6

Q factors for TM modes (solid curves) and TE modes (dashed curves) of the first three orders as a function of the LCORR wall thickness h 0 . The symbols denote δ λ R / δ T = 0 for the TM l = 1 (filled circles), TE l = 1 (open circles), TM l = 2 (filled diamonds), TE l = 2 (open diamonds), TM l = 3 (filled stars), and TE l = 3 (open stars) modes, respectively.

Fig. 7
Fig. 7

1 / ( S × Q ) for TM modes (solid curves) and TE modes (dashed curves) of the first three orders as a function of the LCORR wall thickness h 0 . The symbols denote δ λ R / δ T = 0 for the TM l = 1 (filled circles), TE l = 1 (open circles), TM l = 2 (filled diamonds), TE l = 2 (open diamonds), TM l = 3 (filled stars), and TE l = 3 (open stars) modes, respectively.

Fig. 8
Fig. 8

Detection limit of the first-order TM mode (solid curves) and first-order TE mode (dashed curves) as a function of the LCORR wall thickness h 0 for a temperature fluctuation of δ T = 0 , 0.05, 0.5, and 1 K , respectively.

Fig. 9
Fig. 9

Detection limit at λ R 780 nm as a function of the wall thickness h 0 (a) for the WGMs of the first three orders at δ T = 0 K and (b) for the third-order TM mode at δ T = 0 and 0.05 K , respectively.

Equations (19)

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N 0 H m ( 1 ) ( k 0 n 3 R 2 ) H m ( 1 ) ( k 0 n 3 R 2 ) = B m J m ( k 0 n 2 R 2 ) + H m ( 1 ) ( k 0 n 2 R 2 ) B m J m ( k 0 n 2 R 2 ) + H m ( 1 ) ( k 0 n 2 R 2 ) , N 0 = { n 2 / n 3 , TE modes n 3 / n 2 , TM modes ,
B m = N 1 J m ( k 0 n 1 R 1 ) H m ( 1 ) ( k 0 n 2 R 1 ) J m ( k 0 n 1 R 1 ) H m ( 1 ) ( k 0 n 2 R 1 ) J m ( k 0 n 1 R 1 ) J m ( k 0 n 2 R 1 ) N 1 J m ( k 0 n 1 R 1 ) J m ( k 0 n 2 R 1 ) , N 0 = { n 1 / n 2 , TE modes n 2 / n 1 , TM modes .
δ λ R δ T = λ R ( 1 n eff d n eff d T + α ) ,
δ λ R δ T λ R ( i = 1 3 η i ( d n i / d T ) i = 1 3 ( η i n i ) + α ) ,
η i = I i I 1 + I 2 + I 3 , i = 1 , 2 , 3 ( TE modes ) ,
η i = n i 2 I i n 1 2 I 1 + n 2 2 I 2 + n 3 2 I 3 , i = 1 , 2 , 3 ( TM modes ) ,
I 1 = 0 R 1 | A m J m ( k 0 n 1 r ) | 2 d r , I 3 = R 2 | C m H m ( 1 ) ( k 0 n 3 r ) | 2 d r , I 2 = R 1 R 2 | B m J m ( k 0 n 2 r ) + H m ( 1 ) ( k 0 n 2 r ) | 2 d r .
A m = B m J m ( k 0 n 2 R 1 ) + H m ( 1 ) ( k 0 n 2 R 1 ) J m ( k 0 n 1 R 1 ) , C m = B m J m ( k 0 n 2 R 2 ) + H m ( 1 ) ( k 0 n 2 R 2 ) H m ( 1 ) ( k 0 n 3 R 2 ) .
( δ λ R δ T ) TE λ R ( i = 1 3 I i ( d n i / d T ) i = 1 3 ( I i n i ) + α ) ,
( δ λ R δ T ) TM λ R ( i = 1 3 I i n i 2 ( d n i / d T ) i = 1 3 ( I i n i 3 ) + α ) .
S = δ λ R δ n 1 = λ R δ n 1 · δ k k 0 ,
( δ k k 0 ) TE = δ ( n 1 2 ) [ T 0 ( R 1 ) T 0 ( R 1 ) + n 1 2 k 0 2 I 1 ] 2 n 1 4 k 0 2 i = 1 3 I i , TE modes ,
( δ k k 0 ) TM = δ ( n 1 2 ) I 1 2 i = 1 3 n i 2 I i , TM modes ,
T ( r ) = { A m J m ( k 0 n 1 r ) r < R 1 B m J m ( k 0 n 2 r ) + H m ( 1 ) ( k 0 n 2 r ) R 1 < r < R 2 C m H m ( 1 ) ( k 0 n 3 r ) r > R 2 .
S TM = n 1 λ R I 1 i = 1 3 n i 2 I i = λ R n 1 η 1 ,
S TE = λ R 2 [ k 0 n 1 I 1 + A m 2 J m ( k 0 n 1 R 1 ) J m ( k 0 n 1 R 1 ) ] 2 π n 1 2 i = 1 3 I i = λ R n 1 η 1 + A m 2 λ R 2 J m ( k 0 n 1 R 1 ) J m ( k 0 n 1 R 1 ) 2 π n 1 2 i = 1 3 I i .
1 Q 1 Q sca + 1 ( Q abs ) wall + 1 ( Q abs ) core ,
1 S TM × Q n 1 η 1 λ R × η 1 λ R σ 2 π n 1 = σ 2 π .
DL λ R 100 × 1 S × Q + ( δ λ R δ T ) × δ T S .

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