Abstract

In an effort to improve and simplify refractive index sensors, we identified a basic operation mode at the critical angle. Sensitivity to the refractive index is higher than in standard surface plasmon resonance sensors, and we have been able to demonstrate analytically that it is virtually an unbounded value. We describe this approach and submit a complete analytical study demonstrating its unlimited sensing power. To test the approach, we constructed an economical and basic sensor. Despite its simplicity, we demonstrated the discrimination capability to be of the order of 106, as far as we know close to the best sensitivity ever recorded. This detection method is generally applicable to any optical system and may pave the way for the next generation of optical sensing devices.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  11. R. Micheletto, K. Hamamoto, S. Kawai, and Y. Kawakami, Sens. Actuators A 119, 283 (2005).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2005 (1)

R. Micheletto, K. Hamamoto, S. Kawai, and Y. Kawakami, Sens. Actuators A 119, 283 (2005).
[CrossRef]

2003 (3)

Y. Xinglong, W. Dingxin, and Y. Zibo, Sens. Actuators B 91, 285 (2003).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

Q. Zhan and J. R. Leger, J. Microsc. 210, 214 (2003).
[CrossRef] [PubMed]

2002 (1)

K. Kurihara, K. Nakamura, and K. Suzuki, Sens. Actuators B 86, 49 (2002).
[CrossRef]

1997 (1)

1996 (1)

S. G. Nelson, K. S. Johnston, and S. S. Yee, Sens. Actuators B 35-36, 187 (1996).
[CrossRef]

1994 (2)

W. J. H. Bender and R. E. Dessy, Anal. Chem. 66, 963 (1994).
[CrossRef]

R. Garabedian, C. Gonzales, J. Richards, A. Knoesen, R. Spencer, S. D. Collins, R. L. Smith, Sens. Actuators, A 43, 202 (1994).
[CrossRef]

1993 (2)

M. Malmqvist, Nature 361, 186 (1993).
[CrossRef] [PubMed]

R. C. Jorgenson and S. S. Yee, Sens. Actuators B 12, 213 (1993).
[CrossRef]

1988 (1)

1971 (1)

E. Kretschmann and H. Raether, Z. Phys. 241, 313 (1971).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

Bender, W. J.

W. J. H. Bender and R. E. Dessy, Anal. Chem. 66, 963 (1994).
[CrossRef]

Collins, S. D.

R. Garabedian, C. Gonzales, J. Richards, A. Knoesen, R. Spencer, S. D. Collins, R. L. Smith, Sens. Actuators, A 43, 202 (1994).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

Dessy, R. E.

W. J. H. Bender and R. E. Dessy, Anal. Chem. 66, 963 (1994).
[CrossRef]

Dingxin, W.

Y. Xinglong, W. Dingxin, and Y. Zibo, Sens. Actuators B 91, 285 (2003).
[CrossRef]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

Garabedian, R.

R. Garabedian, C. Gonzales, J. Richards, A. Knoesen, R. Spencer, S. D. Collins, R. L. Smith, Sens. Actuators, A 43, 202 (1994).
[CrossRef]

Giles, I. P.

Gonzales, C.

R. Garabedian, C. Gonzales, J. Richards, A. Knoesen, R. Spencer, S. D. Collins, R. L. Smith, Sens. Actuators, A 43, 202 (1994).
[CrossRef]

Hamamoto, K.

R. Micheletto, K. Hamamoto, S. Kawai, and Y. Kawakami, Sens. Actuators A 119, 283 (2005).
[CrossRef]

Homola, J.

Johnston, K. S.

S. G. Nelson, K. S. Johnston, and S. S. Yee, Sens. Actuators B 35-36, 187 (1996).
[CrossRef]

Jorgenson, R. C.

R. C. Jorgenson and S. S. Yee, Sens. Actuators B 12, 213 (1993).
[CrossRef]

Kawai, S.

R. Micheletto, K. Hamamoto, S. Kawai, and Y. Kawakami, Sens. Actuators A 119, 283 (2005).
[CrossRef]

Kawakami, Y.

R. Micheletto, K. Hamamoto, S. Kawai, and Y. Kawakami, Sens. Actuators A 119, 283 (2005).
[CrossRef]

Knoesen, A.

R. Garabedian, C. Gonzales, J. Richards, A. Knoesen, R. Spencer, S. D. Collins, R. L. Smith, Sens. Actuators, A 43, 202 (1994).
[CrossRef]

Kretschmann, E.

E. Kretschmann and H. Raether, Z. Phys. 241, 313 (1971).
[CrossRef]

Kurihara, K.

K. Kurihara, K. Nakamura, and K. Suzuki, Sens. Actuators B 86, 49 (2002).
[CrossRef]

Leger, J. R.

Q. Zhan and J. R. Leger, J. Microsc. 210, 214 (2003).
[CrossRef] [PubMed]

Malmqvist, M.

M. Malmqvist, Nature 361, 186 (1993).
[CrossRef] [PubMed]

Micheletto, R.

R. Micheletto, K. Hamamoto, S. Kawai, and Y. Kawakami, Sens. Actuators A 119, 283 (2005).
[CrossRef]

Nakamura, K.

K. Kurihara, K. Nakamura, and K. Suzuki, Sens. Actuators B 86, 49 (2002).
[CrossRef]

Nelson, S. G.

S. G. Nelson, K. S. Johnston, and S. S. Yee, Sens. Actuators B 35-36, 187 (1996).
[CrossRef]

Raether, H.

E. Kretschmann and H. Raether, Z. Phys. 241, 313 (1971).
[CrossRef]

Richards, J.

R. Garabedian, C. Gonzales, J. Richards, A. Knoesen, R. Spencer, S. D. Collins, R. L. Smith, Sens. Actuators, A 43, 202 (1994).
[CrossRef]

Smith, R. L.

R. Garabedian, C. Gonzales, J. Richards, A. Knoesen, R. Spencer, S. D. Collins, R. L. Smith, Sens. Actuators, A 43, 202 (1994).
[CrossRef]

Spencer, R.

R. Garabedian, C. Gonzales, J. Richards, A. Knoesen, R. Spencer, S. D. Collins, R. L. Smith, Sens. Actuators, A 43, 202 (1994).
[CrossRef]

Suzuki, K.

K. Kurihara, K. Nakamura, and K. Suzuki, Sens. Actuators B 86, 49 (2002).
[CrossRef]

Xinglong, Y.

Y. Xinglong, W. Dingxin, and Y. Zibo, Sens. Actuators B 91, 285 (2003).
[CrossRef]

Yee, S. S.

S. G. Nelson, K. S. Johnston, and S. S. Yee, Sens. Actuators B 35-36, 187 (1996).
[CrossRef]

R. C. Jorgenson and S. S. Yee, Sens. Actuators B 12, 213 (1993).
[CrossRef]

Zervas, M. N.

Zhan, Q.

Q. Zhan and J. R. Leger, J. Microsc. 210, 214 (2003).
[CrossRef] [PubMed]

Zibo, Y.

Y. Xinglong, W. Dingxin, and Y. Zibo, Sens. Actuators B 91, 285 (2003).
[CrossRef]

Anal. Chem. (1)

W. J. H. Bender and R. E. Dessy, Anal. Chem. 66, 963 (1994).
[CrossRef]

J. Microsc. (1)

Q. Zhan and J. R. Leger, J. Microsc. 210, 214 (2003).
[CrossRef] [PubMed]

Nature (2)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

M. Malmqvist, Nature 361, 186 (1993).
[CrossRef] [PubMed]

Opt. Lett. (2)

Sens. Actuators A (1)

R. Micheletto, K. Hamamoto, S. Kawai, and Y. Kawakami, Sens. Actuators A 119, 283 (2005).
[CrossRef]

Sens. Actuators B (4)

Y. Xinglong, W. Dingxin, and Y. Zibo, Sens. Actuators B 91, 285 (2003).
[CrossRef]

S. G. Nelson, K. S. Johnston, and S. S. Yee, Sens. Actuators B 35-36, 187 (1996).
[CrossRef]

R. C. Jorgenson and S. S. Yee, Sens. Actuators B 12, 213 (1993).
[CrossRef]

K. Kurihara, K. Nakamura, and K. Suzuki, Sens. Actuators B 86, 49 (2002).
[CrossRef]

Sens. Actuators, A (1)

R. Garabedian, C. Gonzales, J. Richards, A. Knoesen, R. Spencer, S. D. Collins, R. L. Smith, Sens. Actuators, A 43, 202 (1994).
[CrossRef]

Z. Phys. (1)

E. Kretschmann and H. Raether, Z. Phys. 241, 313 (1971).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

(Color online) Sensitivity curve for a Kretschmann three-layer system. Calculations include the SPR effect as a comparison between the critical angle and SPR sensitivity peaks. Curve R (gray background) is the reflectivity in relation to the angle α (radians). Curve d R is the numerical derivative of R, where a very sharp and narrow peak is evident at the critical angle. These plots are obtained from a three-layer Fresnel planar model under illumination of λ = 670 nm . Materials are glass ( n p = 1.52 ) , a gold ( ω p = 1.3610 16 , ω t = 1.4510 14 , ϵ i = 9.75 ) layer d = 52 nm thick, and water ( n s = 1.33 ) or air ( n s = 1 ) as sample materials. It is noticeable how the SPR peak deteriorates with an increase of the refractive index. The sensitivity peak at α c appears extremely sharp and unaltered.

Fig. 2
Fig. 2

Plot of the analytical expressions for the sensitivity curve d R d k x ; h ( u ¯ ) and p ( u ¯ ) are nonzero functions; g ( u ¯ ) is null at the critical angle α c . On the gray background, d R d k x , Eq. (2), is calculated for g ( u ¯ ) = 1 and p ( u ¯ ) = 1 to show their relevance to the sensing effect.

Fig. 3
Fig. 3

(Color online) Core of the test device. (a) Planar glass is immersed in a flow cell with the analyte liquid. Light is applied at incidence angle t from a χ = 45 ° surface. (b) Three-dimensional sketch of the planar glass.

Fig. 4
Fig. 4

(Color online) The reflectivity curve depends on the number of reflections, indicated as 1, 20, 40, and 60.

Fig. 5
Fig. 5

Calculated sensitivity of the planar system in Fig. 3. The number of reflections depends on the length of the device. This plot shows the extreme sharpness of the critical angle peak and reveals the potential for sensing. Incidence angle t as defined in Fig. 3. the axis units are degrees × 100 , as we plot the index of an array that has a 0.01° increment.

Fig. 6
Fig. 6

(Color online) Test of sensitivity measured as a response difference between water and methanol. A sharp sensitivity peak at the critical angle is evident; the theoretical curve is also shown. The angle t is defined in Fig. 3.

Fig. 7
Fig. 7

Experimental data with a highly diluted ethanol sample. The theoretical behavior is represented by the dashed curve. The top curve is pure water at (0% ethanol). Less reflective curves are solutions of water and ethanol, 0.2%, 0.4%, 0.6%, 0.8%, and 1% in volume concentration. The A/D converter is 8 bit; data angular resolution is 0.1°, corresponding to the degrees × 10 horizontal scale.

Fig. 8
Fig. 8

(Color online) Response in relation to the sample index of refraction. Data are taken at fixed incidence angle t = 21.7 ° as indicated by the gray box in Fig. 7.

Equations (6)

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

R = r p m + r m s exp ( i 2 k m z d ) 1 + r p m r m s exp ( i 2 k m z d ) 2 ,
d R d k x = h ( u ¯ ) g ( u ¯ ) p ( u ¯ ) .
h ( u ¯ ) = 4 ϵ m ϵ p [ ϵ p k m z ( ϵ s e + k m z ϵ m e + + k s z ) + ϵ m k p z ( ϵ s e k m z + ϵ m e + k s z ) ] { e 4 i d k m z ϵ m p k s z ( ϵ s k m z ϵ m k s z ) 2 ϵ m p k s z ( ϵ s k m z + ϵ m k s z ) 2 + 4 e 2 i d k m z k m z k p z 2 × [ ϵ m ϵ m s ϵ s i d ϵ s 2 k m z 2 k s z + i d ϵ m 2 ( k s z 3 ) ] } k x ,
g ( u ¯ ) = k s z k m z k p z ,
p ( u ¯ ) = { ϵ p k m z ( ϵ s e + k m z ϵ m e + + k s z ) + [ ϵ m k p z ( ϵ s e k m z + ϵ m e + k s z ) ] } 3 .
g ( u ¯ ) = ϵ s ω 2 c 2 k x 2 ϵ m ω 2 c 2 k x 2 ϵ p ω 2 c 2 k x 2

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