Abstract

A high-sensitivity small-angle sensor based on surface plasmon resonance technology and heterodyne interferometry is proposed that uses a new technique with two right-angle prisms. Interestingly, the technique provides a novel method for designing small-angle sensors with high sensitivity and high resolution. Its theoretical resolution can reach 1.2×107 rad over the measurement range of 0.15°θ0.15°. The method has some merits, e.g., a simple optical setup, easy operation, high resolution, high sensitivity, and rapid measurement. Its feasibility is demonstrated.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. Shi and E. Stijns, "Improving the linearity of the Mechelson interferometric angular measurement by a parameter-compensation method," Appl. Opt. 32, 44-51 (1993).
    [CrossRef] [PubMed]
  2. P. S. Huang and J. Ni, "Angle measurement based on the internal-reflection effect and the use of right-angle prisms," Appl. Opt. 34, 4976-4981 (1995).
    [CrossRef] [PubMed]
  3. P. S. Huang and J. Ni, "Angle measurement based on the internal-reflection effect using elongated critical-angle prisms," Appl. Opt. 35, 2239-2241 (1996).
    [CrossRef] [PubMed]
  4. P. S. Huang, "Use of thin films for high-sensitivity angle measurement," Appl. Opt. 38, 4831-4836 (1999).
    [CrossRef]
  5. M. H. Chiu and D. C. Su, "Angle measurement using total-internal-reflection heterodyne interferometry," Opt. Eng. 36, 1750-1753 (1997).
    [CrossRef]
  6. M. H. Chiu and D. C. Su, "Improved technique for measuring small angles," Appl. Opt. 36, 7104-7106 (1997).
    [CrossRef]
  7. M. H. Chiu, S. F. Wang, and R. S. Chang, "Instrument for measuring small angles by use of multiple total internal reflections in heterodyne interferometry," Appl. Opt. 43, 5438-5442 (2004).
    [CrossRef] [PubMed]
  8. W. Zhou and L. Cai, "Interferometer for small-angle measurement based on total internal reflection," Appl. Opt. 37, 5957-5963 (1998).
    [CrossRef]
  9. P. Shi and E. Stijns, "New optical method for measuring small-angle rotations," Appl. Opt. 27, 4342-4346 (1988).
    [CrossRef] [PubMed]
  10. W. M. Robertson and E. Fullerton, "Reexamination of the surface-plasma-wave technique for determining the dielectric constant and thickness of metal films," J. Opt. Soc. Am. B 6, 1584-1589 (1989).
    [CrossRef]
  11. P. Pfeifer, U. Aldinger, G. Schwotzer, and S. Diekmann, "Real time sensing of specific molecular binding using surface plasmon resonance spectroscopy," Sens. Actuators B 54, 166-175 (1999).
    [CrossRef]
  12. B. Lieberg, C. Nylander, and I. Lundström, "Surface plasmon resonance for gas detection and biosensing," Sens. Actuators 4, 299-304 (1983).
    [CrossRef]
  13. H. Melendez, R. Carr, D. U. Bartholomew, K. Kukanskis, J. Elkind, S. Yee, C. Furlong, and R. Woodbury, "A commercial solution for surface plasmon sensing," Sens. Actuators B 35, 212-216 (1996).
    [CrossRef]
  14. Y. Xinglong, Z. Lequn, J. Hong, and W. Haojuan, "Immunosensor based on optical heterodyne phase detection," Sens. Actuators B 76, 199-202 (2001).
    [CrossRef]
  15. L. Lévesque and B. E. Paton, "Detection of defects in multiple-layer structures by using surface plasmon resonance," Appl. Opt. 36, 7199-7203 (1997).
    [CrossRef]
  16. G. Margheri, A. Mannoni, and F. Quercioli, "High-resolution angular and displacement sensing based on the excitation of surface plasma waves," Appl. Opt. 36, 4521-4525 (1997).
    [CrossRef] [PubMed]
  17. S. Shen, T. Liu, and J. Guo, "Optical phase-shift detection of surface plasmon resonance," Appl. Opt. 37, 1747-1751 (1998).
    [CrossRef]
  18. J. Guo, Z. Zhu, W. Deng, and S. Shen, "Angle measurement using surface-plasmon-resonance heterodyne interferometry: a new method," Opt. Eng. 37, 2998-3001 (1998).
    [CrossRef]
  19. E. Kretshmann, "Die Bestimmung optischer Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen," Z. Phys. 241, 313-324 (1971).
    [CrossRef]
  20. Y. C. Cheng, W. K. Su, and J. H. Liou, "Application of a liquid sensor based on surface plasmon wave excitation to distinguish methyl alcohol from ethyl alcohol," Opt. Eng. 39, 311-314 (2000).
    [CrossRef]
  21. H. E. de Bruijn, R. P. H. Kooyman, and J. Greve, "Determination of dielectric permittivity and thickness of a metal layer from a surface plasmon resonance experiment," Appl. Opt. 29, 1974-1978 (1990).
    [CrossRef]
  22. C. C. Lee and Y. J. Jen, "Influence of surface roughness on the calculation of optical constants of a metallic film by attenuated total reflection," Appl. Opt. 38, 6029-6033 (1999).
    [CrossRef]

2004

2001

Y. Xinglong, Z. Lequn, J. Hong, and W. Haojuan, "Immunosensor based on optical heterodyne phase detection," Sens. Actuators B 76, 199-202 (2001).
[CrossRef]

2000

Y. C. Cheng, W. K. Su, and J. H. Liou, "Application of a liquid sensor based on surface plasmon wave excitation to distinguish methyl alcohol from ethyl alcohol," Opt. Eng. 39, 311-314 (2000).
[CrossRef]

1999

1998

1997

1996

H. Melendez, R. Carr, D. U. Bartholomew, K. Kukanskis, J. Elkind, S. Yee, C. Furlong, and R. Woodbury, "A commercial solution for surface plasmon sensing," Sens. Actuators B 35, 212-216 (1996).
[CrossRef]

P. S. Huang and J. Ni, "Angle measurement based on the internal-reflection effect using elongated critical-angle prisms," Appl. Opt. 35, 2239-2241 (1996).
[CrossRef] [PubMed]

1995

1993

1990

1989

1988

1983

B. Lieberg, C. Nylander, and I. Lundström, "Surface plasmon resonance for gas detection and biosensing," Sens. Actuators 4, 299-304 (1983).
[CrossRef]

1971

E. Kretshmann, "Die Bestimmung optischer Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen," Z. Phys. 241, 313-324 (1971).
[CrossRef]

Aldinger, U.

P. Pfeifer, U. Aldinger, G. Schwotzer, and S. Diekmann, "Real time sensing of specific molecular binding using surface plasmon resonance spectroscopy," Sens. Actuators B 54, 166-175 (1999).
[CrossRef]

Bartholomew, D. U.

H. Melendez, R. Carr, D. U. Bartholomew, K. Kukanskis, J. Elkind, S. Yee, C. Furlong, and R. Woodbury, "A commercial solution for surface plasmon sensing," Sens. Actuators B 35, 212-216 (1996).
[CrossRef]

Cai, L.

Carr, R.

H. Melendez, R. Carr, D. U. Bartholomew, K. Kukanskis, J. Elkind, S. Yee, C. Furlong, and R. Woodbury, "A commercial solution for surface plasmon sensing," Sens. Actuators B 35, 212-216 (1996).
[CrossRef]

Chang, R. S.

Cheng, Y. C.

Y. C. Cheng, W. K. Su, and J. H. Liou, "Application of a liquid sensor based on surface plasmon wave excitation to distinguish methyl alcohol from ethyl alcohol," Opt. Eng. 39, 311-314 (2000).
[CrossRef]

Chiu, M. H.

de Bruijn, H. E.

Deng, W.

J. Guo, Z. Zhu, W. Deng, and S. Shen, "Angle measurement using surface-plasmon-resonance heterodyne interferometry: a new method," Opt. Eng. 37, 2998-3001 (1998).
[CrossRef]

Diekmann, S.

P. Pfeifer, U. Aldinger, G. Schwotzer, and S. Diekmann, "Real time sensing of specific molecular binding using surface plasmon resonance spectroscopy," Sens. Actuators B 54, 166-175 (1999).
[CrossRef]

Elkind, J.

H. Melendez, R. Carr, D. U. Bartholomew, K. Kukanskis, J. Elkind, S. Yee, C. Furlong, and R. Woodbury, "A commercial solution for surface plasmon sensing," Sens. Actuators B 35, 212-216 (1996).
[CrossRef]

Fullerton, E.

Furlong, C.

H. Melendez, R. Carr, D. U. Bartholomew, K. Kukanskis, J. Elkind, S. Yee, C. Furlong, and R. Woodbury, "A commercial solution for surface plasmon sensing," Sens. Actuators B 35, 212-216 (1996).
[CrossRef]

Greve, J.

Guo, J.

S. Shen, T. Liu, and J. Guo, "Optical phase-shift detection of surface plasmon resonance," Appl. Opt. 37, 1747-1751 (1998).
[CrossRef]

J. Guo, Z. Zhu, W. Deng, and S. Shen, "Angle measurement using surface-plasmon-resonance heterodyne interferometry: a new method," Opt. Eng. 37, 2998-3001 (1998).
[CrossRef]

Haojuan, W.

Y. Xinglong, Z. Lequn, J. Hong, and W. Haojuan, "Immunosensor based on optical heterodyne phase detection," Sens. Actuators B 76, 199-202 (2001).
[CrossRef]

Hong, J.

Y. Xinglong, Z. Lequn, J. Hong, and W. Haojuan, "Immunosensor based on optical heterodyne phase detection," Sens. Actuators B 76, 199-202 (2001).
[CrossRef]

Huang, P. S.

Jen, Y. J.

Kooyman, R. P. H.

Kretshmann, E.

E. Kretshmann, "Die Bestimmung optischer Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen," Z. Phys. 241, 313-324 (1971).
[CrossRef]

Kukanskis, K.

H. Melendez, R. Carr, D. U. Bartholomew, K. Kukanskis, J. Elkind, S. Yee, C. Furlong, and R. Woodbury, "A commercial solution for surface plasmon sensing," Sens. Actuators B 35, 212-216 (1996).
[CrossRef]

Lee, C. C.

Lequn, Z.

Y. Xinglong, Z. Lequn, J. Hong, and W. Haojuan, "Immunosensor based on optical heterodyne phase detection," Sens. Actuators B 76, 199-202 (2001).
[CrossRef]

Lévesque, L.

Lieberg, B.

B. Lieberg, C. Nylander, and I. Lundström, "Surface plasmon resonance for gas detection and biosensing," Sens. Actuators 4, 299-304 (1983).
[CrossRef]

Liou, J. H.

Y. C. Cheng, W. K. Su, and J. H. Liou, "Application of a liquid sensor based on surface plasmon wave excitation to distinguish methyl alcohol from ethyl alcohol," Opt. Eng. 39, 311-314 (2000).
[CrossRef]

Liu, T.

Lundström, I.

B. Lieberg, C. Nylander, and I. Lundström, "Surface plasmon resonance for gas detection and biosensing," Sens. Actuators 4, 299-304 (1983).
[CrossRef]

Mannoni, A.

Margheri, G.

Melendez, H.

H. Melendez, R. Carr, D. U. Bartholomew, K. Kukanskis, J. Elkind, S. Yee, C. Furlong, and R. Woodbury, "A commercial solution for surface plasmon sensing," Sens. Actuators B 35, 212-216 (1996).
[CrossRef]

Ni, J.

Nylander, C.

B. Lieberg, C. Nylander, and I. Lundström, "Surface plasmon resonance for gas detection and biosensing," Sens. Actuators 4, 299-304 (1983).
[CrossRef]

Paton, B. E.

Pfeifer, P.

P. Pfeifer, U. Aldinger, G. Schwotzer, and S. Diekmann, "Real time sensing of specific molecular binding using surface plasmon resonance spectroscopy," Sens. Actuators B 54, 166-175 (1999).
[CrossRef]

Quercioli, F.

Robertson, W. M.

Schwotzer, G.

P. Pfeifer, U. Aldinger, G. Schwotzer, and S. Diekmann, "Real time sensing of specific molecular binding using surface plasmon resonance spectroscopy," Sens. Actuators B 54, 166-175 (1999).
[CrossRef]

Shen, S.

S. Shen, T. Liu, and J. Guo, "Optical phase-shift detection of surface plasmon resonance," Appl. Opt. 37, 1747-1751 (1998).
[CrossRef]

J. Guo, Z. Zhu, W. Deng, and S. Shen, "Angle measurement using surface-plasmon-resonance heterodyne interferometry: a new method," Opt. Eng. 37, 2998-3001 (1998).
[CrossRef]

Shi, P.

Stijns, E.

Su, D. C.

M. H. Chiu and D. C. Su, "Angle measurement using total-internal-reflection heterodyne interferometry," Opt. Eng. 36, 1750-1753 (1997).
[CrossRef]

M. H. Chiu and D. C. Su, "Improved technique for measuring small angles," Appl. Opt. 36, 7104-7106 (1997).
[CrossRef]

Su, W. K.

Y. C. Cheng, W. K. Su, and J. H. Liou, "Application of a liquid sensor based on surface plasmon wave excitation to distinguish methyl alcohol from ethyl alcohol," Opt. Eng. 39, 311-314 (2000).
[CrossRef]

Wang, S. F.

Woodbury, R.

H. Melendez, R. Carr, D. U. Bartholomew, K. Kukanskis, J. Elkind, S. Yee, C. Furlong, and R. Woodbury, "A commercial solution for surface plasmon sensing," Sens. Actuators B 35, 212-216 (1996).
[CrossRef]

Xinglong, Y.

Y. Xinglong, Z. Lequn, J. Hong, and W. Haojuan, "Immunosensor based on optical heterodyne phase detection," Sens. Actuators B 76, 199-202 (2001).
[CrossRef]

Yee, S.

H. Melendez, R. Carr, D. U. Bartholomew, K. Kukanskis, J. Elkind, S. Yee, C. Furlong, and R. Woodbury, "A commercial solution for surface plasmon sensing," Sens. Actuators B 35, 212-216 (1996).
[CrossRef]

Zhou, W.

Zhu, Z.

J. Guo, Z. Zhu, W. Deng, and S. Shen, "Angle measurement using surface-plasmon-resonance heterodyne interferometry: a new method," Opt. Eng. 37, 2998-3001 (1998).
[CrossRef]

Appl. Opt.

P. Shi and E. Stijns, "Improving the linearity of the Mechelson interferometric angular measurement by a parameter-compensation method," Appl. Opt. 32, 44-51 (1993).
[CrossRef] [PubMed]

P. S. Huang and J. Ni, "Angle measurement based on the internal-reflection effect and the use of right-angle prisms," Appl. Opt. 34, 4976-4981 (1995).
[CrossRef] [PubMed]

P. S. Huang and J. Ni, "Angle measurement based on the internal-reflection effect using elongated critical-angle prisms," Appl. Opt. 35, 2239-2241 (1996).
[CrossRef] [PubMed]

P. S. Huang, "Use of thin films for high-sensitivity angle measurement," Appl. Opt. 38, 4831-4836 (1999).
[CrossRef]

M. H. Chiu and D. C. Su, "Improved technique for measuring small angles," Appl. Opt. 36, 7104-7106 (1997).
[CrossRef]

M. H. Chiu, S. F. Wang, and R. S. Chang, "Instrument for measuring small angles by use of multiple total internal reflections in heterodyne interferometry," Appl. Opt. 43, 5438-5442 (2004).
[CrossRef] [PubMed]

W. Zhou and L. Cai, "Interferometer for small-angle measurement based on total internal reflection," Appl. Opt. 37, 5957-5963 (1998).
[CrossRef]

P. Shi and E. Stijns, "New optical method for measuring small-angle rotations," Appl. Opt. 27, 4342-4346 (1988).
[CrossRef] [PubMed]

L. Lévesque and B. E. Paton, "Detection of defects in multiple-layer structures by using surface plasmon resonance," Appl. Opt. 36, 7199-7203 (1997).
[CrossRef]

G. Margheri, A. Mannoni, and F. Quercioli, "High-resolution angular and displacement sensing based on the excitation of surface plasma waves," Appl. Opt. 36, 4521-4525 (1997).
[CrossRef] [PubMed]

S. Shen, T. Liu, and J. Guo, "Optical phase-shift detection of surface plasmon resonance," Appl. Opt. 37, 1747-1751 (1998).
[CrossRef]

H. E. de Bruijn, R. P. H. Kooyman, and J. Greve, "Determination of dielectric permittivity and thickness of a metal layer from a surface plasmon resonance experiment," Appl. Opt. 29, 1974-1978 (1990).
[CrossRef]

C. C. Lee and Y. J. Jen, "Influence of surface roughness on the calculation of optical constants of a metallic film by attenuated total reflection," Appl. Opt. 38, 6029-6033 (1999).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Eng.

M. H. Chiu and D. C. Su, "Angle measurement using total-internal-reflection heterodyne interferometry," Opt. Eng. 36, 1750-1753 (1997).
[CrossRef]

J. Guo, Z. Zhu, W. Deng, and S. Shen, "Angle measurement using surface-plasmon-resonance heterodyne interferometry: a new method," Opt. Eng. 37, 2998-3001 (1998).
[CrossRef]

Y. C. Cheng, W. K. Su, and J. H. Liou, "Application of a liquid sensor based on surface plasmon wave excitation to distinguish methyl alcohol from ethyl alcohol," Opt. Eng. 39, 311-314 (2000).
[CrossRef]

Sens. Actuators

B. Lieberg, C. Nylander, and I. Lundström, "Surface plasmon resonance for gas detection and biosensing," Sens. Actuators 4, 299-304 (1983).
[CrossRef]

Sens. Actuators B

H. Melendez, R. Carr, D. U. Bartholomew, K. Kukanskis, J. Elkind, S. Yee, C. Furlong, and R. Woodbury, "A commercial solution for surface plasmon sensing," Sens. Actuators B 35, 212-216 (1996).
[CrossRef]

Y. Xinglong, Z. Lequn, J. Hong, and W. Haojuan, "Immunosensor based on optical heterodyne phase detection," Sens. Actuators B 76, 199-202 (2001).
[CrossRef]

P. Pfeifer, U. Aldinger, G. Schwotzer, and S. Diekmann, "Real time sensing of specific molecular binding using surface plasmon resonance spectroscopy," Sens. Actuators B 54, 166-175 (1999).
[CrossRef]

Z. Phys.

E. Kretshmann, "Die Bestimmung optischer Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen," Z. Phys. 241, 313-324 (1971).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Kretchmann's configuration for the generation of surface plasmon resonance. n 1 is the refractive index of the prism, n 2 is the refractive index of the Ti metal, n 3 is the refractive index of the Au metal, n 4 is the refractive index of air, and d 2 and d 3 are the thicknesses of Ti and Au, respectively.

Fig. 2
Fig. 2

Plot of the reflectivity of p polarizatin versus the incident angle α.

Fig. 3
Fig. 3

Phase difference ϕ as a function of the incident angle α for different d 2 at a constant wavelength of λ = 632.8   nm (only one prism is used).

Fig. 4
Fig. 4

Experimental setup (AN1 and AN2, analyzers; D1 and D2, photodetectors; P1 and P2, right-angle prisms).

Fig. 5
Fig. 5

Geometric relations between θ and α 1 or α 2 .

Fig. 6
Fig. 6

Experimental and theoretical curves of Δ ϕ versus Δ θ for d 2 = 2   nm and d 3 = 43.1   nm at a constant wavelength of λ = 632.8   nm .

Fig. 7
Fig. 7

Resolution versus Δ θ .

Fig. 8
Fig. 8

Sensitivity S versus Δ θ .

Fig. 9
Fig. 9

Phase difference Δ ϕ versus the rotation angle Δ θ for a different thickness d 2 of the Ti metal in the measurement range of ± 0.05 ° .

Fig. 10
Fig. 10

Relative error (%) versus the rotation angle Δ θ .

Equations (139)

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

1.2 × 10 7
0.15 ° θ 0.15 °
2.2 × 10 6
2 × 10 5
1.2 × 10 7
400 ( deg / deg )
0.15 ° θ 0.15 °
α sp
r 1234 t = r 12 t + r 234 t e i 2 k z 2 d 2 1 + r 12 t r 234 t e i 2 k z 2 d 2 ,
r 234 t = r 23 t + r 34 t e i 2 k z 3 d 3 1 + r 23 t r 34 t e i 2 k z 3 d 3 ,
r i j       t = ( E i     t E j     t ) / ( E i     t + E j     t )
d 2
d 3
t = p , s
E I t = { n I 2 / k zI , t = p k zI , t = s , I = i , j ; i , j = 1 , 2 , 3 , 4.
k z i ( j )
k z i ( j ) = k 0 [ n i ( j ) 2 n 1 2 sin 2 α ] ,
k 0
r 1234 p
r 1234 s
r 1234 p = | r 1234 p | e i ϕ p , r 1234 s = | r 1234 s | e i ϕ s ,
ϕ = ϕ p ϕ s .
R p = | r 1234 p | 2
R s = | r 1234 s | 2
d 2
2   nm
d 3
43.1   nm
632.8   nm
( ε 1 = n 1     2 )
( ε 2 = n 2     2 )
( ε 3 = n 3     2 )
( ε 4 = n 4     2 )
ε 1 = ( 1.51509 ) 2
ε 2 = 3.84 + 12.5 i
ε 3 = 12 + 1.26 i
ε 4 = ( 1.0003 ) 2
α sp ( α sp = 43.85 ° )
α sp
d 2
λ = 632.8   nm
α sp
d 2
α sp
θ i
n 1
α = 45 ° + sin - 1 ( n 4 sin θ i n 1 ) ,
n 4
α sp
θ i
θ 0
θ 0 = sin 1 [ n 1 sin ( 45 ° θ sp ) n 4 ] 1.742 ° .
Δ f = 2.5   MHz
λ = 632.8   nm
ϕ BS
θ i 1 = θ i 2 = θ 0
α 1
α 2
α sp
θ i 1
θ i 2
θ 0
Δ θ
α 1 = 45 ° sin - 1 [ n 4 sin ( θ 0 Δ θ ) n 1 ] ,
α 2 = 45 ° sin - 1 [ n 4 sin ( θ 0 + Δ θ ) n 1 ] .
I 1
I 2
D 1
D2
I 1 = I 10 [ 1 + V 1 cos ( 2 π Δ f t + ϕ 1 ) ] ,
I 2 = I 20 [ 1 + V 2 cos ( 2 π Δ f t + ϕ 2 + ϕ BS ) ] ,
V 1
V 2
I 1
I 2
ϕ 1
ϕ 2
P 1
P 2
Δ f
ϕ = ϕ 1 ϕ 2 ϕ BS .
n 1 = 1.51509
ϕ BS
n = 3.57
k = 4.36
D 1
D 2
P 1
P 2
Δ ϕ
Δ θ
Δ ϕ
A resolution
A resolution = δ θ δ ϕ Δ ϕ ,
1.2 × 10 7
8 × 10 5
+ 0.01 °
0.01 °
30 min ;
2.4 × 10 7   rad
2.4 × 10 7   rad
S = d ϕ d θ ,
d ϕ
d θ
400 ( deg / deg )
0.15 ° Δ θ 0.15 °
Δ θ
Δ θ = θ θ 0
d 2
λ = 632.8   nm
Δ ϕ
d 2
Δ ϕ
Δ θ
( Δ ϕ )
1.2 × 10 7   rad
0.15 ° Δ θ 0.15 °
n 1
n 2
n 3
n 4
d 2
d 3
d 2
λ = 632.8   nm
α 1
α 2
Δ ϕ
Δ θ
d 2 = 2   nm
d 3 = 43.1   nm
λ = 632.8   nm
Δ θ
Δ θ
Δ ϕ
Δ θ
d 2
± 0.05 °
Δ θ

Metrics