Abstract

We have theoretically analyzed the influence of skew rays on the performance of a fiber-optic sensor based on surface plasmon resonance. The performance of the sensor has been evaluated in terms of its sensitivity and signal-to-noise ratio (SNR). The theoretical model for skewness dependence includes the material dispersion in fiber cores and metal layers, simultaneous excitation of skew rays, and meridional rays in the fiber core along with all guided rays launching from a collimated light source. The effect of skew rays on the SNR and the sensitivity of the sensor with two different metals has been compared. The same comparison is carried out for the different values of design parameters such as numerical aperture, fiber core diameter, and the length of the surface-plasmon-resonance (SPR) active sensing region. This detailed analysis for the effect of skewness on the SNR and the sensitivity of the sensor leads us to achieve the best possible performance from a fiber-optic SPR sensor against the skewness in the optical fiber.

© 2007 Optical Society of America

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References

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  1. I. Pockrand, J. D. Swalen, J. G. Gordan, and M. R. Philpott, "Surface plasmon spectroscopy of organic monolayer assemblies," Surf. Sci. 74, 237-244 (1978).
    [CrossRef]
  2. B. Liedberg, C. Nylander, and I. Sundstrom, "Surface plasmon resonance for gas detection and biosensing," Sens. Actuators 4, 299-304 (1983).
    [CrossRef]
  3. E. Kretschmann, "Radiative decay of non-radiative surface plasmons excited by light," Z. Naturforsch. A 23, 2135-2136 (1968).
  4. E. Kretchmann, "Die eestimmung optischer konstanten von metallen durch anregung von oberflachenplasmashwingungen," Z. Phys. 241, 313-324 (1971).
    [CrossRef]
  5. R. C. Jorgenson and S. S. Yee, "A fiber-optic chemical sensor based on surface plasmon resonance," Sens. Actuators B 12, 213-220 (1993).
    [CrossRef]
  6. W. B. Lin, N. Jaffrezic-Renault, A. Gagnaire, and H. Gagnaire, "The effects of polarization of the incident light-modeling and analysis of a SPR multimode optical fiber sensor," Sens. Actuators , A 84, 198-204 (2000).
    [CrossRef]
  7. R. Slavík, J. Homola, J. Ctyroký, and E. Brynda, "Novel spectral fiber optic sensor based on surface plasmon resonance," Sens. Actuators B 74, 106-111 (2001).
    [CrossRef]
  8. M. Piliarik, J. Homola, Z. Maníková, and J. Ctyroký, "Surface plasmon resonance sensor based on a single-mode polarization-maintaining optical fiber," Sens. Actuators B 90, 236-242 (2003).
    [CrossRef]
  9. D. J. Gentleman, L. A. Obando, J. F. Masson, J. R. Holloway, and K. Booksh, "Calibration of fiber optic based surface plasmon resonance sensors in aqueous systems," Anal. Chim. Acta 515, 291-302 (2004).
    [CrossRef]
  10. A. K. Sharma and B. D. Gupta, "Absorption-based fiber optic surface plasmon resonance sensor: a theoretical evaluation," Sens. Actuators B 100, 423-431 (2004).
    [CrossRef]
  11. Y. Kim, W. Peng, S. Banerji, and K. S. Booksh, "Tapered fiber optic surface plasmon resonance sensor for analyses of vapor and liquid phases," Opt. Lett. 30, 2218-2220 (2005).
    [CrossRef] [PubMed]
  12. Rajan, S. Chand, and B. D. Gupta, "Fabrication and characterization of a surface plasmon resonance based fiber-optic sensor for bittering component--Naringin," Sens. Actuators B 115, 344-348 (2006).
    [CrossRef]
  13. R. D. Harris and J. S. Wilkinson, "Waveguide surface plasmon resonance sensors," Sens. Actuators B 29, 261-267 (1995).
    [CrossRef]
  14. A. K. Sharma and B. D. Gupta, "On the sensitivity and signal to noise ratio of a step-index fiber optic surface plasmon resonance sensor with bimetallic layers," J. Opt. Commun. 245, 159-169 (2005).
    [CrossRef]
  15. B. D. Gupta and A. K. Sharma, "Sensitivity evaluation of a multi-layered surface plasmon resonance-based fiber optic sensor: a theoretical study," Sens. Actuators B 107, 40-46 (2005).
    [CrossRef]
  16. M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, Jr., and C. A. Ward, "Optical properties of metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared," Appl. Opt. 11, 1099-1119 (1983).
    [CrossRef]
  17. H. Raether, Surface Plasmon on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).
  18. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1985).
  19. B. D. Gupta, A. Sharma, and C. D. Singh, "Evanescent wave absorption sensors based on uniform and tapered fibers," Int. J. Optoelectron. 8, 409-418 (1993).

2006 (1)

Rajan, S. Chand, and B. D. Gupta, "Fabrication and characterization of a surface plasmon resonance based fiber-optic sensor for bittering component--Naringin," Sens. Actuators B 115, 344-348 (2006).
[CrossRef]

2005 (3)

A. K. Sharma and B. D. Gupta, "On the sensitivity and signal to noise ratio of a step-index fiber optic surface plasmon resonance sensor with bimetallic layers," J. Opt. Commun. 245, 159-169 (2005).
[CrossRef]

B. D. Gupta and A. K. Sharma, "Sensitivity evaluation of a multi-layered surface plasmon resonance-based fiber optic sensor: a theoretical study," Sens. Actuators B 107, 40-46 (2005).
[CrossRef]

Y. Kim, W. Peng, S. Banerji, and K. S. Booksh, "Tapered fiber optic surface plasmon resonance sensor for analyses of vapor and liquid phases," Opt. Lett. 30, 2218-2220 (2005).
[CrossRef] [PubMed]

2004 (2)

D. J. Gentleman, L. A. Obando, J. F. Masson, J. R. Holloway, and K. Booksh, "Calibration of fiber optic based surface plasmon resonance sensors in aqueous systems," Anal. Chim. Acta 515, 291-302 (2004).
[CrossRef]

A. K. Sharma and B. D. Gupta, "Absorption-based fiber optic surface plasmon resonance sensor: a theoretical evaluation," Sens. Actuators B 100, 423-431 (2004).
[CrossRef]

2003 (1)

M. Piliarik, J. Homola, Z. Maníková, and J. Ctyroký, "Surface plasmon resonance sensor based on a single-mode polarization-maintaining optical fiber," Sens. Actuators B 90, 236-242 (2003).
[CrossRef]

2001 (1)

R. Slavík, J. Homola, J. Ctyroký, and E. Brynda, "Novel spectral fiber optic sensor based on surface plasmon resonance," Sens. Actuators B 74, 106-111 (2001).
[CrossRef]

2000 (1)

W. B. Lin, N. Jaffrezic-Renault, A. Gagnaire, and H. Gagnaire, "The effects of polarization of the incident light-modeling and analysis of a SPR multimode optical fiber sensor," Sens. Actuators , A 84, 198-204 (2000).
[CrossRef]

1995 (1)

R. D. Harris and J. S. Wilkinson, "Waveguide surface plasmon resonance sensors," Sens. Actuators B 29, 261-267 (1995).
[CrossRef]

1993 (2)

B. D. Gupta, A. Sharma, and C. D. Singh, "Evanescent wave absorption sensors based on uniform and tapered fibers," Int. J. Optoelectron. 8, 409-418 (1993).

R. C. Jorgenson and S. S. Yee, "A fiber-optic chemical sensor based on surface plasmon resonance," Sens. Actuators B 12, 213-220 (1993).
[CrossRef]

1983 (2)

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

M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, Jr., and C. A. Ward, "Optical properties of metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared," Appl. Opt. 11, 1099-1119 (1983).
[CrossRef]

1978 (1)

I. Pockrand, J. D. Swalen, J. G. Gordan, and M. R. Philpott, "Surface plasmon spectroscopy of organic monolayer assemblies," Surf. Sci. 74, 237-244 (1978).
[CrossRef]

1971 (1)

E. Kretchmann, "Die eestimmung optischer konstanten von metallen durch anregung von oberflachenplasmashwingungen," Z. Phys. 241, 313-324 (1971).
[CrossRef]

1968 (1)

E. Kretschmann, "Radiative decay of non-radiative surface plasmons excited by light," Z. Naturforsch. A 23, 2135-2136 (1968).

Anal. Chim. Acta (1)

D. J. Gentleman, L. A. Obando, J. F. Masson, J. R. Holloway, and K. Booksh, "Calibration of fiber optic based surface plasmon resonance sensors in aqueous systems," Anal. Chim. Acta 515, 291-302 (2004).
[CrossRef]

Appl. Opt. (1)

M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, Jr., and C. A. Ward, "Optical properties of metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared," Appl. Opt. 11, 1099-1119 (1983).
[CrossRef]

Int. J. Optoelectron. (1)

B. D. Gupta, A. Sharma, and C. D. Singh, "Evanescent wave absorption sensors based on uniform and tapered fibers," Int. J. Optoelectron. 8, 409-418 (1993).

J. Opt. Commun. (1)

A. K. Sharma and B. D. Gupta, "On the sensitivity and signal to noise ratio of a step-index fiber optic surface plasmon resonance sensor with bimetallic layers," J. Opt. Commun. 245, 159-169 (2005).
[CrossRef]

Opt. Lett. (1)

Sens. Actuators (3)

W. B. Lin, N. Jaffrezic-Renault, A. Gagnaire, and H. Gagnaire, "The effects of polarization of the incident light-modeling and analysis of a SPR multimode optical fiber sensor," Sens. Actuators , A 84, 198-204 (2000).
[CrossRef]

R. Slavík, J. Homola, J. Ctyroký, and E. Brynda, "Novel spectral fiber optic sensor based on surface plasmon resonance," Sens. Actuators B 74, 106-111 (2001).
[CrossRef]

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

Sens. Actuators B (6)

R. C. Jorgenson and S. S. Yee, "A fiber-optic chemical sensor based on surface plasmon resonance," Sens. Actuators B 12, 213-220 (1993).
[CrossRef]

A. K. Sharma and B. D. Gupta, "Absorption-based fiber optic surface plasmon resonance sensor: a theoretical evaluation," Sens. Actuators B 100, 423-431 (2004).
[CrossRef]

Rajan, S. Chand, and B. D. Gupta, "Fabrication and characterization of a surface plasmon resonance based fiber-optic sensor for bittering component--Naringin," Sens. Actuators B 115, 344-348 (2006).
[CrossRef]

R. D. Harris and J. S. Wilkinson, "Waveguide surface plasmon resonance sensors," Sens. Actuators B 29, 261-267 (1995).
[CrossRef]

M. Piliarik, J. Homola, Z. Maníková, and J. Ctyroký, "Surface plasmon resonance sensor based on a single-mode polarization-maintaining optical fiber," Sens. Actuators B 90, 236-242 (2003).
[CrossRef]

B. D. Gupta and A. K. Sharma, "Sensitivity evaluation of a multi-layered surface plasmon resonance-based fiber optic sensor: a theoretical study," Sens. Actuators B 107, 40-46 (2005).
[CrossRef]

Surf. Sci. (1)

I. Pockrand, J. D. Swalen, J. G. Gordan, and M. R. Philpott, "Surface plasmon spectroscopy of organic monolayer assemblies," Surf. Sci. 74, 237-244 (1978).
[CrossRef]

Z. Naturforsch. A (1)

E. Kretschmann, "Radiative decay of non-radiative surface plasmons excited by light," Z. Naturforsch. A 23, 2135-2136 (1968).

Z. Phys. (1)

E. Kretchmann, "Die eestimmung optischer konstanten von metallen durch anregung von oberflachenplasmashwingungen," Z. Phys. 241, 313-324 (1971).
[CrossRef]

Other (2)

H. Raether, Surface Plasmon on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1985).

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Figures (10)

Fig. 1
Fig. 1

Fiber-optic sensor configuration based on SPR.

Fig. 2
Fig. 2

Representation of skew ray and skewness angle in an optical fiber.

Fig. 3
Fig. 3

Launching mechanism for excitation of both skew and meridional rays.

Fig. 4
Fig. 4

N-layer model to determine the reflection coefficient.

Fig. 5
Fig. 5

Illustration of sensitivity and SNR for a fiber-optic SPR sensor.

Fig. 6
Fig. 6

SPR transmittance curves between transmitted power and wavelength for four different values of the skewness parameter. The silver has been used for the metallic film.

Fig. 7
Fig. 7

Variation of (a) sensitivity and (b) SNR with the skewness parameter for different values of the fiber core diameter (D, in micrometers). The silver has been used for the metallic film.

Fig. 8
Fig. 8

Variation of (a) sensitivity and (b) SNR with the skewness parameter for different values of NA. The silver has been used for the metallic film.

Fig. 9
Fig. 9

Variation of (a) sensitivity and (b) SNR with the skewness parameter for different values of the sensing region length (L in millimeters). The silver has been used for the metallic film.

Fig. 10
Fig. 10

Variation of (a) sensitivity and (b) SNR with the skewness parameter for two different metals (silver and gold).

Equations (17)

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n 1 ( λ ) = 1 + A 1 λ 2 λ 2 B 1 2 + A 2 λ 2 λ 2 B 2 2 + A 3 λ 2 λ 2 B 3 2 ,
ε m ( λ ) = ε m r + i ε m i = 1 λ 2 λ c λ p 2 ( λ c + i λ ) ,
r s = ρ sin α ,
r s = f tan θ s ,
[ U 1 V 1 ] = M [ U N 1 V N 1 ] ,
M = k = 2 N 1 M k = [ M 11 M 12 M 21 M 22 ] ,
M k = [ cos β k ( i sin β k ) / q k i q k sin β k cos β k ] ,
q k = ( μ k ε k ) 1 / 2 cos θ k = ( ε k n 1 2 sin 2 θ 1 ) 1 / 2 ε k ,
β k = 2 π λ n k cos θ k ( z k z k 1 ) = 2 π d k λ ( ε k n 1 2 sin 2 θ 1 ) 1 / 2 .
r p = ( M 11 + M 12 q N ) q 1 ( M 21 + M 22 q N ) ( M 11 + M 12 q N ) q 1 + ( M 21 + M 22 q N ) .
R p = | r p | 2 .
d P n 1 2 sin θ cos θ ( 1 n 1 2 cos 2 θ ) 2 cos θ s d θ ,
P trans = 0 α max θ c r π / 2 R p N r e f ( θ , α ) n 1 2 sin θ cos θ ( 1 n 1 2 cos 2 θ ) 2 cos θ s d θ d α 0 α max θ c r π / 2 n 1 2 sin θ cos θ ( 1 n 1 2 cos 2 θ ) 2 cos θ s d θ d α ,
N r e f ( θ , α ) = L D cos α tan θ ,
θ c r = sin 1 ( n c l n 1 i ) .
S n = δ λ r e s δ n s .
SNR = δ λ r e s δ λ 0.5 .

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