Abstract

The sensitivities of surface plasmon resonance spectroscopy were examined at incident angles of 66–76 deg. The sensitivities were calculated for various refractive indices of liquid samples and for various thicknesses of deposited dielectric thin layers. Furthermore, the sensitivities were confirmed experimentally. The experimentally measured refractive indices and thicknesses were 1.3311–1.3463 and 0–89 nm, respectively. From these results it was demonstrated that the sensing system showed higher sensitivities with smaller incident angles. For example, the sensitivity for a refractive index at a 66° incident angle was seven times larger than that at 76°. It was also demonstrated that the resonant wavelength has a linear relation to the refractive index and the thickness at refractive indices and thicknesses of 1.33–1.345 and 0–100 nm, respectively, except for a 66° incident angle.

© 1999 Optical Society of America

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References

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  1. H. Raether, “Surface plasmons on smooth and rough surfaces on gratings,” in Vol. 111 of Springer Tracts in Modern Physics (Springer-Verlag, Berlin, 1988), pp. 1–39.
  2. B. Liedberg, C. Nylander, I. Lundstrom, “Surface plasmon resonance for gas detection and biosensing,” Sensors Actuators 4, 299–304 (1983).
    [CrossRef]
  3. K. Matsubara, S. Kawata, S. Minami, “Optical chemical sensor based on surface plasmon measurement,” Appl. Opt. 27, 1160–1163 (1988).
    [CrossRef] [PubMed]
  4. G. Brink, H. Sigl, E. Sackmann, “Near-infrared surface plasmon resonance in silicon-based sensor: new opportunities in sensitive detection of biomolecules from aqueous solutions by applying microstep for discriminating specific and non-specific binding,” Sensors Actuators B 24–25, 756–761 (1995).
    [CrossRef]
  5. E. Stenberg, B. Persson, H. Roos, C. Urbaniczky, “Quantitative determination of surface concentration of protein with surface-plasmon resonance using radiolabeled proteins,” J. Colloid. Interf. Sci. 143, 513–526 (1991).
    [CrossRef]
  6. X. Sun, S. Shiokawa, Y. Matsui, “Experimental studies on biosensing by SPR,” J. Appl. Phys. 28, 1725–1727 (1989).
    [CrossRef]
  7. R. C. Jorgenson, S. S. Yee, “A fiber-optic chemical sensor based on surface plasmon resonance,” Sensors Actuators B 12, 213–220 (1993).
    [CrossRef]
  8. R. C. Jorgenson, S. S. Yee, “Control of the dynamic range and sensitivity of a surface plasmon resonance based fiber optic sensor,” Sensors Actuators A 43, 44–48 (1994).
    [CrossRef]
  9. U. Kunz, A. Katerkamp, R. Renneberg, F. Spener, K. Cammann, “Sensing fatty acid binding protein with planar and fiber-optical surface plasmon resonance spectroscopy devices,” Sensors Actuators B 32, 149–155 (1996).
    [CrossRef]
  10. J. Homola, P. Pfeifer, E. Brynda, J. Skvor, M. Housaka, G. Schwotzer, I. Latka, R. Willsch, “Optical biosensing using surface plasmon resonance spectroscopy,” in Chemical, Biochemical, and Environmental Fiber Sensors IX, R. A. Lieberman, ed., Proc. SPIE3105, 318–324 (1997).
    [CrossRef]
  11. A. A. Kolomenskii, P. D. Gershon, H. A. Schuessler, “Sensitivity and detection limit of concentration and adsorption measurements by laser-induced surface-plasmon resonance,” Appl. Opt. 36, 6539–6547 (1997).
    [CrossRef]
  12. R. P. H. Kooyman, H. Kolkman, J. Van Gent, J. Greve, “Surface plasmon resonance immunosensors: sensitivity considerations,” Anal. Chim. Acta 231, 35–45 (1988).
    [CrossRef]
  13. H. E. de Bruijin, R. P. H. Kooyman, J. Greve, “Choice of metal and wavelength for surface-plasmon resonance sensors: some considerations,” Appl. Opt. 31, 440–442 (1992).
  14. H. Kano, S. Kawata, “Surface-plasmon for adsorption-sensitivity enhancement,” Appl. Opt. 33, 5166–5170 (1994).
    [CrossRef] [PubMed]
  15. J. Homola, “On the sensitivity of surface plasmon resonance sensors with spectral interrogation,” Sensors Actuators B 41, 207–211 (1997).
    [CrossRef]
  16. E. Kretschmann, “Die Bestimmung optischer Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen,” Z. Phys. 241, 313–324 (1971).
    [CrossRef]
  17. R. A. Innes, J. R. Sambles, “Optical characterisation of gold using surface plasmon-polaritons,” J. Phys. F 17, 277–287 (1987).
    [CrossRef]
  18. J. R. Sambles, G. W. Bradbery, F. Yang, “Optical excitation of surface plasmons: an introduction,” Contemp. Phys. 32, 173–183 (1991).
    [CrossRef]

1997

1996

U. Kunz, A. Katerkamp, R. Renneberg, F. Spener, K. Cammann, “Sensing fatty acid binding protein with planar and fiber-optical surface plasmon resonance spectroscopy devices,” Sensors Actuators B 32, 149–155 (1996).
[CrossRef]

1995

G. Brink, H. Sigl, E. Sackmann, “Near-infrared surface plasmon resonance in silicon-based sensor: new opportunities in sensitive detection of biomolecules from aqueous solutions by applying microstep for discriminating specific and non-specific binding,” Sensors Actuators B 24–25, 756–761 (1995).
[CrossRef]

1994

R. C. Jorgenson, S. S. Yee, “Control of the dynamic range and sensitivity of a surface plasmon resonance based fiber optic sensor,” Sensors Actuators A 43, 44–48 (1994).
[CrossRef]

H. Kano, S. Kawata, “Surface-plasmon for adsorption-sensitivity enhancement,” Appl. Opt. 33, 5166–5170 (1994).
[CrossRef] [PubMed]

1993

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

1992

1991

J. R. Sambles, G. W. Bradbery, F. Yang, “Optical excitation of surface plasmons: an introduction,” Contemp. Phys. 32, 173–183 (1991).
[CrossRef]

E. Stenberg, B. Persson, H. Roos, C. Urbaniczky, “Quantitative determination of surface concentration of protein with surface-plasmon resonance using radiolabeled proteins,” J. Colloid. Interf. Sci. 143, 513–526 (1991).
[CrossRef]

1989

X. Sun, S. Shiokawa, Y. Matsui, “Experimental studies on biosensing by SPR,” J. Appl. Phys. 28, 1725–1727 (1989).
[CrossRef]

1988

K. Matsubara, S. Kawata, S. Minami, “Optical chemical sensor based on surface plasmon measurement,” Appl. Opt. 27, 1160–1163 (1988).
[CrossRef] [PubMed]

R. P. H. Kooyman, H. Kolkman, J. Van Gent, J. Greve, “Surface plasmon resonance immunosensors: sensitivity considerations,” Anal. Chim. Acta 231, 35–45 (1988).
[CrossRef]

1987

R. A. Innes, J. R. Sambles, “Optical characterisation of gold using surface plasmon-polaritons,” J. Phys. F 17, 277–287 (1987).
[CrossRef]

1983

B. Liedberg, C. Nylander, I. Lundstrom, “Surface plasmon resonance for gas detection and biosensing,” Sensors Actuators 4, 299–304 (1983).
[CrossRef]

1971

E. Kretschmann, “Die Bestimmung optischer Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen,” Z. Phys. 241, 313–324 (1971).
[CrossRef]

Bradbery, G. W.

J. R. Sambles, G. W. Bradbery, F. Yang, “Optical excitation of surface plasmons: an introduction,” Contemp. Phys. 32, 173–183 (1991).
[CrossRef]

Brink, G.

G. Brink, H. Sigl, E. Sackmann, “Near-infrared surface plasmon resonance in silicon-based sensor: new opportunities in sensitive detection of biomolecules from aqueous solutions by applying microstep for discriminating specific and non-specific binding,” Sensors Actuators B 24–25, 756–761 (1995).
[CrossRef]

Brynda, E.

J. Homola, P. Pfeifer, E. Brynda, J. Skvor, M. Housaka, G. Schwotzer, I. Latka, R. Willsch, “Optical biosensing using surface plasmon resonance spectroscopy,” in Chemical, Biochemical, and Environmental Fiber Sensors IX, R. A. Lieberman, ed., Proc. SPIE3105, 318–324 (1997).
[CrossRef]

Cammann, K.

U. Kunz, A. Katerkamp, R. Renneberg, F. Spener, K. Cammann, “Sensing fatty acid binding protein with planar and fiber-optical surface plasmon resonance spectroscopy devices,” Sensors Actuators B 32, 149–155 (1996).
[CrossRef]

de Bruijin, H. E.

Gershon, P. D.

Greve, J.

H. E. de Bruijin, R. P. H. Kooyman, J. Greve, “Choice of metal and wavelength for surface-plasmon resonance sensors: some considerations,” Appl. Opt. 31, 440–442 (1992).

R. P. H. Kooyman, H. Kolkman, J. Van Gent, J. Greve, “Surface plasmon resonance immunosensors: sensitivity considerations,” Anal. Chim. Acta 231, 35–45 (1988).
[CrossRef]

Homola, J.

J. Homola, “On the sensitivity of surface plasmon resonance sensors with spectral interrogation,” Sensors Actuators B 41, 207–211 (1997).
[CrossRef]

J. Homola, P. Pfeifer, E. Brynda, J. Skvor, M. Housaka, G. Schwotzer, I. Latka, R. Willsch, “Optical biosensing using surface plasmon resonance spectroscopy,” in Chemical, Biochemical, and Environmental Fiber Sensors IX, R. A. Lieberman, ed., Proc. SPIE3105, 318–324 (1997).
[CrossRef]

Housaka, M.

J. Homola, P. Pfeifer, E. Brynda, J. Skvor, M. Housaka, G. Schwotzer, I. Latka, R. Willsch, “Optical biosensing using surface plasmon resonance spectroscopy,” in Chemical, Biochemical, and Environmental Fiber Sensors IX, R. A. Lieberman, ed., Proc. SPIE3105, 318–324 (1997).
[CrossRef]

Innes, R. A.

R. A. Innes, J. R. Sambles, “Optical characterisation of gold using surface plasmon-polaritons,” J. Phys. F 17, 277–287 (1987).
[CrossRef]

Jorgenson, R. C.

R. C. Jorgenson, S. S. Yee, “Control of the dynamic range and sensitivity of a surface plasmon resonance based fiber optic sensor,” Sensors Actuators A 43, 44–48 (1994).
[CrossRef]

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

Kano, H.

Katerkamp, A.

U. Kunz, A. Katerkamp, R. Renneberg, F. Spener, K. Cammann, “Sensing fatty acid binding protein with planar and fiber-optical surface plasmon resonance spectroscopy devices,” Sensors Actuators B 32, 149–155 (1996).
[CrossRef]

Kawata, S.

Kolkman, H.

R. P. H. Kooyman, H. Kolkman, J. Van Gent, J. Greve, “Surface plasmon resonance immunosensors: sensitivity considerations,” Anal. Chim. Acta 231, 35–45 (1988).
[CrossRef]

Kolomenskii, A. A.

Kooyman, R. P. H.

H. E. de Bruijin, R. P. H. Kooyman, J. Greve, “Choice of metal and wavelength for surface-plasmon resonance sensors: some considerations,” Appl. Opt. 31, 440–442 (1992).

R. P. H. Kooyman, H. Kolkman, J. Van Gent, J. Greve, “Surface plasmon resonance immunosensors: sensitivity considerations,” Anal. Chim. Acta 231, 35–45 (1988).
[CrossRef]

Kretschmann, E.

E. Kretschmann, “Die Bestimmung optischer Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen,” Z. Phys. 241, 313–324 (1971).
[CrossRef]

Kunz, U.

U. Kunz, A. Katerkamp, R. Renneberg, F. Spener, K. Cammann, “Sensing fatty acid binding protein with planar and fiber-optical surface plasmon resonance spectroscopy devices,” Sensors Actuators B 32, 149–155 (1996).
[CrossRef]

Latka, I.

J. Homola, P. Pfeifer, E. Brynda, J. Skvor, M. Housaka, G. Schwotzer, I. Latka, R. Willsch, “Optical biosensing using surface plasmon resonance spectroscopy,” in Chemical, Biochemical, and Environmental Fiber Sensors IX, R. A. Lieberman, ed., Proc. SPIE3105, 318–324 (1997).
[CrossRef]

Liedberg, B.

B. Liedberg, C. Nylander, I. Lundstrom, “Surface plasmon resonance for gas detection and biosensing,” Sensors Actuators 4, 299–304 (1983).
[CrossRef]

Lundstrom, I.

B. Liedberg, C. Nylander, I. Lundstrom, “Surface plasmon resonance for gas detection and biosensing,” Sensors Actuators 4, 299–304 (1983).
[CrossRef]

Matsubara, K.

Matsui, Y.

X. Sun, S. Shiokawa, Y. Matsui, “Experimental studies on biosensing by SPR,” J. Appl. Phys. 28, 1725–1727 (1989).
[CrossRef]

Minami, S.

Nylander, C.

B. Liedberg, C. Nylander, I. Lundstrom, “Surface plasmon resonance for gas detection and biosensing,” Sensors Actuators 4, 299–304 (1983).
[CrossRef]

Persson, B.

E. Stenberg, B. Persson, H. Roos, C. Urbaniczky, “Quantitative determination of surface concentration of protein with surface-plasmon resonance using radiolabeled proteins,” J. Colloid. Interf. Sci. 143, 513–526 (1991).
[CrossRef]

Pfeifer, P.

J. Homola, P. Pfeifer, E. Brynda, J. Skvor, M. Housaka, G. Schwotzer, I. Latka, R. Willsch, “Optical biosensing using surface plasmon resonance spectroscopy,” in Chemical, Biochemical, and Environmental Fiber Sensors IX, R. A. Lieberman, ed., Proc. SPIE3105, 318–324 (1997).
[CrossRef]

Raether, H.

H. Raether, “Surface plasmons on smooth and rough surfaces on gratings,” in Vol. 111 of Springer Tracts in Modern Physics (Springer-Verlag, Berlin, 1988), pp. 1–39.

Renneberg, R.

U. Kunz, A. Katerkamp, R. Renneberg, F. Spener, K. Cammann, “Sensing fatty acid binding protein with planar and fiber-optical surface plasmon resonance spectroscopy devices,” Sensors Actuators B 32, 149–155 (1996).
[CrossRef]

Roos, H.

E. Stenberg, B. Persson, H. Roos, C. Urbaniczky, “Quantitative determination of surface concentration of protein with surface-plasmon resonance using radiolabeled proteins,” J. Colloid. Interf. Sci. 143, 513–526 (1991).
[CrossRef]

Sackmann, E.

G. Brink, H. Sigl, E. Sackmann, “Near-infrared surface plasmon resonance in silicon-based sensor: new opportunities in sensitive detection of biomolecules from aqueous solutions by applying microstep for discriminating specific and non-specific binding,” Sensors Actuators B 24–25, 756–761 (1995).
[CrossRef]

Sambles, J. R.

J. R. Sambles, G. W. Bradbery, F. Yang, “Optical excitation of surface plasmons: an introduction,” Contemp. Phys. 32, 173–183 (1991).
[CrossRef]

R. A. Innes, J. R. Sambles, “Optical characterisation of gold using surface plasmon-polaritons,” J. Phys. F 17, 277–287 (1987).
[CrossRef]

Schuessler, H. A.

Schwotzer, G.

J. Homola, P. Pfeifer, E. Brynda, J. Skvor, M. Housaka, G. Schwotzer, I. Latka, R. Willsch, “Optical biosensing using surface plasmon resonance spectroscopy,” in Chemical, Biochemical, and Environmental Fiber Sensors IX, R. A. Lieberman, ed., Proc. SPIE3105, 318–324 (1997).
[CrossRef]

Shiokawa, S.

X. Sun, S. Shiokawa, Y. Matsui, “Experimental studies on biosensing by SPR,” J. Appl. Phys. 28, 1725–1727 (1989).
[CrossRef]

Sigl, H.

G. Brink, H. Sigl, E. Sackmann, “Near-infrared surface plasmon resonance in silicon-based sensor: new opportunities in sensitive detection of biomolecules from aqueous solutions by applying microstep for discriminating specific and non-specific binding,” Sensors Actuators B 24–25, 756–761 (1995).
[CrossRef]

Skvor, J.

J. Homola, P. Pfeifer, E. Brynda, J. Skvor, M. Housaka, G. Schwotzer, I. Latka, R. Willsch, “Optical biosensing using surface plasmon resonance spectroscopy,” in Chemical, Biochemical, and Environmental Fiber Sensors IX, R. A. Lieberman, ed., Proc. SPIE3105, 318–324 (1997).
[CrossRef]

Spener, F.

U. Kunz, A. Katerkamp, R. Renneberg, F. Spener, K. Cammann, “Sensing fatty acid binding protein with planar and fiber-optical surface plasmon resonance spectroscopy devices,” Sensors Actuators B 32, 149–155 (1996).
[CrossRef]

Stenberg, E.

E. Stenberg, B. Persson, H. Roos, C. Urbaniczky, “Quantitative determination of surface concentration of protein with surface-plasmon resonance using radiolabeled proteins,” J. Colloid. Interf. Sci. 143, 513–526 (1991).
[CrossRef]

Sun, X.

X. Sun, S. Shiokawa, Y. Matsui, “Experimental studies on biosensing by SPR,” J. Appl. Phys. 28, 1725–1727 (1989).
[CrossRef]

Urbaniczky, C.

E. Stenberg, B. Persson, H. Roos, C. Urbaniczky, “Quantitative determination of surface concentration of protein with surface-plasmon resonance using radiolabeled proteins,” J. Colloid. Interf. Sci. 143, 513–526 (1991).
[CrossRef]

Van Gent, J.

R. P. H. Kooyman, H. Kolkman, J. Van Gent, J. Greve, “Surface plasmon resonance immunosensors: sensitivity considerations,” Anal. Chim. Acta 231, 35–45 (1988).
[CrossRef]

Willsch, R.

J. Homola, P. Pfeifer, E. Brynda, J. Skvor, M. Housaka, G. Schwotzer, I. Latka, R. Willsch, “Optical biosensing using surface plasmon resonance spectroscopy,” in Chemical, Biochemical, and Environmental Fiber Sensors IX, R. A. Lieberman, ed., Proc. SPIE3105, 318–324 (1997).
[CrossRef]

Yang, F.

J. R. Sambles, G. W. Bradbery, F. Yang, “Optical excitation of surface plasmons: an introduction,” Contemp. Phys. 32, 173–183 (1991).
[CrossRef]

Yee, S. S.

R. C. Jorgenson, S. S. Yee, “Control of the dynamic range and sensitivity of a surface plasmon resonance based fiber optic sensor,” Sensors Actuators A 43, 44–48 (1994).
[CrossRef]

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

Anal. Chim. Acta

R. P. H. Kooyman, H. Kolkman, J. Van Gent, J. Greve, “Surface plasmon resonance immunosensors: sensitivity considerations,” Anal. Chim. Acta 231, 35–45 (1988).
[CrossRef]

Appl. Opt.

Contemp. Phys.

J. R. Sambles, G. W. Bradbery, F. Yang, “Optical excitation of surface plasmons: an introduction,” Contemp. Phys. 32, 173–183 (1991).
[CrossRef]

J. Appl. Phys.

X. Sun, S. Shiokawa, Y. Matsui, “Experimental studies on biosensing by SPR,” J. Appl. Phys. 28, 1725–1727 (1989).
[CrossRef]

J. Colloid. Interf. Sci.

E. Stenberg, B. Persson, H. Roos, C. Urbaniczky, “Quantitative determination of surface concentration of protein with surface-plasmon resonance using radiolabeled proteins,” J. Colloid. Interf. Sci. 143, 513–526 (1991).
[CrossRef]

J. Phys. F

R. A. Innes, J. R. Sambles, “Optical characterisation of gold using surface plasmon-polaritons,” J. Phys. F 17, 277–287 (1987).
[CrossRef]

Sensors Actuators

B. Liedberg, C. Nylander, I. Lundstrom, “Surface plasmon resonance for gas detection and biosensing,” Sensors Actuators 4, 299–304 (1983).
[CrossRef]

Sensors Actuators A

R. C. Jorgenson, S. S. Yee, “Control of the dynamic range and sensitivity of a surface plasmon resonance based fiber optic sensor,” Sensors Actuators A 43, 44–48 (1994).
[CrossRef]

Sensors Actuators B

U. Kunz, A. Katerkamp, R. Renneberg, F. Spener, K. Cammann, “Sensing fatty acid binding protein with planar and fiber-optical surface plasmon resonance spectroscopy devices,” Sensors Actuators B 32, 149–155 (1996).
[CrossRef]

G. Brink, H. Sigl, E. Sackmann, “Near-infrared surface plasmon resonance in silicon-based sensor: new opportunities in sensitive detection of biomolecules from aqueous solutions by applying microstep for discriminating specific and non-specific binding,” Sensors Actuators B 24–25, 756–761 (1995).
[CrossRef]

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

J. Homola, “On the sensitivity of surface plasmon resonance sensors with spectral interrogation,” Sensors Actuators B 41, 207–211 (1997).
[CrossRef]

Z. Phys.

E. Kretschmann, “Die Bestimmung optischer Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen,” Z. Phys. 241, 313–324 (1971).
[CrossRef]

Other

J. Homola, P. Pfeifer, E. Brynda, J. Skvor, M. Housaka, G. Schwotzer, I. Latka, R. Willsch, “Optical biosensing using surface plasmon resonance spectroscopy,” in Chemical, Biochemical, and Environmental Fiber Sensors IX, R. A. Lieberman, ed., Proc. SPIE3105, 318–324 (1997).
[CrossRef]

H. Raether, “Surface plasmons on smooth and rough surfaces on gratings,” in Vol. 111 of Springer Tracts in Modern Physics (Springer-Verlag, Berlin, 1988), pp. 1–39.

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Figures (8)

Fig. 1
Fig. 1

Geometry of a prism, a metal film, a deposited dielectric thin layer, and a liquid sample.

Fig. 2
Fig. 2

Relation among the resonant wavelength and the refractive index of a liquid sample and the thickness of a deposited thin layer. The incident angle of the light was (a) 66°, (b) 68°, (c) 70°, (d) 72°, (e) 74°, and (f) 76°.

Fig. 3
Fig. 3

Spectral SPR instrument system: W, 30-W tungsten white-light source; M1–M4, spherical mirrors; P1–P3, apertures; B, polarizer; S, spectroscope with charge-coupled device; F, metal film.

Fig. 4
Fig. 4

Measured and calculated spectral SPR. Refractive index of the liquid sample, 1.3311; thickness of the deposited dielectric thin layer, 0 nm; incident angle, 70°.

Fig. 5
Fig. 5

Resonant wavelength as a function of the refractive index of a liquid sample for various thicknessess of deposited dielectric thin layers. The incident angle of the light was 70°. The thicknessess of the layers were (a) 89, (b) 37, (c) 21, and (d) 0 nm.

Fig. 6
Fig. 6

Intercept as a function of the thickness of a deposited dielectric thin layer. The incident angle of the light was 70°. The values of the intercepts were calculated from the lines of the resonant wavelength versus the refractive index for various thicknesses of deposited dielectric thin layers (shown in Fig. 5).

Fig. 7
Fig. 7

Slope as a function of the thickness of a deposited dielectric thin layer. The incident angle of the light was 70°. The values of the slope were calculated from the lines of the resonant wavelength versus the refractive index for various thicknesses of deposited dielectric thin layers (shown in Fig. 5).

Fig. 8
Fig. 8

Calculated resonant wavelengths as functions of the refractive index of a liquid sample. Solid lines, data calculated with the empirical equation. Markers, data theoretically calculated with Fresnel formulas in a four-layer system. The incident angle of the light was 70°. The thicknesses of the layers were (a, a′) 0, (b, b′) 100, and (c, c′) 200 nm.

Tables (1)

Tables Icon

Table 1 Constant Values C1, C2, C3, and λ0 for 66°–76° Incident Angles

Equations (10)

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

εr=ε-ωp2/ω2,
εi=ε-εr/ωτ0,
nBK7=1.52-1.17×104×λ-9.79×10-1×λ2,
nSiO2=1.46-5.93×103×λ-2.55×λ2,
λ=F1t+F2tn,
F1t=A+Bt,
F2t=C+Dt,
λ=A+Bt+Cn+Dtn.
n=n0+δn,  t=t0+δt,  A=λ0,
λ=λ0+C1δt+C2δn+C3δnδt,

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