Abstract

In the context of surface plasmon resonance (SPR) kinetic biochips, it is important to model the SPR phenomenon (i.e., extinction of reflectivity) toward biochip design and optimization. The Rouard approach that models reflectivity off a thin-film stack is shown to be extendable to any number of absorbing layers with no added complexity. Using the generalized Rouard method, the effect of SPR is simulated as a function of the wavelength for various metal thicknesses. Given an optimal metal thickness, the dependence of SPR on the angle of incidence and wavelength is also demonstrated. Such a model constitutes a potential basis for the efficient design and optimization of multidimensional sensors.

© 2006 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  12. E. Kretschmann and H. Raether, "Radiative decay of non-radiative surface plaasmons excited by light," Z. Naturforsch 23A, 2135-2136 (1968).
  13. Available: http://www.sopra-sa.com/index2.htm.

1997

1988

B. Rothenhausler and W. Knoll, "Surface plasmon microscopy," Nature 332, 615-617 (1988).
[CrossRef]

1968

A. Otto, "Excitation of surface plasma waves in silver by the method of frustrated total reflection," Z. Physik 216, 398-410 (1968).
[CrossRef]

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

1964

1950

F. Abeles, "Recherches sur la propagation des ondes électromagnétiques sinusoïdales dans les milieux stratifiés. Application aux couches minces," Ann. Phys. (Paris) 5, 596-640 (1950).

1941

1937

M. P. Rouard, "Etudes des propriétés optiques des lames métalliques très minces," Ann. Phys. (Paris) Ser. II 7, 291-384 (1937).

Abeles, F.

F. Abeles, "Recherches sur la propagation des ondes électromagnétiques sinusoïdales dans les milieux stratifiés. Application aux couches minces," Ann. Phys. (Paris) 5, 596-640 (1950).

Baumeister, P. W.

P. W. Baumeister, Optical Coating Technology (SPIE, 2004).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, 1959).
[PubMed]

Dankner, Y.

Fano, U.

Katzir, A.

Knoll, W.

B. Rothenhausler and W. Knoll, "Surface plasmon microscopy," Nature 332, 615-617 (1988).
[CrossRef]

Kretschmann, E.

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

McLeod, H. A.

H. A. McLeod, Thin Film Optical Filters, 3rd ed. (Institute of Physics, 2002).

Otto, A.

A. Otto, "Excitation of surface plasma waves in silver by the method of frustrated total reflection," Z. Physik 216, 398-410 (1968).
[CrossRef]

Park, K. C.

Raether, H.

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

Rothenhausler, B.

B. Rothenhausler and W. Knoll, "Surface plasmon microscopy," Nature 332, 615-617 (1988).
[CrossRef]

Rouard, M. P.

M. P. Rouard, "Etudes des propriétés optiques des lames métalliques très minces," Ann. Phys. (Paris) Ser. II 7, 291-384 (1937).

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, 1959).
[PubMed]

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, 1988), p. 406.

Ann. Phys.

F. Abeles, "Recherches sur la propagation des ondes électromagnétiques sinusoïdales dans les milieux stratifiés. Application aux couches minces," Ann. Phys. (Paris) 5, 596-640 (1950).

M. P. Rouard, "Etudes des propriétés optiques des lames métalliques très minces," Ann. Phys. (Paris) Ser. II 7, 291-384 (1937).

Appl. Opt.

J. Opt. Soc. Am.

Nature

B. Rothenhausler and W. Knoll, "Surface plasmon microscopy," Nature 332, 615-617 (1988).
[CrossRef]

Z. Naturforsch

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

Z. Physik

A. Otto, "Excitation of surface plasma waves in silver by the method of frustrated total reflection," Z. Physik 216, 398-410 (1968).
[CrossRef]

Other

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, 1959).
[PubMed]

P. Yeh, Optical Waves in Layered Media (Wiley, 1988), p. 406.

P. W. Baumeister, Optical Coating Technology (SPIE, 2004).
[CrossRef]

H. A. McLeod, Thin Film Optical Filters, 3rd ed. (Institute of Physics, 2002).

Available: http://www.sopra-sa.com/index2.htm.

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic of a nonabsorbing thin film ( e 2 , n 2 ) deposited between a glass substrate ( e 1 , n 1 ) and a dielectric medium ( e 3 , n 3 ) ; (b) schematic of a multiple layer stack with absorbing layers.

Fig. 2
Fig. 2

Typical stack of multiple thin films and substrates of various thicknesses and refractive indices for surface plasmon resonance biosensors based on a Kretschmann configuration.

Fig. 3
Fig. 3

(a) Variation of plasmon curves with wavelength and Ag metal thickness at angle of incidence (a) 60 ° 42 and (b) 51 ° 3 3 .

Fig. 4
Fig. 4

Reflectivity surface plot of the configuration SF11–Ag–water (a) in 3D between 50° and 70° in the visible range and (b) in 2D as a function of the angle of incidence for 450   nm and 750   nm for the optimized thicknesses.

Equations (15)

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r 1 2 s = n 1  cos   θ 1 n 2  cos   θ 2 n 1  cos   θ 1 + n 2  cos   θ 2 ,
r 1 2 p = n 1  cos   θ 2 n 2  cos   θ 1 n 1  cos   θ 2 + n 2  cos   θ 1 ,
t 1 2 s = 2 n 1  cos   θ 1 n 1  cos   θ 1 + n 2  cos   θ 2 ,
t 1 2 p = 2 n 1  cos   θ 1 n 1  cos   θ 2 + n 2  cos   θ 1 ,
R 1 2 / p s = r 1 2 / p s 2 ,
T 1 2 / p s = n 2  cos   θ 2 n 1  cos   θ 1 t 1 2 / p s 2 .
r 2 = r 1 2 + t 1 2 e j φ 2 r 2 3 e j φ 2 t 2 1 + t 1 2 e j φ 2 r 2 3 e j φ 2 r 2 1 × e j φ 2 r 2 3 e j φ 2 t 2 1 + = r 1 2 + t 1 2 r 2 3 t 2 1 e 2 j φ 2 1 r 2 1 r 2 3 e 2 j φ 2 ,
φ k = 2 π λ n k e k  cos   θ k ,
t 1 2 t 2 1 = 1 r 1 2 2 .
r 2 = r 1 2 + r 2 3 e 2 j φ 2 1 + r 1 2 r 2 3 e 2 j φ 2 .
r 4 = r 3 4 + r 4 5 e 2 j φ 4 1 + r 3 4 r 4 5 e 2 j φ 4 .
r 3 = r 2 3 + r 4 e 2 j φ 3 1 + r 2 3 r 4 e 2 j φ 3 .
r 2 = r 1 2 + r 3 e 2 j φ 2 1 + r 1 2 r 3 e 2 j φ 2 .
I = n 1  sin   θ 1 = n 2  sin   θ 2 = n 3  sin   θ 3 = n 4  sin   θ 4 = n 5  sin   θ 5 ,
sin   θ 2 = n 1  sin   θ 1 a n 2 + j b n 2 .

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