Abstract

We propose an exact design, analysis, and visualization method for multiple surface plasmon resonance (MSPR) mode excitation phenomena for a structure composed of an optimized-thickness polymethyl-methacrylate layer and a gold thin-film layer. The proposed simulation method is based on a recursive transfer matrix method (R-TMM) and Gaussian angular spectrum decomposition. Our method illustrates, under the Kretchmann-Raether attenuated total reflection (ATR) geometry, the response for an angle-modulated Gaussian incident beam. To verify the simulation results we also performed experiments to excite MSPR modes under the ATR geometry. Our fast and exact R-TMM with the Gaussian angular spectrum method can be widely applied to the design and analysis of metal- and dielectric-composed thin film structures.

© 2005 Optical Society of America

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References

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  1. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).
  2. A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys Reports 408, 131-314 (2005).
    [CrossRef]
  3. J. Homola, S. Yee, and G. Gauglitz, "Surface plasmon resonance sensors: review," Sens. Actuators B 54, 3- 15 (1999).
    [CrossRef]
  4. B. Rothenhausler and W. Knoll, "Surface plasmon microscopy," Nature 332, 615-617 (1988).
  5. W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824- 830 (2003).
    [CrossRef] [PubMed]
  6. P. Andrew and W. L. Barnes, "Energy transfer across a metal film mediated by surface plasmon polaritons," Science 306, 1002-1005 (2004).
    [CrossRef] [PubMed]
  7. O. J. F. Martin, C. Girard, and A. Dereux, "Generalized field propagator for electromagnetic scattering and light confinement," Phys. Rev. Lett. 74, 526-529 (1995).
    [CrossRef] [PubMed]
  8. C. Hafner, The Generalized Multiple Multipole Technique for Computational Electromagnetics (Artech House, Boston, 1990).
  9. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Boston, 2000).
  10. Y. Xie, A. R. Zakharian, J. V. Moloney, and M. Mansuripur, "Transmission of light through a periodic array of slits in a thick metallic film," Opt. Express 13, 4485-4491 (2005), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-12-4485">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-12-4485</a>
    [CrossRef] [PubMed]
  11. P. Drude, "Zur Elektronentheorie der Metalle," Ann. Phys. 1, 566-613 (1900).
    [CrossRef]
  12. G. Mie, "Beiträge zur Optik trüber Medien, speziell Kolloidalen Metall-lösungen," Ann. Phys. 25, 377�??445 (1908).
    [CrossRef]
  13. Handbook of Optical Constants of Solids, edited by E. D. Palik (Academic, New York, 1985).
  14. F.-C. Chien and S.-J. Chenb, "A sensitivity comparison of optical biosensors based on four different surface plasmon resonance modes," Biosensors and Bioelec. 20, 633-642 (2004).
    [CrossRef]
  15. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley & Sons, New York, 1991).
    [CrossRef]
  16. F. I. Baida, D. V. Labeke, and J.-M. Vigoureux, "Near-field surface plasmon microscopy: A numerical study of plasmon excitation, propagation, and edge interaction using a three-dimensional Gaussian beam," Phys. Rev. B 60, 7812-7815 (1999).
    [CrossRef]
  17. F. I. Baida, D. V. Labeke, and J.-M. Vigoureux, "Theoretical study of near-field surface plasmon excitation, propagation and diffraction," Opt. Commun. 171, 317-331 (1999).
    [CrossRef]

Ann. Phys. (2)

P. Drude, "Zur Elektronentheorie der Metalle," Ann. Phys. 1, 566-613 (1900).
[CrossRef]

G. Mie, "Beiträge zur Optik trüber Medien, speziell Kolloidalen Metall-lösungen," Ann. Phys. 25, 377�??445 (1908).
[CrossRef]

Biosensors and Bioelec. (1)

F.-C. Chien and S.-J. Chenb, "A sensitivity comparison of optical biosensors based on four different surface plasmon resonance modes," Biosensors and Bioelec. 20, 633-642 (2004).
[CrossRef]

Nature (2)

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

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824- 830 (2003).
[CrossRef] [PubMed]

Opt. Commun. (1)

F. I. Baida, D. V. Labeke, and J.-M. Vigoureux, "Theoretical study of near-field surface plasmon excitation, propagation and diffraction," Opt. Commun. 171, 317-331 (1999).
[CrossRef]

Opt. Express (1)

Phys Reports (1)

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys Reports 408, 131-314 (2005).
[CrossRef]

Phys. Rev. B (1)

F. I. Baida, D. V. Labeke, and J.-M. Vigoureux, "Near-field surface plasmon microscopy: A numerical study of plasmon excitation, propagation, and edge interaction using a three-dimensional Gaussian beam," Phys. Rev. B 60, 7812-7815 (1999).
[CrossRef]

Phys. Rev. Lett. (1)

O. J. F. Martin, C. Girard, and A. Dereux, "Generalized field propagator for electromagnetic scattering and light confinement," Phys. Rev. Lett. 74, 526-529 (1995).
[CrossRef] [PubMed]

Science (1)

P. Andrew and W. L. Barnes, "Energy transfer across a metal film mediated by surface plasmon polaritons," Science 306, 1002-1005 (2004).
[CrossRef] [PubMed]

Sens. Actuators B (1)

J. Homola, S. Yee, and G. Gauglitz, "Surface plasmon resonance sensors: review," Sens. Actuators B 54, 3- 15 (1999).
[CrossRef]

Other (5)

C. Hafner, The Generalized Multiple Multipole Technique for Computational Electromagnetics (Artech House, Boston, 1990).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Boston, 2000).

Handbook of Optical Constants of Solids, edited by E. D. Palik (Academic, New York, 1985).

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

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley & Sons, New York, 1991).
[CrossRef]

Supplementary Material (2)

» Media 1: MPG (1284 KB)     
» Media 2: MPG (1706 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

(a) General Kretschmann-Raether’s SPR structure and calculated (b) dispersion relation, (c) reflectance with respect to the incident angle variation, and (d) penetration depth with reconstruction wavelengths of 532nm and 632.8nm. The following parameters were used in the calculations: the refractive index of the substrate and SiO2 prism is 1.460; the refractive index of the gold film is 0.402 + i2.540 @532nm, 0.1726 + i3.4218 @632.8nm, and its thickness is 50 nm. θ is the variable incident angle of the probing beam.

Fig. 2.
Fig. 2.

(a) Proposed multiple SPR sensor structure and calculated (b) dispersion relation, (c) reflectance with respect to the incident angle variation, and (d) penetration depth with two different reconstruction wavelengths of 532nm and 632.8nm. The following parameters were used in the calculations: the refractive index of the substrate and SiO2 prism is 1.460; the refractive index of the Cr film is 2.9 + i4.44 at the wavelength of 532nm, 1.44 + i3.40 at the wavelength of 632.8nm and its thickness is 1nm; the refractive index of the Au film is 0.402 + i2.540 at the wavelength of 532nm, 0.1726 + i3.4218 at the wavelength of 632.8nm, and its thickness is 30nm; the refractive index and the thickness of the PMMA layer are 1.490 and 450nm, respectively.

Fig. 3.
Fig. 3.

Simulation results for MSPR excitation phenomena for the structure with four-layer (prism/Au/PMMA/air) using the proposed R-TMM with Gaussian angular spectrum decomposition method; (a) Ex -field and (b) Ez -field distribution of our proposed MSPR structure under the incident angle of 66.8° with the wavelength of 532 nm, (c) simulated movie for MSPR excitation with respect to the angle modulation for the Gaussian beam input with the wavelength of 632.8 nm, and (d) simulated movie for MSPR excitation with respect to the angle modulation for the Gaussian beam input with the wavelength of 532 nm. [Media 1] [Media 2]

Fig. 4.
Fig. 4.

(a) Kretchmann-Raether ATR coupling system and (b) its experimental result.

Equations (10)

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k s = ε 0 ω c sin θ = k sp = ω c ε 1 · ε 2 ε 1 + ε 2 , k zi = ε i ( ω c ) 2 k x 2 , ( i = 1,2 )
R = r 012 2 , r 012 = E ref E inc = r 01 + r 12 e 2 1 + r 01 r 12 e 2 , r ij = ( k zi ε i k zj ε k ) / ( k zi ε i + k zj ε k )
[ U 1 V 1 ] = M 2 M 3 M N 1 [ U N 1 V N 1 ] = k = 2 N 1 M k [ U N 1 V N 1 ] ,
R p = r p 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 ) ,
M ij = ( k = 2 N 1 M k ) ij , i , j = 1,2 ,
H i = k 0 n i ω μ 0 { M i , 11 exp [ i k zi ( z l i 1 ) ] + M i , 12 exp [ i k zi ( z l i 1 ) ] } exp ( i k xi x ) ,
E i = k zi k 0 n i { M i , 11 exp [ i k zi ( z l i 1 ) ] + M i , 12 exp [ i k zi ( z l i 1 ) ] } exp ( i k xi x ) ,
U ( x , z ) = E 0 w 0 w ( z ) exp [ x 2 w 2 ( z ) ] exp [ j ( kz + k x 2 2 R ( z ) ζ ( z ) ) ] ,
A ( f x ; z = 0 ) = E ( x , z = 0 ) exp [ i 2 π f x x ] dx .
E ( x , z = 0 ) = A ( f x ; z = 0 ) exp [ i 2 π f x x ] d f x .

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