Abstract

The transmission of light along the surface normal through an air-quartz-glass interface covered with a periodic array of thin, rectangular gold patches has been studied over the visible to infrared range. The various structures that are observed can be qualitatively understood as arising from standing-wave resonances set by the size and surroundings of the metal patches. A method-of-moments calculational scheme provides simulations in good quantitative agreement with the data. It is shown how the standing-wave picture provides a useful conceptual framework to understand and exploit such systems.

© 2003 Optical Society of America

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References

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  1. R. Mittra, C. H. Chan, T. Cwik, “Techniques for analyzing frequency selective surfaces—a review,” Proc. IEEE 76, 1593–1615 (1988).
    [CrossRef]
  2. J. C. Vardaxoglou, Frequency Selective Surfaces: Analysis and Design (Research Studies, Taunton, UK, 1997).
  3. T. K. Wu, Frequency Selective Surface and Grid Array (Wiley, New York, 1995).
  4. V. Kettunen, M. Kuittnen, J. Tarunen, P. Vahimaa, “Spectral filtering with finitely conducting inductive grids,” J. Opt. Soc. Am. A 15, 2783–2785 (1998).
    [CrossRef]
  5. K. D. Möller, O. Sternberg, H. Grebel, P. Lahanne, “Thick inductive cross shaped metal meshes,” J. Appl. Phys. 91, 9461–9465 (2002).
    [CrossRef]
  6. S. T. Chase, R. D. Joseph, “Resonant array bandpass filters for the far infrared,” Appl. Opt. 22, 1775–1779 (1983).
    [CrossRef] [PubMed]
  7. T. Schimert, M. E. Koch, “Analysis of scattering from frequency-selective surfaces in the infrared,” J. Opt. Soc. Am. A 7, 1545–1553 (1990).
    [CrossRef]
  8. T. R. Schimert, A. J. Brouns, C. H. Chan, R. Mittra, “Investigation of millimeter-wave scattering from frequency selective surface,” IEEE Trans. Microwave Theory Tech. 39, 315–322 (1991).
    [CrossRef]
  9. I. Puscasu, D. Spencer, G. Boreman, “Refractive-index and element-spacing effects on the spectral behavior of infrared frequency-selective surfaces,” Appl. Opt. 39, 1570–1574 (2000).
    [CrossRef]
  10. I. Puscasu, W. L. Schaich, G. Boreman, “Modeling parameters for the spectral behavior of infrared frequency-selective surfaces,” Appl. Opt. 40, 118–124 (2001).
    [CrossRef]
  11. I. Puscasu, W. L. Schaich, G. Boreman, “Resonant enhancement of emission and absorption using frequency selective surfaces in the infrared,” Infrared Phys. Technol. 43, 101–107 (2002).
    [CrossRef]
  12. W. Gotschy, K. Vonmetz, A. Lectner, F. R. Aussenegg, “Thin films by regular patterns of metal nanoparticles: tailoring the optical properties by nanodesign,” Appl. Phys. B 63, 381–384 (1996).
  13. J. R. Krenn, G. Schider, W. Rechberger, B. Lamprecht, A. Leitner, F. R. Aussenegg, J. C. Weeber, “Design of multipolar plasmon excitations in silver nanoparticles,” Appl. Phys. Lett. 77, 3379–3381 (2000).
    [CrossRef]
  14. P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]
  15. M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Opt. 22, 1099–1119 (1983).
    [CrossRef] [PubMed]
  16. E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985).
  17. J. Van Bladel, Singular Electromagnetic Fields and Sources (Oxford U. Press, Oxford, UK, 1991).
  18. R. F. Harrington, Field Computation by Moment Methods (Institute of Electrical and Electronics Engineers, New York, 1992).
  19. B. Lamprecht, J. R. Krenn, A. Leitner, F. R. Aussenegg, “Metal nanoparticle gratings: influence of dipolar particle interaction on the plasmon resonance,” Phys. Rev. Lett. 84, 4721–4724 (2000).
    [CrossRef] [PubMed]
  20. R. W. Wood, “Anomalous diffraction gratings,” Phys. Rev. 48, 928–936 (1935).
    [CrossRef]
  21. M. G. Cottam, D. R. Tilley, Introduction to Surface and Superlattice Excitations (Cambridge U. Press, New York, 1989).
    [CrossRef]
  22. M. Cardona, “Fresnel reflection and surface plasmons,” Am. J. Phys. 39, 1277 (1971).
    [CrossRef]
  23. Of course one may include the coupling among surface wave vectors and, as shown in Section 3, good agreement is then found for the mode locations.

2002 (2)

K. D. Möller, O. Sternberg, H. Grebel, P. Lahanne, “Thick inductive cross shaped metal meshes,” J. Appl. Phys. 91, 9461–9465 (2002).
[CrossRef]

I. Puscasu, W. L. Schaich, G. Boreman, “Resonant enhancement of emission and absorption using frequency selective surfaces in the infrared,” Infrared Phys. Technol. 43, 101–107 (2002).
[CrossRef]

2001 (1)

2000 (3)

I. Puscasu, D. Spencer, G. Boreman, “Refractive-index and element-spacing effects on the spectral behavior of infrared frequency-selective surfaces,” Appl. Opt. 39, 1570–1574 (2000).
[CrossRef]

J. R. Krenn, G. Schider, W. Rechberger, B. Lamprecht, A. Leitner, F. R. Aussenegg, J. C. Weeber, “Design of multipolar plasmon excitations in silver nanoparticles,” Appl. Phys. Lett. 77, 3379–3381 (2000).
[CrossRef]

B. Lamprecht, J. R. Krenn, A. Leitner, F. R. Aussenegg, “Metal nanoparticle gratings: influence of dipolar particle interaction on the plasmon resonance,” Phys. Rev. Lett. 84, 4721–4724 (2000).
[CrossRef] [PubMed]

1998 (1)

1996 (1)

W. Gotschy, K. Vonmetz, A. Lectner, F. R. Aussenegg, “Thin films by regular patterns of metal nanoparticles: tailoring the optical properties by nanodesign,” Appl. Phys. B 63, 381–384 (1996).

1991 (1)

T. R. Schimert, A. J. Brouns, C. H. Chan, R. Mittra, “Investigation of millimeter-wave scattering from frequency selective surface,” IEEE Trans. Microwave Theory Tech. 39, 315–322 (1991).
[CrossRef]

1990 (1)

1988 (1)

R. Mittra, C. H. Chan, T. Cwik, “Techniques for analyzing frequency selective surfaces—a review,” Proc. IEEE 76, 1593–1615 (1988).
[CrossRef]

1983 (2)

1972 (1)

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

1971 (1)

M. Cardona, “Fresnel reflection and surface plasmons,” Am. J. Phys. 39, 1277 (1971).
[CrossRef]

1935 (1)

R. W. Wood, “Anomalous diffraction gratings,” Phys. Rev. 48, 928–936 (1935).
[CrossRef]

Alexander, R. W.

Aussenegg, F. R.

J. R. Krenn, G. Schider, W. Rechberger, B. Lamprecht, A. Leitner, F. R. Aussenegg, J. C. Weeber, “Design of multipolar plasmon excitations in silver nanoparticles,” Appl. Phys. Lett. 77, 3379–3381 (2000).
[CrossRef]

B. Lamprecht, J. R. Krenn, A. Leitner, F. R. Aussenegg, “Metal nanoparticle gratings: influence of dipolar particle interaction on the plasmon resonance,” Phys. Rev. Lett. 84, 4721–4724 (2000).
[CrossRef] [PubMed]

W. Gotschy, K. Vonmetz, A. Lectner, F. R. Aussenegg, “Thin films by regular patterns of metal nanoparticles: tailoring the optical properties by nanodesign,” Appl. Phys. B 63, 381–384 (1996).

Bell, R. J.

Bell, R. R.

Bell, S. E.

Boreman, G.

Brouns, A. J.

T. R. Schimert, A. J. Brouns, C. H. Chan, R. Mittra, “Investigation of millimeter-wave scattering from frequency selective surface,” IEEE Trans. Microwave Theory Tech. 39, 315–322 (1991).
[CrossRef]

Cardona, M.

M. Cardona, “Fresnel reflection and surface plasmons,” Am. J. Phys. 39, 1277 (1971).
[CrossRef]

Chan, C. H.

T. R. Schimert, A. J. Brouns, C. H. Chan, R. Mittra, “Investigation of millimeter-wave scattering from frequency selective surface,” IEEE Trans. Microwave Theory Tech. 39, 315–322 (1991).
[CrossRef]

R. Mittra, C. H. Chan, T. Cwik, “Techniques for analyzing frequency selective surfaces—a review,” Proc. IEEE 76, 1593–1615 (1988).
[CrossRef]

Chase, S. T.

Christy, R. W.

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Cottam, M. G.

M. G. Cottam, D. R. Tilley, Introduction to Surface and Superlattice Excitations (Cambridge U. Press, New York, 1989).
[CrossRef]

Cwik, T.

R. Mittra, C. H. Chan, T. Cwik, “Techniques for analyzing frequency selective surfaces—a review,” Proc. IEEE 76, 1593–1615 (1988).
[CrossRef]

Gotschy, W.

W. Gotschy, K. Vonmetz, A. Lectner, F. R. Aussenegg, “Thin films by regular patterns of metal nanoparticles: tailoring the optical properties by nanodesign,” Appl. Phys. B 63, 381–384 (1996).

Grebel, H.

K. D. Möller, O. Sternberg, H. Grebel, P. Lahanne, “Thick inductive cross shaped metal meshes,” J. Appl. Phys. 91, 9461–9465 (2002).
[CrossRef]

Harrington, R. F.

R. F. Harrington, Field Computation by Moment Methods (Institute of Electrical and Electronics Engineers, New York, 1992).

Johnson, P. B.

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Joseph, R. D.

Kettunen, V.

Koch, M. E.

Krenn, J. R.

J. R. Krenn, G. Schider, W. Rechberger, B. Lamprecht, A. Leitner, F. R. Aussenegg, J. C. Weeber, “Design of multipolar plasmon excitations in silver nanoparticles,” Appl. Phys. Lett. 77, 3379–3381 (2000).
[CrossRef]

B. Lamprecht, J. R. Krenn, A. Leitner, F. R. Aussenegg, “Metal nanoparticle gratings: influence of dipolar particle interaction on the plasmon resonance,” Phys. Rev. Lett. 84, 4721–4724 (2000).
[CrossRef] [PubMed]

Kuittnen, M.

Lahanne, P.

K. D. Möller, O. Sternberg, H. Grebel, P. Lahanne, “Thick inductive cross shaped metal meshes,” J. Appl. Phys. 91, 9461–9465 (2002).
[CrossRef]

Lamprecht, B.

J. R. Krenn, G. Schider, W. Rechberger, B. Lamprecht, A. Leitner, F. R. Aussenegg, J. C. Weeber, “Design of multipolar plasmon excitations in silver nanoparticles,” Appl. Phys. Lett. 77, 3379–3381 (2000).
[CrossRef]

B. Lamprecht, J. R. Krenn, A. Leitner, F. R. Aussenegg, “Metal nanoparticle gratings: influence of dipolar particle interaction on the plasmon resonance,” Phys. Rev. Lett. 84, 4721–4724 (2000).
[CrossRef] [PubMed]

Lectner, A.

W. Gotschy, K. Vonmetz, A. Lectner, F. R. Aussenegg, “Thin films by regular patterns of metal nanoparticles: tailoring the optical properties by nanodesign,” Appl. Phys. B 63, 381–384 (1996).

Leitner, A.

J. R. Krenn, G. Schider, W. Rechberger, B. Lamprecht, A. Leitner, F. R. Aussenegg, J. C. Weeber, “Design of multipolar plasmon excitations in silver nanoparticles,” Appl. Phys. Lett. 77, 3379–3381 (2000).
[CrossRef]

B. Lamprecht, J. R. Krenn, A. Leitner, F. R. Aussenegg, “Metal nanoparticle gratings: influence of dipolar particle interaction on the plasmon resonance,” Phys. Rev. Lett. 84, 4721–4724 (2000).
[CrossRef] [PubMed]

Long, L. L.

Mittra, R.

T. R. Schimert, A. J. Brouns, C. H. Chan, R. Mittra, “Investigation of millimeter-wave scattering from frequency selective surface,” IEEE Trans. Microwave Theory Tech. 39, 315–322 (1991).
[CrossRef]

R. Mittra, C. H. Chan, T. Cwik, “Techniques for analyzing frequency selective surfaces—a review,” Proc. IEEE 76, 1593–1615 (1988).
[CrossRef]

Möller, K. D.

K. D. Möller, O. Sternberg, H. Grebel, P. Lahanne, “Thick inductive cross shaped metal meshes,” J. Appl. Phys. 91, 9461–9465 (2002).
[CrossRef]

Ordal, M. A.

Palik, E. D.

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

Puscasu, I.

Rechberger, W.

J. R. Krenn, G. Schider, W. Rechberger, B. Lamprecht, A. Leitner, F. R. Aussenegg, J. C. Weeber, “Design of multipolar plasmon excitations in silver nanoparticles,” Appl. Phys. Lett. 77, 3379–3381 (2000).
[CrossRef]

Schaich, W. L.

I. Puscasu, W. L. Schaich, G. Boreman, “Resonant enhancement of emission and absorption using frequency selective surfaces in the infrared,” Infrared Phys. Technol. 43, 101–107 (2002).
[CrossRef]

I. Puscasu, W. L. Schaich, G. Boreman, “Modeling parameters for the spectral behavior of infrared frequency-selective surfaces,” Appl. Opt. 40, 118–124 (2001).
[CrossRef]

Schider, G.

J. R. Krenn, G. Schider, W. Rechberger, B. Lamprecht, A. Leitner, F. R. Aussenegg, J. C. Weeber, “Design of multipolar plasmon excitations in silver nanoparticles,” Appl. Phys. Lett. 77, 3379–3381 (2000).
[CrossRef]

Schimert, T.

Schimert, T. R.

T. R. Schimert, A. J. Brouns, C. H. Chan, R. Mittra, “Investigation of millimeter-wave scattering from frequency selective surface,” IEEE Trans. Microwave Theory Tech. 39, 315–322 (1991).
[CrossRef]

Spencer, D.

Sternberg, O.

K. D. Möller, O. Sternberg, H. Grebel, P. Lahanne, “Thick inductive cross shaped metal meshes,” J. Appl. Phys. 91, 9461–9465 (2002).
[CrossRef]

Tarunen, J.

Tilley, D. R.

M. G. Cottam, D. R. Tilley, Introduction to Surface and Superlattice Excitations (Cambridge U. Press, New York, 1989).
[CrossRef]

Vahimaa, P.

Van Bladel, J.

J. Van Bladel, Singular Electromagnetic Fields and Sources (Oxford U. Press, Oxford, UK, 1991).

Vardaxoglou, J. C.

J. C. Vardaxoglou, Frequency Selective Surfaces: Analysis and Design (Research Studies, Taunton, UK, 1997).

Vonmetz, K.

W. Gotschy, K. Vonmetz, A. Lectner, F. R. Aussenegg, “Thin films by regular patterns of metal nanoparticles: tailoring the optical properties by nanodesign,” Appl. Phys. B 63, 381–384 (1996).

Ward, C. A.

Weeber, J. C.

J. R. Krenn, G. Schider, W. Rechberger, B. Lamprecht, A. Leitner, F. R. Aussenegg, J. C. Weeber, “Design of multipolar plasmon excitations in silver nanoparticles,” Appl. Phys. Lett. 77, 3379–3381 (2000).
[CrossRef]

Wood, R. W.

R. W. Wood, “Anomalous diffraction gratings,” Phys. Rev. 48, 928–936 (1935).
[CrossRef]

Wu, T. K.

T. K. Wu, Frequency Selective Surface and Grid Array (Wiley, New York, 1995).

Am. J. Phys. (1)

M. Cardona, “Fresnel reflection and surface plasmons,” Am. J. Phys. 39, 1277 (1971).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. B (1)

W. Gotschy, K. Vonmetz, A. Lectner, F. R. Aussenegg, “Thin films by regular patterns of metal nanoparticles: tailoring the optical properties by nanodesign,” Appl. Phys. B 63, 381–384 (1996).

Appl. Phys. Lett. (1)

J. R. Krenn, G. Schider, W. Rechberger, B. Lamprecht, A. Leitner, F. R. Aussenegg, J. C. Weeber, “Design of multipolar plasmon excitations in silver nanoparticles,” Appl. Phys. Lett. 77, 3379–3381 (2000).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

T. R. Schimert, A. J. Brouns, C. H. Chan, R. Mittra, “Investigation of millimeter-wave scattering from frequency selective surface,” IEEE Trans. Microwave Theory Tech. 39, 315–322 (1991).
[CrossRef]

Infrared Phys. Technol. (1)

I. Puscasu, W. L. Schaich, G. Boreman, “Resonant enhancement of emission and absorption using frequency selective surfaces in the infrared,” Infrared Phys. Technol. 43, 101–107 (2002).
[CrossRef]

J. Appl. Phys. (1)

K. D. Möller, O. Sternberg, H. Grebel, P. Lahanne, “Thick inductive cross shaped metal meshes,” J. Appl. Phys. 91, 9461–9465 (2002).
[CrossRef]

J. Opt. Soc. Am. A (2)

Phys. Rev. (1)

R. W. Wood, “Anomalous diffraction gratings,” Phys. Rev. 48, 928–936 (1935).
[CrossRef]

Phys. Rev. B (1)

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Phys. Rev. Lett. (1)

B. Lamprecht, J. R. Krenn, A. Leitner, F. R. Aussenegg, “Metal nanoparticle gratings: influence of dipolar particle interaction on the plasmon resonance,” Phys. Rev. Lett. 84, 4721–4724 (2000).
[CrossRef] [PubMed]

Proc. IEEE (1)

R. Mittra, C. H. Chan, T. Cwik, “Techniques for analyzing frequency selective surfaces—a review,” Proc. IEEE 76, 1593–1615 (1988).
[CrossRef]

Other (7)

J. C. Vardaxoglou, Frequency Selective Surfaces: Analysis and Design (Research Studies, Taunton, UK, 1997).

T. K. Wu, Frequency Selective Surface and Grid Array (Wiley, New York, 1995).

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

J. Van Bladel, Singular Electromagnetic Fields and Sources (Oxford U. Press, Oxford, UK, 1991).

R. F. Harrington, Field Computation by Moment Methods (Institute of Electrical and Electronics Engineers, New York, 1992).

M. G. Cottam, D. R. Tilley, Introduction to Surface and Superlattice Excitations (Cambridge U. Press, New York, 1989).
[CrossRef]

Of course one may include the coupling among surface wave vectors and, as shown in Section 3, good agreement is then found for the mode locations.

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Figures (10)

Fig. 1
Fig. 1

Scanning electron micrograph of a patch array.

Fig. 2
Fig. 2

Extinction versus vacuum wavelength for different values of w y . Results for successive patterns are shifted by 0.005, and each pattern was fabricated and measured twice at different places on the substrate. Moving from the bottom to the top curves, the values of w y are 0.091, 0.32, 0.58, 0.85, 1.10, 1.34, and 1.62 μm. The value of w z = 0.091 μm.

Fig. 3
Fig. 3

Calculated extinction versus wavelength for w y = 1.10 μm. The solid (dashed) curve is calculated with a scattering rate 1/ω p τ = 0.024 (0.008) and patch thickness h = 16 nm (17 nm). See text for other parameter values. The circles are from a calculation that uses a tabulated (rather than Drude) dielectric function plus h = 16 nm.

Fig. 4
Fig. 4

Calculated extinction versus wavelength for various w y . Results for successive patterns are shifted by 0.005. The labeling scheme is the same as in Fig. 2.

Fig. 5
Fig. 5

Calculated relative transmission versus wavelength for w y = 1.10 μm. For the solid (dashed) curve the incident polarization is along the y (z) direction. For the thin solid curve the current is allowed to flow only along ŷ and is independent of z within a patch.

Fig. 6
Fig. 6

Relative transmission versus wavelength for unpolarized incident light. The dashed curve is from the model calculation based on Eq. (5). The values of w y in micrometers are (a) 1.62, (b) 1.34, (c) 1.10, (d) 0.85, (e) 0.58, and (f) 0.32. Results for different w y are shifted by 0.5.

Fig. 7
Fig. 7

Calculated transmission versus wavelength for w y = 1.62 μm. The light is incident in the xy plane at an angle θ with respect to the surface normal. We use Eq. (5) for the unpolarized light. The θ = 0 result is the same as the theory curve in Fig. 6(a).

Fig. 8
Fig. 8

Expansion coefficients versus wavelength for w y = 1.10 μm. The location of structures correlates well with the minima and threshold anomalies in the T/ T 0 of Fig. 5.

Fig. 9
Fig. 9

Possible surface dispersion of resonance locations ∊ = ℏω versus wave vector Q. The points are extracted from the results of Figs. 2 and 6 by Eq. (9). Some even j modes, excited off normal incidence in the infrared, are included. The long- (short-) dashed curves are the light lines for glass (vacuum). At frequencies above them light can propagate away from the surface. The solid curve is the (lowest) retarded surface plasmon for a homogeneous Au layer of thickness h = 16 nm between vacuum and glass.

Fig. 10
Fig. 10

Extinction versus wavelength for different values of w y with incident polarization along . The theoretical curves in (b) are calculated with the same parameters used for Figs. 4 and 6.

Equations (12)

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

Z0=-2πi/0-1hλ,
=d-0ωp2/ωω+i/τ,
Jyy, z=j,k dj,kycosj π2 y˜cosk π2 z˜,
Jzy, z=j,k dj,kzsinj π2 y˜sink π2 z˜,
Tun/T0un= 12Ty/T0y+Tz/T0z 12Ty/T0y+1,
/01/22πλ=G˜+yˆ 2πλsin θ,
G˜=2πnydy yˆ+ nzdz zˆ
-11dy˜ -11dz˜Jyy, z= 8πj dj,0y-1j-12/j,
jπwy= 2πλeff=Qω
ω2=ωp2Qh0g+0,
Q¯=Q2- ω2c201/2,
jyπwy=Q=jzπwz.

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