periodic lattice of voids in such a way that the planar real The light absorption exhibits resonant enhancement at the surface of metal and the imaginary plane located below frequencies of plasma resonances in nanovoids. Almost Физика твердого тела, 2005, том 47, вып. Total resonant absorption of light by plasmons on the nanoporous surface of a metal absorption can also be achieved at high-order plasma resonances by choosing the appropriate parameters of the porous layer (Fig. 3).
In conclusion, we have shown theoretically that nearly total light absorption on a nanoporous surface of metal can be achieved at the plasma resonance. This phenomenon occurs when the lattice of spherical voids is buried in the metal substrate at a specific distance from the metal surface, which ensures optimal coupling of plasmons in the voids to the external light. Based upon a simple model, corroborated by detailed calculations later on, we have found a physical criterion for the optimal coupling, which reads that the radiative broadening of the plasma resonance must be equal to its dissipative broadening in order to produce total light Figure 3. Absorption spectra of light incident normally onto a absorption at the resonance. It is worth mentioning that silver surface with spherical inclusions of a material with dielectric the resonant light absorption must be accompanied by high constant = 4.5 (solid curve) and = 3.3 (dashed curve). The local-field enhancement near or inside the voids, and this absorption of light on the surface of bulk silver is shown by dashcould be used to trigger non-linear effects. The frequencies dotted curve. Vertical arrows mark the energies of the fundamental of absorption resonances can be easily tuned by varying (l = 1), second (l = 2), and third (l = 3) plasmon modes of a the diameter of the voids or by filling them with dielectric single void in bulk silver.
materials. This makes this type of nanoporous metals very attractive for variety of applications from nanophotonics to biophysics.
total resonant light absorption (the effect of black silver“) ” We thank S.V. Gaponenko, V.G. Golubev and S.G. Tikhooccurs when the lattice of voids is buried in the silver deev for inspiring conversations. Helpful discussions with substrate at distance smaller than the skin depth (the latter A.N. Ponyavina and O. Stenzel are gratefully appreciated.
is about 23 nm for silver). Although the frequency of the plasma resonance on the porous metal surface is close to the frequency of the fundamental (with the orbital quantum References number l = 1) Mie plasmon mode of a single spherical  T. Klar, M. Perner, S. Grosse, G. von Plessen, W. Spirkl, void in an infinite metallic medium, they do not coincide.
J. Feldmann. Phys. Rev. Lett. 80, 4249 (1998).
As clearly seen in Fig. 2, a, the shift between these two  B. Lamprecht, J.R. Krenn, A. Leitner, F.R. Aussenegg. Phys.
frequencies grows with decreasing the inter-void spacing, Rev. Lett. 83, 4421 (1999).
which shows that the reason for such a shift is the coupling  S. Coyle, M.C. Netti, J.J. Baumberg, M.A. Ghanem, P.R. Birof plasmons in adjacent voids. Note that the spectra are kin, P.N. Bartlett, D.M. Whittaker. Phys. Rev. Lett. 87, 176 independent of the polarization for normally incident light (2001).
due to the symmetry of the void lattice, |a| = |b|.
 E. Prodan, P. Nordlander, N.J. Halas. Chem. Phys. Lett. 368, Now we can estimate free parameters | f |2/ and l l 94 (2003).
|l|2/ introduced in the previous section by fitting Eqs. (2)  E. Prodan, C. Radloff, N.J. Halas, P. Nordlander. Science 302, l and (5) to the resonance frequency and FWHM in the 419 (2003).
 T.V. Teperik, V.V. Popov, F.J. Garca de Abajo. Phys.
case of total light absorption. In this case the FWHM is Rev. B 69, 155 402 (2004).
equal to 4l as shown in the previous section. We obtain  N. Stefanou, V. Yannopapas, A. Modinos. Comput. Phys.
free parameters | f |2/ 1 and |l|2/ l 0.1 for every l l Commun. 113, 49 (1998); 132, 189 (2000).
resonance shown in Fig. 2, b.
 J.D. Jackson. Classical Electrodynamics. Wiley, N. Y. (1975).
Fig. 2 depicts the resonant absorption caused by the  C. Bohren, D. Hufmann. Absorption and Scattering of Light excitation of the fundamental plasmon mode (l = 1) in by Small Particles. J. Wiley, N. Y. (1998).
voids. The frequencies of high-order plasma resonances  F.J. Garca de Abajo. Phys. Rev. B 60, 6086 (1999).
fall within the interband absorption spectra (at frequencies  P.B. Johnson, R.W. Christy. Phys. Rev. B 6, 4370 (1972).
higher than 3.5 eV for silver ) and, therefore, these resonances can hardly be observed in the reflectivity spectra.
The frequencies of plasmon resonances on a nanoporous metal surface can be reduced by filling the pores with a dielectric material. Fig. 3 shows the calculated absorption spectra of light incident normally onto a silver surface with filled spherical nanopores. In this case the second and the third plasmon resonances along with the fundamental plasma resonance show up in the visible. A giant light Физика твердого тела, 2005, том 47, вып.
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