Plasmon frequencies of cube shaped metal clusters

Abstract

Abstract. The plasmon frequencies of a cube shaped metal cluster are calculated by two different methods. Unlike the spherical cluster, which has a single plasmon frequency, cop/~, the cube has a series of optically active plasmon frequencies. The two dominant peaks appear at frequencies which are considerably lower than that of a spherical cluster. PACS: 36.40The plasma resonance absorption in metal clusters is usually interpreted in terms of the Mie resonance [1], which is characteristic of a spherical cluster. For a free electron like spherical cluster in air, the resonance occurs at the frequency co = cop/,~. In optical measurements on metal clusters, the spherical shape is indeed prevalent, but other geometrical shapes may occur [2]. We calculate here the optical absorption spectrum of a cube shaped metal cluster, having a frequency dependent dielectric constant of the formwhere cop is the plasma frequency and ? is a damping constant. Two different methods will be employed. The method of FuchsFuchs [3] discussed the case of ionic crystal cubes, and developed a method for calculating their infi'ared absorption spectrum. However, his approach is quite general, and is applicable to any material described by a frequency dependent dielectric constant e(co). The only assumption is that the cube is much smaller than the wavelength of light, so that retardation can be neglected. Fuchs has shown that the susceptibility of the cube can be written as a sum over normal modes in the formwhere eh is the dielectric constant of the surrounding medium. The depolarization factors nm determine the normal mode resonance frequencies, whereas C(m) gives the strength of the m-th peak. The C(m) satisfy the sum rulem For a sphere only the uniformly polarized mode contributes to the optical absorption, and its depolarization factor is n = 1/3, so that the susceptibility assumes the form 1 1 Z((]J) = 4T(, (,f,/,S h --This susceptibility yields the resonance at the frequency cop/V/3 (assuming that eh = 1). Assuming an external uniform field, the surface polarization at a discrete set of points on the surfaces of the cube was obtained by We have calculated the absorption cross section of a cube of edge a = 3 nm, in air, assuming a dielectric constant of the form (1), with cop = 8.65 x 1015, the sodium value. For the damping constant the value 7 = 0.02c% was used. In

Initial growth of Au on oxides

“…For instance, recent calculations indicate that cube-shaped metal clusters are considerably lower in energy than that of spherical clusters. 27 Because in our experiments we have used the same primary energy and temperature as well as the same incident and scattering angles, the change in loss energy observed must be caused by either a cluster size effect or interaction between Au clusters and the substrate (alumina film). This is quite different from Au/TiO 2 (110), in which the surface plasmon of Au is not detected at initial growth of Au.…”

Substrate-Mediated Broadband Tunability in Plasmonic Resonances of Metal Nanoantennas on Finite High-Permittivity Dielectric Substrate

“…Within electrostatic limit, the extinction cross section of nanocubes with length L (of the order of ∼10 nm) can be obtained using the methods demonstrated by Fuchs [31] and Ruppin [32], where radiative damping and other retardation effects are negligible. However, for larger nanocubes, the estimation of the optical properties must include the radiation loss effects.…”

Study of Plasmonic Resonances on Platonic Solids

“…Gelder et al () and Fuchs () are probably the first who studied the resonances of cubic clusters and inclusions. Indicative numerical studies (Avelin et al, ; Hohenester & Krenn, ; Klimov et al, ; Ruppin, ; Sihvola et al, ; Tzarouchis et al, , ), and several experimental studies (Akselrod et al, ; Cortie et al, ; Lagos et al, ; Zhang et al, ), reveal a vibrant interest for the resonant behavior of the cube.…”

“…The inset figures indicate the surface charge distribution for the two first absorption resonances, that is, (a) the imaginary part of charge distribution at = 549.2 nm (electric dipole) and (b) the real part of the charge distribution at = 461.5 nm. Hohenester & Krenn, 2005;Klimov et al, 2014;Ruppin, 1996;Sihvola et al, 2004;Tzarouchis et al, 2016aTzarouchis et al, , 2016b, and several experimental studies (Akselrod et al, 2014;Cortie et al, 2012;Lagos et al, 2017;Zhang et al, 2011), reveal a vibrant interest for the resonant behavior of the cube. Figure 5 depicts the resonant spectra of the cube.…”