Plasmon dispersion

Solving Maxwell s equations at the metal/dielectric interface at the appropriate boundary conditions yields the surface plasmon dispersion relation, that is, the relation of the angular frequency co and the x-component of the surface plasmon wave vector kSP,... 

Holland WR, Hall DG (1983) Surface-plasmon dispersion relation shifts induced by the interaction with localized plasma resonances. Phys Rev B 27 7765-7768... 

Shin H., Catrysse P. B., and Fan S. (2005). Effect of the plasmonic dispersion relation on the transmission properties of subwavelength cylindrical holes. Plys. Rev. B 72 085436. 

Fig. 3. The solid line represents the RPA (linear) contribution to the stopping power of equation (15), for Zj = 1 andr = 2.07, as a function of the velocity of the probe particle. Dashed and dotted lines represent contributions from momentum transfers below q < q ) and above (q > q ) the critical momentum q where the plasmon dispersion enters the e-h pair continuum.

Fig. 4 A Schematic cross section of metal film growth and corresponding scanning electron micrographs (below) of the gold nanocavities fabricated with a = 350 nm latex spheres of thickness t for (a) ajl, (b) a, and (c) 2.1a [91]. B Measured energy dispersion of the reflectivity for TM polarized light as a function of the in-plane wave vector for increasing relative void depth, i=t/(2a) (a-c). Log color scale white dotted lines show a zone-folded plasmon dispersion, sample orientations of 4> = 30° in all cases, (i-iv) k space cuts through dispersion relation at (i) (i,E) = (0.25,2.2 eV) (ii) (i,E) = (0.4,2.2 eV) (in) (i,E) = (0.4,1.7 eV) (iv) (f, ) = (0.6,2.2 eV), symmetry shown above (i). Light shade corresponds to absorption features [93]...

This asymptotic trend is indicated by the dotted continuation of the peak frequency. It becomes more than obvious that the limitation of nuclear sizes inhibits a clear empirical confirmation of this trend. The Mie resonance in the clusters, on the other hand, approaches a finite value in the bulk limit. This is due to the long-range Coulomb force, which generally produces a plasmon dispersion co a q. The overall trends for very large clusters complies with a linear growth of the surface plasmon frequency. 

As has been discussed in great detail, the grating effectively imposes a Brillouin Zone structure upon the surface plasmon dispersion, resulting in various dispersion... 

The plasmon dispersion is obtained from the roots of e q,o)) = 0. Cappellini et al. (1993) have generalized their expression (4.2.9) for the static dielectric constant of semi-conductors to include dynamic processes, in a one-pole approximation (Hybertsen and Louie, 1986) ... 

FIGURE 38. Surface plasmon dispersion curve (o(k ). k Wave vector due to roughness. The experimental arrangements due to Otto and Kretschmann for surface plasmon excitation in ATR are also shown. 

FIGURE 39, Surface plasmon dispersion curves for Ag single-crystal electrodes in 0.5 M NaC104. Note the anisotropy in the optical response for Ag(llO). After Ref. 111. 

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