Surface modes-plasmons

The considerable distinctions between optical spectra of a metal nanostmcture and corresponding bulk metal appear due to surface modes (plasmon-polariton resonances) in nanoparticles and size dependence of their optical constants. In the case of partially-ordered nanoparticle arrays these effects are of the collective nature because of strong electrodynamic coupling. The theoretical approach for regarding... 

Vp(fO is peaked at the surface. Many collective oscillations manifest themselves as predominantly surface modes. As a result, already one separable term generating by (74) usually delivers a quite good description of collective excitations like plasmons in atomic clusters and giant resonances in atomic nuclei. The detailed distributions depends on a subtle interplay of surface and volume vibrations. This can be resolved by taking into account the nuclear interior. For this aim, the radial parts with larger powers and spherical Bessel functions can be used, much similar as in the local RPA [24]. This results in the shift of the maxima of the operators (If), (12) and (65) to the interior. Exploring different conceivable combinations, one may found a most efficient set of the initial operators. 

Following (9.27) we discussed the physical interpretation of the plasma frequency for a simple metal and introduced the concept of a plasmon, a quantized plasma oscillation. It may help our understanding of the physics of surface modes in small particles and the terminology sometimes encountered in their description if we expand that discussion. 

Ions in the lattice of a solid can also partake in a collective oscillation which, when quantized, is called a phonon. Again, as with plasmons, the presence of a boundary can modify the characteristics of such lattice vibrations. Thus, the infrared surface modes that we discussed previously are sometimes called surface phonons. Such surface phonons in ionic crystals have been clearly discussed in a landmark paper by Ruppin and Englman (1970), who distinguish between polariton and pure phonon modes. In the classical language of Chapter 4 a polariton mode is merely a normal mode where no restriction is made on the size of the sphere pure phonon modes come about when the sphere is sufficiently small that retardation effects can be neglected. In the language of elementary excitations a polariton is a kind of hybrid excitation that exhibits mixed photon and phonon behavior. 

By means of this combination of the cross section for an ellipsoid with the Drude dielectric function we arrive at resonance absorption where there is no comparable structure in the bulk metal absorption. The absorption cross section is a maximum at co = ojs and falls to approximately one-half its maximum value at the frequencies = us y/2 (provided that v2 ). That is, the surface mode frequency is us or, in quantum-mechanical language, the surface plasmon energy is hcos. We have assumed that the dielectric function of the surrounding medium is constant or weakly dependent on frequency. 

Another interesting variant of the total reflection technique is the so-called Surface Electromagnetic Wave Spectroscopy (SEWS), which consists of the generation of a surface plasmon on a substrate by frustrated total internal reflection in a prism located a few microns from the surface. This plasmon is decoupled by a second prism. Some interesting data relating to surface modes on alumina have been reported with this technique [30]. 

Figure 8. Surface-plasmon microscopy, (a) The coupling of the incident photons to the surface mode can be accomplished by using a prism. The evanescent field of the surface plasmon extends into the monolayer coating, and the light that is scattered or diffracted when the resonance condition is not fulfilled can be imaged by the lens. After Rothenhausler and Knoll. (b) SPM images of a monolayer of DMPA in the LE-LC region transferred to a solid support.

Fig. la. Schematic showing the optical field (magnetic component) at an interface which supports surface plasmons. The dielectric function in the dielectric medium is the diectric function in the metal can be approximated hy the Drude-Lorentz expression given in the upper right hand corner. Notice that the field extends much farther into the dielectric than the metal, b. The reflectivity in an ATR configuration. The 0 is the critical angle and 0gp is the angle at which the surface plasmon is excited. Reflectivity extends from zero to one. Notice that the reflectivity from s waves, i.e., those waves with their electric vector perpendicular to the plane of incidence do not excite a surface mode.. 

Surface plasmon waves are surface electromagnetic modes that travel along a metal-dielectric interface as bound nonradiative waves with their field amplitude decaying exponentially perpendicular to the interface (Raether 1988). Surface plasmons are usually excited by coupling them to an evanescent wave at a dielectric surface. A plasmon wave atom mirror can be formed on a glass surface with a thin deposited... 

Kovacs G (1982) Optical excitation of surface plasmon-polaritons in layered media. In Broadman AD (ed) Electromagnetic Surface Modes, pp 143-200. New York Wiley. 

As already mentioned, collective excitations are associated with a diverging dynamic response to a perturbation. Equations (4.3.1) and (4.3.2) suggest that a collective surface mode occurs when 1 + e(cu) = 0. By replacing 6(( ) by its bulk expression (4.2.15), one obtains the surface plasmon energy ho)s equal to ... 

Not only do the new and old surfaces produce surface plasmons in the island-growth mode, but the interlace between the growing film and the substrate is also capable of producing an interphase plasmon excitation. Typically an interphase plasmon will appear at an energy intermediate between the surface plasmons of the two phases. Its intensity will grow as the island phase grows laterally but will eventually disappear as the interface retreats below the thickening island layer. 

Since the confined modes (whether they are waveguide modes or surface plasmons) are nonradiative (i.e., their wavevector parallel to the interface, is greater than the wavevector of the... 

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