Plasmon frequencies

Within a jellium atom, the electron frequency is of order 1017/sec. compared with the plasmon frequency for jellium (1.1 x 1016/sec.) so an isolated jellium atom behaves as a dielectric. However, the valence electron screens any electric field caused by polarization. The screening length (Thomas-Fermi) is 0.47Ang., or 0.36 of the radius of the jellium atom. Thus the field of the positive ion is reduced by about 30% at R. 

One source of EM enhancement may be attributed to the excitation of surface plasmons (SP) in the metal. A plasmon is a collective excitation in which all of the conduction electrons in a metal oscillate in phase. In the bulk, there is essentially only one allowed fundamental plasmon frequency. 

The ficos peak is ascribed to an interface plasmon. Assuming that the aluminium conduction electrons are well described by a free-electron gas, the interface plasmon frequency is related to the relative dielectric constant e of the molecular film through the relation ... 

One-electron wave function Ae-electron wave function cos Interface plasmon frequency... 

Metals are characterized by a plasmon frequency Ep proportional to the square-root of the number of conduction electrons per A3. Metallic lithium (162) shows E-p—7.5 and 2.Ep = 14.8 eV above / (Lils) =54.8 eV and sodium (162, 163) five almost equidistant plasmon signals with consecutive distances 5.8 to 5.9 eV... 

Measurements of the polarized reflectance in the NIR have frequently been used to obtain estimates for the transfer integrals. The method consists in fitting a reflectance model based on the Drude expression [Eq. (1)] to the experimental data. The Drude expression should be considered as a tool in estimating the plasmon frequency, ftp the background dielectric constants, e0 plasma frequency, (op and so on. The validity of the Drude analysis is limited to the conducting organic materials, with the electrical conductivity not less than a few S cm-1. 

In general, low-dimensional, low-density systems offer the best prospects for strong effects of xc phenomena on plasmon frequencies. A case in point is a pair of parallel quasi-two-dimensional electron layers in a semiconductor doublequantum well experiment. Interesting effects are predicted for this case [200]. 

Metal type of the nanoparticles The plasmon frequency for most metals corresponds to that of an ultraviold photon. For silver, gold, alkali metals, and a few other materials, the plasmon frequency is low compared to that of a visible or nearultraviolet range indicating the possibility of exciting plasmon by light. 

Since enhanced electromagnetic fields in proximity to metal nanoparticles are the basis for the increased system absorption, various computational methods are available to predict the extent of the net system absorption and therefore potentially model the relative increase in singlet oxygen generation from photosensitizers. " In comparison to traditional Mie theory, more accurate computational methods, such as discrete dipole approximation (DDA/ or finite difference time domain (FDTD) methods, are often implemented to more accurately approximate field distributions for larger particles with quadruple plasmon resonances, plasmon frequencies of silver nanoparticles, or non-spherical nanoparticles in complex media or arrangements. ... 

Pockrand et also find that the decay into the surface plasmons becomes inefficient at distances smaller than 18 nm, when the dye is not in resonance with the plasmon frequency. 

Fig. 12.19. Trend of the giant resonance or surface plasmon frequencies towards the bulk limit as a function of the number of atoms in the cluster (after J.H. Parks and S.A. Donald [712]).

The optical properties of shapes other than spheres are generally more complex. If the metal nanocrystal is in the form of an ellipsoid or rod, then its surface plasmon frequency shifts drastically because the restoring force on the conduction electrons is extraordinarily sensitive to particle curvature [2]. For the general case of an ellipsoid, the extinction cross-section of a rod-like particle is given by... 

The absorption spectra of spherical particles of colloidal dimensions can be calculated by Mie theory from a wavelength dependence of optical constants of the particles relative to the surrounding medium [7]. Spherical particles that do not interact with each other exhibit a single resonance as long as r T is valid, where r and A are the particle size and wavelength of the incident light, respectively. In this size regime the surface plasmon frequency is essentially size independent. Colloidal metallic particles produced by laser ablation have dimensions typically on the... 

In the bulk, the dielectric constant becomes zero at a frequency that is by definition equal to the plasmon frequency. Equation (2.288) is the solution of the free-electron analog of expression ... 

This is the surface plasmon frequency. It is shifted by compared to the bulk... 

At certain incident angles the wavelength of the light matches the plasmon frequency and resonance occurs. This reduces the intensity of the reflected light, and the magnitude of the effect depends on the refractive index of the material into which the evanescent wave penetrates. 

Fig. 7. Schematic representation of the collective dipole spectra of sodium clusters obtained in linear response theory [57], The quantity plotted is a m) as the percentage of the total dipole strength, mi, normalized to 100% (see Eq. (42)). The lowest spectrum (Na ) represents the classical limit, where 100% of the strength lies in the surface plasmon (frequency (Ouu) and the volume plasmon (frequency co,) has zero strength. For finite clusters the surface plasmon is red-shifted and its missing strength is distributed over the remainder of the strongly fragmented volume plasmon.

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