Charge density oscillations

Valence electrons also can be excited by interacting with the electron beam to produce a collective, longitudinal charge density oscillation called a plasmon. Plas-mons can exist only in solids and liquids, and not in gases because they require electronic states with a strong overlap between atoms. Even insulators can exhibit... 

Theoretically, SPW is described as a charge density oscillation that goierates highly confined electromagnetic fields on the surfoce of a metal film (24, 26, 31-35). The criterion for the excitation of SPW is that the incident laser beam must be matched in both frequency and momentum with that of SPW. This can only occur, for example, if P wave (TM wave) is incident from the glass side at a specific angle of which the projection of k vector of the incident photon matches SPW s k vector (26, 36, 37). The dispersion relation for a semi-infinite metal plane surface of... 

FIGURE 30 Charge density oscillation and redistribution at a metal-vacuum interface. 

The charge density oscillation of electron which gives rise to the SPR at the interface of metal and dielectric constant has to fulfill some criteria regarding dielectric constant (Fig. 13.7). 

Sur ce plasmons are excited if an electromagnetic wave is coupled into a metal/dielectric interface. These plasmons are charge density oscillations propagating at that surface of the metal. The wave is a perturbation of the electron plasma extending several tens of nm into the metal (depending on the skin depth) and decays exponentially up to 500 nm into the adjacent medium. 

From the surface plasmon-polariton wavevector (Eq. (1.163)) we can then obtain the wavelength of the surface plasmon-polariton A-spp which represents the period of the surface charge density oscillation and of the associated field distribution of the mode (see Fig. 1.6). In particular, the SPP wavelength can be found from the complex dispersion relation Eq. (1.163) by taking the real part. Writing the complex relative permittivity of the metal as m(ft>) = —1 I-pie" we can write the complex SPP wavevector as kx =... 

Hence the charge density oscillations at the surface are characterized by a wave vector 2kp. In our simple one-dimensional model, the oscillations drop off with 1/z, where z is the distance from the surface. In three dimensions, the oscillations are damped as 1/z. The charge density oscillations at the surface are called Friedel oscillations. ... 

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