Solids phonon-polaritons

The elementary excitations mentioned so far are not related in any special way to the solid state and will therefore not be treated in this article. We will discuss here the following low-lying quantized excitations or quasi-particles which have been investigated by Raman spectroscopic methods phonons, polaritons, plasmons and coupled plasmon-phonon states, plasmaritons, mag-nons, and Landau levels. Finally, phase transitions were also studied by light scattering experiments however, they cannot be dealt with in this article. 

The use of lasers for the excitation of Raman spectra of solids has led to the detection of many new elementary excitations of crystals and to the observation of nonlinear effects. In this review we have tried to lead the reader to a basic understanding of these elementary excitations or quasi-particles, namely, phonons, polaritons, plasmons, plasmaritons, Landau levels, and magnons. Particular emphasis was placed upon linear and stimulated Raman scattering at polaritons, because the authors are most familiar with this part of the field and because it facilitates understanding of the other quasi-particles. 

Figure 1 Phonon-polariton dispersion in LiTa03. The solid lines describe the dispersion of the upper and lower branches of the polariton, the dashed line describes the dispersion of light at frequencies below the phonon resonance, and the dotted line describes the dispersion of light at frequencies above the phonon resonance.

The experimental and theoretical investigation of higher order vibrational motion and relaxation in solids should now advance quite rapidly as, in fact, there are no lack of suitable problems and the methods to tackle them. We note in this context, and in anticipation of the section on vibrational energy propagation, that the existance of polariton bound states has been inferred from the production of additional gaps in the phonon-polariton dispersion curves of ionic crystals having a molecular subgroup. ... 

Figure 8.2.19 Dispersion of the transversal and longitudinal phonon branches (solid blue lines) for small wave vectors. The asymptotic linear behaviors for fc and /t > -j, respectively, are outline by dashed black lines. The dispersion of the surface phonon-polariton, which exists in the gap of the bulk transversal and longitudinal phonon branches, is shown as a red line. Asymptotically, it converges for larger wave vectors to the constant frequency a). ...

Figure 8.2.20 Snapshot of the electrical field lines E x,z) above the solid surface (side view) for a surface phonon-polariton (Fuchs-Kliewer phonon) with wavelength X. Blue and red circles emphasize the positive and negative sign of surface charges.

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. 

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