Longitudinal polarization waves

Fig. 10. Schematic diagram of a longitudinal polarization wave in a condensed medium consisting of nonpolar molecules.

The Relationship of Observation to Cause and Effect Polarizations of Photons and EM Waves Imperfect Longitudinal EM Waves... 

The x and polarizations (or any combination) are the familiar transverse photon and the transverse wave. The z polarization along the line of propagation gives the longitudinal photon and the longitudinal EM wave. 

Fig. 4.19 Lattice distortion in Rayleigh wave defining the saggital plane (a) longitudinal (bulk) wave (b) y-polarized (shear bulk) wave (c) y-0-z polarized Rayleigh waves (SAW waves) all propagating in the z-direction...

Phonons are quanta of crystal vibration [2,4], The physics of phonons is quite similar to that of photons in that they follow Bose-Einstein statistics. However, there are some key differences, namely (1) phonons have a lower cut-off in wavelength and upper cut-off in frequency whereas photon wavelength and frequency are not limited (2) phonons can have longitudinal polarization whereas photons are transverse waves (3) phonon-phonon interaction can emit or annihilate phonons and thereby restore thermodynamic equilibrium. Despite these differences, heat conduction by phonons can be studied as a radiative transfer problem. 

Figure 34. Surface phonon dispersion for 2H-TaSe2. The HAS data are shown as solid circles except for weak points which appear in the TOP spectra as hybridized longitudinal modes that are shown as crosses. All the data were obtained at 60 K, well into the low-temperature phase. The calculated striped and shaded regions, corresponding to transverse and longitudinal polarizations respectively, are the slab-adapted bulk phonon bands, while the solid line is a calculation for the Rayleigh wave based on the Dispersive Linear Chain Model (shown schematically in Fig. 35). The open circles at g = 0 are from Raman scattering experiments. (This figure has been corrected from Fig. 23 in Ref. 54.)...

Another important feature of the intermolecular contributions to the relaxation energy is the dependence of their average value on the dielectric response of the medium. If e ( , to ) is the non-local dielectric function of the medium associated with wave vector and frequency v = d)/2 x, then the longitudinal polarization fluctuations of the medium are defined by... 

The first equation is scalar, and has a wave solution with velocity Vi = -J c /p). This is the longitudinal wave of eqn (6.7). It is sometimes called an irrotational wave, because V x u = 0 and there is no rotation of the medium. The second equation is vector, and has two degenerate orthogonal solutions with velocity v = s/(cu/p)- These are the transverse or shear waves of eqn (6.6) the degenerate solutions correspond to perpendicular polarization. They are sometimes called divergence-free waves, because V u = 0 and there is no dilation of the medium. Waves in fluids may be considered as a special case with C44 = 0, so that the transverse solutions vanish, and C = B, the adiabatic bulk modulus. 

---