Biphonons longitudinal

Macroscopic theory - Transverse, longitudinal, and surface biphonons... 

Note that the microscopic theory of Fermi resonance with polaritons, developed above, cannot be directly applied to cubic crystals, because triply degenerate states correspond to dipole-active transitions in such crystals (for the corresponding generalization of the theory, see (41)). However, as was mentioned previously, the polariton spectrum can also be found within the framework of macroscopic electrodynamics, which requires that the dielectric tensor of the crystal be known. The results of a proper analysis, as could be expected, are equivalent to those obtained in microscopic theory. We shall use the macroscopic theory in the following in application to cubic crystals. Using this approach we shall show additionally how the longitudinal and surface biphonons can also be found (see also (15)). 

FlG. 6.8. Dependence of the dielectric function on the frequency in the region of overtone frequencies E b and E b are the energies of the longitudinal and transverse biphonons, respectively m n and emax are the minimum and maximum energy values in the band of two-particle states. 

In the region of longitudinal-transverse splitting 0yb < u> < Op, where e(u>) < 0, surface biphonons should also exist. At the boundary with the vacuum, their dispersion law satisfies the relation... 

FlG. 6.11. Polariton dispersion in the NH4CI crystal. Longitudinal-transverse splitting of the biphonon is observed in the frequency region v 1460 cm-1 (from (61)). 

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