Surface biphonons

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)). 

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... 

Surface biphonons could be investigated, for example, by the attenuated total reflection (ATR) method. In contrast to RSL by polaritons, this method is effective, as is well known, both for crystals with and without inversion center. In this sense, it is a more universal method. In conclusion we point out that in degenerate semiconductors Fermi resonance with plasmons (47) is also possible along with Fermi resonance with phonons and polaritons. The spectrum of plasmophonons has been measured in many semiconductors by the RSL method (see, e.g. Mooradian and McWhorter (48)). 

Also worthy of further development is the theory of surface biphonons. The conditions required for the formation of these states are different from those of the formation of surface states for the spectral region of the fundamental vibrations. It was demonstrated on the model of a one-dimensional crystal (26) that situations may exist, in general, in which the surface state of the phonon is not formed and the spectrum of surface states begins only in the frequency region of the overtones or combination tones of the vibrations. 

When the frequency of the surface biphonon lies within the band of the surface polariton, Fermi resonance occurs and the dispersion curve of the po-lariton is subject to a number of essential changes (gaps appear, etc. (86)). Consequently, experimental research of surface polariton dispersion under these conditions could yield, like similar investigations of bulk polaritons, a great deal of interesting information, not only about the surface biphonons themselves, but about the density of states of surface phonons and the magnitude of their anharmonicity constants as well. 

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