Nonlinear polarizability biphonons

A generalization of biphonon theory beyond the Van Kranendonk model was made later (14)—(17). Subsequently, the effect of biphonons on polariton dispersion in the spectral region of two-particle states was investigated in a number of papers (18)—(22), and the contribution of biphonons to the nonlinear polarizability of a crystal was discussed in (23)-(25). Problems of the theory of local and quasilocal biphonons in disordered media were discussed in a number of papers (14), (26) -(28). The influence of anharmonicity in crystals on the spectra of inelastically scattered neutrons was considered by Krauzman et al. (29), Prevot et al. (30), and in Ref. (31). 

Biphonons and biexcitons and the gigantic nonlinear polarizability effect... 

In the preceding section it was shown that the formation of bound states of phonons leads to the appearance of a new type of resonance of the dielectric tensor ij(co). It is clear, of course (23), that the nonlinear polarizabilities should have analogous resonances, and this also concerns, besides biphonons, other types of bound states of quasiparticles, such as biexcitons, electron-exciton complexes, etc. 

Note that for H(uj + uj ) = Eb it is necessary to take the damping of the biphonon into account in the expression for A(w + u/,0). In this case, along with the real part of the tensor Xije u>,uj), an imaginary part is also present. This corresponds, as is well known, to the occurrence of two-photon absorption that is accompanied, in the given case, by the excitation of a biphonon. As applied to excitons this question has been discussed by Hanamura (51) within the framework of a somewhat different approach. We refer to it here (see also Fly-tzanis (52)) because both the generation of a second harmonic and two-photon absorption are processes that are completely described by the nonlinear polarizability of the crystal found above with bound states taken into account. Actually, these processes can be investigated by a single method. 

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