Abstract: We studied intensity of the Stokes component of the four-wave scattering by coherently excited phonon polaritons as a function of phase mismatches. Experiments in homogeneous LiIO$-3$/, differently doped LiNbO$-3$/:Mg, and periodically poled Nd:Mg:LiNbO$-3$/ crystals are discussed from the scope of the conventional model. We found sufficient discrepancies between the model predictions and observed linewidths in LiNbO$-3$/ crystals. The general expressions for the four-wave signal dependence from phase mismatches in periodically-poled crystals and in spatially-limited crystal areas are derived. !11
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