Абдуллин У.А., Ляхов Г.А., Руденко О.В., Чиркин А.С. «Возбуждение разностных частот в нелинейной оптике и условия черенковского излучения» Журнал экспериментальной и теоретической физики, 66, № 4, с. 1295-1304 (1974)

A theory of nonlinear optical effects is developed for the case when the transverse dimension of the region occupied by the nonlinear-polarization wave is of the order of the wavelength of the emitted wave. There arise in this case specific emission conditions similar to those under which the Vavilov-Cerenkov radiation is emitted. This case is of special interest in connection with the problem of the generation of far infrared radiation as a difference frequency. In contrast to other nonlinear optics problems in which the quasioptical approximation is widely used, the solution of the indicated problem requires the solution of the complete wave equation. The emission of Cerenkov difference frequency radiation (DFR) by a monochromatic-wave doublet, as well as by an ultrashort light pulse, is considered. In the latter case the Cerenkov radiation, which is inevitably generated in many media, can be treated as additional nonlinear losses. It is shown that in ordinary anisotropic media Cerenkov-radiation emission should be possible for both the forward and backward waves. This radiation possesses interesting distinctive features in optically active media, in which four Cerenkov angles can exist simultaneously. It is also shown that in DFR generation the Cerenkov condition can, besides the usual interference interpretation, also be accounted for on the basis of' the vector interaction between the angular components of the beams. The advantage of the Cerenkov DFR generation over the synchronous vector interaction of the beams is noted.