Method of integral equations and extinction theorem in volumetric and surface phenomena in nonlinear optics

The method of integral equations of molecular optics [1] is based on the representation of the medium as the system of discrete oscillators and gives self-consistent description of the electromagnetic phenomena in medium without using operation of averaging when one comes from micro to macro-scopic field. In [2] the attempt has been made to apply method of integral equations to the nonlinear optics within the limits of the conception of local (microscopic) field. For justification of the corner-stone assumption that non-lineal polarization satisfies the wave equation it is necessary to assume the number of rather strict restrictions — plane pumping wave, plane interface between the media, approximation of given field and so on. In [3] this problem was solved in a general case without the above-mentioned assumptions but only for nonmagnetic medium with dipole mechanism of nonlinearity.