V. V. Yatsyk

In resonant area of frequencies the analysis of a problem of scattering and generation of waves is carried out at excitation isotropic, not magnetic, linearly polarised (Е polarisation), nonlinear layered dielectric structure with cubic polarizability of medium a package of the flat waves consisting of flat waves on multiple frequencies. Electromagnetic waves in the non-linear medium with a cubic polarisability are described by an infinite system of non-linear equations. At the study of particular non-linear effects it proves to be possible to restrict the examination to a finite number of equations, and also to leave certain terms in the representation of the polarisation coefficients, which characterize the physical problem under investigation. The analysis of excitation of transverse non-homogeneous nonlinear dielectric layered structure with a package of quasi-homogeneous electromagnetic fields has allowed receiving down a condition of phase synchronism of waves. Having added classical statement of a problem by a condition of phase synchronism, in strict statement the boundary-value problem diffraction of a package of flat waves on nonlinear layered dielectric structure taking into account generation of the third harmonic is considered. The investigated boundary-value problem is reduces to system one-dimensional (along structure height) nonlinear integrated Fredholm equations of the second sort concerning making complex Fourier amplitudes of the scattered and generated fields by a nonlinear layer.