V.V. Yatsyk

Results of the numerical analysis of a problem of resonant scattering and generation of the third harmonic are resulted at excitation nonlinear, isotropic, cubically polarisable, non-magnetic, linearly polarised (Е-polarisation), the layered dielectric structure by a plane wave. Decisions of system of the one-dimensional nonlinear integrated equations (equivalent a considered boundary-value problem) concerning complex Fourier amplitudes of fields scattering and generated by a non-linear layer on the basic and trebled frequency are investigated. The algorithm of the solution of the system of non-linear integral equations is given. It is based on one of possible iterative schemes, with application of a quadrature rule to each of the non-linear integrated equations of system. Results of calculations of values non-linear dielectric constants and diffraction characteristics of the scattered and generated fields depending on value of amplitude and angle of falling of a plane wave are presented. The dependence characterizing the portions of generated energy in the third harmonic on the value of the falling corner and the amplitude of the excitation field of the non-linear structure is given. In particular, within the framework of the closed system under consideration it is shown that the imaginary part of the dielectric constant, determined by the value of the non-linear part of the polarization at the excitation frequency, characterises the loss of energy in the non-linear medium (at the frequency of the incident field) due to the generation of the electromagnetic field of the third harmonic (at the triple frequency).