Energy characteristics of a nonlinear layer at resonant frequencies of wave scattering and generation

Abstract

This work presents a mathematical model, a computational scheme and experimental results describing the electrodynamic characteristics of a nonmagnetic, isotropic, E-polarized, nonlinear layered dielectric object with a cubically polarizable medium. The nonlinear object is irradiated by a quasi-homogeneous field, where the incident field constitutes of a packet of phase-synchronized plane oscillations. In the case under consideration the excitation may consist both of a highly intense electromagnetic field at a basic (fundamental) frequency, which results in the generation of the third harmonic, as well as of weakly intense fields at multiples of the basic frequency which produce no harmonics, but only have an influencing effect on the processes of wave radiation. The investigations were carried out within the setting of a coupled system approach at resonant excitation frequencies determined by the eigenvalues of the induced eigenvalue problems. A verification of the energy balance law is carried out. By means of estimations for the conditionalities of the occuring matrices, the level of degeneration of the induced non-self-adjoint spectral problems as well as the sensitivity of the coupled system of nonlinear boundary value problems with respect to computational errors are verified.