Abstract
An iterative algorithm is presented for analyzing the optimal resonant radiation properties of electromagnetic waves by cubically polarized nonlinear layers. The analysis is based on mathematical models for the rigorous treatment of the following problems: Self-consistent solution of both the system of boundary value problems of electrodynamics at resonant frequencies of excitation and generation, as well as the corresponding linearized eigenvalue problems with induced dielectric coefficients. The choice of the resonant excitation frequency of a nonlinear object in dependence on the real parts of the eigen frequencies of the spectral problems is discussed.
Highlights
The interest in the study of the properties of nonlinear objects has not diminished over the decades
We show that it is due to the resonant properties of the generated oscillations, that is, the coincidence of the real part of the eigenvalue of the spectral problem at the frequency of the generated oscillations with the generation frequency
The incident field acts in normal direction jnk = 00, n = 1, 2, 3, with amplitudes akinc 1 0, ainc 2k
Summary
The interest in the study of the properties of nonlinear objects has not diminished over the decades. It should be pointed out that, for a small amplitude of the irradiating field (that is if the generation of higher harmonics can be neglected) it is possible to describe a nonlinear medium by means of the simplest Kerr approximation. In such a situation, it is possible to analyze nonlinear layered structures as objects of resonant wave scattering only. In the general case of excitation by a packet of harmonic oscillations at multiple frequencies, the problem of numerical computation is reduced to a system of coupled boundary value problems with nonlinear Kerr-type permittivities induced at the multiple frequencies. Certain properties of the numerical method were checked computationally to confirm the validity of the proposed mathematical model and the results of the calculations obtained
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