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Abstract
The paper focuses on the development of a mathematical model, an effective algorithm and a self-consistent numerical analysis of the multifunctional properties of resonant scattering and generation of oscillations by nonlinear, cubically polarizable layered structures. The multifunctionality of such layered media is caused by the nonlinear mechanism between interacting oscillations—the incident oscillations (exciting the nonlinear layer from the upper and lower half-spaces) as well as the scattered and generated oscillations at the frequencies of excitation/scattering and generation. The study of the resonance properties of scattering and generation of oscillations by a nonlinear structure with a controllable permittivity in dependence on the variation of the intensities of the components of the exciting wave package is of particular interest. In the present paper, we extend our former results, and furthermore we analyze the realizability of multifunctional properties of nonlinear electromagnetic objects with a controllable permittivity. The results of our investigations (i) demonstrate the possibility to control the scattering and generation properties of the nonlinear structure via the intensity of the incident field, (ii) indicate the possibility of increasing the multifunctionality of electronic devices, of designing frequency multipliers, and other electrodynamic devices containing nonlinear dielectrics with controllable permittivity.
Public Interest Statement
Nonlinear dielectrics with controllable permittivity are intensively investigated and begin to find broad applications in device technology. The development of new types of dielectrics, the introduction, and production of modern functional electronic devices require a comprehensive knowledge about the properties of these materials. In this context, the properties of such solid and liquid nonlinear materials are of important, which practically enable the conversion of energy or information, modulation, detection, amplification, recording, storing, displaying, and other types of conversion of electrical, magnetic, and optical signals carrying information. The paper is devoted to the mathematical and computational investigation of a model of resonance scattering and generation of waves by an isotropic, nonmagnetic, nonlinear, layered, dielectric structure which is excited by two-sided acting packets of plane waves in the resonance frequency range. In particular, an algorithm for the numerical determination of the eigenfrequencies (resonance frequencies) and eigenfields is developed.
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Notes on contributors
Lutz Angermann
The authors perform joint research about scattering and generation of electromagnetic waves on nonlinear structures since more than 10 years.
Lutz Angermann is a professor of Numerical Mathematics at the Department of Mathematics of the Clausthal University of Technology since 2001. His research is concerned with the mathematical analysis of numerical algorithms for partial differential equations with special interests in finite-volume and finite-element methods and their application to problems in Physics and Engineering. He is the author of more than 100 research papers.
Vasyl V. Yatsyk
Vasyl V. Yatsyk is a senior scientist at the O.Ya. Usikov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine (O.Ya. Usikov IRE NASU) 1998, Kharkiv, Ukraine. He authored more than 100 papers. His research interests include scattering and generation effects on nonlinear materials, numerical–analytical methods of electromagnetic theory, resonant interaction, and dispersion of waves.