© 2019

Resonant Scattering and Generation of Waves

Cubically Polarizable Layers


Part of the Mathematical Engineering book series (MATHENGIN)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Lutz Angermann, Vasyl V. Yatsyk
    Pages 1-43
  3. Lutz Angermann, Vasyl V. Yatsyk
    Pages 55-76
  4. Lutz Angermann, Vasyl V. Yatsyk
    Pages 77-100
  5. Lutz Angermann, Vasyl V. Yatsyk
    Pages 101-113
  6. Lutz Angermann, Vasyl V. Yatsyk
    Pages 115-122
  7. Lutz Angermann, Vasyl V. Yatsyk
    Pages 123-186
  8. Lutz Angermann, Vasyl V. Yatsyk
    Pages 187-196
  9. Back Matter
    Pages 197-208

About this book


This monograph deals with theoretical aspects and numerical simulations of the interaction of electromagnetic fields with nonlinear materials. It focuses in particular on media with nonlinear polarization properties. It addresses the direct problem of nonlinear Electrodynamics, that is to understand the nonlinear behavior in the induced polarization and to analyze or even to control its impact on the propagation of electromagnetic fields in the matter. 
The book gives a comprehensive presentation of the results obtained by the authors during the last decade and put those findings in a broader, unified context and extends them in several directions.
It is divided into eight chapters and three appendices. Chapter 1 starts from the Maxwell’s equations and develops a wave propagation theory in plate-like media with nonlinear polarizability. In chapter 2 a theoretical framework in terms of weak solutions is given in order to prove the existence and uniqueness of a solution of the semilinear boundary-value problem derived in the first chapter. Chapter 3 presents a different approach to the solvability theory of the reduced frequency-domain model. Here the boundary-value problem is reduced to finding solutions of a system of one-dimensional nonlinear Hammerstein integral equations. Chapter 4 describes an approach to the spectral analysis of the linearized system of integral equations. Chapters 5 and 6 are devoted to the numerical approximation of the solutions of the corresponding mathematical models. Chapter 7 contains detailed descriptions, discussions and evaluations of the numerical experiments. Finally, chapter 8 gives a summary of the results and an outlook for future work.


third-harmonic generation finite element methods Q-factor analysis nonlinear boundary value problem cubic susceptibility frequency tripling Maxwell's equations nonlinear polarizability nonlinear integral equations Sturm-Liouville boundary value problems wave propagation frequency domain model Hemmerstein integral equation Kerr nonlinearity cubic polarization trace inequality spectral analysis spectral energy relationships solvability theory numerical spectral analysis

Authors and affiliations

  1. 1.Institut für MathematikTechnische Universität ClausthalClausthal-ZellerfeldGermany
  2. 2.O.Ya. Usikov Insitute for Radiophysics and ElectronicsNational Academy of Sciences of UkraineKharkivUkraine

Bibliographic information

Industry Sectors
Energy, Utilities & Environment


“The book is a useful reference work, not only for professional theoreticians dealing with problems of nonlinear electrodynamics, but also for graduate students who can widely benefit from it.” (Vladimir Čadež, zbMATH 1414.78001, 2019)