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E-raamat: Resonant Scattering and Generation of Waves: Cubically Polarizable Layers

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  • Formaat: PDF+DRM
  • Sari: Mathematical Engineering
  • Ilmumisaeg: 26-Jul-2018
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319963013
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Resonant Scattering and Generation of Waves: Cubically Polarizable LayersSuurem pilt
  • Formaat: PDF+DRM
  • Sari: Mathematical Engineering
  • Ilmumisaeg: 26-Jul-2018
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319963013
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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.

Arvustused

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 ade, zbMATH 1414.78001, 2019)

The mathematical model.- Maxwells equations and wave propagation in
media withnonlinear polarizability.- The reduced frequency-domain model.- The
condition of phase synchronism.- Packets of plane waves.- Energy conservation
laws.- Existence and uniqueness of a weak solution.- Weak formulation.-
Existence and uniqueness of a weak solution.- The equivalent system of
nonlinear integral equations.- The operator equation.- A sufficient condition
for the existence of a continuous solution.- A sufficient condition for the
existence of a unique continuous solution.- Relation to the system of
nonlinear Sturm-Liouville boundary value problems.- Spectral analysis.-
Motivation.- Eigen-modes of the linearized problems.- Spectral energy
relationships and the quality factor of eigen-fields.- Numerical solution of
the nonlinear boundary value problem.- The finite element method.- Existence
and uniqueness of a finite element solution.- Error estimate.- Numerical
treatment of the systemof integral equations.- Numerical quadrature.-
Iterative solution.- Numerical spectral analysis.- Numerical experiments.-
Quantitative characteristics of the fields.- Description of the model
problems.- The problem with the Kerr nonlinearity.- The self-consistent
approach.- A single layer with negative cubic susceptibility.- A single layer
with positive cubic susceptibility.- A three-layered structure.- Conclusion
and outlook.- A Cubic polarization.- A.1 The case without any static field.-
A.2 The case of a nontrivial static field.- B Tools from Functional
Analysis.- B.1 Poincar´e-Friedrichs inequality.- B.2 Trace inequality.- B.3
Interpolation error estimates.- Notation.- References.- Index.
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