Resonant Scattering and Generation of Waves

Cubically Polarizable Layers

Lutz Angermann, Vasyl V. Yatsyk (Autoren)

Buch | Hardcover

XX, 208 Seiten

2018 | 1st ed. 2019
Springer International Publishing (Verlag)
978-3-319-96300-6 (ISBN)

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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.

The mathematical model.- Maxwell's 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.

"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 Cadez, zbMATH 1414.78001, 2019)

“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)

Erscheinungsdatum	09.08.2018
Reihe/Serie	Mathematical Engineering
Zusatzinfo	XX, 208 p. 72 illus., 68 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	508 g
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	cubic polarization • cubic susceptibility • Finite Element Methods • Frequency Domain Model • frequency tripling • Hemmerstein integral equation • Kerr nonlinearity • Maxwell's equations • Nonlinear Boundary Value Problem • Nonlinear integral equations • nonlinear polarizability • numerical spectral analysis • Q-factor analysis • solvability theory • Spectral Analysis • spectral energy relationships • Sturm-Liouville boundary value problems • third-harmonic generation • trace inequality • wave propagation
ISBN-10	3-319-96300-7 / 3319963007
ISBN-13	978-3-319-96300-6 / 9783319963006
Zustand	Neuware