Resonant Scattering and Generation of Waves
Springer International Publishing (Verlag)
978-3-319-96300-6 (ISBN)
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 |
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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 |
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 |
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