Resonant Scattering and Generation of Waves: Cubically Polarizable Layers - Couverture souple

Livre 31 sur 45: Mathematical Engineering

Angermann, Lutz; Yatsyk, Vasyl V.

 
9783030071721: Resonant Scattering and Generation of Waves: Cubically Polarizable Layers
Couverture souple
ISBN 10 : 3030071723 ISBN 13 : 9783030071721
Editeur : Springer, 2018

Synopsis

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 system of 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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Éditeur
Springer
Date d'édition
2018
Langue
anglais
ISBN 10 
3030071723
ISBN 13 
9783030071721
Reliure
Broché
Nombre de pages
228
Coordonnées du fabricant
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Poststr. 9
Darmstadt
64293
Allemagne

Autres éditions populaires du même titre

9783319963006: Resonant Scattering and Generation of Waves: Cubically Polarizable Layers

Edition présentée

ISBN 10 :  3319963007 ISBN 13 :  9783319963006
Editeur : Springer International Publishin..., 2018
Couverture rigide