Resonant Scattering and Generation of Waves Cubically Polarizable Layers /

• Κύριοι συγγραφείς: Angermann, Lutz (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut), Yatsyk, Vasyl V. (http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Έκδοση: 1st ed. 2019.
• Σειρά: Mathematical Engineering,
• Θέματα: Physics.; Computer mathematics.; Optical materials.; Electronic materials.; Solid state physics.; Engineering mathematics.; Computer science-Mathematics.; Numerical and Computational Physics, Simulation.; Computational Science and Engineering.; Optical and Electronic Materials.; Solid State Physics.; Engineering Mathematics.; Mathematics of Computing.

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...

Πίνακας περιεχομένων:

• The mathematical model
• Maxwell's equations and wave propagation in media with nonlinear 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.