Resonant Scattering and Generation of Waves
-15%
portes grátis
Resonant Scattering and Generation of Waves
Cubically Polarizable Layers
Yatsyk, Vasyl V.; Angermann, Lutz
Springer International Publishing AG
08/2018
208
Dura
Inglês
9783319963006
15 a 20 dias
3421
Descrição não disponível.
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.
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third-harmonic generation;finite element methods;Q-factor analysis;nonlinear boundary value problem;cubic susceptibility;frequency tripling;Maxwell's equations;nonlinear polarizability;nonlinear integral equations;Sturm-Liouville boundary value problems;wave propagation;frequency domain model;Hemmerstein integral equation;Kerr nonlinearity;cubic polarization;trace inequality;spectral analysis;spectral energy relationships;solvability theory;numerical spectral analysis
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.
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
third-harmonic generation;finite element methods;Q-factor analysis;nonlinear boundary value problem;cubic susceptibility;frequency tripling;Maxwell's equations;nonlinear polarizability;nonlinear integral equations;Sturm-Liouville boundary value problems;wave propagation;frequency domain model;Hemmerstein integral equation;Kerr nonlinearity;cubic polarization;trace inequality;spectral analysis;spectral energy relationships;solvability theory;numerical spectral analysis
