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Resonant Scattering and Generation of Waves: Cubically Polarizable Layers
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Titel: | Resonant Scattering and Generation of Waves: Cubically Polarizable Layers/ by Lutz Angermann, Vasyl V. Yatsyk |
Format: | E-Book |
Sprache: | Englisch |
veröffentlicht: |
Cham
Springer International Publishing
2019
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Mathematical Engineering Springer eBook Collection SpringerLink |
Schlagwörter: | |
Quelle: | Verbunddaten SWB |
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520 | |a 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 | ||
520 | |a 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 | ||
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author | Angermann, Lutz, Yatsyk, Vasyl V. |
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contents | 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 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 |
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spelling | Angermann, Lutz VerfasserIn aut, Resonant Scattering and Generation of Waves Cubically Polarizable Layers by Lutz Angermann, Vasyl V. Yatsyk, Cham Springer International Publishing 2019, Online-Ressource (XX, 208 p. 72 illus., 68 illus. in color, online resource), Text txt rdacontent, Computermedien c rdamedia, Online-Ressource cr rdacarrier, Mathematical Engineering, Springer eBook Collection, SpringerLink Bücher, 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 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, Springer eBook Collection. Engineering, Physics, Computer science Mathematics, Computer mathematics, Solid state physics, Optical materials, Electronic materials, Engineering mathematics., Yatsyk, Vasyl V. VerfasserIn aut, 9783319963006, Erscheint auch als Druck-Ausgabe 978-3-319-96300-6, Printed edition 9783319963006, http://dx.doi.org/10.1007/978-3-319-96301-3 Verlag Volltext, https://doi.org/10.1007/978-3-319-96301-3 X:SPRINGER Resolving-System lizenzpflichtig, https://swbplus.bsz-bw.de/bsz508132088cov.jpg V:DE-576 X:Springer image/jpeg 20180802141106 Cover, https://zbmath.org/?q=an:1414.78001 B:ZBM 2021-04-12 Verlag Zentralblatt MATH Inhaltstext, http://dx.doi.org/10.1007/978-3-319-96301-3 DE-14, DE-14 epn:3588575782 2020-02-06T11:11:32Z, http://dx.doi.org/10.1007/978-3-319-96301-3 DE-Ch1, DE-Ch1 epn:337664179X 2018-11-30T16:17:09Z, DE-105 epn:3376641897 2018-12-10T12:24:33Z, http://dx.doi.org/10.1007/978-3-319-96301-3 DE-Zwi2, DE-Zwi2 epn:3376642052 2018-11-08T17:30:15Z |
spellingShingle | Angermann, Lutz, Yatsyk, Vasyl V., Resonant Scattering and Generation of Waves: Cubically Polarizable Layers, 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 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, Physics, Computer science Mathematics, Computer mathematics, Solid state physics, Optical materials, Electronic materials, Engineering mathematics. |
swb_id_str | 508132088 |
title | Resonant Scattering and Generation of Waves: Cubically Polarizable Layers |
title_auth | Resonant Scattering and Generation of Waves Cubically Polarizable Layers |
title_full | Resonant Scattering and Generation of Waves Cubically Polarizable Layers by Lutz Angermann, Vasyl V. Yatsyk |
title_fullStr | Resonant Scattering and Generation of Waves Cubically Polarizable Layers by Lutz Angermann, Vasyl V. Yatsyk |
title_full_unstemmed | Resonant Scattering and Generation of Waves Cubically Polarizable Layers by Lutz Angermann, Vasyl V. Yatsyk |
title_short | Resonant Scattering and Generation of Waves |
title_sort | resonant scattering and generation of waves cubically polarizable layers |
title_sub | Cubically Polarizable Layers |
title_unstemmed | Resonant Scattering and Generation of Waves: Cubically Polarizable Layers |
topic | Physics, Computer science Mathematics, Computer mathematics, Solid state physics, Optical materials, Electronic materials, Engineering mathematics. |
topic_facet | Physics, Computer science, Computer mathematics, Solid state physics, Optical materials, Electronic materials, Engineering mathematics., Mathematics |
url | http://dx.doi.org/10.1007/978-3-319-96301-3, https://doi.org/10.1007/978-3-319-96301-3, https://swbplus.bsz-bw.de/bsz508132088cov.jpg, https://zbmath.org/?q=an:1414.78001 |
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