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020 _a9783319963013
_9978-3-319-96301-3
024 7 _a10.1007/978-3-319-96301-3
_2doi
050 4 _aQC19.2-20.85
072 7 _aPHU
_2bicssc
072 7 _aSCI040000
_2bisacsh
072 7 _aPHU
_2thema
082 0 4 _a530.1
_223
100 1 _aAngermann, Lutz.
_eauthor.
_0(orcid)0000-0003-3474-2160
_1https://orcid.org/0000-0003-3474-2160
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_938083
245 1 0 _aResonant Scattering and Generation of Waves
_h[electronic resource] :
_bCubically Polarizable Layers /
_cby Lutz Angermann, Vasyl V. Yatsyk.
250 _a1st ed. 2019.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2019.
300 _aXX, 208 p. 72 illus., 68 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aMathematical Engineering,
_x2192-4740
505 0 _aThe 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.
520 _aThis 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.
650 0 _aMathematical physics.
_911013
650 0 _aMathematics—Data processing.
_931594
650 0 _aOptical materials.
_97729
650 0 _aCondensed matter.
_917064
650 0 _aEngineering mathematics.
_93254
650 0 _aComputer science—Mathematics.
_931682
650 1 4 _aTheoretical, Mathematical and Computational Physics.
_931560
650 2 4 _aComputational Science and Engineering.
_938084
650 2 4 _aOptical Materials.
_97729
650 2 4 _aCondensed Matter Physics.
_914649
650 2 4 _aEngineering Mathematics.
_93254
650 2 4 _aMathematics of Computing.
_931875
700 1 _aYatsyk, Vasyl V.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_938085
710 2 _aSpringerLink (Online service)
_938086
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783319963006
776 0 8 _iPrinted edition:
_z9783319963020
776 0 8 _iPrinted edition:
_z9783030071721
830 0 _aMathematical Engineering,
_x2192-4740
_938087
856 4 0 _uhttps://doi.org/10.1007/978-3-319-96301-3
912 _aZDB-2-ENG
912 _aZDB-2-SXE
942 _cEBK
999 _c76293
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