Authors:
Develops a theory that opens the way for practitioners to design or to optimize optical, optoelectronic or electromagnetic devices which make use of nonlinear material properties
Shows how artificial materials such as virtual gratings could be developed
Presents the first detailed mathematical and computational analysis of the effect of third-harmonic generation
Part of the book series: Mathematical Engineering (MATHENGIN)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
About this book
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.
Keywords
- 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
Reviews
Authors and Affiliations
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Institut für Mathematik, Technische Universität Clausthal, Clausthal-Zellerfeld, Germany
Lutz Angermann
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O.Ya. Usikov Insitute for Radiophysics and Electronics, National Academy of Sciences of Ukraine, Kharkiv, Ukraine
Vasyl V. Yatsyk
Bibliographic Information
Book Title: Resonant Scattering and Generation of Waves
Book Subtitle: Cubically Polarizable Layers
Authors: Lutz Angermann, Vasyl V. Yatsyk
Series Title: Mathematical Engineering
DOI: https://doi.org/10.1007/978-3-319-96301-3
Publisher: Springer Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-319-96300-6Published: 07 August 2018
Softcover ISBN: 978-3-030-07172-1Published: 28 December 2018
eBook ISBN: 978-3-319-96301-3Published: 26 July 2018
Series ISSN: 2192-4732
Series E-ISSN: 2192-4740
Edition Number: 1
Number of Pages: XX, 208
Number of Illustrations: 4 b/w illustrations, 68 illustrations in colour
Topics: Numerical and Computational Physics, Simulation, Computational Science and Engineering, Optical and Electronic Materials, Solid State Physics, Engineering Mathematics, Mathematics of Computing