Overview
- 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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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.
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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
Table of contents (8 chapters)
Reviews
Authors and Affiliations
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