Overview
- Contains a general introduction to the so-called Floquet-Bloch theory, which provides analytical tools to investigate the spectrum of periodic differential operators.
- Describes the numerical technique to solve Maxwell eigenvalue problems to compute the bandstructure of 3D photonic crystals.
- Introduces the theory of direct and inverse scattering and applies it to periodic media.
- Investigation of nonlinear optical effects in wave guides that can be described by the nonlinear Schrödinger equation.
- Includes supplementary material: sn.pub/extras
Part of the book series: Oberwolfach Seminars (OWS, volume 42)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (5 chapters)
Keywords
About this book
<p>This book concentrates on the mathematics of photonic crystals, which form an important class of physical structures investigated in nanotechnology. Photonic crystals are materials which are composed of two or more different dielectrics or metals, and which exhibit a spatially periodic structure, typically at the length scale of hundred nanometers.</p>
<p>In the mathematical analysis and the numerical simulation of the partial differential equations describing nanostructures, several mathematical difficulties arise, e. g., the appropriate treatment of nonlinearities, simultaneous occurrence of continuous and discrete spectrum, multiple scales in space and time, and the ill-posedness of these problems.</p>
<p>This volume collects a series of lectures which introduce into the mathematical background needed for the modeling and simulation of light, in particular in periodic media, and for its applications in optical devices.</p>
Authors and Affiliations
Bibliographic Information
Book Title: Photonic Crystals: Mathematical Analysis and Numerical Approximation
Authors: Willy Dörfler, Armin Lechleiter, Michael Plum, Guido Schneider, Christian Wieners
Series Title: Oberwolfach Seminars
DOI: https://doi.org/10.1007/978-3-0348-0113-3
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2011
Softcover ISBN: 978-3-0348-0112-6Published: 18 May 2011
eBook ISBN: 978-3-0348-0113-3Published: 18 May 2011
Series ISSN: 1661-237X
Series E-ISSN: 2296-5041
Edition Number: 1
Number of Pages: VIII, 162
Topics: Mathematics, general