Advertisement

© 2011

Photonic Crystals: Mathematical Analysis and Numerical Approximation

Benefits

  • 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.

Book

Part of the Oberwolfach Seminars book series (OWS, volume 42)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Willy Dörfler, Armin Lechleiter, Michael Plum, Guido Schneider, Christian Wieners
    Pages 1-21
  3. Willy Dörfler, Armin Lechleiter, Michael Plum, Guido Schneider, Christian Wieners
    Pages 23-62
  4. Willy Dörfler, Armin Lechleiter, Michael Plum, Guido Schneider, Christian Wieners
    Pages 63-77
  5. Willy Dörfler, Armin Lechleiter, Michael Plum, Guido Schneider, Christian Wieners
    Pages 79-126
  6. Willy Dörfler, Armin Lechleiter, Michael Plum, Guido Schneider, Christian Wieners
    Pages 127-162
  7. Back Matter
    Pages 163-163

About this book

Introduction

This volume collects a series of lectures which provide an introduction to the mathematical background needed for the modeling and simulation of light, in particular in periodic media, and for its applications in optical devices.

The 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.

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.

Keywords

inverse problems nonlinear dynamics of modulated pulses numerical approximation spectral theory of periodic differential equations

Authors and affiliations

  1. 1., Institut für Angewandte und Numerische MKarlsruhe Institut für TechnologieKarlsruheGermany
  2. 2., INRIA Saclay and CMAPEcole PolytechniquePalaiseau CedexFrance
  3. 3.Institut für AnalysisKarlsruher Institut für TechnologieKarlsruheGermany
  4. 4., Department of MathematicsUniversity of StuttgartStuttgartGermany
  5. 5., Institut für Angewandte und Numerische MKarlsruhe Institut für TechnologieKarlsruheGermany

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
  • Copyright Information Springer Basel AG 2011
  • Publisher Name Springer, Basel
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-0348-0112-6
  • eBook ISBN 978-3-0348-0113-3
  • Edition Number 1
  • Number of Pages VIII, 162
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Mathematics, general
  • Buy this book on publisher's site
Industry Sectors
Aerospace
Automotive
Finance, Business & Banking