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Photonic Crystals: Mathematical Analysis and Numerical Approximation

  • Book
  • © 2011

Overview

Authors:
  1. Willy Dörfler

    1. , Institut für Angewandte und Numerische M, Karlsruhe Institut für Technologie, Karlsruhe, Germany

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  2. Armin Lechleiter

    1. , INRIA Saclay and CMAP, Ecole Polytechnique, Palaiseau Cedex, France

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  3. Michael Plum

    1. Institut für Analysis, Karlsruher Institut für Technologie, Karlsruhe, Germany

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  4. Guido Schneider

    1. , Department of Mathematics, University of Stuttgart, Stuttgart, Germany

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  5. Christian Wieners

    1. , Institut für Angewandte und Numerische M, Karlsruhe Institut für Technologie, Karlsruhe, Germany

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  • 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)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-viii
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  2. Introduction

    • Willy Dörfler, Armin Lechleiter, Michael Plum, Guido Schneider, Christian Wieners
    Pages 1-21

  3. Photonic bandstructure calculations

    • Willy Dörfler, Armin Lechleiter, Michael Plum, Guido Schneider, Christian Wieners
    Pages 23-62

  4. On the spectra of periodic differential operators

    • Willy Dörfler, Armin Lechleiter, Michael Plum, Guido Schneider, Christian Wieners
    Pages 63-77

  5. An introduction to direct and inverse scattering theory

    • Willy Dörfler, Armin Lechleiter, Michael Plum, Guido Schneider, Christian Wieners
    Pages 79-126

  6. The role of the nonlinear Schrödinger equation in nonlinear optics

    • Willy Dörfler, Armin Lechleiter, Michael Plum, Guido Schneider, Christian Wieners
    Pages 127-162

  7. Back Matter

    Pages 163-163
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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

  • , Institut für Angewandte und Numerische M, Karlsruhe Institut für Technologie, Karlsruhe, Germany

    Willy Dörfler, Christian Wieners

  • , INRIA Saclay and CMAP, Ecole Polytechnique, Palaiseau Cedex, France

    Armin Lechleiter

  • Institut für Analysis, Karlsruher Institut für Technologie, Karlsruhe, Germany

    Michael Plum

  • , Department of Mathematics, University of Stuttgart, Stuttgart, Germany

    Guido Schneider

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: Springer Basel 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

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