Scattering Theory for Diffraction Gratings

  • Calvin H. Wilcox

Part of the Applied Mathematical Sciences book series (AMS, volume 46)

Table of contents

  1. Front Matter
    Pages N1-ix
  2. Calvin H. Wilcox
    Pages 1-3
  3. Calvin H. Wilcox
    Pages 5-19
  4. Calvin H. Wilcox
    Pages 21-159
  5. Back Matter
    Pages 160-165

About this book

Introduction

The scattering of acoustic and electromagnetic waves by periodic sur­ faces plays a role in many areas of applied physics and engineering. Opti­ cal diffraction gratings date from the nineteenth century and are still widely used by spectroscopists. More recently, diffraction gratings have been used as coupling devices for optical waveguides. Trains of surface waves on the oceans are natural diffraction gratings which influence the scattering of electromagnetic waves and underwater sound. Similarly, the surface of a crystal acts as a diffraction grating for the scattering of atomic beams. This list of natural and artificial diffraction gratings could easily be extended. The purpose of this monograph is to develop from first principles a theory of the scattering of acoustic and electromagnetic waves by periodic surfaces. In physical terms, the scattering of both time-harmonic and transient fields is analyzed. The corresponding mathematical model leads to the study of boundary value problems for the Helmholtz and d'Alembert wave equations in plane domains bounded by periodic curves. In the formal­ ism adopted here these problems are intimately related to the spectral analysis of the Laplace operator, acting in a Hilbert space of functions defined in the domain adjacent to the grating.

Keywords

Beugungsgitter Boundary value problem Linearer partieller Differentialoperator Raleigh-Blochsche Welle Spektralanalyse Streutheorie scattering theory

Authors and affiliations

  • Calvin H. Wilcox
    • 1
  1. 1.Department of MathematicsUniversity of UtahSalt Lake CityUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1130-3
  • Copyright Information Springer-Verlag New York Inc. 1984
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-90924-0
  • Online ISBN 978-1-4612-1130-3
  • Series Print ISSN 0066-5452
  • About this book
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