Applied Mathematical Sciences

Scattering Theory for Diffraction Gratings

Authors: Wilcox, Calvin H.

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About this book

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.

Table of contents (3 chapters)

Table of contents (3 chapters)

Buy this book

eBook $84.99
price for USA in USD
  • ISBN 978-1-4612-1130-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $109.99
price for USA in USD
  • ISBN 978-0-387-90924-0
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Scattering Theory for Diffraction Gratings
Authors
Series Title
Applied Mathematical Sciences
Series Volume
46
Copyright
1984
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-1130-3
DOI
10.1007/978-1-4612-1130-3
Softcover ISBN
978-0-387-90924-0
Series ISSN
0066-5452
Edition Number
1
Number of Pages
180
Topics