Oberwolfach Seminars

Photonic Crystals: Mathematical Analysis and Numerical Approximation

Authors: Dörfler, W., Lechleiter, A., Plum, M., Schneider, G., Wieners, C.

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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.
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About this book

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.

Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook $39.99
price for USA in USD
  • ISBN 978-3-0348-0113-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • Immediate eBook download after purchase and usable on all devices
  • Bulk discounts available
Softcover $49.99
price for USA in USD
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Photonic Crystals: Mathematical Analysis and Numerical Approximation
Authors
Series Title
Oberwolfach Seminars
Series Volume
42
Copyright
2011
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-0113-3
DOI
10.1007/978-3-0348-0113-3
Softcover ISBN
978-3-0348-0112-6
Series ISSN
1661-237X
Edition Number
1
Number of Pages
VIII, 162
Topics