Photonic Crystals: Mathematical Analysis and Numerical Approximation

✍ Scribed by Willy Dörfler, Armin Lechleiter, Michael Plum, Guido Schneider, Christian Wieners (auth.)

• Publisher: Birkhäuser Basel
• Year: 2011
• Tongue: English
• Leaves: 172
• Series: Oberwolfach Seminars 42
• Edition: 1
• Category: Library

✦ Synopsis

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

Front Matter....Pages i-viii
Introduction....Pages 1-21
Photonic bandstructure calculations....Pages 23-62
On the spectra of periodic differential operators....Pages 63-77
An introduction to direct and inverse scattering theory....Pages 79-126
The role of the nonlinear Schrödinger equation in nonlinear optics....Pages 127-162
Back Matter....Pages 163-163

✦ Subjects

Mathematics, general