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.
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.
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.
General
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