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Contributed Talks 1
Speaker: Jichun Li, UNLV
Title: Error analysis of time-domain finite element
methods for 3-D Maxwell's equations in dispersive media
Abstract:
We consider the time dependent Maxwell's equations in
dispersive media on a bounded three-dimensional domain.
The standard finite element method and
mixed finite element method are developed
and error estimates are provided for both semi- and
fully-discrete schemes. We believe this is the first error
analysis carried out for time-domain finite element
methods for solving Maxwell's equations in dispersive media.
Speaker: Mikhail Erementchouk, CUNY
Title:
Exciton polaritons in one-dimensional resonant photonic crystals
Abstract:
Lately a significant attention is paid to a new class of problems
appeared at a merging point of traditional photonic crystals and
systems with a periodic arrangement of optically active elements.
These are resonant photonic crystals. The simplest model of such
structures is given by the Maxwell equations inside an elementary cell
with a rank one perturbation. For this (one-dimensional) model the
transfer matrix can be written in terms of corresponding solutions of
a Cauchy problem for the Maxwell equations without the perturbation.
This establishes a relation between the polariton dispersion law in
the resonant photonic crystal and that in purely passive and purely
active systems. The consideration is illustrated by several examples.
A special attention is paid to a resonance condition.
Speaker: Valery Smyshlyaev, Bath
Title:
Localised eigenstates for defects in high contrast periodic media
via homogenization
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