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Sofiane Soussi's Abstract
Defect modes calculations in photonic crystals and guided waves
We will address some of the basic issues of the supercell method
and prove the convergence of this technique. We prove an
exponential convergence of the defect frequencies with the {\em
supercell} size and give a justification of the quasi
independence of the corresponding eigenfunctions on the wave
vector. We also give a characterization of the {\em supercell}
eigenvalues corresponding to the background photonic crystal.
We will also study guidance of electromagnetic waves in photonic
fibers. We characterize guided modes in the fiber as
eigenfunctions of compact integral operators and prove their
exponential decay in the cladding. Then, we prove the possiblity
of opening gaps in the spectrum of the background medium making
it possible to guide electromagnetic waves with suitable cores.
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