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Mathematical Modeling in Optics

Abstract : In the first part of the thesis, we study electromagnetic diffraction by bounded objects surrounded by nonlinear dielectric thin coating. We give a development of the fundamental and second-harmonic wave based on integral equation techniques.

In the second part, we study the convergence of the (\em supercell) method, used by physicists for approaching modes introduced by compactly supported defects in a photonic crystal. We study the convergence of this method giving a sense to the spectrum convergence. The exponential convergence of defect eigenvalues is proved.

The third part is dedicated to the study of wave propagation in photonic fibers. We derive a mathematical modelisation of these fibers which cladding is a 2D photonic crystal. Guided modes are characterized as eigenvalues of integral operators.
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Contributor : Sofiane Soussi <>
Submitted on : Friday, March 11, 2005 - 2:44:32 PM
Last modification on : Friday, January 10, 2020 - 3:42:10 PM
Long-term archiving on: : Friday, April 2, 2010 - 9:16:52 PM


  • HAL Id : tel-00008756, version 1



Sofiane Soussi. Mathematical Modeling in Optics. Mathematics [math]. Ecole Polytechnique X, 2004. English. ⟨tel-00008756⟩



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