Joint Summer Research Conference in the Mathematical Sciences
Mathematical Modeling of Novel Optical Materials and Devices
Topics

Invited Speakers

Schedule

Organizing Committee

Contact

Participants

Maps & Directions

Financial Assistance

Accommodation

Registration

Home

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.

Snowbird, Utah     June 11 - 17, 2005