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Accurate and efficient solutions of wave propagation problems in periodic media – Catalin Turc

Date: Mon. January 31st, 2011, 12:30 pm-1:30 pm
Location: Rockefeller 221

Many devices designed to guide and control waves rely on periodic structures on the wavelength scale: these include diffraction gratings (used to squeeze multiple signals onto a single optical fiber, and in our highest-powered lasers), photonic crystals (the most promising route to energy-efficient ultra-fast optical computation on a chip), meta-materials (allowing the control of waves in ways impossible in naturally-occurring media), and solar cells. I will present a class of efficient and accurate numerical methods based on boundary integral equations for the solution of wave propagation problems in piece-wise homogeneous periodic media. The main ideas behind these algorithms are (1) a novel representation of quasi-periodic Green’s functions that converges fast and (2) acceleration techniques based on equivalent sources and FFTs. The resulting solvers are fast and accurate, as we will demonstrate through a variety of numerical examples.

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