Homogenization of Quasi-Periodic Photonic Crystals: The Cut-and-Project Multiple Scale Method

Explore an advanced mathematics seminar presentation where Professor Sebastian Guenneau from CNRS discusses a novel asymptotic procedure for homogenizing wave equations in quasiperiodic inhomogeneous media. Learn about the cut-and-project multiple scale method developed in collaboration with Elena Cherkaev, Niklas Wellander, and Frederic Zolla, which projects partial differential operators from a higher-dimensional space onto quasiperiodic functions in physical space. Discover how heterogeneous photonic quasicrystals can be approximated by homogeneous media using anisotropic tensors when wavelengths exceed periodic cell dimensions. Understand the broader applications of this mathematical approach to various wave problems involving linear partial differential equations in quasiperiodic structures derived from cut-and-projection techniques.