US-Cameroon Cooperative Research: Pade Approximants and the Physics of Waves

Denison University, Granville OH

Investigators

Abstract

0218015 Paul This award supports a two-year collaborative research project between Professor Prabasaj Paul, with the Department of Physics and Astronomy at Colgate University, and Professor Daniel Nkemzi, with the Department of Physics at the University of Buea, in Cameroon. They will investigate the application of Pade approximants to the problems of scattering of electromagnetic waves, and of photonic materials with maximal bandgaps. The problem of electromagnetic wave scattering from rough surfaces is important to many branches of physics and mathematics. Using some powerful mathematical techniques, the multipoint Pade approximants, the two researchers will investigate the scattering of waves off uneven surfaces with very large roughness parameters, as well as the transmission of light through regions with a spatially varying refractive index. The Pade approximants of the scattering matrix will preserve two important properties, reciprocity and unitarity. The investigators expect their model to yield better results than existing mathematical models that are based on a classical perturbation series. The study combines Professor Paul's expertise in condensed matter and quantum physics with Professor Nkemzi's knowledge of applied mathematics, principally in wave propagation. The results are expected to add new knowledge about wave scattering from rough surfaces, and will have application to many areas of mathematics and physics.