Nonlinear Optics: Physics, Analysis, and Numerics

Abstract

When high-intensity electromagnetic waves at optical frequencies interact with solids and/or nanostructures the materials’ response cannot anymore be described via simple linear relations. The resulting science of nonlinear optics has recently witnessed exiting developments that have brought to the fore numerous mathematical challenges that need to be addressed in order to fully exploit the opportunities that result from these developments. The mathematical modeling involves a system of partial differential equations where the Maxwell equations are coupled to evolution equations of the materials and their response to electromagnetic fields. Typically, the full coupled systems are quite complicated or even intractable so that the derivation, the analysis, and the numerical treatment of simplified effective models is often indispensable. In turn, this requires the close cooperation between researchers from theoretical physics and analysis/numerics in order to push forward the field on nonlinear optics.