Applications of Applied Mathematics to Extreme Nonlinear Optics Research
Abstract: The Arizona Center for Mathematical Sciences is a Mathematics Department research center operated within the College of Optical Sciences. There has been a long tradition of applied math students, working in various areas of nonlinear optics, who have graduated over the years. I will provide a brief overview of current ongoing research in the general area of extreme nonlinear optics. The relevant mathematical models range from full 3D Vector Maxwell, a Multiphysics Maxwell-Hydrodynamics model that captures water droplet shattering by ultrashort laser pulses etc and an in-house developed set of nonlinear pdes that capture the dynamical evolution of subcycle shock waves on the propagating E.M fields. A parallel experimental laboratory has been operated where theoretical designs of semiconductor laser structures are fabricated and converted into new classes of operating lasers.
