Novel photonic materials such as photonic crystals and metamaterials are scientifically engineered to interact with and control electromagnetic waves in ways that cannot be achieved with conventional materials. Photonic crystals exhibit bandgap phenomena and have proven very important as an integrated component in many optical devices. At sub-wavelength scales, the interaction between electromagnetic waves and conduction electrons at metallic interfaces leads to surface plasmon polaritons and to the confinement of electromagnetic fields over very small spatial dimensions with applications in heat transfer, energy harvesting and sensing. I will describe a range of numerical simulation and optimization algorithms for the design of photonic and plasmonic structures. These will include a multi-scale high order Hybridized Discontinuous Galerkin method, including novel approaches for accurate wave propagation, our topology optimization approach via convex optimization techniques, particularly semi-definite programming (SDP), and our fabrication adaptive optimization algorithm. We will illustrate our algorithms with examples in both photonic crystal design and plasmonics.
Professor of Aeronautics and Astronautics at MIT with an interest in numerical simulation, computational mechanics, and aerodynamics.