Our research is focused on novel structures for controlling the interaction between electromagnetic waves and matter ranging from radio to optical frequencies. Periodic structures such as metasurfaces provide a medium for incorporating nonlinear or active circuit elements for applications such as antenna isolation, scattering control, improved absorption, and bandwidth enhancement for microwave structures. They can also enable extreme electric field enhancement for photoemission based microelectronic and plasmonic devices. Specific techniques include mathematics for arbitrary anisotropic impedance surface patterning, nonlinear or non-Foster based active materials, and nano-scale periodic structures for new optical effects. We also develop small broadband antennas, and new devices for biological applications of electromagnetics.