My research falls in to 3 general areas: fundamental properties of superconductors, particularly electrodynamic properties; near-field microwave microscopy; classical and quantum chaos. My laboratory was originally built to explore the fundamental electrodynamic properties of superconductors at RF, microwave, and mm-wave frequencies. We use superconducting resonators and other instruments to measure the surface impedance and complex conductivity as a function of temperature, frequency, and magnetic field. This research has led to many insights about the fundamental properties of cuprate superconductors, and the proximity effect. We invented the near-field microwave microscope as an outgrowth of our superconductivity research. This instrument measures the electrodynamic properties (linear and nonlinear dielectric constant, resistivity, magnetic permeability, local superconducitng nonlinearities, etc.) of materials on scales between the nm and the mm length scales. We have multiple US patents on this instrument, and a small company (Neocera) has developed a version of our microscope for the semiconductor metrology industry (NeoMetriK). Our chaos work includes investigation of nonlinear circuits containing the semiconductor p/n junction. We have developed new ways to generate chaos at GHz frequencies using nonlinear feedback. We also work on the fundamental physics of quantum chaos. This is the study of quantum mechanical systems whose classical counterpart displays classical chaos. We test the predictions of random matrix theory using our microwave analog of the Schrodinger equation. This work also has a practical aspect associated with predictions of induced voltages on electronic components inside complicated enclosures. Our electromagnetic compatibility work has received a great deal of attention recently. This work is funded by the National Science Foundation, the Air Force, the US Government, and the CNAM.
condensed matter physics, superconductivity, near field microscopy, scanning probe microscopy, nonlinear circuit chaos, quantum chaos, nanotechnology, metamaterials, negative index of refraction, fluctuations, proximity effect, scanning laser microscopy, nonlinear superconductor