Prof. Steven G Johnson

Having joined both the faculty of Applied Mathematics and the Research Lab or Electronics (RLE) in the fall of 2004, Johnson's group has focused on two main directions of research. The first is that of understanding problems of wave propagation in nanostructured media, primarily photonic crystals -- periodic dielectric media that can mold the flow of light to yield unusual optical phenomena from confinement in air cavities to negative refraction. Because these are complicated structures, there are many open problems in their theoretical understanding, from what phenomena are possible to how to predict their behavior without resorting to brute-force computation. In this modeling, we have made strides in developing semi-analytical approaches that have shed new light on the problems of loss from disorder and other mechanisms. However, large-scale computation is of inevitable importance as well, and enabling such computation is the second focus of the group. In particular, we have developed one of the most widely used software libraries for fast Fourier transforms (FFTs) by continuing innovations in self-optimizing software, which deals in an automated fashion with the burgeoning complexity of today’s computer hardware.