Prof. Steven G Johnson
Professor of Applied Mathematics and Physics
Areas of Interest and Expertise
Photonic Crystals
Nanostructures and Computation
Electromagnetism
Structured Media
High Performance Computation
Fast Fourier Transforms
LargeScale Eignesolvers
Modeling and Simulation
Nanostructures and Computation
Electromagnetism
Structured Media
High Performance Computation
Fast Fourier Transforms
LargeScale Eignesolvers
Modeling and Simulation
Research Summary
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 bruteforce computation. In this modeling, we have made strides in developing semianalytical approaches that have shed new light on the problems of loss from disorder and other mechanisms. However, largescale 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 selfoptimizing software, which deals in an automated fashion with the burgeoning complexity of today’s computer hardware.

Projects
November 18, 2005Department of Mathematics
Nanostructures and Computation Group
Principal Investigator Steven Johnson
September 27, 2005Department of MathematicsMIT PhotonicBands (MPB)
Principal Investigator Steven Johnson
September 27, 2005Department of MathematicsPhotonic Crystals: Periodic Surprises in Electromagnetism
Principal Investigator Steven Johnson