New capabilities for fabricating materials at nanometer length scales have created the possibility of materials with new optical scattering properties. These materials are nano-scale dielectric and metallic scatterers, arranged in a periodic structure to harness resonant phenomena in their interaction with electric fields. Examples include photonic crystals, in which patterned dielectric structures are used as nano-scale optical waveguides. Multiple groups in the Electromagnetics Division are studying meta-materials, whose surfaces reflect or transmit light at very controlled frequencies with high efficiency and selectivity. These structures present challenges for mathematical modeling. For a precise simulation of these fields, this project requires the full vectorial solution to Maxwell's Equations, capable of capturing both near and far fields, to bridge the coupling of resonances dictated by both the nanometer scale structures and the macroscopic scale structures. Convergence properties of resulting mathematical sums are extremely subtle and careful scalings are necessary.

A huge amount of data comes out of these calculations. We are using immersive visualization to examine the complex dynamics of the electromagnetic fields. Field vectors are represented as geometric arrows in our three-dimensional immersive scene, and simulations of the periodic behavior of these vectors over time and frequency ranges give a complete picture of the outcome of these mathematical calculations.We visualized data for the electric, magnetic, and energy field vectors in and around an array of a sheet of atoms in a nanostructure. These vectors vary in a time-periodic function, and vary over a wide frequency range.