Relaxation approach for the generation of inhomogeneous distributions of uniformly sized particles

For many applications in gradient index devices and photonic crystals, it is necessary to be able to design semicrystalline distributions of particles where the lattice constant of the distribution is an arbitrary function of position. We propose a method to generate such distributions which is physically motivated by a system of interacting particles, and apply it to the design and implementation of a microwave gradient index lens. While the demonstration was preformed at microwave wavelengths, this technique would also be particularly useful for designing devices for operation at IR and visible wavelengths where the fabrication of distributions of uniformly sized holes or columns is very easy. © 2010 American Institute of Physics.