  Using adaptive algorithms, the design of nano-scale dielectric structures for
photonic applications is explored. Widths of dielectric layers in a linear
array are adjusted to match target responses of optical transmission as a
function of energy. Two complementary approaches are discussed. The first
approach uses adaptive local random updates and progressively adjusts
individual dielectric layer widths. The second approach is based on global
updating functions in which large subgroups of layers are adjusted
simultaneously. Both schemes are applied to obtain specific target responses of
the transmission function within selected energy windows, such as discontinuous
cut-off or power-law decay filters close to a photonic band edge. These
adaptive algorithms are found to be effective tools in the custom design of
nano-scale photonic dielectric structures.
