Photonic bandgap optimization in inverted fcc photonic crystals

We present results of photonic band-structure calculations for inverted photonic crystal structures. We consider a structure of air spheres in a dielectric background, arranged in an fcc lattice, with a cylindrical tunnel connecting each pair of neighboring spheres. We derive (semi)analytical expressions for the Fourier coefficients of the dielectric susceptibility, which are used as input in a standard plane-wave expansion method. We optimize the width of the photonic bandgap by applying a gradient search method and varying two geometrical parameters in the system: the ratios R/a and Rc/R, where a is the lattice constant, R is the sphere radius, and Rc is the cylinder radius. It follows from our calculations that the maximal gap width in this type of photonic-crystal structure with air spheres and cylinders in silicon is Δω/ω0 = 9.59%.