Marcel Doosje

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%.

Scattering of light on the surfaces of photonic crystals

We present a new method to calculate the scattering of light at the surface of a photonic crystal. The problem is solved in terms of virtual surface-current distributions and the calculation takes full advantage of the existing infinite-space plane-wave expansion method for obtaining the photonic band structure. Working with surface currents makes the calculations less time-consuming by means of reduction of the dimensionality in the problem. The method is tested and illustrated for semi-infinite two-dimensional photonic crystals of small and large dielectric contrast.

Scattering of light on the surface of photonic crystals

We present a new method to calculate the scattering of light at the surface of a photonic crystal. The problem is solved in terms of virtual surface-current distributions and the calculation takes full advantage of the existing infinite-space plane-wave expansion method for obtaining the photonic band structure. Working with surface currents makes the calculations less-time consuming by means of reduction of the dimensionality in the problem. The method is tested and illustrated for semi-infinite two-dimensional photonic crystals of small and large dielectric contrast.