Fast multipole method for periodic scattering problems

This presentation discusses an FMM for periodic boundary value problems for Maxwellpsilas equations in 3D. The periodic Green function and its derivatives, which are essential to the present method, are derived with Fourier analysis. We then apply the proposed method to scattering problems for two dimensional array of spheres and silicon woodpile structures, which are standard models in the field of photonic crystals. For the silicon woodpile structures, we compare the obtained energy transmittances with those in the previous studies. We observe good agreements.