Advanced Numerical Methods in Diffractive Optics and Applications to Periodic Photonic Nanostructures

In this thesis, we present the Fourier Modal Method for computing periodic nanophotonic systems. We investigate waveguides and cavities inside woodpile photonic crystals and compare our numerical results with experimental measurements. Also, the polarization properties of opal photonic crystals are investigated. Additionally, we report on our efforts in improving the convergence of the method by adaptive spatial resolution for arbitrarily shaped structures.