The topic of my project is the numerical investigation of optical nanostructures. In detail, Maxwell's equations are solved in frequency domain by the Fourier modal method with the scattering matrix approach. The investigated nanostructures consist of metallic materials ('metamaterials') and dielectric materials ('photonic crystals'). On the one hand the aim of my thesis is the improvement of the existing simulation tool in terms faster convergence, and on the other hand to obtain a better understanding of the optical properties of these materials.