The present work deals with the diffraction of visible, coherent light from three-dimensional photonic crystals as well as three-dimensional phase lattices. The difference between the latter structures is their refractive index modulation. Although the periodic modulation of the refractive index in three dimensions is in both cases of the order of a few micrometers, the photonic phase lattices have a continuous modulation of the refractive index while the photonic crystals have a discontinuous modulation, respectively.
The scattering properties of the photonic crystals / phase lattices are investigated in this thesis. The major investigation is done experimentally, but a modelling of the scattering curves is done as well. This modelling focuses on the applicability of approximate solution approaches. Therefore, a short primer on the numerical solution methods of Maxwell’s equations is given. Subsequently, approximate solutions are discussed where the attention is especially directed to the dependence and strength of the refractive index modulation. Furthermore, a short introduction of the used scattering geometry is given as well as a depiction of the experimental setup.
The scattering properties of the photonic crystals, given by the so-called woodpile structure, are specifically investigated regarding their refractive index dependence. Experimentally, this is achieved via infiltration of special refractive index liquids. Moreover, a classification of scattering regimes is sought which is based on the refractive index difference. In particular a transition of the so-called kinematic scattering which can be described by the Laue equations to a more dynamic scattering regime is investigated. In order to substantiate the experimental findings, simulations based on a rigorous numerical solution of Maxwell's equations are presented. Those results confirm the experimental classification of the scattering regimes.
Due to their differing refractive index modulation the holographic phase lattices are investigated in a separate part. Since the maximum refractive index difference is much smaller than the one for the previously mentioned photonic crystals and since such an investigation has been already published, a comparison of the experimental scattering efficiency of a phase lattice with a rigorous solution is omitted in favour of an approximate solution approach. This approach relies on the kinematic scattering theory. Furthermore, it is shown that this rather simple approach can well explain the light scattering from the considered structures. Merely, the scattering efficiencies cannot be described properly by the model.