Dynamic wave field synthesis: enabling the generation of field distributions with a large space-bandwidth product

The generation and manipulation of electromagnetic field distributions plays an essential role in physics in general, and particularly in the vast field of physical optics. In the current state of the art, one of the most convenient methods of performing this task is provided by either static or dynamic diffractive as well as holographic optical elements. Currently available dynamic optical elements, such as spatial light modulators, do offer on the one hand high temporal flexibility. They however have a limited space-bandwidth product (SBWP), and thus limited degrees of freedom. This arises primarily from a limitation in the number of controllable elements, their inherent two dimensional nature and limited lateral extent. Conventional static optical elements, such as planar or volume holographic elements, have on the other hand high degrees of freedom but low flexibility in terms of temporal applications. An optical system that facilitates dynamic synthesis of field distributions with high SBWP is thus highly desirable. This thesis presents a novel approach that facilitates the generation of a set of arbitrary orthogonal elementary waves, which can in turn be coherently superposed in order to generate optical fields with a high SBWP. To achieve this goal a hybrid system that consists of an angular multiplexed computer generated volume hologram (CGVH) as a static element and a spatial light modulator as a dynamic element is investigated, developed and characterized. CGVHs are volumetric holographic optical elements whose complex transmission function can be modeled mathematically in terms of the scattering potential of a given dielectric medium. This work presents an approach that employs perturbation theory in deriving a more elaborate mathematical model that is based on a series approximation of the complex wave field scattered from a volume hologram. The mathematical model behind this approach essentially incorporates various physical constraints that account for the discretized numerical design and a laser lithography based fabrication of the holograms in a non-linear optical material. Initial simulations and experimental work done to characterize this system show that the proposed approach facilitates a dynamic decoupling of single or a linear combination of far field projections without any detectable cross-talk between them. This work furthermore demonstrates that Bragg selectivity on the order of (change in angle = 1.1 x 10^10, i.e. approximately 4 orders of magnitude higher than the current state of the art, which is based on cascaded computer generated holograms