Subwellenlängenstrukturen zur Erzeugung allgemeiner Phasenfunktionen

Data transmission through optical fibers, lithographic production of semiconductor components, and sensors for autonomous driving are just a few examples for optical technologies in modern societies. The usage of diffractive optical elements (DOEs) offers possibilities for almost arbitrary manipulation of light within small available spaces. One popular approach is the use of metamaterials, which can have properties that are impossible for classical materials. Here, mainly effective-index structures of dielectric materials have been considered. Computer-generated holograms (CGHs), a special type of DOEs, can be used to generate almost arbitrary intensity distributions by their diffraction pattern. The simulation of light propagation through DOEs can be quite challenging. A rigorous simulation of the entire element is often too difficult due to the enormous computational requirements. The aim of this work is to overcome the limitations of established algorithms. For this purpose, new methods for the optical simulation of general DOEs have been developed: On the one hand, the use of suitable approximations allows a significant reduction of the computational effort to solve Maxwell's equations. On the other hand, physical simulations can be bypassed by machine learning to predict the optical function. In addition, the application of the new methods to design and optimization tasks is demonstrated. The presented methods can be used to optimize a variety of DOEs, for example metalenses or beamsplitters with high numerical aperture. In particular, the design of pattern generators for three-dimensional measurement of objects, face recognition, or camera calibration are promising application areas.