| Abstract [eng] |
Analytical expressions are convenient because their numerical calculations demand considerably lower computing resources. The algorithms based on these expressions are highly adaptable for parallel computing. For these reasons analytical computed modeling can be used to evaluate a number of different systems at once. Laser beam propagation can also be visualized in high definition. In this thesis theory essential to analytical modeling of LASER beams will be introduced namely, Wave equation, Gaussian beams, analytical expressions for Electric field. Calculations will be based on tensor method for describing the Electric field distribution. This will be important in modeling and visualizing of elliptical Gaussian beams, calculating their propagation as well as analysis of Flattened Gaussian Beams. Models acquired using the software package created will be introduced. New results from modeling a real entire optical system will be discussed. Modeling was done with the goal to compensate astigmatism introduced by a reflective beam expander. Computational toolkit developed during this Masters project allows the user to evaluate and visualize beam propagation. While evaluating a number of different systems at once and plotting the parameters of interest in 3D space the astigmatism values obtained for TEM00 mode Gaussian and Flattened Gaussian beams agree with the theory and expand upon the empirical methods of evaluating astigmatism. It has been noticed, that astigmatism can be compensated for Flattened Gaussian beams in the same manner as for the fundamental Gaussian beams. This is important, because Flattened Beams need to be channeled using reflective telescopes or 4F systems as they are not modes of free space and their intensity distribution changes shape under free space propagation. |
