Matematické metody v diagnostice a v optimalizaci optických multivrstev

Abstract

The aim of this work is the description and optimization of optical multilayer parameters using selected mathematical methods. The algebraic, analytical, numerical and/or statistical approaches are used and combined for this purpose. The most of presented results were obtained using matrix algorithm for Rigorous coupled-wave analysis (Chapter 3). A solving of inverse problems by the use of minimizing numerical methods (Chapter 4) is one of the other applied methods. Besides the statistical data processing and testing hypotheses (Chapter 5) the application of the Green's electromagnetic tensor serves to a homogenization of anisotropic nanostructures by the EMA – effective medium approximation (Chapter 6). Also, a cost functional of several types for optical characteristics fitting in optical systems was designed and analysed. From the practical point of view, the optical nano-systems with plasmonic and magneto-plasmonic response were studied. Presented numerical as well as graphical outputs were performed with the help of own algorithms implemented as Matlab codes.