Tečná pole v matematickém modelu optické difrakce na periodických strukturách

Abstract

The aim of the work was to formulate and to solve the periodical diffraction problem using the boundary integral equations for the scalar components of the vector tangential fields on the one period of the common boundary. The periodical Green function is of key importance and its properties are discussed. The computational algorithm of the problem is based on the collocation method with the equidistant nodes and the system of trigonometric polynomials seems to be the best choice of the basis functions. The mathematical model is used to solve some chosen application problems of the optical diffraction, the results are compared to values obtained by the referential method. Further, the variational formulation of the periodical diffraction problem is presented together with the resume of the known related theoretical results.

In particular, the main contributions of the dissertation thesis are as follows: 1. Formulation of the diffraction problem on a periodical interface as the boundary integral equations for the scalar components of the tangential fields of intensity vectors. 2. Property analysis of the periodical fundamental solution of the Helmholtz equation. 3. Numerical implementation of the designed mathematical model. 4. Examples of the model applications and verification of the model by comparison to the referential method.