الفهرس 
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Abstract
Among the optical devices that have been adopted in different photonics applications, the cylindrical optical devices have played a dominant role. They have an enormous number of uses and applications starting from the optical connections that link photonic devices through any optical network as well as the variety of laser sources with a cylindrical shape such as the Vertical Cavity Surface Emitting Lasers (VCSELs). Along the continuous development in photonic technologies and the increasing interest in their related applications, the approximate computational models have been considered as a perfect candidate in characterizing these applications and evaluating their performance as well as determining the best designs for them in terms of geometry and manufacturing materials. Therefore, the aim of this thesis is presenting a mathematical approach that achieves the previous objectives and obtains the most accurate results in a fast and stable manner in order to characterize the cylindrical symmetric optical devices even those with multiple discontinuities. There is a number of numerical modelling techniques that have been adopted especially in computational photonics, including the finite element method (FEM). FEM proves its reliability in the analysis and design of photonic devices due to its flexibility and its ability to discretize the structure of the problem domain into different order of elements that can be interpolated with various orders of shape functions. In the presented thesis, we have developed a numerical approach based on FEM in order to simulate the optical devices of circular symmetry, and the modal analysis has been integrated with the beam propagation method (BPM) to analyze the waves propagation along these structures by one of the non-Iterative techniques of BPM. One of the main problems facing the modelling of cylindrical devices with multiple discontinuities, which in turn changes the behavior and the nature of the propagated waves, is the instability and divergence. Such problem has been considered in the introduced work by using blocked Schur algorithm (BSA). In which, the speed of processing through the elements of the resulted matrices has increased comparing to the other iterative methods such as Padé approximation and Taylor series expansion. The proposed model achieves efficient, fast, and accurate results through studying different structures of cylindrical optical devices. The results have been validated with numerical approaches and commercial softwares.