Finite Elements Method (FEM) and Finite Difference Method (FDM) in the Euler implicit approach, were used in order to determine the bi-dimensional electromagnetic field. of an oscillating punctual source inside a square geometry with three reflective boundaries and an absorbing one. Although the main approach consist in solving the wave equation for the electric field., it was decided to use the approach of electromagnetic potentials V and A because those potentials give a simpler solution for both, the electric and magnetic field. Besides, a comparison with theory was made, solving for an electromagnetic field without boundaries produced by an oscillating punctual source.
The properties of Kummer beams propagation and transformation in optical metamaterials are studied. The possibility is established and conditions are determined for unidirectional and opposite directional propagation of Kummer light beams phase and the longitudinal component of its energy flux in metamaterials. The reflection and refraction coefficients of arbitrary Kummer beam are represented as superposition of linear combinations of reflection and refraction ones of TM- and TE- polarized Kummer beams. These properties are studied in the LG (Laguerre-Gaussian) beams and in Bessel beams. The main goal is to compare these three beams and to show the Kummer´s advantage. To use these mathematical functions a Computer Algebra Software has been used, specifically Maple.