Aplicação das Wavelets de Daubechies em conjunto com o método de propagação vetorial de feixes na análise de estruturas fotônicas
In the Finite Element Method (FEM), the elements are connected by points, which are called nodes or nodal points. The set of elements and nodes, local and global, is known as mesh. In this case, what is subdivided into the mesh is the geometry of the structure to be analyzed. In order to analyze...
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| Formato: | doctoralThesis |
| Idioma: | pt_BR |
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| Endereço do item: | https://repositorio.ufrn.br/jspui/handle/123456789/27573 |
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| Resumo: | In the Finite Element Method (FEM), the elements are connected by points, which are
called nodes or nodal points. The set of elements and nodes, local and global, is known as
mesh. In this case, what is subdivided into the mesh is the geometry of the structure to be
analyzed. In order to analyze the physical behavior of the structure, we use mathematical
equations that do not have an exact solution, but can be approximated numerically. The
precision of the FEM depends on the number of nodes, the number of elements and the
size and types of elements that make up the mesh. That is, the smaller the size of the
element and the greater the number of them in a given mesh, the greater the precision
in the results of the analysis. In this context, the computer simulation software has been
evolving and seeks to improve the analyzes addressed by the FEM, improving the choice
of types and the generation of the mesh, leading to a good performance of the modeling
techniques. In this work, the search is for a better performance of FEM, when applied in
conjunction with other techniques, to simulate the propagation of electromagnetic waves
in dielectric waveguides. For this, we used the Daubechies wavelet as a mathematical tool
to obtain the coefficients of the elementary matrices, which arise in the analysis, due to
the geometry of the elements that form the mesh. Therefore, the proposal is to develop
a Daubechies base to be used in conjunction with the Vector Beam Propagation Method
(VBPM), in the analysis of the electromagnetic propagation in guided media. The VBPM
uses as a numerical basis the FEM and the method of the propagation of light beams in
optical structures. In order to reach the main objective of this work, a moment-generating
function was developed to generate functions of type x
k
, starting from a base of wavelets.
The function x
k was expressed by means of a Daubechies wavelet base which gave rise
to the elementary matrices of the VBPM, also known as base functions. To verify the
accuracy of the VBPM with the new set of base functions, wave propagation was analyzed
in a weak electromagnetic coupling dielectric guide and the transfer of energy between a
photonic crystal optical fiber and a conventional optical fiber. |
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