Daubechies Wavelets Aplication in Conjunction with the Vectorial Beam Propagation Method in the Analysis of Photonics Structures.
Daubechies Wavelets, VBPM, Photonics Structures
Wavelets are mathematical tools that allow the decomposition, description and representation of a given function. In this context, the propagation of signals in electrical, magnetic and optical devices can be numerically analyzed with the help of wavelets. Among the various types of wavelets, Daubechies has a peculiar property of having the compact support, which allows to describe the behavior of functions with discontinuities or abrupt variations of values in frequency and / or time domain. The numerical and computational performance of this type of wavelet presents a characteristic of special attention, regarding the time of simulation and obtaining accurate results when applied in the analysis of specific problems. It is important to highlight applications that use wavelets in antenna modeling, image study, oil detection, file compression, signal and image study, and artificial neural networks. In this work, the Daubechies wavelets are used in conjunction with the Vector Beam Propagation Method (VBPM) for photonic structure analysis. The work aims at the generation of base functions obtained through the translations and resolutions of this type of wavelet using the moment generating function.