Daubechies wavelets as basis functions for the vectorial beam propagation method

ABSTRACTWe analyze the propagation of electromagnetic signals in optical waveguides using the Daubechies wavelets as basis functions applied in a mathematical model based in finite element method (FEM). The Daubechies wavelets have the peculiar property of having the compact support, which allows describing the behavior of functions with discontinuities or some abrupt variations of values in frequency and/or time domain. Then, the basis functions and the Galerkin method (GM) are applied together with the vector beam propagation method (VBPM) to develop a new mathematical approach. In order to validate the proposed formulation performance, we analyze a new polished-type optical fiber coupler, for which two cores are curved in a parabolic shape, and between them, a leaky-waveguide with an index-matching liquid layer is included. The distance between cores has variable parameters. Due to the inclusion of the leaky-waveguide, the coupling distance drastically reduces.