Optical Fiber Coupler Analysis Using Daubechies Wavelets

Abstract

This article presents the theoretical analysis of a signal coupling between a proposed Photonic Crystal Fiber (PCF) and a Conventional Fiber with Step Index (CFSI) system. In this analysis, the Finite Element Method (FEM) and Beam Propagation Method (BPM) are applied together with Daubechies wavelets as basis function and described in the mathematical formulation. The simulations were performed casting the PCF signal into CFSI core using the PCF refractive index. For simulation purposes, the cladding material refractive index was set as 1.5% lower than the core index. The application of Daubechies wavelets as basis functions in BPM analysis presented insertion loss around 3.8% during the fiber coupling.

Use of Daubechies Wavelets in the Representation of Analytical Functions

“…Wavelets are widely used in the solution of numerical problems in several areas of knowledge such as image compression, Numerical Harmonic Analysis [2], financial analysis, oil detection, differential Equations [3,4], biomedical signals, analysis of electromagnetic integral Equations [5], optical fibers [6], among others. Many of these applications use the specific properties of wavelets, such as coefficients that are determined numerically, multi-resolution analysis to decompose a signal, integrals, and derivatives obtained numerically, energy concentrated in its compact and base with orthogonal elements.…”