The Finite Element Beam Propagation Method Based on Adaptive Pad´e Approximation for Analyzing a Wide-Angle Waveguide

Abstract

This paper proposed a mathematical model for wide-angle structure to analyze and compare results from the first and second order of Pad´e approximation. The proposed method aims to improve accuracy and efficiency of the Vectorial Finite Element Beam Propagation Method (FE-VBPM) using the Pad´e approximation in the wide-angle formulation of the waveguide structure. The computational complexity is greatly reduced by using the transverse FE-BPM with rectangular nodal elements. The boundary condition includes the 2D perfectly matched layer (PML) in its calculation. The proposed method studies wave equations in the frequency domain of an isotropic medium. The relative power is calculated in the tapered waveguide, which is the non-uniform structure formulation. The simulation results are obtained and analyzed on four different angles of tapered waveguide structure.