Padé boundary conditions for finite element time domain beam propagation method

Abstract

In this paper, we present Pade approximation boundary conditions for domain truncation in time domain analysis using finite element (FEM) beam propagation method. The method removes the number of unknowns required for the conventional perfectly matched layer (PML). The line integral resulted from FEM discretization is treated by solving the one dimensional Helmholtz wave equation at domain ports. The square root resulted from the solution is handled using the conventional Pade approximation. A waveguide example is introduced to measure the Reflection of the proposed boundary condition. The comparison between our approach and the conventional PML shows that our method produces reflection far less than the conventional PML.