An Explicit Finite Difference Wide Angle Beam Propagation Method

Abstract

In recent years, significant improvements in the beam propagation method(BPM) have taken place mostly to be able to design and analyze various photonic integrated circuits(PIC). The efficiency of the scalar paraxial BPM has been improved through finite difference algorithms. The vector nature of the wave propagation in PICs has been studied using the paraxial vector BPM. In addition, several wide angle beam propagation algorithms have been developed using a higher order expansion of a Helmholtz propagation operator[l] with the operator splitting or using a recursive Pade formula[2][3]. All the reported algorithms are implicit schemes which require the solution of linear matrix equation[2][3] or that in combination with the fast Fourier transform[l]. The purpose of this paper is to introduce a simple explicit finite difference wide angle BPM. This wide angle propagation technique is compared with the paraxial BPM through numerical examples which are a tilted propagation in a dielectric waveguide and the diffraction of a focused gaussian beam in homogeneous media.