Oblique Du-Fort Frankel Beam Propagation Method

The oblique BPM based on the Du-Fort Frankel method is presented. The paper demonstrates the accuracy and the computational improvements of the scheme compared to the oblique BPM based on Crank-Nicholson (CN) scheme. 1. Introduction Increasingly complex optical devices demand computationally fast and memory efficient algorithms for modelling purposes. Finite difference beam propagation method (FD-BPM) is a popular numerical technique for simulating large network of optical components due to its computational advantages over classical numerical techniques such as Finite Difference Time Domain (FDTD) method. The BPM method is commonly applied in the Cartesian coordinate system. However when the boundaries of an optical component are not aligned to the Cartesian mesh, for example in the case of tilted waveguides, bends and Mach-Zehnder modulators, sampling on the Cartesian mesh introduces nonphysical staircasing noise. The noise can be minimised by using very fine mesh but that in return incurs large computational costs. To more efficiently reduce the sampling error an improved three-point formulas are used at the interface which take into account the distance between the boundary and the transverse sampling points [1–3]. Further increase in accuracy of the Cartesian BPM, particularly for strongly guided waveguides, is achieved by considering the longitudinal component of magnetic field which is commonly neglected in the standard FD-BPM method [4]. In contrast to Cartesian system, Oblique and Structure Related (SR) coordinate system offers an accurate and efficient alternative for modelling nonorthogonal structures and automatically satisfies . The sampling grid of the SR mesh is aligned with the component material boundary thus eliminating staircase error and allowing relaxation in mesh size. Various SR-BPM schemes have been introduced [5–11] and different schemes can be combined together to map out the optical component. Furthermore, the SR coordinate system ensures high accuracy for the simple paraxial BPM formulation even without the use of wide-angled schemes [10]. The oblique equation takes into account the propagation direction, which is usually parallel to the structure boundary. Hence the mode-mismatch error is small. One of the motivations for implementation in oblique coordinates is to remove the need for high-order wide-angle scheme which requires substantial computational resources. Wide-angle for oblique coordinate has been developed by Sujecki [11]. However the author has also confirmed that the wide-angle oblique approach should in