The threaded BPM: A novel extension to the two-dimensional scalar beam propagation method

The two-dimensional scalar beam propagation method (BPM) is a widely used, computationally efficient tool for the analysis of planar optical waveguides and devices. The inherent paraxial limitations and rectilinear analysis grid limit its application to slightly curved structures and waveguides. In this novel extention to the BPM algorithm, the curvature restrictions are removed and in many cases the paraxial restrictions can be avoided, allowing for the first time, the efficient analysis of arbitrarily curved structures, such as S- or U-shaped bends, curved transitions of progressively varying curvature, and curved couplers. It can also handle concatenated devices and the curved interconnect sections between them. The process operates by the concatenation of micro-conformal maps, which progressively re-orientate the problem optimally towards a straight BPM analysis.