The general theory of a class of structure related (SR) non-orthogonal coordinate systems is introduced for the first time. Special cases of this type of coordinate system used separately or in combination can automatically follow the local geometry of many common optical waveguide designs, thereby facilitating the fast and accurate simulation of photonic circuits, when incorporated within a FD-BPM algorithm. Substantial savings in run time and memory are possible in comparison with standard FD-BPM in rectangular coordinates.
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