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The structure-related (SR) finite-difference beam-propagation method is applied to integrated optical couplers employing curved waveguide sections. A general nonorthogonal coordinate system is introduced that matches the local structure geometry, yielding a more accurate analysis with coarser meshes than standard schemes, thus providing significant computational resource savings. Furthermore, the algorithm is easily interfaced with conventional schemes. Examples of curved two-dimensional and three-dimensional directional waveguide couplers are examined to show the advantages and generality of SR schemes as well as to explore the role of the extra degrees of freedom offered by nonorthogonal meshing.