Optical waveguide devices typically have dimensions transverse to the main propagation direction on the order of a fraction of a millimeter and therefore, cannot be modeled by ray or beam tracing techniques. In this small domain, numerical solutions of the fundamental field equations are usually employed. Two such implicit FD-BPM (Finite- Difference Beam Propagation Method) techniques have been integrated into a general optical engineering code: a full vector paraxial and scalar non-paraxial. Along with a more rigorous FDTD (Finite-Difference Time-Domain) calculation, their relative accuracies and efficiencies are compared on the practical 3D problem of coupling an optical system's focused spot into a single-mode fiber using a tapered mode converter. In all but the most extreme cases, the agreement between all three is better than expected especially considering that the runtimes vary drastically on a manycore desktop, with and without the help of a modern number-crunching GPU (Graphics Processing Unit).

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Alan W. Greynolds, "Comparison of 3D finite-difference methods for modeling waveguide components embedded in a general optical system," Proc. SPIE 11103, Optical Modeling and System Alignment, 111030L (Presented at SPIE Optical Engineering + Applications: August 13, 2019; Published: 11 September 2019); https://doi.org/10.1117/12.2526531.