Note that the simulation time and RAM scale differently for BPM and FDTD. This is because the BPM equation is solved along the propagation axis, whereas the FDTD algorithm solves for all grid points at each time step during the simulation. Therefore, the simulation time for BPM is linear with the structure length, while for FDTD a 2x increase in length results in a 4x time increase. The required RAM for BPM is constant with structure length because the algorithm only saves field data over the cross-section; for FDTD, the required RAM increases linearly with the structure length since field data is saved over the entire structure.
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1) Watts et al. "Integrated mode-evolution-based polarization rotators," Optics Letters, 30 (2005).