Some applications of a fundamental scheme to simple implementations of the finite-difference time-domain method and the beam-propagation method

A fundamental scheme has recently been developed for simple implementations of the implicit finite-difference time-domain (FDTD) methods based on the alternating-direction implicit and locally one-dimensional (LOD) schemes. The advantage of the fundamental scheme is that the number of arithmetic operations of the resultant equations is significantly reduced in the right-hand sides, when compared to that without the fundamental scheme. In this article, we develop a frequency-dependent LOD body-of-revolution FDTD based on the fundamental scheme. For the assessment of the developed method, a plasmonic rod waveguide is analyzed with attention to the time step size beyond the stability limit. We also apply the fundamental scheme to a reformulation of the full-vectorial beam-propagation method for the eigenmode analysis of optical waveguides.