Dispersive media in the body-centered tetragonal FDTD method via auxiliary differential equations

The body-centered tetragonal finite-difference time-domain (BCT-FDTD) method collocates all three electric- and magnetic-field components at each lattice node, removing the inter-component staggering of the standard Yee grid. We extend BCT-FDTD to dispersive media by porting the unified multi-pole auxiliary-differential-equation (ADE) formulation to the collocated grid. Material dispersion is carried by one complex polarization-pole current per pole, advanced by a single scalar recursion identical for the Drude, Debye, Lorentz, and critical-point models; the recursion enters only the local field-update coefficients and leaves the BCT curl stencil unchanged. We validate the scheme against Lorentz and Drude slabs (within 0.4% of the analytic spectra), a crystalline-silicon thin film (a Drude pole and three critical points), and periodic arrays of silver and gold nanospheres, with the Maxwell–Garnett effective medium used as a quasistatic reference. The primary Yee comparisons use matched three-dimensional sampling density. At the finest resolution the two grids place the plasmon resonance within 0.9% of each other in all six metal–radius combinations, and on production-scale grids the collocated solver runs at equal or lower cost. The method makes BCT-FDTD directly applicable to plasmonic and semiconductor nanophotonics, and generalizes naturally to anisotropic and nonlinear dispersive media.