Quantitative Benchmarking of a Split-Field PML FDTD Solver: Slit Diffraction, and Scattering from PEC and Dielectric Cylinders
This paper presents a two-dimensional TMz finite-difference time-domain (FDTD) solver based on Yee's scheme for modeling radiation from an infinitely long z-directed line current, with the open region truncated by a Berenger split-field perfectly matched layer (PML). After validating cylindrical-wave propagation and negligible late-time reflections in free space, the solver is applied to three inhomogeneous configurations: (i) diffraction through a one-cell-thick perfectly electrically conducting (PEC) sheet with single and double slits; (ii) scattering from infinitely long PEC cylinders of circular and rectangular cross section; and (iii) scattering from infinitely long dielectric cylinders of varying cross section and permittivity. Beyond qualitative field maps, the diffraction case is characterized quantitatively: a steady-state phasor extracted by a running discrete Fourier transform yields the transmitted intensity, from which the fringe visibility and the far-field pattern are computed and compared against the closed-form Fraunhofer prediction. The single- and double-slit cases are cleanly separated by a visibility that rises from near zero to near unity, and the double-slit interference maxima agree with the grating condition arcsin(m λ_0 / d) to within a fraction of a degree. For dielectric cylinders, the field penetrates the obstacle with the expected reduced internal wavelength λ_0 / \sqrt{ε_r}, and the scattered field strength grows with permittivity contrast. A reference-subtraction method isolates the scattered field throughout. The results confirm that the FDTD-PML framework accurately captures open-region diffraction and geometry- and material-dependent scattering.