Abstract
This paper presents a rigorous validation of Finite-Difference Time-Domain (FDTD) simulations against two-dimensional (2D) analytical frameworks for dielectric slab waveguides. A systematic methodology is introduced to resolve common discrepancies arising from dimensional reduction and coordinate mismatch between 3D physical geometries and 2D numerical domains. By implementing a two-step Effective Index Method (EIM) to achieve a 2.5D simulation framework, and utilizing a geometry-aligned rotated coordinate system, the study successfully maps analytical transverse-electric (TE) and transverse-magnetic (TM) modes to their FDTD counterparts (TM แถป and ๐ ๐แถป ) at a source wavelength of ๐. ๐ ๐ ฮผ ๐ฆ . Results demonstrate a high degree of correlation between the numerical field profiles and analytical mode shapes, validating the proposed mapping strategy for smooth dielectric waveguides.