FDTD Simulation of 2D TE Wave Propagation

For simulating 2D Transverse Electric (TE) wave propagation problems, we can conduct research using the Finite-Difference Time-Domain (FDTD) method. During the simulation process, to better approximate real-world environments, we must consider the impact of boundary conditions. Therefore, we implement Uniaxial Perfectly Matched Layer (UPML) boundary conditions to eliminate boundary reflections and simulate free-space propagation effects. This boundary condition approach significantly reduces computational errors and enhances simulation accuracy through proper impedance matching at domain boundaries.

Key implementation aspects include: - Discretizing Maxwell's equations using central-difference approximations in both space and time domains - Implementing TE-wave specific field components (Ez, Hx, Hy) update equations with leapfrog time stepping - Configuring UPML parameters through graded conductivity profiles to absorb outgoing waves - Applying convolutional perfect matched layer (CPML) formulations for improved numerical stability - Validating results through numerical dispersion analysis and reflection coefficient measurements