Finite-Difference Time-Domain (FDTD) Simulation of 2D Transverse Magnetic (TM) Wave Propagation

To simulate the propagation of two-dimensional (2D) Transverse Magnetic (TM) waves, we employ the Finite-Difference Time-Domain (FDTD) method. This numerical approach discretizes Maxwell's equations in both space and time domains using central difference approximations. The implementation typically involves updating electric and magnetic field components in leapfrog fashion: electric fields at integer time steps and magnetic fields at half-time steps. A critical aspect of this simulation is implementing absorbing boundary conditions to prevent unwanted reflections from computational domain boundaries. The Perfectly Matched Layer (PML) serves as an effective absorbing boundary condition that theoretically provides zero reflection at all frequencies and incidence angles. In code implementation, PML is realized by adding specially designed lossy layers around the main simulation domain, where field components are split and attenuated using conductivity profiles that gradually increase toward the outer boundaries. This approach enables more accurate wave propagation modeling and yields higher-quality simulation results by effectively minimizing boundary reflections.