2D FDTD Program with PML Boundary Conditions and TM Wave Implementation

The two-dimensional finite-difference time-domain (FDTD) program represents a powerful numerical method for electromagnetic analysis, widely employed for simulating wave propagation in complex geometries. The implementation utilizes Yee's algorithm for spatial discretization, where electric and magnetic field components are staggered in both space and time to satisfy Maxwell's equations numerically. The program incorporates Perfectly Matched Layer (PML) absorption boundary conditions, which are implemented through complex coordinate stretching factors that create a lossy medium matching the impedance of the computational domain. The PML implementation involves splitting field components and applying anisotropic material parameters to effectively absorb outgoing waves without significant reflections. The simulation specifically handles transverse magnetic (TM) wave incidence, where the magnetic field remains perpendicular to the propagation direction. For TM mode implementation, the code tracks Ez, Hx, and Hy field components using central difference approximations for temporal and spatial derivatives. The update equations typically follow the leapfrog scheme, where electric fields are updated at integer time steps and magnetic fields at half-integer steps. Key implementation aspects include: - Field initialization routines that set up TM wave source conditions - PML parameter calculation for optimal absorption performance - Time-stepping loops implementing the core FDTD update equations - Boundary condition applications at each iteration - Field monitoring and data collection mechanisms This FDTD program with PML boundaries and TM wave configuration enables accurate analysis of electromagnetic behavior in various structures, making it particularly valuable for applications in microwave engineering, optical fiber design, and integrated optics systems. The code structure ensures numerical stability through careful consideration of Courant-Friedrichs-Lewy (CFL) conditions and proper handling of material interfaces.