MATLAB Implementation of 2D FDTD for TM Wave Simulation

This 2D Finite-Difference Time-Domain (FDTD) program is designed to simulate Transverse Magnetic (TM) wave propagation, primarily used for analyzing electromagnetic wave behavior. The implementation utilizes Yee's algorithm with staggered grid arrangement for electric and magnetic field components (Ez, Hx, Hy). The program simulates plane wave incidence through proper source implementation, typically using a total-field/scattered-field (TF/SF) boundary condition setup to inject plane waves into the computational domain.

Key algorithmic features include: Perfectly Matched Layer (PML) boundary conditions to minimize reflections from domain edges, material property assignment for different media regions, and time-stepping updates based on Maxwell's curl equations. The code calculates wave propagation through media, capturing reflection and refraction phenomena at material interfaces by enforcing continuity conditions for electromagnetic fields.

Users need to configure simulation parameters including grid resolution (dx, dy), time step (dt) satisfying Courant stability condition, domain size, PML layers, and material properties (permittivity, permeability). The program outputs time-domain field distributions that can be processed to analyze various electromagnetic phenomena like scattering patterns, transmission coefficients, and resonant behaviors in structured media.

This 2D FDTD implementation serves as a valuable computational tool for studying wave propagation problems, with applications in photonic device design, antenna analysis, and electromagnetic compatibility studies. The modular code structure allows for extensions to include dispersive materials, nonlinear effects, or additional boundary conditions.