FDTD Plane Wave Simulation with UPML Boundary Conditions

The Finite-Difference Time-Domain (FDTD) method is a widely used numerical technique for electromagnetic field simulation. Plane wave simulation represents one of the fundamental applications of FDTD, enabling the study of electromagnetic wave propagation characteristics in free space or various media.

To minimize the impact of boundary reflections on simulation results, Uniaxial Perfectly Matched Layer (UPML) is typically implemented as an absorbing boundary condition. The UPML effectively absorbs outgoing waves, ensuring that the field distribution within the simulation domain remains undisturbed by boundary reflections.

Implementing this simulation in MATLAB involves several critical steps with corresponding code implementations: Grid Discretization: The computational domain is discretized into spatial grids with defined spatial steps (dx, dy, dz) and time steps (dt) that must satisfy the Courant stability condition. Code implementation typically involves defining grid dimensions using meshgrid functions. Plane Wave Excitation: Plane waves are introduced through either hard sources (direct field assignment) or soft sources (added to existing fields) using excitation waveforms like Gaussian pulses or sine-modulated Gaussian pulses. MATLAB implementation requires creating source functions and applying them to specific grid locations. UPML Boundary Processing: UPML layers are established at computational domain boundaries with optimized parameters including layer thickness and conductivity distribution profiles. The implementation involves modifying update equations within PML regions using stretched coordinate formulations. Field Update Iteration: Electric and magnetic field components are alternately updated according to FDTD's finite-difference scheme using central difference approximations. This involves implementing the core update loops that apply Maxwell's equations in discrete form, typically using vectorized operations for efficiency.

With proper parameter configuration, one can observe electromagnetic wave propagation, reflection, and transmission phenomena, providing valuable insights for antenna design, electromagnetic scattering studies, and wave-matter interactions.