FDTD Plane Wave Simulation with UPML in MATLAB

In the fields of electromagnetics and computational modeling, the Finite-Difference Time-Domain (FDTD) method serves as a widely-used numerical solution technique for solving Maxwell's equations. MATLAB, as a prominent scientific computing platform, provides an efficient environment for implementing FDTD numerical simulations. Plane waves represent a fundamental electromagnetic wave type that can model various application scenarios in wave propagation studies. The Uniaxial Perfectly Matched Layer (UPML) constitutes an advanced boundary condition algorithm designed to minimize unwanted reflections at computational domain boundaries, effectively simulating wave absorption and transmission characteristics.

The implementation typically involves discretizing Maxwell's equations using central difference approximations in both time and space domains. Key components include: electric and magnetic field update equations using Yee's grid arrangement, plane wave source implementation through total-field/scattered-field (TF/SF) formulation, and UPML boundary conditions implemented through stretched coordinate PML formulations. The MATLAB code structure generally comprises: field initialization arrays (Ex, Ey, Ez, Hx, Hy, Hz), material parameter definitions, time-stepping loops with field update equations, source excitation functions, and UPML absorption layers with complex coordinate stretching parameters.

By integrating FDTD-based plane wave simulation with UPML boundary conditions in MATLAB, researchers can accurately model electromagnetic field behavior across diverse scenarios. This approach provides scientists with a robust computational tool for investigating various challenges in electromagnetics research and computational modeling applications, enabling studies on wave propagation, scattering phenomena, and antenna design optimization.