MATLAB Implementation of Yee Algorithm and FDTD Method

The Yee algorithm and Finite-Difference Time-Domain (FDTD) method represent classical numerical simulation approaches in computational electromagnetics, widely applied in electromagnetic wave propagation, antenna design, and related fields. The core concept involves discretizing Maxwell's equations in both time and spatial domains for numerical solution. MATLAB implementation of Yee+FDTD typically involves these critical steps: First, establishing a three-dimensional spatial grid where electric and magnetic field components are arranged using staggered grids (Yee cells) to satisfy natural discretization requirements. The implementation then employs central difference approximations for time-stepping through curl equations, incorporating absorbing boundary conditions (such as Perfectly Matched Layers - PML) to simulate infinite space. The MATLAB code implementation includes update loops for electric and magnetic fields, where electric field components update at integer time steps while magnetic field components update at half-time steps. For performance optimization, vectorized operations are typically employed to avoid explicit loops. A complete implementation must also consider modules for excitation source setup (e.g., Gaussian pulses), material parameter mapping, and near-to-far-field transformations. This implementation provides significant reference value for understanding electromagnetic wave interactions with complex structures. With minor modifications, it can be adapted for cutting-edge research applications including photonic crystals and metamaterials studies. Key functions in the implementation would include grid generation using meshgrid, field update equations based on finite differences, and PML boundary condition implementation using conductivity profiling.