Analysis of FDTD Numerical Dispersion Issues

This article explores the significance and impact of numerical dispersion in FDTD (Finite-Difference Time-Domain) simulations. We present a MATLAB implementation that helps users analyze how numerical dispersion affects electromagnetic wave propagation. The program incorporates key FDTD algorithm components including Yee cell discretization, leapfrog time stepping, and boundary condition handling. Through parameter variation studies, users can observe how spatial discretization (dx, dy, dz) and temporal sampling (dt) affect phase velocity errors across different frequency components. The implementation includes visualization functions to plot dispersion relationships and compare numerical results against theoretical models. Since numerical dispersion significantly impacts simulation accuracy across various electromagnetic applications, we recommend utilizing this program to understand dispersion mitigation techniques and optimize FDTD parameters for specific wavelength ranges and material properties.