1D FDTD Matlab Code Implementation for Electromagnetic Wave Simulation

In this article, we provide a detailed discussion of the 1D FDTD (Finite-Difference Time-Domain) method along with comprehensive Matlab code implementation. The 1D FDTD is a numerical computational method specifically designed for analyzing electromagnetic wave behavior and propagation characteristics. The code implementation utilizes Matlab's efficient matrix operations and includes key components such as: - Field update equations using central difference approximations - Perfectly Matched Layer (PML) boundary conditions implementation - Source excitation functions (Gaussian pulse and sinusoidal sources) - Time-stepping algorithm with stability condition (Courant condition) - Field visualization and data analysis modules This numerical method finds extensive applications in wireless communications, radar technology, antenna design, and optical systems. Our implementation provides a clear understanding of the fundamental principles behind the FDTD method, including the Yee algorithm spatial discretization and leapfrog time integration scheme. The Matlab code is structured with modular functions for easy customization and includes comprehensive comments explaining each computational step. Key functions implement the electric and magnetic field updates using discrete differential operators, ensuring numerical stability through proper spatial and temporal sampling. Even for users unfamiliar with the FDTD method, our code provides an accessible platform for electromagnetic simulations with features including parameter customization, real-time field visualization, and result analysis capabilities. The implementation emphasizes computational efficiency through vectorized operations and optimized memory management.