1D, 2D, and 3D Finite-Difference Time-Domain (FDTD) Methods with MATLAB Implementation

Sullivan's comprehensive reference provides detailed implementations of 1D, 2D, and 3D Finite-Difference Time-Domain (FDTD) methods specifically designed for MATLAB. These numerical techniques have demonstrated exceptional effectiveness in solving diverse problems across multiple domains including electromagnetics, optics, and acoustics. The FDTD method operates as a time-domain numerical analysis approach that solves Maxwell's differential equations governing electromagnetic wave propagation through various media. In MATLAB implementations, this typically involves discretizing the computational domain using Yee's grid algorithm and implementing leapfrog time-stepping schemes for stable time evolution. The implementation structure commonly includes defining material parameters using arrays, setting up boundary conditions through functions like PML (Perfectly Matched Layer), and processing field updates using central difference approximations. Key functions often involve vectorized operations for electric and magnetic field updates, with 1D implementations using simple array operations, 2D requiring matrix manipulations, and 3D simulations employing three-dimensional array operations for efficient computation. Through these MATLAB implementations, researchers can accurately model electromagnetic wave behavior in complex structures such as waveguides, antennas, and photonic devices. The method also enables crucial studies of electromagnetic wave interactions with biological tissues, making it invaluable for medical applications including hyperthermia treatment planning and biomedical imaging. MATLAB's computational environment provides an ideal platform for FDTD implementation, offering built-in visualization tools for field pattern analysis and optimization capabilities for performance enhancement. Overall, these FDTD methods represent powerful computational tools with broad applicability across scientific and engineering disciplines.