Simulation of Beam Propagation in 2D and 3D Media

The Finite-Difference Time-Domain (FDTD) method provides a robust approach for simulating light beam propagation in two- and three-dimensional media. This technique involves discretizing both spatial and temporal domains to numerically solve Maxwell's equations. In MATLAB implementation, key components include defining Yee's grid for field components, implementing absorbing boundary conditions (e.g., PML), and solving coupled electric and magnetic field updates through leapfrog time stepping. The algorithm typically handles field updates using central difference approximations, with E-field components calculated from prior H-field values and vice versa. MATLAB's matrix operations efficiently manage the 2D/3D grid structures, while built-in visualization tools enable analysis of propagation patterns, diffraction effects, and interactions with different material geometries. This approach allows researchers to model optical phenomena like waveguide coupling, photonic crystal behavior, and light-matter interactions through customizable permittivity/permeability distributions and source excitation setups.