FDTD Simulations of EM Waves
Maxwell’s Equations describe the spatial and time derivative relationships between electric and magnetic fields (in 1D shown below). One notable analytic solution, the simplest analytic solution, to this set of differential equations is the wave solution which underpins our understanding of modern RF engineering.
However, analytic solutions are hard work and it is much more common to analyze these equations using numerical methods. An easily implemented numerical solution is the Finite-Difference-Time-Domain (FDTD) method. By staggering the time domain, the derivative at x can be estimated by using f(x+-1/2).
This allows Maxwell’s Equations to be solved numerically, without all the hassle of actually doing rigorous math. This can be efficiently implemented using Matlab (or any language). Below is the FDTD code for a 1D implentation.
Using this various simulation environments can be created. The above code uses a soft source.