Simulation Of Em Wave Propagation In Three-Dimensional Structures By A Finite-Difference Method

We have developed a finite-difference time-domain solution to Maxwell’s equations for<br>simulating electromagnetic wave propagation in three-dimensional media. The algorithm<br>allows arbitrary variations of electrical conductivity and permittivity within a model. It<br>uses the Yee’s staggered grid technique to discretize the model and approximates spatial<br>derivatives with optimized second-order, finite differences everywhere except close to the<br>computational domain boundary where it uses conventional central differences. The pointwise<br>computational time of the optimized second-order difference scheme is the same as<br>that of the conventional fourth-order difference scheme, but the former has better dispersion<br>characteristics. Although the optimized difference scheme imposes stricter limitations<br>on the size of time steps allowed for an explicit time-marching scheme, a simple calculation<br>shows that this scheme is more cost-effective, due to its lower required spatial sampling rate,<br>than the conventional second- or fourth-order difference scheme. The temporal derivatives<br>are approximated by second-order central differences throughout.<br>We used the Liao transmitting boundary conditions to truncate an open problem. A<br>reflection coefficient analysis shows that this transmitting boundary condition works very<br>well. However, it is subject to instability. We propose a method which stabilizes the<br>boundary condition and which can be easily implemented.<br>The finite-difference solution was compared to closed-form solutions for both conducting<br>and non-conducting whole spaces and for a non-conducting half-space. In all cases, the<br>finite-difference results are in good agreement with the closed-form solutions.