Incorporating lossy materials and PML into the split-field update FDTD method

Periodic structures, such as frequency selective surfaces, photonic bandgap structures, and antenna arrays, are being more widely used in electromagnetic systems. To make the numerical modeling of a periodic structure more practical, usually a single unit cell of the structure is modeled and periodic boundary conditions are used to incorporate the periodic nature. Traditionally, frequency-domain techniques are used to numerically model such structures because of the simple way in which the boundary condition can be applied. However, when broadband data is needed, a time-domain approach is desirable. Unfortunately, periodic boundary conditions in the time-domain introduce the need for time-advanced data, obviously a problem for a time-domain approach. To get around this, a field transformation can be applied which simplifies the boundary conditions, but results in a more complex set of equations to be solved. The FDTD algorithm can be applied to the transformed field equations; however, additional variables must be introduced because of stability considerations. One technique that has been developed for discretizing and solving the transformed field equations is the split-field method. This paper extends the method to include general anisotropic dielectric and magnetic media.