The methods described in the previous chapter for analytically treating outgoing waves and preventing reflections can be very effective under certain circumstances. However, a number of drawbacks are evident. The reflection coefficient that results from these analytical ABCs is a function of incident angle, and can be very high for grazing angles, as shown in Figure 8.4. Furthermore, as can be seen from the Higdon operators, for higher accuracy the one-way wave equation that must be applied at the boundary becomes increasingly complex, and requires the storage of fields at previous time steps (i.e., n − 1). One of the great advantages of the FDTD method is that it does not require the storage of any fields more than one time step back, so one would prefer a boundary method that also utilizes this advantageous property.

Those methods in the previous chapter should most accurately be referred to as “radiation” boundary conditions. This type of boundary emulates a one-way wave equation at the boundary, as a method for circumventing the need for field values outside the boundary, which would be required in the normal update equation. Strictly speaking, however, they are not “absorbing” boundary conditions.

The family of methods that will be discussed in this chapter are absorbing boundaries. These methods involve modifying the medium of the simulation in a thin layer around the boundary, as shown in Figure 9.1, so that this layer becomes an artifically “absorbing” or lossy medium.