The time domain discrete Green's function as a boundary condition for three dimensional waveguide problems

For the calculation of the Green's function, the boundary layer is excited by a space-time impulse. The field within the computational domain is initially set to zero. By using the FDTD equations beyond the boundary, this impulse generates an output at the boundary, which allows the desired Green's function to be written in the form of a matrix. This matrix is subsequently used in the boundary condition, which is applicable for all types of excitations, including evanescent waves. A rectangular waveguide is used for a 3D demonstration of this method. The Green's function condition is applied at the one end of the waveguide in an FDTD computation with, say, TE/sub 10/ excitation. As expected, the profiles of E/sub y/ along the z and y axes are sinusoidal and uniform, respectively, both ending abruptly at the boundary. These numerical results agree quite closely with the known analytical solutions to this problem.