A numerical absorbing boundary condition for finite difference and finite element analysis of open periodic structures

We introduce a numerical absorbing boundary condition that effects a complete absorption of all of the significant Floquet modes impinging upon the boundary, including both the propagating and the dominant evanescent modes. Using this requirement as the specification, we go on to derive linear relationships that link the field values at the boundary grid points to those of their neighbors. This procedure differs from the classical approaches to deriving the local boundary conditions, since in this method only the field values at the prescribed grid points are used. In this respect, it is somewhat similar to the measured equation of invariance (MEI) boundary condition. However, and in contrast to the MEI method, the present method uses the Floquet modes which depend only upon the periodicity and the excitation, and not on the geometry of the periodic element. This has an important advantage of using simple and analytically-known functions, and eliminating the need to carry out the surface integrations needed in other approaches.