Absorbing boundary conditions for the finite-element analysis ofplanar devices

The finite-element method is used to determine the scattering matrices of open devices in two dimensions. Microwave and optical devices in which the fields are not confined to a finite region can be analyzed with the finite-element method if special boundary conditions are used to absorb outgoing radiation. The absorbing boundary conditions can be imposed by the addition of two terms to the usual functional for the scalar Helmholtz equation. Universal matrices are introduced to allow the additional terms to be easily assembled, for polynomial orders one through four. Results are given for the impedance of a parallel-plate waveguide radiating into free space and for the scattering parameters of three dielectric slab waveguide devices: a rectangular discontinuity, a feed structure, and a junction