New boundary integral equations for computer-aided design of dielectric waveguide circuits

New forms of boundary integral equations are presented for the exact treatment of wave propagation in two-dimensional complicated dielectric waveguide circuits. Since the new boundary integral equations can be solved numerically by the conventional boundary-element method, they are suitable for the basic theory of computer-aided-design software for dielectric waveguide circuits. The new boundary integral equations are derived for a two-dimensional dielectric waveguide bend. They can be obtained by considering specific conditions at points far away from the bend. The numerical solution of the corner bend by the boundary-element method establishes the validity of the new boundary integral equations. The numerical results are evaluated on the bases of the law of energy conservation and the reciprocity condition. Since the theory is based on the exact theory, the solution is exact if sufficiently large computer memory and computational time are used.