Efficient eigenmode analysis for lossy dielectric waveguides using a hybrid (frontal-FE)/BIE technique

Abstract

Conventional numerical techniques, such as FDTD, finite elements (FE) and boundary integral equation techniques (BIE) have been studied thoroughly and applied extensively in electromagnetic problem solving. Each of these methods has its advantages and drawbacks. If one uses FE or FDTD techniques, mesh truncation schemes in combination with absorbing boundary conditions are necessary to model open structures. The BIE method can incorporate the infinite extent of unbounded simulation regions using an appropriate Green's function, occurring as the kernel of the integral equation. Such Green's functions however can only be generated efficiently for structures consisting of sufficiently large homogeneous regions. Since modern interconnection technology relies more and more on complex waveguides exhibiting a large amount of inhomogeneity and even anisotropy, the limitations of the above methods become more and more stringent. The combination of finite elements with boundary integral techniques was proposed to circumvent such problems. We show that a hybrid technique can be applied to find the eigenmodes of open waveguides, containing bounded but inhomogeneous and anisotropic regions. In addition, homogeneous regions are considered with arbitrary losses. The losses due to the skin effect are rigorously taken into account by using a BIE approach for such materials.