A new variational finite element analysis of microwave and optical waveguides without spurious solutions

The method presented can deal with waveguides of arbitrary cross-section and transverse inhomogeneity, including anisotropy and loss (or gain). It gives directly solutions for the (complex) propagation constant and totally eliminates the spurious solutions which ordinarily appear interspersed with the correct results of many vectorial finite element formulations. Additionally, efficiency has been maximized by using only two vector components to describe the problem. A very efficient new solver for the sparse nonsymmetric matrix eigenequation has been developed for the formulation and it is also reported. This new finite element method with the efficient matrix solver which drastically reduces computing time and storage has been thoroughly tested showing its effectiveness and applicability