Quasi-mode-matching technique for unbounded waveguide discontinuities

The mode matching technique is an established method for the analysis of various waveguide discontinuities. As the method is based on complete, countable and orthogonal sets of eigenmodes it is not simply applicable to open waveguide structures such as fiber optics or dielectric slab guides. In this paper we show two methods for dealing with open structures. While the first method is a simple construction of a semi-open situation by adding artificial boundaries, the second method extends the mode matching technique to the dense mode spectra of open waveguides by employing Laguerre polynomial expansions.