The electric field of the modes of waveguides with edges, like rectangular guides or rib guides, is known to diverge along the edges of the guide. The divergence makes the design of rapidly converging numerical algorithms for vector mode field computations in such waveguides difficult. Two closely related methods that have overcome the difficulties to some extent are the method of lines and the transverse resonance (mode matching) method. The common merits of these methods are discussed, and some results are presented for mode field distributions in practical rib waveguides, calculated with the transverse resonance method.
Aasmund Sudbo, Aasmund Sudbo,
"Problems in vector mode calculations for dielectric waveguides", Proc. SPIE 2212, Linear and Nonlinear Integrated Optics, (25 August 1994); doi: 10.1117/12.185118; https://doi.org/10.1117/12.185118