  We analyse theoretically for the first time to our knowledge the perfect
phase matching of guided TE and TM modes with a multilayer waveguide composed
of linear isotropic dielectric materials. Alongside strict investigation into
dispersion relations for multilayer systems, we give an explicit qualitative
explanation for the phenomenon of mode matching on the basis of the standard
one-dimensional homogenization technique, and discuss the minimum number of
layers and the refractive index profile for the proposed device scheme. Direct
applications of the scheme include polarization-insensitive, intermodal
dispersion-free planar propagation, efficient fibre-to-planar waveguide
coupling and, potentially, mode filtering. As a self-sufficient result, we
present compact analytical expressions for the mode dispersion in a finite,
N-period, three-layer dielectric superlattice.
