A general transform for regularizing planar open waveguide dispersion relation

Recently, conformal mapping technique has been introduced to unfold the characteristic equation of multilayered dielectric waveguides. The previous transformations have various deficiencies, i.e., the corresponding transformed functions are either multivalued, or have a singular point. Also one of them is not generally applicable. We introduce a new mapping that has none of the above deficiencies. Furthermore, in the new plane, the modal zones are rectangular strips which facilitate the implementation of the corresponding numerical routines. By this transformation, various modes of general planar dielectric waveguides can be traced easily.