A uniform approximation for the eigenmodes of a planar dielectric waveguide

This paper derives a new approximation for the eigenmodes of a planar waveguide. The approximation is uniformly valid at both the high and low frequency regions of the dispersion relation. It is shown that a Pade approximation of the frequency equation leads to very accurate solutions. The new approximate solution is used to compute the frequency spectrum and the results compared with the exact analytical solution. The solutions presented here are ideal for analytically studying transient wave fields by means of modal summation.