Analysis of single mode inhomogeneous planar waveguides

A new method for obtaining the propagation characteristics of single mode inhomogeneous planar waveguides is presented. The method is based on the scalar variational principle and a new trial field-the cosine-exponential field-is proposed. A comparison with other methods and the exact numerical results shows that our method is much more accurate than the existing methods. The method also allows one to define an equivalent slab waveguide which is then used to obtain an accurate approximation for the propagation constant of the TM
0
-mode.