A simple method is presented to obtain the scattering parameters of the two dimensional tapered dielectric waveguide, by discrete approximation to tapering, consisting of series of steps. The two dimensional step discontinuity of the junction of two different dielectric rectangular waveguides has been solved using integral equation arising from the field matching of the discrete modes and the continuous spectrum. Accurate numerical solution has been obtained using Ritz-Galerkin variational approach with appropriate sets of expanding functions. The results in the form of scattering parameters for varying tapered length have been depicted graphically. Computed results from generalized integral expressions are found to be in excellent agreement with results obtained in two-dimensional case. With this method it is possible to design the structure to enlarge the cross section of a mode in a slow and controlled manner.
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