Application of the Wiener-Hopf technique to dielectric slab waveguide discontinuities

The analysis, based on the Wiener-Hopf technique, of a step discontinuity in relative permittivity is presented for a single-mode dielectric slab waveguide excited in the dominant TE mode. The Wiener-Hopf equation is obtained by applying the Fourier transform together with the proper boundary and edge conditions. Because of the complicated functions involved, the factorisation and decomposition are obtained numerically by applying Lee-Mittra and Noble techniques. The solutions for the reflected and transmitted fields contain infinite number of constants which satisfy the infinite dimensional algebraic simultaneous linear equations. However, convergent solutions of field components can be obtained by using only a few terms. The accuracy of the results is confirmed by good agreement with previously reported data.