Mutual coupling between two circular waveguides

The problem of coupling between two circular waveguides is solved using the Wiener-Hopf technique. Expressions for the radiated, reflected, and the transmitted fields are obtained and are expressed by three terms. The first term in these expressions represents the solution for an open ended circular waveguide, while the other two are due to the interaction between the two waveguides. It is shown that, the radiated, reflected, and the transmitted fields can also be found from the reflection coefficient of an open ended circular waveguide and an evaluation of a semi-infinite integral involving the fourier transformed Green´s function of the Weiner-Hopf equation. Exact solutions are used to generate the approximate solution of the ray theory of diffraction. This is achieved by expanding the exact solution and using the modified diffraction coefficient of Lee in conjunction with a spherical wave-factor.