Theoretical analysis of the junction discontinuity between a straight and a curved section of rectangular waveguide

The asymptotic form of orthonormal eigenfunctions in the curved guide is obtained, and an integral equation is set up for the junction field. The latter is found as a power series in theguide curvature, and the first-order coefficient is determined explicitly. The odd-order mode-conversion coefficients are found to the first order and vary asymptotically as the inverse cubeof the mode order. A variational technique then determines the reflection coefficient exactly, to the second order in the curvature expansion parameter. The junction parameters are found to this order of accuracy, and are shown to involve a junction transformer which represents the radiation coupling between the dominant modes in the straight and curved guide sections. The even-order mode-conversion coefficients are found by a formulation analgous to that used for the reflection coefficient, and are shown to vary as the square of the curvature and asymptotically asthe inverse cube of the mode number. The form of the junction field is determined and is shown to possess a logarithmic singularity in its second derivative at the guide wall.