High-frequency description of the Kirchhoff-type modal coupling between open ended waveguides

The Kirchhoff-type aperture integration (AI) is the simplest way to calculate the radiation from an open-ended waveguide (OEW). Recently, a rigorous equivalence between the field predicted by AI and that radiated by the physical optics (PO) wall-current was demonstrated, in which the PO currents are defined as that associated to the unperturbed mode. By using this equivalence, a method for asymptotically reducing the AI into a line integration (LI) of incremental diffraction coefficients along the waveguide edge was previously presented. A LI representation of the aperture field is well suited for introducing a fringe contribution as provided by the physical theory of diffraction (PTD) or by the incremental theory of diffraction (ITD). In this paper, the equivalence between PO and AI is extended to evaluate the coupling between two OEWs of arbitrary cross-section. Furthermore, a Kirchhoff-type coupling coefficient is derived in terms of a double line integration of incremental coupling coefficients. This may provide a useful tool when the mutual impedance of two modal distributions has to be calculated in the framework of a method of moments (MoM) procedure which is formulated in terms of mode-shaped basis functions.