Equivalence between physical optics and aperture integration for radiation from open-ended waveguides

The eigen-mode radiation from an open-ended waveguide of arbitrary cross section is considered. The following theorem is demonstrated: the Kirchhoff-Kottler aperture integration for the radiated field is equivalent to the physical-optics (PO) approach applied to the wall currents. This theorem allows one to resort to aperture integration for those structures involving complicated PO integration. On the other hand, based on the same theorem the aperture integration may be reduced to a line integral along the edge of the waveguide for those configurations that allow a simple PO integration. It can also be useful in developing more efficient solutions in the framework of incremental theories.