  This paper presents a modal analysis based on the reciprocity theorem to
calculate the coupled/penetrated fields into an open-ended waveguide mounted on
a finite flange. Although there is no limitation on the geometry and type of
the external source, an infinitesimal dipole is chosen to produce a plane wave
incident to the waveguide aperture. The proposed method relates the amplitude
of each penetrated mode into the waveguide to the far-field radiation
components of that mode from the waveguide aperture. The accuracy of the final
result depends on the accuracy of the calculated radiated fields. The radiated
field components are calculated considering the reflected fields due to the
aperture and the diffracted fields due to the flange edges. For the first time,
the impact of a finite flange on the penetrated fields into a waveguide is
discussed comprehensively. The geometry of a rectangular waveguide mounted on a
thick square flange is selected to be evaluated. The effects of changing the
main parameters of the geometry on the penetrated fields are discussed
rigorously in various examples. Our results are compared with 3D full-wave
simulations, and an excellent agreement was found between the results while our
analytical approach showing a 60 times faster performance. In addition, we
compared our results with the measurement reported in a previous study.
