Multimode solution for the reflection properties of an open-ended rectangular waveguide radiating into a dielectric half-space: the forward and inverse problems

Open-ended rectangular waveguides are extensively used in nondestructive dielectric material evaluation. The dielectric properties of an infinite-half space of a material are calculated from the measured reflection properties referenced to the waveguide aperture. This calculation relies on a theoretical and numerical derivation of the reflection coefficient likewise referenced to the waveguide aperture. Most of these derivations assume the dominant mode field distribution across the waveguide aperture. However, when dealing with low permittivity and low loss dielectric materials, there may exist significant errors when calculating the dielectric properties from the measured reflection coefficient. These errors have also shown to be more significant in the upper frequency portion of a waveguide band. More accurate results are obtained when higher order modes are considered in addition to the dominant waveguide mode. However, most studies incorporating higher-order modes have used various approximations when calculating the reflection properties and have not provided a full discussion on the influences of dielectric properties of the infinite-half space and the frequency of operation. This paper gives a rigorous and exact formulation in which the dominant mode and the evanescent higher-order modes are used as basis functions to obtain the solution for the reflection coefficient at the waveguide aperture. The analytic formulation uses Fourier analysis in addition to the forcing of the necessary boundary conditions at the waveguide aperture. The solution also readily accounts for the complex contributions of both TE and TM higher-order modes. Finally, the influences of the dielectric properties of the infinite-half space and the frequency of operation are investigated