A Multi-Mode Solution for Analysis of the Reflection Coefficient of Open-Ended Rectangular Waveguides Radiating into a Dielectric Infinite Half-Space

Abstract

The open-ended rectangular waveguide probe is a powerful tool for characterizing the dielectric and reflection properties of various materials and structures [1][2][3][4][5][6][7][8][9][10][11]. In these applications the measurable parameter, r (i.e. the reflection coefficient), is used to determine the sought-for parameters. The said reflection coefficient is defmed as the ratio of the reflected electric field at the aperture of the waveguide to that of the incident electric field.In light of this, many studies have dealt with the radiation properties of the openended waveguide probe radiating into an infinite dielectric half-space. The original studies, using variational principles, approximate the field distribution at the aperture to that of the dominant propagating TE IO mode [12][13]. Although these derivations are reasonably accurate and computationally efficient for most practical cases, they lead to significant errors when attempting to re-calculate the dielectric properties of the infinite half-space from the measured rfor a certain range of dielectric properties and frequency of operation in the waveguide band [10]. These errors are primarily due to the exclusion of higher-order modes in the theoretical fonnulation. To remedy this problem several attempts have been made which incorporate the effect of higher-order modes in the derivations [1][2][3][14][15][16][17][18][19][20][21],