Nondestructive Determination of the Permittivity Tensor of a Uniaxial Material Using a Two-Port Clamped Coaxial Probe

Abstract

A two-port coaxial probe is introduced to nondestructively determine the permittivity tensor of a uniaxial material. The proposed approach possesses several advantages over existing techniques, e.g., only a single sample is required, the sample does not need to be rotated, and only a single measurement system is needed. The derivation of the theoretical scattering parameters is shown. This is accomplished by applying Love’s equivalence theorem and the continuity of transverse magnetic fields to formulate a system of coupled integral equations. A necessary step in this approach is the derivation of the magnetic-current-excited uniaxial parallel-plate Green’s function. The development of this Green’s function is presented here using a new scalar potential formulation, which significantly reduces the difficulty of the probe’s theoretical development. The system of coupled integral equations is solved using the method of moments to yield the theoretical scattering parameters. The permittivity tensor is found by minimizing the two-norm of the vector difference between the theoretical and measured scattering parameters via nonlinear least squares. To validate the probe, measurement results of a uniaxial absorber are presented and compared to those obtained using a focused-beam (free-space) measurement system. The probe’s sensitivity to uncertainties in measured scattering parameters, sample thickness, and coaxial line properties is also investigated.