In Situ Measurements of the Complex Permittivity of Materials Using Reflection Ellipsometry in the Microwave Band: Theory (Part I)

Abstract

Abstract-The aim of this series of two papers is to propose an original and low-cost tool dedicated to industrial applications and based on the reflection ellipsometry technique for in situ characterization of dielectric materials at microwave frequencies. In this first paper, different theoretical developments are presented that concern first a specific numerical method for calculating the complex permittivity of a single-layer sample from the measured parameters. Based on contour line charts, this method allows obtaining simultaneously the relative uncertainties on the real and imaginary parts of the complex permittivity. Secondly, for experimental comparisons with the classical Fresnel method, a numerical data processing method based on contour line charts has also been developed, which aims at the determination of the reflection coefficients in both parallel and perpendicular polarizations of the material.

Specular Reflectance Measurements of Dielectric Plates in Millimeter Frequency Range

“…1(a), the specular reflection coefficient of the dielectric plate is given by [11] , (1) where sin is the propagation factor through the dielectric plate, 2 ⁄ is the free-space wavenumber, is the free-space wavelength, is the complex relative permittivity of the dielectric plate, and , respectively, are the incident and reflected angles, and is the perpendicular-polarized reflection coefficient at the air-dielectric interface, which is given by .…”

“…Various methods have been developed in millimeter and submillimeter frequency ranges to measure material properties (usually complex permittivity and permeability), e.g., the open resonator [3,4], free space [5][6][7][8][9][10], and reflection ellipsometry methods [11][12][13]. The open resonator method provides accurate material properties at discrete resonance frequencies.…”

“…Their bandwidths have been broadening and operating frequency bands have been moving to the submillimeter frequency range. Measurements of the electrical properties of EM materials have gained considerable importance, particularly in the millimeter and submillimeter frequency ranges, as material parameters are fundamental parameters in the natural and application sciences fields [1,2].Various methods have been developed in millimeter and submillimeter frequency ranges to measure material properties (usually complex permittivity and permeability), e.g., the open resonator [3,4], free space [5][6][7][8][9][10], and reflection ellipsometry methods [11][12][13]. The open resonator method provides accurate material properties at discrete resonance frequencies.…”

Characterization of material anisotropy using microwave ellipsometry

“…The majority of microwaves techniques are based on the measurement of the transmission and the reflexion electromagnetic energy using a vector network analyzer [1]. Some other techniques are based on free-space measurement, which are known to be nondestructive, contactless, and they do not require sample preparation [2][3][4][5].…”

Retrieval of refractive index over specular surfaces for remote sensing applications

“…A number of experimental methods have been devised to determine refractive index by means of measurements of reflectance [2,3]. The complex dielectric constant of the material can be deduced back from the power of the reflected or/and transmitted part of the wave, as a function of the angle of incidence (Fresnel method) or of the polarization of the receiving antenna (reflection or transmission ellipsometry) [4].…”