Fabry-Perot Open Resonator Research Articles

Bulk glass-ceramic composites and ULTCC substrates for microwave and millimetre-wave applications

In this study, a new ultra-low-temperature co-fired ceramic (ULTCC) glass-ZnO-SiO2-B2O3CeO2−MgO-Al2O3 composite was developed and its applicability as a dielectric substrate in emerging high-performance communication technologies in the microwave and millimetre-wave frequency ranges was investigated. The novel material composition enables achieving good sinterability at a low fabrication temperature of 470 °C. Extensive studies have been conducted on the microstructure, porosity, water absorption, surface roughness, and thermal expansion coefficient. Following this analysis, the dielectric properties of the bulk glass-ceramic composites and the final ULTCC substrates were characterised. These measurements were conducted within a broad frequency range of 5 GHz–1.1 THz using split-post dielectric resonators, a Fabry-Perot open resonator, and a time-domain spectrometer, resulting in quasi-continuous frequency characteristics of the complex permittivity. Furthermore, the fabricated ULTCC substrates were subjected to surface-wise measurements, which provided 2D maps of the dielectric properties as qualitative and quantitative measures of the uniformity and quality of the material.

Measurement Errors and Uncertainties in the Complex Permittivity Extraction With a Fabry–Perot Open Resonator

A Fabry–Perot open resonator (FPOR) has recently become one of the most popular fixtures dedicated to the characterization of dielectric materials in the microwave and millimeter-wave range, mainly due to its quasi-broadband operation combined with large accuracy typical for resonant methods. However, to become a widely recognized measurement standard, an error budget of this approach has to be evaluated, accounting for systematic and random errors in the extraction of the dielectric constant (Dk) and loss tangent. It will be shown in this article that the main sources of the systematic and random Dk errors are the choice of the electromagnetic (EM) model and variation of the thickness of the dielectric sheet, respectively. The first one can be controlled to some extent by the developer of the measurement system, however, thickness variation cannot be easily controlled. Therefore, it has to be accounted for in the form of uncertainty bars. In the case of the loss tangent, systematic and random errors are mainly due to the electric energy filling factor error and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$</tex-math> </inline-formula> -factor variation, respectively. Moreover, it is shown in this article that the loss tangent uncertainty (LTU) is the lowest when the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$</tex-math> </inline-formula> -factor with the sample is 40%–50% of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$</tex-math> </inline-formula> -factor of the empty cavity. In addition to that, it is shown that the noise floor of the measurement is much less important when the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$</tex-math> </inline-formula> -factor is estimated with the aid of curve-fitting algorithms instead of the 3-dB-point method. However, complete knowledge on the LTU cannot be acquired from just one measurement as it does not account for the finite repeatability of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$</tex-math> </inline-formula> -factor measurement. It is, therefore, proposed in this article how to practically evaluate and suppress this error. Although the main attention has been focused on the FPOR, many conclusions presented in this study are not limited to a particular type of resonant technique.

Microwave Characterization of Dielectric Sheets in a Plano-Concave Fabry-Perot Open Resonator

Despite its long history, a double-concave (DC) Fabry-Perot open resonator (FPOR) has recently gained popularity in the characterization of dielectrics in the 20–110 GHz range, mainly due to such novel accomplishments as full automation of the measurement process and the development of even more accurate and computationally efficient electromagnetic model. However, it has been discovered that such a DC resonator suffers from unwanted mode coupling present for electrically thick samples. Such limitations are missing in a plano-concave (PC) FPOR. For those reasons, the aim in this article is to apply the newly proposed scattering matrix method in the study of major properties of that kind of a resonator and, subsequently, to propose a new tool dedicated to the measurement of dielectrics without the aforementioned limits. For the first time in the literature, major properties of the PC FPOR with and without the sample, such as resonance frequencies, geometric factors, energy filling factors, and the resulting quality factor, are rigorously computed. Moreover, their impact on the accuracy of the loss tangent extraction is investigated. Such a study, which opens the way for accurate microwave characterization of electrically thick dielectric sheets above 20 GHz, has never been performed before. The whole complex permittivity extraction algorithm presented in this article is validated experimentally by measuring well-known materials, namely, C-plane sapphire, silicon, and Z-cut monocrystalline quartz.

Characterization of Low-Loss Dielectric Materials for High-Speed and High-Frequency Applications.

In this study, the Df (dissipation factor or loss tangent) and Dk (dielectric constant or permittivity) of the low-loss dielectric material from three different vendors are measured by the Fabry–Perot open resonator (FPOR) technique. Emphasis is placed on the sample preparation, data collection, and the comparison with the data sheet values provided from vendors. A coplanar waveguide with ground (CPWG) test vehicle with one of these raw dielectric materials (vendor 1) is designed (through Polar and simulation) and fabricated. The impedance of the test vehicle is measured by TDR (time-domain reflectometer), and the effective Dk of the test vehicle is calculated by the real cross-section of the metal line width, spacing, and thickness of the test vehicle and a closed-form equation. In parallel, the insertion loss and return loss are measured with the VNA (vector network analyzer) of the test vehicle. Finally, the measurement and simulation results are correlated. Some recommendations on the low-loss dielectric materials of the Dk and Df are also provided.

Mode Coupling in a Fabry-Perot Open Resonator

A Fabry-Perot open resonator (FPOR) is a tool dedicated to broadband accurate microwave and millimeter-wave characterization of dielectric sheets. Despite the various advantages of that method, one of the major challenges limiting its applicability is unintentional coupling of Gaussian modes of interest with a particular family of parasitic higher order modes. The coupling affects the resonance frequency of the resonator loaded with the material under test, thus disturbing the extracted permittivity. It has already been shown that spectral properties of these parasitic modes can be predicted using a recently developed electromagnetic model of a FPOR based on the scattering matrix method. It is shown in this article that the systematic analysis of experimental results supplemented with accurate numerical computations allows us to suppress the impact of mode coupling on the measured permittivity.

Rigorous Scattering Matrix Analysis of a Fabry–Perot Open Resonator

A completely novel electromagnetic model of a Fabry-Perot open resonator is proposed and validated in this article. The idea that led to the invention of this model is to split the analysis of the resonator into a few nonresonant sections, thus, substantially alleviating computational effort involved in the analysis of such a large high-Q structure. Each section of the resonator, including mirrors, is represented as a multimode scattering matrix and the whole resonator is considered as a cascade of two-port networks. Mode analysis applied in the proposed model allows representing fields propagating along the resonator in the form of an orthogonal set of cylindrical waveguide modes. Due to versatility and large computational efficiency, the method can be used to account for electromagnetic phenomena that cannot be solved with commonly used models of the Fabry-Perot open resonator based on a scalar paraxial approximation. The obtained solution is validated against experimental data. It is also shown that the spurious mode coupling occurring in the measurement of electrically thick dielectric sheet materials can be explained using the proposed scattering matrix method.

Measurement of Dielectrics From 20 to 50 GHz With a Fabry–Pérot Open Resonator

A novel approach to the measurement of complex permittivity of low-loss dielectric materials with the aid of an open Fabry–Perot resonator with concave Gaussian mirrors is presented in this paper. For that purpose, a new scalar 1-D layered electromagnetic (EM) model of the resonator is proposed. The model takes the advantage of Cartesian-to-Gaussian coordinate transformation and axisymmetrical properties of the TEM modes of interest. There are several advantages of the proposed approach. The first is the use of Gaussian mirrors instead of spherical ones, which better fit to the shape of Gaussian wavefronts. Second, the model more accurately accounts for oblique incidence of the wave onto the surface of the sample, which is one of the major challenges in case of alternative models based on a characteristic equation. An automated measurement setup operating in the 20–50-GHz range has been designed and manufactured to experimentally validate the proposed measurement method. A real part of permittivity of a few well-known materials, such as silicon, quartz, polystyrene, or polyethylene terephthalate (PET) foil, has been measured with the accuracy better than 0.5%, which means a significant improvement as compared to the state of the art in this area.

Terahertz Dielectric Properties of Polycrystalline MgAl2O4 Spinel Obtained by Microwave Sintering and Hot Pressing

This paper describes the fabrication of polycrystalline magnesium aluminate spinel (MgAl2O4) by microwave sintering and hot pressing and the investigation of its dielectric properties in the millimeter-wave and terahertz frequency range. The dielectric properties were studied in the frequency range 50–300 GHz using a spectrometer based on an open Fabry–Perot resonator with a high quality factor and in the range 0.6–3.3 THz using the time-domain spectroscopy method. The terahertz radiation was generated as a result of air breakdown using two-color laser pulses with carrier wavelengths of 800 and 400 nm. The dielectric characteristics of MgAl2O4 ceramics obtained from high-purity nanosized powders by microwave sintering and by hot pressing are compared. The refractive index of the materials varies from 2.85 to 2.95, and the dielectric loss tangent increases from 1.5 × 10−4 to 1.5 × 10−2 within the frequency range 0.05–3.3 THz. The possible use of magnesium aluminate spinel for millimeter-wave and terahertz applications is discussed.

Experimental demonstration of Fabry-Perot open resonators in a surface-wave bandgap crystal

We report on the proposal and experimental realization of a type of retardation-based Fabry-Perot (FP) open resonator in a surface-wave bandgap crystal implemented on a single structured metal surface. This surface-wave FP open resonator is formed by introducing a finite line defect in the surface-wave bandgap crystal, whose resonance frequencies lie exactly within the forbidden bandgap of the surrounding crystal. Due to the complete surface-wave forbidden bandgap, a new FP plasmonic resonance mode exhibiting monopolar features which is missing in both traditional FP resonators and plasmonic resonators is emerged. Near-field response spectra and imaged mode profiles are presented to characterize the properties of these FP open resonators in the microwave regime.

Charles Hard Townes

Charles Hard Townes

Modern Resonator Spectroscopy at Submillimeter Wavelengths

Classical resonator spectroscopy methods have been realized for the first time in the submillimeter wave range. A resonator spectrometer was developed earlier at the IAP RAS on the basis of an open Fabry-Perot resonator excited by the radiation of a backward wave oscillator whose frequency is stabilized by the phase lock loop system. This spectrometer is successfully used for high-precision measurements of the dielectric properties of solid, liquid, and gaseous dielectrics as well as for the metal and coating reflection measurements in the 36-370 GHz range. In this paper, we report an extension of the upper limit of the spectrometer operation frequency to 520 GHz. Features of operation of the main spectrometer systems in the extended frequency range are analyzed. The broadband measurements of absorption in modern MPCVD diamonds are presented. A continuous record of the absorption spectrum of the laboratory atmosphere in the 350-500 GHz range obtained for the first time by the high-sensitivity microwave method is demonstrated. Further prospects for extension of the spectrometer range to terahertz frequencies are discussed.

The Influence of a Coupling Film on Ultra-Low-Loss Dielectric Measurement Using an Open Resonator

A Fabry-Perot open resonator excited through a coupling film and loaded with a plane-parallel dielectric plate is analyzed. The eigen equation of the field in the resonator is obtained. The quality factors of the resonator with and without a coupling film are compared. The quality factors of the resonator loaded with a plate that is in resonance and off resonance are also compared. It is shown that the difference in coupling losses between a loaded resonator and an unloaded resonator may strongly affect the accuracy in measuring ultra-low loss dielectric material. Some ways to reduce the influence of coupling loss are discussed. Our experiment results are consistent with the numerical analysis.

Bulk and In-Circuit Dielectric Characterization of LTCC Tape Systems Through Millimeter Wave Frequency Range

Low Temperature Co-fired Ceramic (LTCC) material systems offer a highly versatile microwave and millimeter wave packaging platform. Extremely low microwave loss, excellent control of dielectric constant, uniform dielectric thickness, non-existent water absorption leading to very high hermeticity, ability to support multilayer structure leading to 3-dimensional packaging, ability to embed passive functions within the tape layers, availability of a wide range of metallizations, etc. are some of the key advantages of LTCC for microwave packaging. One of the important parameters which needs to be determined at the very early stages of circuit designs are the dielectric properties - dielectric constant and loss tangent, both of which are functions of frequency. These properties need to be known accurately over the entire frequency range of operation for the circuit. For LTCC based designs, the use of dielectric constant of bulk material can lead to deviations between the performance expected at the design stage and for the fabricated circuit. Such deviations are a significant concern for broadband circuits as well as for circuits with sharp resonant behavior such as filters. One of the significant sources of deviation between bulk LTCC and “in-circuit” dielectric constant is the nature of the thick film metallizations used in LTCC technology. Work described here is a comprehensive characterization of three DuPont™ GreenTape™ LTCC systems 951, 943, and 9K7 - in the frequency range 10 to 70 GHz. Both bulk and “in-circuit” dielectric properties with silver and gold metallizations are studied to quantify the deviations in dielectric properties. A Fabry-Perot open resonator technique is used for the bulk characterization while printed ring resonators are used for the in-circuit characterization. This comprehensive characterization will provide key design data for LTCC designers in the 10 – 70 GHz frequency range.

Methods for investigating thin dielectric films in the millimeter range

An original method based on determining the characteristics of open Fabry-Perot resonator modes with different polarizations is proposed for measuring parameters of dielectric plates and films with a thickness smaller than λ/2 in the millimeter and submillimeter wavelength ranges. This method is used for determining the refractive index and tanδ, as well as the thickness of films made of isotropic materials. For anisotropic films of known thickness, the method makes it possible to measure the permittivity tensor components. Popular film materials such as Teflon (polytetrafluoroethylene, PTFE), lavsan (Mylar, polyethyleneterephthalate, PETP), and polyamide with a minimal thickness of ∼5 μm are investigated. Appreciable anisotropy of roll film materials and the dependence of the dielectric properties on the thickness, which is associated with manufacturing technology, are revealed. The dependence of the refractive index and tanδ on the air humidity is investigated

Fabry–Perot Open Resonator Technique for Dielectric Permittivity and Loss Tangent Measurements of Yttrium Iron Garnet

This paper presents a Fabry-Perot open resonator system for the precision measurement of real part of permittivity and loss tangent of yttrium iron garnet specimens at 60 GHz. This system allows us to vary the cavity length at 10-nm step size to study the resonance profile of each excited fundamental mode with great stability and reproducibility. The obtained highly symmetrical, fully resolved Gaussian resonance profile results in a significantly high Q factor for the overall system. It enables us to determine the dielectric permittivity and loss tangent of ferrite materials accurately and reliably for the first time. Measurements have been performed on a 99.9% pure yttrium iron garnet and a gadolinium substituted yttrium iron garnet specimen at 60 GHz. A temperature dependence study has also been conducted at a limited temperature range near room temperature

Dielectric Measurements of CVD Diamonds at Millimeter Wavelength Using a Fabry-Perot Open Resonator

Precise dielectric property measurements at a millimeter wave frequency band are attractive. A Fabry-Perot open resonator consisting of hemispherical and plane mirrors, coupling holes is designed by the use of analytic theories and a numerical simulation code. HFSS. Dielectric constant measurements on CVD diamonds are performed by a frequency variation method. Measurements show that permittivity and loss tangent range from 5.59 to 6.46, and from 1.1 × 10−3, to 5.3 × 10−2. respectively, in the frequency range of 95–100 GHz depending on sample preparation of the CVD diamonds.

Development Trend of Millimeter-Wave Evaluation Techniques of Low-Loss Dielectrics and High Temperature Superconductors

Recent development trends of several resonance methods are reviewed to measure the complex relative permittivity (relative permittivity εr and loss tangent tanδ of low-loss dielectric materials and the surface resistance Rs of high temperature superconductors (HTS) in microwave and millimeter-wave regions; that is, a cavity resonator method, a cut-off circular waveguide method, a balanced-type circular disc resonator method, a Fabry-Perot open resonator method, a whispering-gallery mode resonator method, a Hakki-Coleman method, a two-dielectric-resonator method, a one-dielectric-resonator method, a dielectric resonator method using NRD-guides, and a perturbation method.

Modern Millimeter-Wave Resonator Spectroscopy of Broad Lines

Broad line millimeter-wave resonator spectroscopy is shown to have high sensitivity and fast and broad frequency scanning possibilities. Methods of absolute measurement of separate line, sample, and resonator losses are demonstrated and discussed. The primary radiation source (BWO) frequency is controlled digitally with minimal steps of a few hertz and switching time of 200 ns. An open Fabry–Perot resonator with a quality factor of ∼600 000 is used. A resonance-width measurement accuracy of 20 Hz is reached which corresponds to an absorption coefficient sensitivity limit of ∼4 × 10−9 cm−1 (0.0018 dB/km). In situ open atmosphere spectra records at 44–98 and 113–200 GHz are obtained in one experiment each. Lines of atmospheric oxygen and atmospheric water are observed. The water line at 183 GHz fits the Van Vleck–Weisskopf shape up to 20 half-widths from the line center within experimental accuracy. The dry-air broadening parameter for this water line is defined as 3.985(40) MHz/Torr. Atmosphere absorption in a 140-GHz window is measured. Results from other authors are compared. Possible applications of the modern broad line millimeter-wave resonator spectroscopy including real-time monitoring of open-air atmosphere and technological processes and measurement of absorption in thin dielectric films and conducting surfaces and metals are discussed.

Nonlinear Bragg scattering and mode superradiance in an open Fabry—Perot resonator

Mode superradiance (i.e. superfluorescence) in an open Fabry—Perot resonator is characterised by simultaneous emission of counterpropagating coherent pulses even when the mirrors have very low (but finite) reflection coefficients, beginning from Rcr ≪ 1. It is shown that for any value of the resonator Q factor, even when R ≫ Rcr or R ~ 1, a self-matched λ/2 grating of the population inversion in a two-level medium does not result in significant Bragg reflection which would exceed the reflection from the mirrors. A consistent allowance for the interference of inhomogeneous conterpropagating waves significantly alters the spatial and temporal dynamics of depletion of the population inversion and, consequently, greatly changes he profile of collective spontaneous radiation pulses, compared with the predictions of the mean field and unidirectional superradiance theories. A new nonlinear equation for superradiance in an open resonator is derived.

A novel high-field/high-frequency EPR and ENDOR spectrometer operating at 3 mm wavelength

A high-field/high-frequency EPR and ENDOR system operating at 3 mm wavelength is described. The probe-head designs of two different resonator types, i.e. an open Fabry-Perot resonator and a cylindrical TE011 cavity, are presented in detail. The advantages and limitations of high-field/high-frequency EPR and ENDOR spectroscopy are demonstrated for selected examples. The performance data of the spectrometer suggest that it will be very useful for broad applications in physics, chemistry and biology.