Microwave Resonance Frequencies Research Articles

On-Chip Microwave Frequency Combs in a Superconducting Nanoelectromechanical Device.

Nanomechanical resonances coupled to microwave cavities can be excited, measured, and controlled simultaneously using electromechanical back-action phenomena. Examples of these effects include sideband cooling and amplification, which are commonly described through linear equations of motion governed by an effective optomechanical Hamiltonian. However, this linear approximation is invalid when the pump-induced cavity microwave field is large enough to trigger optomechanical nonlinearities, resulting in phenomena like frequency combs. Here, we employ a niobium-based superconducting electromechanical device to explore the generation of microwave frequency combs. We observe the formation of combs around a microwave resonant frequency (3.78 GHz) with 8-MHz frequency spacing, equal to the mechanical resonant frequency. We investigate their dynamics for different optomechanical parameters, including detuning, pump powers, and cavity decay rates. Our experimental results show excellent agreement with numerical modeling. These electromechanical frequency combs can be beneficial in nanomechanical sensing applications that require precise electrical tracking of mechanical resonant frequencies.

Resonance frequency measurement with accuracy and stability at the 10−12 level in a copper microwave cavity below 26 K by experimental optimization

Single-pressure refractive index gas thermometry (SPRIGT) is a novel primary thermometry technique, developed jointly by the Technical Institute of Physics and Chemistry (TIPC) of the Chinese Academy of Sciences (CAS) in China and LNE-Cnam in France. To help obtain a competitive uncertainty of 0.25 mK in thermodynamic temperature measurements, high-stability and low-uncertainty of microwave resonance frequency measurements better than 2 ppb have been demonstrated. This article describes how high-stability and low-uncertainty resonance frequency measurements were achieved using a copper microwave cavity. Microwave measurements were carried out under vacuum and isobarically at helium-4 pressures of 30, 60, 90, and 120 kPa over the temperature range of 5–26 K, with good consistency among microwave modes for the thermodynamic temperatures determined. Performance was optimized using an Allan variance analysis. In this way, with an integration time of 3 h, a stability and accuracy at the 10–12 level were obtained, an almost 20-fold improvement upon our previous result (Zhang et al 2019 Sci. Bull. 64 286–8).

Functional Magnetic Composites Based on Hexaferrites: Correlation of the Composition, Magnetic and High-Frequency Properties.

The paper describes preparation features of functional composites based on ferrites, such as “Ba(Fe1−xGax)12O19/epoxy,” and the results of studying their systems; namely, the correlation between structure, magnetic properties and electromagnetic absorption characteristics. We demonstrated the strong mutual influence of the chemical compositions of magnetic fillers (Ba(Fe1−xGax)12O19 0.01 < x < 0.1 solid solutions), and the main magnetic (coercivity, magnetization, anisotropy field and the first anisotropy constant) and microwave (resonant frequency and amplitude) characteristics of functional composites with 30 wt.% of hexaferrite. The paper presents a correlation between the chemical compositions of composites and amplitude–frequency characteristics. Increase of Ga-content from x = 0 to 0.1 in Ba(Fe1−xGax)12O19/epoxy composites leads to increase of the resonant frequency from 51 to 54 GHz and absorption amplitude from −1.5 to −10.5 dB/mm. The ability to control the electromagnetic properties in these types of composites opens great prospects for their practical applications due to high absorption efficiency, and lower cost in comparison with pure ceramics oxides.

Progress towards a gas-flow standard using microwave and acoustic resonances

We describe our progress in developing a novel gas flow standard that utilizes 1) microwave resonances to measure the volume, and 2) acoustic resonances to measure the average gas density of a collection tank/pressure vessel. The collection tank is a 1.85 m3, nearly-spherical, steel vessel used at pressures up to 7 MPa. Previously, using the cavity's microwave resonance frequencies, we determined the cavity's pressure- and temperature-dependent volume VBBB with the expanded uncertainty of 0.022% (coverage factor k = 2, corresponding to 95% confidence level). This was the first step in developing a pressure, volume, speed of sound, and time (PVwt) primary standard. In the present work, when the shell was filled with argon, measurements of pressure and acoustic resonance frequencies determined the “acoustic mass” Macst that agreed with gravimetric measurements within 0.04%, even when temperature gradients were present. Most of these differences were a linear function of pressure; therefore, they can be reduced by further research. We designed and implemented a novel positive feedback system to measure the acoustic resonance frequencies. Using the measurements of VBBB, pressure, and acoustic resonance frequencies of the enclosed gas (nitrogen or argon), we calibrated 3 critical flow venturis that NIST has used as working standards for over 10 years. The two independent flow calibrations agreed within the long-term reproducibility of each CFV, which is less than 0.053%. Furthermore, the feasibility of a dynamic tracking technique using this feedback loop was tested by comparing ΔMacst computed under no-flow conditions and ΔMacst computed by the rate of fall or rise during a flow. This was done for flows ranging from 0.11 g/s to 3.9 g/s.

Correlated mode analysis of a microwave driven ICP source

Microwave and optical measurements are correlated to identify the mode evolution in a miniature, microwave driven, inductively coupled plasma (ICP) source. The very compact design of the source is derived from previous work (Porteanu et al 2013 Plasma Sources Sci. Technol. 22 035016). Microwave spectroscopy of the system resonances during the simultaneous microwave excitation of the plasma (‘Hot-S-Parameter’ spectroscopy) is a novel method to determine the electron density and to identify the type of coupling mode. The method corresponds directly to the kind of numerical simulations employed. The purpose of this analysis is finally to find the minimum power necessary to drive the source into the ICP mode. The efficiency of microwave energy transfer to the plasma is also discussed. Nitrogen at pressures between 50 and 1000 Pa and a gas flow of 150 sccm is used as test plasma, for which the electron density is determined. Analysis of the microwave resonance frequency shows that the electron density exceeds 1019 m−3 at 50 Pa for 11 W and at 1000 Pa for 26 W absorbed power. 3D theoretical analysis of this source confirms that at this electron density an ICP mode is present.

Broadband ferromagnetic resonance of non-stoichiometric nano Nickle ferrite with different Ni2+content

Four non-stoichiometric nano nickle ferrite samples have molar Ni contents of 0.23, 0.41, 0.62 and 0.82, as they were checked by atomic absorption spectroscopy, were synthesized by precipitation method. The synthesized compositions were checked by x-ray diffraction (XRD), scanning electron microscopy (SEM) and transmission electron microscopy (TEM). All particles showed the spherical shape and inverse spinel structure with average sizes from 21 nm to 29 nm. The maximum magnetization saturation of 4.3 emu g−1 was at Ni content of 0.62. The zero field cooling and field cooling measurement exhibited that the particles had superparamagnetic properties of blocking temperature near room temperature. The synthesized compositions were impeded within an equal amount of epoxy matrix. Different magnetic parameters were measured by conducting the shortcut broadband ferromagnetic resonance (BFMR) tests. The compositions showed a linear proportion between magnetic field and microwave resonance frequency in range 1.5–26.5 GHz. The maximum g-factor with low effective magnetization was Ni content of 0.62. The minimum damping constant was for composition for Ni content 0.41, and generally increasing Ni concentration increases damping factor. The inverse of the quality factor was reduced with frequency increasing.

Determining the mass of gas in large collection volumes with acoustic and microwave resonances

We characterized a 1.8 m3, quasi-spherical resonator, a pressure vessel informally known as the “big blue ball” or “BBB.” The BBB will be the collection volume of a NIST-designed gas-flow standard that will operate at pressures up to 7 MPa. Using microwave resonance frequencies, we determined the volume of the BBB filled with argon as a function of pressure (up to 7 MPa) and temperature (near ambient). The measured pressure- and temperature-dependences of the BBB’s volume are consistent with the published properties of carbon steels. We filled the BBB with 220 kg of argon in weighed increments of approximately 20 kg. We also determined the mass macoust of argon in the BBB by measuring the pressure, the acoustic resonance frequencies facoust of 3 modes, and using the known thermophysical properties of argon. The values of macoust were within ±0.03 % of the gravimetrically determined masses. In a typical application, the BBB will never be isothermal. Nevertheless, the acoustic resonance frequencies quickly and accurately determine the average temperature and mass of the gas in the BBB despite significant, long-lived thermal gradients that are created by pressure changes. A theoretical model for effect of temperature gradients on the acoustic resonance frequencies is presented.

Tunable microwave properties of rhomboid shaped nanomagnet pairs

The magnetization dynamics of a multilayer rhomboid shaped nanomagnet pair is investigated using micro-focused Brillouin light scattering spectroscopy. The multilayer structure consists of two permalloy layers separated by a nonmagnetic Cr spacer layer. As compared with a single-layer rhomboid shaped nanomagnet pair with two distinct magnetic ground states (ferromagnetic and antiferromagnetic), the multilayer nanomagnetic pair displays multiple magnetic ground states upon different initialization fields due to the presence of both in-plane and out-of-plane dipolar coupling. The dynamic response as a function of initialization field has been systematically investigated. Distinct microwave absorption behavior and resonance frequency shift are observed when the nanomagnet pair is switched into different magnetic ground states. Micromagnetic simulations validate our experimental observations.

Efficient quantum microwave-to-optical conversion using electro-optic nanophotonic coupled resonators

We propose a low noise, triply-resonant, electro-optic (EO) scheme for quantum microwave-to-optical conversion based on coupled nanophotonics resonators integrated with a superconducting qubit. Our optical system features a split resonance - a doublet - with a tunable frequency splitting that matches the microwave resonance frequency of the superconducting qubit. This is in contrast to conventional approaches where large optical resonators with free-spectral range comparable to the qubit microwave frequency are used. In our system, EO mixing between the optical pump coupled into the low frequency doublet mode and a resonance microwave photon results in an up-converted optical photon on resonance with high frequency doublet mode. Importantly, the down-conversion process, which is the source of noise, is suppressed in our scheme as the coupled-resonator system does not support modes at that frequency. Our device has at least an order of magnitude smaller footprint than the conventional devices, resulting in large overlap between optical and microwave fields and large photon conversion rate ($g/2\pi$) in the range of $\sim$5-15 kHz. Owing to large $g$ factor and doubly-resonant nature of our device, microwave-to-optical frequency conversion can be achieved with optical pump powers in the range of tens of microwatts, even with moderate values for optical $\it{Q}$ ($\sim 10^6$) and microwave $Q$ ($ \sim10^4$). The performance metrics of our device, with substantial improvement over the previous EO-based approaches, promise a scalable quantum microwave-to-optical conversion and networking of superconducting processors via optical fiber communication.

Determination of the Boltzmann constant with cylindrical acoustic gas thermometry: new and previous results combined

We report a new determination of the Boltzmann constant kB using a cylindrical acoustic gas thermometer. We determined the length of the copper cavity from measurements of its microwave resonance frequencies. This contrasts with our previous work (Zhang et al 2011 Int. J. Thermophys. 32 1297, Lin et al 2013 Metrologia 50 417, Feng et al 2015 Metrologia 52 S343) that determined the length of a different cavity using two-color optical interferometry. In this new study, the half-widths of the acoustic resonances are closer to their theoretical values than in our previous work. Despite significant changes in resonator design and the way in which the cylinder length is determined, the value of kB is substantially unchanged. We combined this result with our four previous results to calculate a global weighted mean of our kB determinations. The calculation follows CODATA’s method (Mohr and Taylor 2000 Rev. Mod. Phys. 72 351) for obtaining the weighted mean value of kB that accounts for the correlations among the measured quantities in this work and in our four previous determinations of kB. The weighted mean is 1.380 6484(28) × 10−23 J K−1 with the relative standard uncertainty of 2.0 × 10−6. The corresponding value of the universal gas constant is 8.314 459(17) J K−1 mol−1 with the relative standard uncertainty of 2.0 × 10−6.

Acoustic and microwave tests in a cylindrical cavity for acoustic gas thermometry at high temperature.

Relative primary acoustic gas thermometry (AGT) determines the ratios of thermodynamic temperatures from measured ratios of acoustic and microwave resonance frequencies in a gas-filled metal cavity on isotherms of interest. When measured in a cavity with known dimensions, the frequencies of acoustic resonances in a gas determine the speed of sound, which is a known function of the thermodynamic temperature T. Changes in the dimensions of the cavity are measured using the frequencies of the cavity's microwave resonances. We explored techniques and materials for AGT at high temperatures using a cylindrical cavity with remote acoustic transducers. We used gas-filled ducts as acoustic waveguides to transmit sound between the cavity at high temperatures and the acoustic transducers at room temperature. We measured non-degenerate acoustic modes in a cylindrical cavity in the range 295 K<T<797 K. The fractional uncertainty of the measured acoustic frequencies increased from 2×10(-6) at 295 K to 5×10(-6) at 797 K. In addition, we measured the frequencies of several transverse magnetic (TM) microwave resonances up to 1000 K in order to track changes in the cavity's length L and radius R. The fractional standard deviation of the values of L deduced from three TM modes increased from 3×10(-6) for T<600 K to 57 × 10(-6) at 1000 K. We observed similar inconsistencies in a previous study.

Comment on “Non-thermal mechanism of weak microwave fields influence on neurons” [J. Appl. Phys. 114, 104701 (2013)

This comment is directly related to previously published work [M. N. Shneider and M. Pekker, J. Appl. Phys. 114, 104701 (2013)], in which we outlined the effect of a non-thermal mechanism of microwave radiation on the activity of neural tissue. In this note, we provide more realistic estimates of the longitudinal sound velocity in the lipid membranes and the corresponding estimates of the microwave resonance frequencies.

Progress towards an acoustic determination of the Boltzmann constant at CEM-UVa

An acoustic gas thermometer was used to achieve a determination of the Boltzmann constant, kB, using a misaligned stainless steel (316L) spherical cavity with an internal volume of approximately 268 cm3. Measurements of the speed of sound while the cavity is filled with argon at the temperature of the triple point of water, 273.16 K, and at different pressures between 78.2 kPa and 0.9 MPa, were used to extrapolate the value of the speed of sound in argon at zero pressure. The internal volume of the resonator was accurately determined by measuring microwave resonance frequencies at the same temperature and pressure conditions as for the acoustic measurements. The measurements were taken at pressures from 78.2 kPa up to 901.3 kPa, and at 273.16 K. As the results of the measurements, we determined kB = (1.380 644 1 ± 0.000 022 1) × 10−23 J K−1 which means a relative standard uncertainty of 16 parts in 106.

‘Weighing’ a gas with microwave and acoustic resonances

With calibrations of large flow meters in mind, we established the feasibility of determining the mass M of argon gas contained within a 0.3 m3 commercially manufactured pressure vessel (‘tank’) with a relative standard uncertainty of ur(M) = 0.0016 at 0.6 MPa by combining the measured argon pressure and the measured microwave and acoustic resonance frequencies within the pressure vessel with an accurate equation of state for argon. (All stated uncertainties correspond to the 68% confidence level.) Previously, we used microwaves to determine the tank’s internal volume Vmicro with ur(V) = 0.0006 and to determine the thermal expansion of the volume (Moldover et al 2015 Meas. Sci. Tech. 26 015304). Here, we show that the microwave results accurately predict the wavenumbers kcalc of the four lowest-frequency acoustic modes of the gas. When we compared kcalc to the measured wavenumbers kmeas, which included corrections for known perturbations, such as the tank’s calculated pressure-dependent center-of-mass motion (but not the tank’s vibrational modes), the inconsistency of the ratio kmeas/kcalc among the modes was the largest component of ur(M). Because the resonance frequencies f calc of the acoustic modes depend on the average speed of sound (and therefore the average temperature) of the gas in the tank, first-order perturbation theory predicts that f calc for a rigid cylindrical cavity is independent of linear temperature gradients. Consistent with this prediction, the average of f meas for the 3 lowest-frequency, non-degenerate longitudinal modes changed only Δfmeas / f meas = (0.2 ± 1.3) × 10−4 when, near ambient temperature, we heated the tank’s top 13 K warmer than its bottom. However, we observed a linear dependence on ΔT for the average of f meas for the nearly-degenerate doublet modes, which the rigid cylinder theory does not predict. We argue that the linear dependence on ΔT was caused by anisotropic changes in the tank’s shape in response to the applied temperature gradient. We conclude that resonance frequencies can be used to ‘weigh’ the compressed gas in much larger tanks, which are possibly made from ferromagnetic steel and possibly at high pressures in un-thermostatted environments; therefore, resonance measurements will have many applications in gas metrology.

A focusing reflectarray and its application in microwave virus sanitizer

AbstractIn this paper, a focusing reflectarray based on the conductor‐backed strip dipole unit cell is proposed and designed for use in the microwave virus sanitizer. Unlike traditional far‐field antennas that form a planar phase front in a specified far‐field direction, the focusing reflectarray is designed to coherently add the fields radiated from the feeding antenna at a predetermined focal point, typically within its radiating near‐field region and to ensure adequate power density to inactivate the H3N2 virus sample. Furthermore, the focusing reflectarray has a simple and planar structure compared with conventional focusing antennas. Since the microwave resonant absorption frequency of the H3N2 virus is at about 8 GHz, an 8 × 8 focusing reflectarray is designed for operation at 8 GHz. A prototype antenna is then fabricated and used for H3N2 virus sanitization. It is demonstrated experimentally that the death rate of the H3N2 virus sample is up to 93%, verifying the feasibility of the microwave virus sanitizer as well as the proposed focusing reflectarray.

Performance of the Au/MgO/Ni photovoltaic devices

A 100μm thick MgO film is used to design a metal semiconductor metal device. The device is characterized by means of current voltage characteristics in the dark and under various light energies in the photon energy range of 3.70–2.15eV. A photovoltaic effect presented by an open circuit voltage of 0.12–0.47V, short circuit current density of 3.9–10.5μA/cm2, quantum efficiency of 0.662–0.052, and responsivity of 0.179–0.024A/W under photoexcitation optical power of 2.2–28.2μW is observed. The device was also tested as a UV optical communication component. The test revealed a wide range of tunability and sensitivity for microwave resonant frequencies of 0.5 and 2.9GHz. The differential resistance of the device exhibited different values at each applied ac signal frequency. When the frequency is fixed, the illuminated to the dark current ratio remained constant for all signal powers in the range of 0.00–20.0dBm.

Optomechanical effects of two-level systems in a back-action evading measurement of micro-mechanical motion

We show that the two-level systems (TLS) in lithographic superconducting circuits act as a power-dependent dielectric leading to non-linear responses in a parametrically coupled electromechanical system. Driven TLS shift the microwave resonance frequency and modulate the mechanical resonance through the optical spring effect. By pumping with two tones in a back-action evading measurement, these effects produce a mechanical parametric instability which limits single quadrature imprecision to 1.4 xzp. The microwave resonator noise is also consistent to a TLS-noise model. These observations suggest design strategies for minimizing TLS effects to improve ground-state cooling and quantum non-demolition measurements of motion.

Magnetostrictive thin films for microwave spintronics

Multiferroic composite materials, consisting of coupled ferromagnetic and piezoelectric phases, are of great importance in the drive towards creating faster, smaller and more energy efficient devices for information and communications technologies. Such devices require thin ferromagnetic films with large magnetostriction and narrow microwave resonance linewidths. Both properties are often degraded, compared to bulk materials, due to structural imperfections and interface effects in the thin films. We report the development of epitaxial thin films of Galfenol (Fe81Ga19) with magnetostriction as large as the best reported values for bulk material. This allows the magnetic anisotropy and microwave resonant frequency to be tuned by voltage-induced strain, with a larger magnetoelectric response and a narrower linewidth than any previously reported Galfenol thin films. The combination of these properties make epitaxial thin films excellent candidates for developing tunable devices for magnetic information storage, processing and microwave communications.

Micromagnetic Simulation on the Microwave Magnetic Properties of Glass-Coated Amorphous Alloy Microwires

The magnetic structure of the glass-coated magnetic alloy microwires were modeled based on the main magnetic domain structure and meshed by finite element method. The magnetic spectrum of the magnetic alloy microwires was calculated based on the micromagnetic theory. The simulation results of the magnetic spectrum of glass-coated magnetic alloy microwires showed that the magnetic anisotropy field increase as the magneto-crystalline anisotropy constants increase. The microwave resonance frequency increased accompanied by the reduction of the permeability and the increase of the magnetic anisotropy field of the glass-coated magnetic alloy microwires.

X- and Q-Band Electron Spin Echo Study of Stochastic Molecular Librations of Spin Labels in Lipid Bilayers

Electron spin echo (ESE) of nitroxide spin labels allows detecting fast nanosecond stochastic restricted rotations (stochastic molecular librations), which is a common property of molecules in disordered media including biological systems. Under the typical experimental conditions, the anisotropic electron paramagnetic resonance (EPR) spectrum of a nitroxide is only partly excited by microwave pulses, which allows selecting an anisotropic contribution to the transverse spin relaxation by comparing echo decays at different spectral positions. On the other hand, for low-amplitude orientational motion, the excitation bandwidth is large enough to cover the range of spectral diffusion occurring during the echo formation. To verify that the two-pulse echo decay is indeed related to fast motions, the stimulated electron spin echo can be used. In addition, theory predicts an increase of the relaxation rates at higher microwave resonance frequency. To check this prediction, in the present work we performed a comparative study of ESE decays at microwave X- and Q-bands, for spin-labeled lipids in the gel phase of a 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) bilayer. A good agreement found between experimental data and computer simulation provides additional justification for the model of fast stochastic molecular librations.