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Simple perovskite crystals undergo structural phase transitions on cooling to low temperatures, which significantly change the material properties of the crystal. In this work we rigorously characterize the temperature evolution of permittivity of a perovskite crystal as it undergoes phase transitions. In particular, we have undertaken precision measurements of a single crystal of Strontium Titanate from 294.6 K to 5.6 K, by measuring the frequency of multiple microwave transverse electric and magnetic resonant modes simultaneously. The multi-mode microwave measurement technique of resonant frequency used in this work allows high precision determination of any induced anisotropy of the permittivity as the crystal undergoes structural phase transitions. Compared with previous results we unequivocally show that the permittivity has an isotropic value of $316.3\pm2.2$ at room temperature, consistent with its well-known cubic structure, and determine the onset of dielectric anisotropy as the crystal is cooled to lower temperatures. We show that the crystal exhibits uniaxial anisotropy in the permittivity below 105 K when the structure becomes tetragonal, and exhibits biaxial anisotropy in the permittivity below 51 K when the structure becomes orthorhombic., Comment: Accepted for publication in TUFFC. arXiv admin note: substantial text overlap with arXiv:1508.07550

Electrodynamic theory applied to the analysis of TEn0p mode resonances in ferromagnetic spheres placed either in metallic cavities or in the free space is compared with Walker-Fletcher's theory of so-called magnetostatic modes. The influence of the diameter of the sample, its permittivity and the permittivity of the surrounding media on the resonance frequencies of a few modes is analyzed. It is shown that the dominant resonances are essentially related either to negative values of the diagonal component of the permeability tensor or, for clockwise circularly polarized magnetic fields, to negative effective permeability. The electrodynamic theory is used to determine the saturation magnetization (Ms) from measured TEn01 frequency differences. Measurements on different samples confirmed that Ms can be determined using an electrodynamic approach with uncertainties of the order of 2% regardless of sample sizes, metal enclosures or static magnetic field values., Comment: preprint - "The author's own write-up of research results and analysis that has not been peer reviewed, nor had any other value added to it by a publisher (such as formatting, copy-editing, technical enhancements, and the like)."

Dielectric resonators are employed to build state-of-the-art low-noise and high- stability oscillators operating at room and cryogenic temperatures. A resonator temperature coefficient of frequency is one criterion of performance. This paper reports on predictions and measurements of this temperature coefficient of frequency for three types of cylindrically-symmetric Bragg resonators operated at microwave frequencies. At room temperature, microwave Bragg resonators have the best potential to reach extremely high Q-factors. Research has been conducted over the last decade on modeling, optimizing and realizing such high Q-factor devices for applications such as filtering, sensing, and frequency metrology. We present an optimized design, which has a temperature sensitivity 2 to 4 times less than current whispering gallery mode resonators without using temperature compensating techniques and about 30% less than other existing Bragg resonators. Also, the performance of a new generation single-layered Bragg resonators, based on a hybrid-Bragg-mode, is reported with a sensitivity of about -12ppm/K at 295K. For a single reflector resonator, it achieves a similar level of performance as a double-Bragg-reflector resonator but with a more compact structure and performs six times better than whispering-gallery-mode resonators. The hybrid resonator promises to deliver a new generation of high-sensitivity sensors and high-stability room-temperature oscillators., Comment: 24 pages, 8 figures, 2 tables, journal article

The dielectric properties of strontium titanate (SrTiO$_3$) have previously been reported from room temperature to low temperatures with conflicting results. In this work, precision measurement of the permittivity is undertaken by simultaneously measuring transverse electric and transverse magnetic resonant modes within a single crystal. It is unequivocally shown that the permittivity is isotropic at room temperature with a permittivity of order $316.3\pm2.2$ by measuring multiple modes of different electric field polarisations. As the crystal is cooled to 5 K and undergoes well known phase transitions, we show the material becomes uniaxial anisotropic with the ratio of the parallel to perpendicular permittivity to the cylinder z-axis of the sample as high as 2.4 below 6 K.

Dielectric resonators are key components for many microwave and millimetre wave applications, including high-Q filters and frequency-determining elements for precision frequency synthesis. These often depend on the quality of the dielectric material. The commonly used material for building the best cryogenic microwave oscillators is sapphire. However sapphire is becoming a limiting factor for higher frequencies design. It is then important to find new candidates that can fulfil the requirements for millimetre wave low noise oscillators at room and cryogenic temperatures. These clocks are used as a reference in many fields, like modern telecommunication systems, radio astronomy (VLBI), and precision measurements at the quantum limit. High-resolution measurements were made of the temperature-dependence of the electromagnetic properties of a polycrystalline diamond disk at temperatures between 35 K and 330 K at microwave to sub-millimetre wave frequencies. The cryogenic measurements were made using a TE01{\delta} dielectric mode resonator placed inside a vacuum chamber connected to a single-stage pulse-tube cryocooler. The high frequency characterization was performed at room temperature using a combination of a quasi-optical two-lens transmission setup, a Fabry-Perot cavity and a whispering gallery mode resonator excited with waveguides. Our CVD diamond sample exhibits a decreasing loss tangent with increasing frequencies. We compare the results with well known crystals. This comparison makes clear that polycrystalline diamond could be an important material to generate stable frequencies at millimetre waves., Comment: 6 pages, 7 figures, 1 table, journal article

The loss tangent of medium, low and very low loss dielectric substrates (including the Rogers RT Duroid 5880 and 6010.2, LaAlO3, (La, Sr)(Al, Ta)O3, MgO and Quartz) was measured at varying temperatures with two TE01{\delta} dielectric resonators to ensure verification of the tests. The accuracy of the measurements has been researched and discussed for split post dielectric resonator (SPDR) in a copper enclosure and a single post dielectric resonator (SuPDR) in a superconducting enclosure in the temperature range from 15K to 300 K., Comment: 4 pages, 7 figures

Yttrium Vanadate (YVO4) is a birefringent crystal material used in optical isolators and circulators with potentials for application in cryogenic microwave devices. As microwave properties of the YVO4 are not known, we measured the complex permittivity at the frequency of 25 GHz, using the Hakki-Coleman dielectric resonator technique in the temperature range from 13 K to 80 K. The real part of relative permittivity of YVO4 turned out to be similar to that of Sapphire - one of popular dielectric materials, used at microwave frequencies. The measured loss tangent tang {\delta} of the YVO4 was of the order of 10^(-6) at cryogenic temperatures. As Yttrium Vanadate (YVO4) is easy to synthesis and machine, it may replace the expensive Sapphire in some microwave applications., Comment: 4 pages, 4 figures, ISBN 981-238-372-7

Surface resistance of HTS films is typically measured using Sapphire dielectric rod resonators enclosed in a copper cavity. In this paper we present surface resistance measurements of YBa2Cu3O7-{\delta} films using Strontium Lanthanum Aluminate (SLAO) at a resonant frequency of 18.2 GHz. We have performed the error analysis of the cavity loaded with SLAO dielectric rod and also verification measurements using two Sapphire (Al2O3) rod resonators operating at resonant frequencies of 24.6 GHz and 10 GHz respectively. Good agreement between the values of Rs of two sets of YBa2Cu3O7-{\delta} films measured using the SLAO and the Sapphire dielectrics has been obtained after a frequency scaling of Rs was applied. Using different dielectric rods of the same size in the same cavity for measurements of Rs of HTS films, it is feasible to do microwave characterization of the same films at differing frequencies., Comment: 4 pages, 10 figures

A split post dielectric resonator in a copper enclosure and a single post dielectric resonator in a cavity with superconducting end-plates have been constructed and used for the complex permittivity measurements of single crystal substrates. (La,Sr)(Al,Ta)O3, LaAlO3, MgO and quartz substrates have been measured at temperatures from 20 K to 300 K in the split post resonator and from 15 K to 80 K in the single post resonator. The TE01delta mode resonant frequencies and unloaded Qo-factors of the empty resonators at temperature of 20 K were: 9.952 GHz and 25,000 for the split post resonator and 10.808 GHz and 240,000 for the single post resonator respectively., Comment: 4 pages, 8 figures, 1 table

Properties of calcium fluoride (CaF2) have been well researched at UV, visible and IR range of frequencies, but not at ultra high frequencies. In this work we report the loss tangent and the real part of relative permittivity of CaF2, measured in the temperatures range of 15 - 81 K and the frequency of 29.25 GHz. The loss tangent and the real part of relative permittivity were determined by measurements of the resonant frequency and the Qo - factor of a TE011 mode cylindrical copper cavity with superconducting plates containing the sample under test. The measured real part of relative permittivity of CaF2 was found to change from 6.484 to 6.505, and the loss tangent from 3.1x10^(-6) to 22.7x10^(-6), when the temperature was varied from 15 to 81 K. Due to the low losses CaF2 can be useful in construction of high Q-factor microwave circuits and devices, operating at the cryogenic temperatures., Comment: 6 pages, 8 figures, 2 tables; http://www.sciencedirect.com/science/article/pii/S0955221903001833

Accurate data of complex permittivity of dielectric substrates are needed for efficient design of HTS microwave planar circuits. We have tested MgO substrates from three different manufacturing batches using a dielectric resonator with superconducting parts recently developed for precise microwave characterization of laminar dielectrics at cryogenic temperatures. The measurement fixture has been fabricated using a SrLaAlO3 post dielectric resonator with DyBa2Cu3O7 end plates and silver-plated copper sidewalls to achieve the resolution of loss tangent measurements of 2 {\times} 10-6. The tested MgO substrates exhibited the average relative permittivity of 9.63 and tan {\delta} from 3.7 {\times} 10-7 to 2 {\times} 10-5 at frequency of 10.5 GHz in the temperature range from 14 to 80 K., Comment: 6 pages, 8 figures, 3 tables

We report on extremely sensitive measurements of changes in the microwave properties of high purity non-intentionally-doped single-crystal semiconductor samples of gallium phosphide, gallium arsenide and 4H-silicon carbide when illuminated with light of different wavelengths at cryogenic temperatures. Whispering gallery modes were excited in the semiconductors whilst they were cooled on the coldfinger of a single-stage cryocooler and their frequencies and Q-factors measured under light and dark conditions. With these materials, the whispering gallery mode technique is able to resolve changes of a few parts per million in the permittivity and the microwave losses as compared with those measured in darkness. A phenomenological model is proposed to explain the observed changes, which result not from direct valence to conduction band transitions but from detrapping and retrapping of carriers from impurity/defect sites with ionization energies that lay in the semiconductor band gap. Detrapping and retrapping relaxation times have been evaluated from comparison with measured data., Comment: 7 pages, 6 figures

A Bragg resonator uses dielectric plates within a metallic cavity to confine the energy within a central free space region. The importance of the permittivity is shown with a better Q-factor possible using higher permittivity materials of larger intrinsic dielectric losses. This is because the electric energy in the reflectors decreases proportionally to the square root of permittivity and the coupling to the metallic losses decrease linearly. In a sapphire resonator with a single reflector pair a Q-factor of 2.34x10^5 is obtained, which may be improved on by up to a factor of 2 using higher permittivity materials.

The authors report on observation of Bragg confined mode in a hollow cylindrical dielectric cavity. A resonance was observed at 13.4 $GHz$ with an unloaded Q-factor of order $2\times10^5$, which is more than a factor of 6 above the dielectric loss limit. Previously such modes have only been realized from pure Transverse Electric modes with no azimuthal variations and only the $E_{\phi}$ component. From rigorous numeric simulations it is shown that the mode is a hybrid mode with non-zero azimuthal variations and with dominant $E_r$ and $E_{\phi}$ electric field components and $H_z$ magnetic field component., Comment: Accepted to be published in Applied Physics Letters