High-Q sapphire-rutile frequency-temperature compensated microwave dielectric resonators

A sapphiro-rutile composite resonator was constructed from a cylindrical sapphire monocrystal with two thin disks of monocrystal rutile held tightly against the ends. Because rutile exhibits low loss and an opposite temperature coefficient of permittivity to sapphire, it is an ideal material for compensating the frequency-temperature dependence of a sapphire resonator. Most of the electromagnetic modes in the composite structure exhibited turning points (or compensation points) in the frequency-temperature characteristic. The temperatures of compensation for the WG quasi TM modes were measured to be below 90 K with Q-factors of the order of a few million depending on the mode. For WG quasi TE modes, the temperatures of compensation were measured to be between 100 to 160 K with Q-factors of the order of a few hundreds of thousands, depending on the mode. The second derivatives of the compensation points were measured to be of the order 0.1 ppm/K(2 ), which agreed well with the predicted values.     

Stabilizing the spectrum of a femtosecond Ti:Sapphire laser

A new scheme for stabilizing the beat frequency of the interacting longitudinal modes in a femtosecond Ti:sapphire laser (Femos-1) has been developed and experimentally studied. The stability and frequency spectrum of mode beats in a modified laser have been monitored. A short-term instability of the beat frequency does not exceed 4.8 × 10^?8 (τ = 10 s) over a time scale of 10 min. The laser linewidth in the regime of self-mode-locking is ≤3 Hz at a laser spectrum width of 20 nm.     

Room temperature measurement of the anisotropic loss tangent of sapphire using the whispering gallery mode technique

The anisotropic loss tangent has been determined in monocrystalline sapphire for components parallel and perpendicular to the crystal axis, using the whispering gallery (WG) mode method. The Q-factors of quasi-TE and quasi-TM modes were measured precisely in four cylindrical sapphire resonators at room temperature, from which was determined a maximum attainable Q-factor of (2.1 +/- 0.2) x 10(5) at 9 GHz in a quasi-TM mode. Sapphire dielectric material from three different manufacturers was compared over the 270-345 K temperature range and the 5-16 GHz frequency range.     

Temperature-compensated cryogenic Fabry-Perot cavity

We show that temperature compensation based on differential thermal expansion between sapphire and fused silica can be used to create a Fabry-Perot cavity with an exceptionally low coefficient of thermal expansion at low temperatures. We describe the design of such a cavity that utilizes shaped fused silica mirrors and a sapphire spacer. The geometry of the fused silica mirror was designed using a finite element model to have a small platform, giving a frequency temperature turning point of 16.6 K. The measured turning point was 16.2 K and the curvature was 6 x 10(-10) K(-2), both of which were consistent with the model.     

Analysis of the rutile-ring method of frequency-temperature compensating a high-Q whispering gallery sapphire resonator

The rutile-ring method of dielectrically frequency-temperature compensating a high-Q whispering gallery (WG) sapphire resonator is presented. Two and three-dimensional finite element (FE) analysis has been implemented to design and analyze the performance of such resonators, with excellent agreement between theory and experiment. A high-Q factor of 30 million at 13 GHz, and compensation temperature of 56 K was obtained. It is shown the frequency-temperature compensation can occur either because the rutile adds a small perturbation to the sapphire resonator or because of a mode interaction with a resonant mode in the rutile. The characteristics of both of these methods are described, and it is shown that for high frequency stability, it is best to compensate perturbatively     

Measurement and analysis of a microwave oscillator stabilized by a sapphire dielectric ring resonator for ultra-low noise

Phase-noise measurements are presented for a microwave oscillator whose frequency is stabilized by a whispering gallery mode sapphire ring resonator with Q of 2x10(5). The nature of the mode, which involves little metallic conduction, allows nearly full use of the very low dielectric loss in sapphire. Several mode families have been identified with good agreement with calculated frequency predictions. Waveguide coupling parameters have been characterized for the principal (lowest frequency) mode family, for n=5 to n =10 full waves around the perimeter. For a 5-cm wheel resonator in a 7.6-cm container, Q-values of above 10(5) were found at room temperature for all of the modes in this sequence. Coupling Q-values for the same modes ranged from 10(4) (n =5) to 10(5) (n=10) for a WR112 waveguide port at the center of the cylinder wall of the containing can. Phase noise measurements for a transistor oscillator locked to the n=10 (7.84-GHz) mode showed a 1/f(3) dependence for low offset frequencies, and a value of L(f)=-55 dB/Hz at an offset of 10 Hz from the carrier. The oscillator shows phase noise below the previously reported for any X-band source.     

Frequency-temperature compensation in Ti(3+) and Ti(4+ ) doped sapphire whispering gallery mode resonators

A new method of compensating the frequency-temperature dependence of high-and monolithic sapphire dielectric resonators near liquid nitrogen temperature is presented. This is achieved by doping monocrystalline sapphire with Ti(3+) ions. This technique offers significant advantages over other methods.     

New method to build a high stability sapphire oscillator from the temperature compensation of the difference frequency between modes of orthogonal polarization

A new method to construct a high stability sapphire oscillator is presented. The method relies on the anisotropic fractional temperature coefficients of frequency (TCF) of orthogonally polarized modes. We show that it is possible to design a resonator with transverse electric and magnetic modes at different frequencies, but with the same TCF in units hertz per kelvin, resulting in temperature compensation of the difference frequency. Compensation was demonstrated between 50 to 77 K by measuring the difference frequency of two microwave oscillators frequency locked to orthogonally polarized whispering gallery modes. Curvature of the compensation points was measured to be 1 to 3 /spl times/ 10/sup -8/ K/sup -2/ between 50 and 77 K. This technique enables the construction of temperature compensated oscillators at any temperature and does not require dielectric, paramagnetic, or mechanical compensation techniques. Considering the above parameters, we show that it is possible to construct oscillators with fractional frequency instability at /spl tau/ = 1 s, of order 7.6 /spl times/ 10/sup -15/ at solid nitrogen temperature (/spl sim/50 K).     

Temperature-compensated sapphire resonator for ultra-stableoscillator capability at temperatures above 77 K

We report on the design and test of a whispering gallery sapphire resonator for which the dominant (WGH_n11) microwave mode family shows frequency-stable, compensated operation for temperatures above 77 K. The resonator makes possible a new ultra-stable oscillator (USO) capability that promises performance improvements over the best available crystal quartz oscillators in a compact cryogenic package. A mechanical compensation mechanism, enabled by the difference between copper and sapphire expansion coefficients, tunes the resonator to cancel the temperature variation of sapphire's dielectric constant. In experimental tests, the WGH₈₁₁ mode showed a frequency turnover temperature of 87 K in agreement with finite element calculations. Preliminary tests of oscillator operation show an Allan Deviation of frequency variation of 1.4-6×10^-12 for measuring times 1 s ⩽τ⩽100 s with unstabilized resonator housing temperature and a mode Q of 2×10⁶. We project a frequency stability 10^-14 for this resonator with stabilized housing temperature and with a mode Q of 10⁷     

Sapphire Whispering Gallery Thermometer

An innovative sapphire whispering gallery thermometer (SWGT) is being explored at the National Institute of Standards and Technology (NIST) as a potential replacement for a standard platinum resistance thermometer (SPRT) for industrial applications that require measurement uncertainties of ≤ 10 mK. The NIST SWGT uses a synthetic sapphire monocrystalline disk configured as a uniaxial, dielectric resonator with whispering gallery modes between 14 GHz and 20 GHz and with Q-factors as large as 90,000. The prototype SWGT stability at the ice melting point (0°C) is ≤ 1 mK with a frequency resolution equivalent to 0.05 mK. The prototype SWGT measurement uncertainty (k= 1) is 10 mK from 0°C to 100°C for all five resonance modes studied. These results for the SWGT approach the capabilities of industrial resistance thermometers. The SWGT promises greatly increased resistance to mechanical shock relative to SPRTs, over the range from −196°C to 500°C while retaining the low uncertainties needed by secondary calibration laboratories. The temperature sensitivity of the SWGT depends upon a well-defined property (the refractive index at microwave frequencies) and the thermal expansion of a pure material. Therefore, it is expected that SWGTs can be calibrated over a wide temperature range using a reference function, along with deviations measured at a few fixed points. This article reports the prototype SWGT stability, resolution, repeatability, and the temperature dependence of five whispering gallery resonance frequencies in the range from 0°C to 100°C. Certain commercial equipments, instruments or materials are identified in this article in order to adequately specify the experimental procedure. Such identification does not imply recommendation or endorsement by the NIST.     

Experimental verification of stress compensation in the SBTC-cut

The authors have demonstrated experimental verification of the stress compensation feature for the fast thickness shear mode of vibration of stress-compensated for B-mode and temperature-compensated for C-mode (SBTC)-cut quartz resonators. For the resonator design used in the cylindrical probe structure, the motional resistance for the B-mode of vibration was approximately 12% of that of the C-mode. The relatively large motional resistance for the C-mode of vibration of the SBTC-cut was found to be largely due to the lower piezoelectric coupling for the thickness excitation of this mode. In addition the proximity of the third overtone of the A-mode to the fifth overtone of the C-mode also contributed to the increase in the motional resistance. The authors have obtained experimental data on the temperature dependence of the planar stress coefficient and pressure dependence of the frequency-temperature characteristic for both the thickness-shear modes of the SBTC-cut. It is noted that such a doubly rotated cut can have applications in the design of either stable frequency sources or sensors for pressure and temperature measurements.     

On the accuracy of Mindlin plate predictions for the frequency-temperature behavior of resonant modes in AT- and SC-cut quartz plates

The frequency spectra of resonant modes in AT- and SC-cut quartz plates and their frequency-temperature behavior were studied using Mindlin first- and third-order plate equations. Both straight-crested wave solutions and two-dimensional plate solutions were studied. The first-order Mindlin plate theory with shear correction factors was previously found to yield inaccurate frequency spectra of the modes in the vicinity of the fundamental thickness-shear frequency. The third-order Mindlin plate equations without correction factors, on the other hand, predict well the frequency spectrum in the same vicinity. In general, the frequency-temperature curves of the fundamental thickness-shear obtained from the first-order Mindlin plate theory are sufficiently different from those of the third-order Mindlin plate theory that they raise concerns. The least accurately predicted mode of vibration is the flexure mode, which results in discrepancies in its frequency-temperature behavior. The accuracy of other modes of vibrations depends on the degree of couplings with the flexure mode. Mindlin first-order plate theory with only the shear correction factors is not sufficiently accurate for high frequency crystal vibrations at the fundamental thickness-shear frequency. Comparison with measured resonant frequencies and frequency-temperature results on an AT-cut quartz plate shows that the third-order plate theory is more accurate than the first-order plate theory; this is especially true for the technically important fundamental thickness shear mode in the AT-cut quartz plate.     

A cryogenic open-cavity sapphire reference oscillator with low spurious mode density

In this paper, we describe the implementation of a microwave cryogenic sapphire oscillator (CSO) at the Laboratoire de Physique et Métrologie des Oscillateurs. In our realization we solved the problem of the spurious modes by operating the sapphire resonator in an open cavity. The CSO compared to a hydrogen maser demonstrates a frequency stability better than 3 x 10(-14) at short term. Its long-term frequency instability of the order of 3 x 10(-12)/day is limited by a random walk process. A first attempt to use this reference oscillator to characterize other signal sources is presented.     

Power stabilized cryogenic sapphire oscillator

Microwave oscillators of exceptional short-term stability have been realized from cryogenic sapphire resonators with loaded Q factors in excess of 10⁹ at 11.9 GHz and 6 K. This has been achieved by a power stabilized loop oscillator with active Pound frequency stabilization. These oscillators have exhibited a fractional frequency stability of 3-4×10^-15 for integration times from 0.3 to 100 s. The relative drift of these two oscillators over one day is a few times 10^-13. To reduce the long-term drift, which is principally due to excessive room temperature sensitivity, we have added cryogenic sensors for the power and frequency stabilization servos to one of these oscillators. We have also implemented a servo to reduce the room temperature sensitivity of our phase modulators. Testing of this oscillator against a Shanghai Observatory H-maser has shown an Allan deviation of 4×10^-15 from 600 to 2000 s     

Sensitivity and optimization of a high-Q sapphire dielectric motion-sensing transducer

A high-Q sapphire dielectric motion sensing transducer that operates at microwave frequencies has been developed. The device uses cylindrical whispering gallery modes of quality factor greater than 10 (5) at room temperature and greater than 10(8) at 4 K. The tuning coefficient of the transducer resonance frequency with respect to displacement was measured to be of the order of a few MHz/mum. An electromagnetic model that predicts the resonant frequency and tuning coefficient has been developed and was verified by experiment. We implemented the model to determine what aspect ratio and what dielectric mode is necessary to maximize the sensitivity. We found that the optimum mode type was a TM whispering gallery mode with azimuthal mode number of about 7 for a resonator of 3 cm in diameter. Also, we determined that the tuning coefficients were maximized by choosing an aspect ratio that has a large diameter with respect to the height. By implementing a microwave pump oscillator of SSB phase noise -125 dBc/Hz at 1 kHz; offset, we have measured a sensitivity of order 10 (-16) m/ radicalHz. We show that this can be improved with existing technology to 10(-18) m/ radicalHz, and that in the near future this may be further improved to 10(-19) m/ radicalHz.     

Cryogenic dual-mode resonator for a fly-wheel oscillator for a caesium frequency standard

A dual-mode, sapphire-loaded cavity (SLC) resonator has been designed and optimized with the aid of finite element software. The resonance frequency was designed to be near the frequency of a Cs atomic frequency standard. Experimental tests are shown to agree very well with calculations. The difference frequency of two differently polarized modes is shown to be a highly sensitive temperature sensor in the 50 to 80 K temperature range. We show that an oscillator based on this resonator has the potential to operate with fractional frequency instability below 10/sup -14/ for measurement times of 1 to 100 seconds. This is sufficient to operate an atomic clock at the quantum projection noise limit.     

Properties of shear horizontal acoustic plate modes in BT-cut quartz

Properties of shear horizontal acoustic plate modes (SHAPMs) in BT-cut quartz were calculated and measured. A delay line with a long interdigital transducer, deposited on -50.5°YX90°-oriented quartz plate, was used for the measurements. For one of the SHAPMs, at a frequency of about 100.4 MHz, insertion loss, turnover temperature, and quadratic temperature coefficient of frequency of about 10 dB, 15°C, and -30 ppb/(°C)(2) in air, respectively, were obtained. Using water and glycerin solutions, insertion loss changes against dynamic viscosity were measured for this mode. In a viscosity range from about 1 mPa·s to 1000 mPa·s, an insertion loss change of about 14 dB was obtained.     

Experimental investigation on a thermoacoustic engine having a looped tube and resonator

The purpose of this paper is to study the impact of regenerator hydraulic radius, resonator length, and mean pressure on the characteristics of the tested thermoacoustic engine, which has a looped tube and resonator. Two different acoustic oscillations are observed in the tested engine [Yu ZB, Li Q, Chen X, Guo FZ, Xie XJ, Wu JH. Investigation on the oscillation modes in a thermoacoustic stirling prime mover: mode stability and mode transition. Cryogenics 2003;43(12):687-91]. In this paper, they are called two acoustic modes, high frequency mode (with a frequency independent of the resonator length) and low frequency mode (with a frequency depending on the resonator length). Experimental results indicate that the relative penetration depth (the ratio of penetration depth over hydraulic radius) plays an important role in the excitation and pressure amplitude of the two acoustic modes. For each tested regenerator hydraulic radius, there is a measured optimal relative penetration depth, which leads to the lowest onset temperature difference. Note that, in the tested engine, the measured optimal relative viscous penetration depths are in the range 3-5 (for low frequency mode). Furthermore, experimental results also show that the resonator length affects the presence of high frequency mode in this engine.     

Room-temperature growth of AlN/TiN epitaxial multi-layer by laser molecular beam epitaxy

We have fabricated epitaxial AlN thin films at room temperature on sapphire (0001) substrates with a TiN (111) epitaxial buffer layer by pulsed laser deposition in ultra-high vacuum (laser molecular beam epitaxy method). The TiN buffer layers were also fabricated at room temperature. Four-circle X-ray diffraction analysis and reflection high-energy electron diffraction results indicate the heteroepitaxial structure of AlN (0001)/TiN (111)/sapphire (0001) with the epitaxial relationship of AlN [10-10]||TiN [11-2]||sapphire [11-20]. The surface of the room-temperature grown AlN film was found to be atomically flat, reflecting the nano-stepped surface of ultrasmooth sapphire substrates. Then, we could achieve the room-temperature epitaxial growth of [AlN/TiN] multi-layer. The temperature dependence of resistivity of the AlN/TiN multi-layer film was also measured.     

Thermal control of a dual mode parametric sapphire transducer

We propose a method to control the thermal stability of a sapphire dielectric transducer made with 2 dielectric disks separated by a thin gap and resonating in the whispering gallery (WG) modes of the electromagnetic field. The simultaneous measurement of the frequencies of both a WGH mode and a WGE mode allows one to discriminate the frequency shifts due to gap variations from those due to temperature instability. A simple model, valid in quasi-equilibrium conditions, describes the frequency shift of the 2 modes in terms of 4 tuning parameters. A procedure for their direct measurement is presented.