Ultra-stable Oscillator Research Articles

Study on the origin of 1/f noise in quartz resonators

Intrinsic frequency fluctuations with a power spectral density limit the short-term stability in quartz crystal ultra-stable oscillators. The physical origin of this noise remains not clearly explained. In this paper, a review of an experimental study on numerous ultra-stable quartz crystal resonators is presented. A comparison with past measurements is given. A theoretical approach, based on the fluctuation–dissipation theorem, is used in order to put numerical constraints on a model of noise caused by an internal (or structural) dissipation proportional to the amplitude and not to the speed, in the limit of low frequencies. The order of the magnitude of the noise is then discussed using a candidate physical process. Comparisons between theoretical and experimental results show that internal damping of thickness fluctuations by any internal friction force proportional to strain and independent of frequency may not be the dominant noise mechanism for the best SC-cut quartz resonators. Finally, we conclude on the work that could be done to solve the remaining open problems.

Characterization of the Individual Short-Term Frequency Stability of Cryogenic Sapphire Oscillators at the 10(-16) Level.

We present the characterization of three cryogenic sapphire oscillators (CSOs)using the three-cornered-hat method. Easily implemented with commercial components and instruments, this method reveals itself very useful to analyze the fractional frequency stability limitations of these state-of-the-art ultrastable oscillators. The best unit presents a fractional frequency stability better than 5 ×10(-16) at 1s and below 2 ×10(-16) for [Formula: see text].

High-Q energy trapping of temperature-stable shear waves with Lamé cross-sectional polarization in a single crystal silicon waveguide

A multi-port electrostatically driven silicon acoustic cavity is implemented that efficiently traps the energy of a temperature-stable eigen-mode with Lamé cross-sectional polarization. Dispersive behavior of propagating and evanescent guided waves in a ⟨100⟩-aligned single crystal silicon waveguide is used to engineer the acoustic energy distribution of a specific shear eigen-mode that is well known for its low temperature sensitivity when implemented in doped single crystal silicon. Such an acoustic energy trapping in the central region of the acoustic cavity geometry and far from substrate obviates the need for narrow tethers that are conventionally used for non-destructive and high quality factor (Q) energy suspension in MEMS resonators; therefore, the acoustically engineered waveguide can simultaneously serve as in-situ self-oven by passing large uniformly distributed DC currents through its body and without any concern about perturbing the mode shape or deforming narrow supports. Such a stable thermo-structural performance besides large turnover temperatures than can be realized in Lamé eigen-modes make this device suitable for implementation of ultra-stable oven-controlled oscillators. 78 MHz prototypes implemented in arsenic-doped single crystal silicon substrates with different resistivity are transduced by in- and out-of-plane narrow-gap capacitive ports, showing high Q of ∼43k. The low resistivity device shows an overall temperature-induced frequency drift of 200 ppm over the range of −20 °C to 80 °C, which is ∼15× smaller compared to overall frequency drift measured for the similar yet high resistivity device in the same temperature range. Furthermore, a frequency tuning of ∼2100 ppm is achieved in high resistivity device by passing 45 mA DC current through its body. Continuous operation of the device under such a self-ovenizing current over 10 days did not induce frequency instability or degradation in Q.

Recent progress in the performances of ultrastable quartz resonators and oscillators

Stressed compensated (SC) cut led recently to the best frequency stability ever obtained with a quartz oscillator, 2.5 × 10−14 for the flicker frequency modulation (FFM) floor. This result is confirmed in this paper with a 3.2 × 10−14 ± 1.1 × 10−14 . The quartz resonator is integrated in a 5 MHz enhanced aging box double oven controlled oscillator. After reminding a bit of history, this paper describes how the first significant development in terms of ultra-stable quartz state-of-the-art oscillators was performed in the last 20 years, how the resonators were chosen, and main information about the development of adequate electronics and how to mechanically and thermally stabilized such an ultra-stable oscillator. We also present how to characterize the expected performances, and hot topics in quartz based oscillators.

Tests of Sapphire Crystals Manufactured With Different Growth Processes for Ultra-Stable Microwave Oscillators

We present the characterization of 8-12 GHz whispering gallery mode resonators machined in high-quality sapphire crystals elaborated with different growth techniques. These microwave resonators are intended to constitute the reference frequency of ultra-stable Cryogenic Sapphire Oscillators. We conducted systematic tests near 4 K on these crystals to determine the unloaded Q-factor and the turnover temperature for whispering gallery modes in the 8-12 GHz frequency range. These characterizations show that high quality sapphire crystals elaborated with the Heat Exchange or the Kyropoulos growth technique are both suitable to meet a fractional frequency stability better than 1x10-15 for 1 s to 10.000 s integration times.

Systematic and quantitative analysis of residual amplitude modulation in Pound-Drever-Hall frequency stabilization

We theoretically analyze the effects of two primary mechanisms of residual amplitude modulation, estimate the resulting frequency instabilities, and discuss relevant experimental countermeasures, providing useful information that are beneficial for the development of ultrastable optical oscillators as well as many precision experiments relying on stable lasers. A Pound-Drever-Hall signal comprising contributions from the birefringence of the electro-optic crystal is derived and used to examine the birefringence-related amplitude modulation and the resultant frequency offset in terms of various experimental parameters. The combined effect of the crystal birefringence and pararsitic 'etalons is further investigated by dividing the etalons into three representative categories according to their locations in the optical path. The analysis shows that introducing a resonant optical cavity only scales the birefringence-generated amplitude modulation by a constant, thereby lending strong support to the active control scheme using a separate detection path. When a parasitic 'etalon is added, the active control scheme can still suppress the resultant instability except for the parasitic 'etalon that is located closely in front of the optical cavity. In this case the etalon produces rather large frequency instability and therefore should be avoided. In addition, numerical calculations are performed to assess the impact of a special situation where the front and end surfaces of an ultrastable optical cavity are potential sources of the parasitic etalon that can strongly couple with the cavity.

Temperature, radiation and aging analysis of the DORIS Ultra Stable Oscillator by means of the Time Transfer by Laser Link experiment on Jason-2

The Time Transfer by Laser Link (T2L2) experiment on-board the Jason-2 satellite was launched in June 2008 at 1335km altitude. It has been designed to use the Satellite Laser Ranging (SLR) space technique as an optical link between ground and space clocks. T2L2, as all the instruments aboard Jason-2, is referenced to the Ultra Stable Oscillator (USO) provided by the Doppler Orbitography and Radio-positioning Integrated by Satellite (DORIS) system. A complex data processing has been developed in order to extract time & frequency products as the relative frequency bias of the USO from ground-to-space time transfer passages. The precision of these products was estimated of a few parts in 10−13 given the very good in-flight performance of T2L2 with a ground-to-space time stability of a few picoseconds (ps) over 100s. Frequency bias from T2L2 were compared with results from operational orbit computation, notably with the DIODE (Détermination Immédiate d’Orbite par Doris Embarqué) outputs (see Jayles et al. (2016) same issue) at the level of 1·10−12.The present paper is focusing on the main physical effects which drive the frequency variations of the Jason-2 USO during its flight, notably over the South Atlantic Anomaly (SAA) area. In addition to the effects of radiation we studied the effect of the residual temperature variations, in the range 8–11°C (measured on-board). A model was established to represent these effects on the short term with empirical coefficients (sensitivities of the USO) to be adjusted. The results of fitting the model over ∼200 10-day periods, from 2008 to 2014, show the sensitivities of the Jason-2 USO to temperature and radiation. The analysis of the 6-year output series of empirical coefficients allows us to conclude that: (i) the temperature to frequency dependence is very stable along time at the level of around −1.2·10−12per°C, (ii) the radiation effects are much lower than those previously detected on the Jason-1 USO with a factor>10. The swept material used by manufacturers for the Jason-2 quartz oscillator has such properties to avoid non-linear effects >1–2·10−12, (iii) the model is available at 1min or less over the Jason-2 mission, with a level of consistency of 5·10−13, which is the average RMS of the post-fit residuals.

Fluctuation-dissipation theorem and 1/f noise of bulk acoustic wave cavities

The short time stability in quartz crystal ultra-stable oscillators is limited by some intrinsic frequency fluctuations with a 1/f power spectral density. The physical origin of this 1/f noise is still unknown. In this paper, the fluctuation dissipation theorem is used to numerically evaluate the importance of the contribution of internal damping of thickness fluctuations on the level of noise for bulk acoustic wave cavities. A 1/f contribution to the power spectral density of frequency noise for the shear mode usually used is obtained. Its study provides a possible explanation for the fact that, for the best resonators, the 1/f noise amplitude is usually disconnected from the quality factor measured at resonance.

Comparison of the frequency estimation of the DORIS/Jason2 oscillator thanks to the onboard DIODE and Time Transfer by Laser Link experiment

The main applications for DORIS are precise orbit determination, and precise Geodesy. Onboard Jason-2 for instance, the DORIS tracking component is the French contribution to the precise orbit determination capability, a key capability for altimetry product scientific result accuracy. T2L2 is a time transfer technique based on the propagation of light pulses for synchronization between two clocks. Hosting T2L2 on-board Jason-2 was to allow for very fine DORIS USO (Ultra-Stable Oscillator) frequency monitoring, and for this purpose T2L2 was connected to the DORIS USO. Thanks to the continuous tracking of T2L2/Jason-2 by the Laser Ranging network it is possible to monitor the USO for several days, weeks, and even much longer, and thus to also compare with the DIODE (the DORIS on-board orbit determination software) frequency bias estimates. The DORIS USO frequency biases estimate comparison between two independent systems, T2L2 and DIODE, can be of benefit to both, allowing the accuracies of both systems to be better understood, and for improvements to be made to both systems. Such comparison is the central topic of the present paper. T2L2 monitors the DORIS on-board USO frequency with an accuracy of much better than 10−12 which is the specification for the Doppler instrumentation.The paper investigates the limits of the DORIS-DIODE frequency bias estimates using T2L2, showing that USO frequency compliance accuracy of 10−12 has been reached.

HY-2A Radar Altimeter Ultrastable Oscillator Drift Estimation Using Reconstructive Transponder With Its Validation By Multimission Cross Calibration

This paper presents a method estimating the HY-2A altimeter ultrastable oscillator (USO) drift with a reconstructive transponder. The frequency of the USO of the in-orbit altimeter changes with age, and a bias between the actual frequency and the nominal one exists. The USO bias contributes a portion of the altimeter range drift. The HY-2A altimeter transmits signals at a fixed time interval during calibration, and the actual interval between adjacent altimeter transitions, which is controlled by the USO, is different from the nominal one due to the USO drift. The reconstructive transponder measures the arrival times of the altimeter transmitted signals accurately with the atomic clock. The drift of the USO on board the HY-2A altimeter can be estimated accurately by using the ranges from the reconstructive transponder and the HY-2A altimeter. The USO drifts of around 40 cm/year are presented. Furthermore, the multimission cross calibration provides preliminary validation of the HY-2A altimeter USO drift.

Direct terrestrial test of Lorentz symmetry in electrodynamics to 10(-18).

Lorentz symmetry is a foundational property of modern physics, underlying the standard model of particles and general relativity. It is anticipated that these two theories are low-energy approximations of a single theory that is unified and consistent at the Planck scale. Many unifying proposals allow Lorentz symmetry to be broken, with observable effects appearing at Planck-suppressed levels; thus, precision tests of Lorentz invariance are needed to assess and guide theoretical efforts. Here we use ultrastable oscillator frequency sources to perform a modern Michelson–Morley experiment and make the most precise direct terrestrial test to date of Lorentz symmetry for the photon, constraining Lorentz violating orientation-dependent relative frequency changes Δν/ν to 9.2±10.7 × 10−19 (95% confidence interval). This order of magnitude improvement over previous Michelson–Morley experiments allows us to set comprehensive simultaneous bounds on nine boost and rotation anisotropies of the speed of light, finding no significant violations of Lorentz symmetry.

Time-delay interferometry with optical frequency comb

Heterodyne laser phase measurements in a space-based gravitational wave interferometer are degraded by the phase fluctuations of the onboard clocks, resulting in unacceptable sensitivity performance levels of the interferometric data. In order to calibrate out the clock phase noises it has been previously suggested that additional inter-spacecraft phase measurements must be performed by modulating the laser beams. This technique, however, considerably increases system complexity and probability of subsystem failure. With the advent of self-referenced optical frequency combs, it is possible to generate the heterodyne microwave signal that is coherently referenced to the onboard laser. We show in this case that the microwave noise can be cancelled directly by applying modified second-generation Time-Delay Interferometric combinations to the heterodyne phase measurements. This approach avoids use of modulated laser beams as well as the need of additional ultra-stable oscillator clocks.

A numerical technique for two‐way radio occultations by oblate axisymmetric atmospheres with zonal winds

AbstractThe Ultra Stable Oscillator aboard the Cassini spacecraft failed in late 2011, which means that all radio occultations after that date have to be done in two‐way mode, using a ground‐based signal transmitted to the spacecraft as the frequency reference. Here we present the numerical technique we use to analyze the data from the two‐way atmospheric radio occultations of both Saturn and Titan that have occurred since the Ultra Stable Oscillator (USO) failure, along with the theoretical reasons behind this technique. Since our two‐way technique is based upon our earlier one‐way technique which used the USO as the frequency reference, we also present our one‐way technique which we used for Saturn occultations prior to the loss of the USO.

Dual transponder ranging performance in the presence of oscillator phase noise

A dual transponder carrier ranging method can be used to measure inter-satellite distance with high precision by combining the reference and the to-and-fro measurements. Based on the differential techniques, the oscillator phase noise, which is the main error source for microwave ranging systems, can be significantly attenuated. Further, since the range measurements are derived on the same satellite, the dual transponder ranging system does not need a time tagging system to synchronize the two satellites. In view of the lack of oscillator noise analysis on the dual transponder ranging model, a comprehensive analysis of oscillator noise effects on ranging accuracy is provided. First, the dual transponder ranging system is described with emphasis on the detailed analysis of oscillator noise on measurement precision. Then, a high-fidelity numerical simulation approach based on the power spectrum density of an actual ultra-stable oscillator is carried out in both frequency domain and time domain to support the presented theoretical analysis. The simulation results under different conditions are consistent with the proposed concepts, which makes the results reliable. Besides, the results demonstrate that a high level of accuracy can be achieved by using this oscillator noise cancelation-oriented ranging method.

Analysis of frequency noise in ultra-stable optical oscillators with active control of residual amplitude modulation

Two 1,064-nm Nd:YAG lasers frequency stabilized by high-finesse optical cavities are developed to investigate various noise mechanisms in ultra-stable optical oscillators. Active control of residual amplitude modulation using a separate sensing path is implemented and its effectiveness in the presence of a resonant optical cavity is theoretically analyzed and experimentally verified by measuring the rejection ratios in optical heterodyne beat between a perturbed laser and a stable reference. Laser frequency noises originated from vibration, residual amplitude modulation, quantum-limited shot noise, and electronic noise are experimentally analyzed. With active control, residual amplitude modulation is suppressed to below 1 x 10(-6) at 0.02-1,000 s, reaching a minimum of 2 x 10(-7) at similar to 2 s. A frequency stability of 2 x 10(-15) is obtained from 0.1 to 10 s, and the optical heterodyne beat of the two Nd: YAG lasers shows 1-Hz linewidth with a measurement time of 4.096 s. In addition, the experimentally determined linewidths agree well with the calculation according to a simplified relationship between the linewidth and the underlying flicker noise that modulates the laser frequency.

Atomic fountain clock with very high frequency stability employing a pulse-tube-cryocooled sapphire oscillator.

The frequency stability of an atomic fountain clock was significantly improved by employing an ultra-stable local oscillator and increasing the number of atoms detected after the Ramsey interrogation, resulting in a measured Allan deviation of 8.3 × 10(-14)τ(-1/2)). A cryogenic sapphire oscillator using an ultra-low-vibration pulse-tube cryocooler and cryostat, without the need for refilling with liquid helium, was applied as a local oscillator and a frequency reference. High atom number was achieved by the high power of the cooling laser beams and optical pumping to the Zeeman sublevel m(F) = 0 employed for a frequency measurement, although vapor-loaded optical molasses with the simple (001) configuration was used for the atomic fountain clock. The resulting stability is not limited by the Dick effect as it is when a BVA quartz oscillator is used as the local oscillator. The stability reached the quantum projection noise limit to within 11%. Using a combination of a cryocooled sapphire oscillator and techniques to enhance the atom number, the frequency stability of any atomic fountain clock, already established as primary frequency standard, may be improved without opening its vacuum chamber.

Barium fluoride and lithium fluoride whispering-gallery-mode resonators for photonics applications

Crystalline whispering-gallery-mode disk resonators are finding an increasing number of applications in photonics. Their exceptional energy storage capacity is of great interest in the area of ultrastable oscillators for aerospace and communication engineerings as well as for sensing applications. Here, we investigate the physi- cal properties of some unconventional crystalline materials. We show that these resonators can display quality factors higher than ten million at 1550 nm and we discuss their potential for various applications. © 2014 Society of

Limit-Cycle Dynamics with Reduced Sensitivity to Perturbations

Limit-cycle oscillators are used to model a broad range of periodic nonlinear phenomena. Using the optically injected semiconductor laser as a paradigmatic example, we demonstrate that at specific operating points, the period-one oscillation frequency is simultaneously insensitive to multiple perturbation sources. In our system these include the temperature fluctuations experienced by the master and slave lasers as well as fluctuations in the bias current applied to the slave laser. Tuning of the oscillation frequency then depends only on the injected optical field amplitude. Experimental measurements are in detailed quantitative agreement with numerical modeling. These special operating points should prove valuable for developing ultrastable nonlinear oscillators, such as a narrow-linewidth, frequency-tunable photonic microwave oscillator.

Improved GRACE kinematic orbit determination using GPS receiver clock modeling

Kinematic positions of Low Earth Orbiters based on GPS tracking are frequently used as pseudo-observations for single satellite gravity field determination. Unfortunately, the accuracy of the satellite trajectory is partly limited because the receiver synchronization error has to be estimated along with the kinematic coordinates at every observation epoch. We review the requirements for GPS receiver clock modeling in Precise Point Positioning (PPP) and analyze its impact on kinematic orbit determination for the two satellites of the Gravity Recovery and Climate Experiment (GRACE) mission using both simulated and real data. We demonstrate that a piecewise linear parameterization can be used to model the ultra-stable oscillators that drive the GPS receivers on board of the GRACE satellites. Using such a continuous clock model allows position estimation even if the number of usable GPS satellites drops to three and improves the robustness of the solution with respect to outliers. Furthermore, simulations indicate a potential accuracy improvement of the satellite trajectory of at least 40 % in the radial direction and up to 7 % in the along-track and cross-track directions when a 60-s piecewise linear clock model is estimated instead of epoch-wise independent receiver clock offsets. For PPP with real GRACE data, the accuracy evaluation is hampered by the lack of a reference orbit of significantly higher accuracy. However, comparisons with a smooth reduced-dynamic orbit indicate a significant reduction of the high-frequency noise in the radial component of the kinematic orbit.

High-Frequency Noise in the Gravity Recovery and Climate Experiment Intersatellite Ranging System

The Gravity Recovery and Climate Experiment mission consists of two satellites flying in tandem with a highprecision intersatellite rangemeasurement system. The rangemeasurements are collected continuously and are used tomake accurate determinations of theEarth’s gravity field atmonthly intervals. The changes in themonthlymodels (i.e., the temporal variations in the gravity field) are manifestations of the global mass change between the Earth’s atmosphere, ocean, and land systems. The primary focus of the study was twofold: 1) to understand the characteristics and sources of the high-frequency noise, in the range of 0.02–0.1Hz, in the dual one-way ranging, and 2) to explore methods for mitigating the effect of the noise. Based on the mathematical model of the dual one-way ranging observation, the Allan variance was computed from the K-band range measurements to establish an upper bound for the frequency instability of the ultrastable oscillators and its contribution to the high-frequency noise. Because the residuals of the time derivative of the dual one-way ranging are dominated by the high-frequency noise, they were also examined to evaluate the contributions of various other factors such as the system noise from the microwave receiver and the antenna offset correction noise. The results indicate that the systemnoise is the dominant source of the excessive high-frequency noise. As one method of mitigation for the ongoing mission, a tighter bandwidth filter for the dual one-way ranging was investigated.