Anthony Mann

Resonant frequencies of higher order modes in cylindrical anisotropic dielectric resonators

A method that calculates the frequency of the lowest order mode in a cylindrical isotropic dielectric is extended to higher order modes in a anisotropic crystal. Four different axial match equations are derived depending on whether they are quasi TE or quasi TM, and have an odd or even axial mode number. A general radial match equation is also derived. Combining it with the relevant axial equation forms a set of two coupled transcendental equations that can be solved numerically. The theory is confirmed by room temperature measurements in two sapphire crystals of different aspect ratios, and in cryogenic sapphire resonators used in high stability fixed and tunable oscillators. The sensitivity of mode frequency to dimensional and permittivity perturbations is analyzed. >

A very high stability sapphire loaded superconducting cavity oscillator

Abstract We have implemented a sapphire loaded superconducting cavity resonator in a novel phase stabilised loop oscillator at 10 Ghz and achieved a fractional frequency stability of 10–14 for 3 to 300 seconds integration time and a resonator Q of 3 x 108. We present here an overview of the oscillator.

Cryogenic sapphire oscillator with exceptionally high frequency stability

Extremely high short-term frequency stability has been realised in oscillators based on liquid helium cooled sapphire resonators with a modified mounting structure. These oscillators have exhibited an Allan deviation of about 5.4/spl times/10/sup -16//spl tau//sup -1/2/ for integration times (/spl tau/) of 1 to 4 s and a minimum of 2.4/spl times/10/sup -16/ at 32 s.

Ultra-stable cryogenic sapphire dielectric microwave resonators: mode frequency-temperature compensation by residual paramagnetic impurities

Residual paramagnetic impurities in a sapphire monocrystal multi-mode resonator can provide a means of temperature compensation so that the effect of temperature fluctuations on the frequency of an ultra-stable cryogenic microwave oscillator can be reduced to second order. Modes investigated at X-band in 3 and 5 cm diameter resonators exhibited a wide range of effective paramagnetic filling factors, and frequency-temperature turning points in the range 5 to 13 K. The observations agree well with theory.

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 10/sup 9/ 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/spl times/10/sup -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/sup -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/spl times/10/sup -15/ from 600 to 2000 s. >

Low noise 9-GHz sapphire resonator-oscillator with thermoelectric temperature stabilization at 300 Kelvin

The authors report on an X-band microwave oscillator incorporating a room temperature thermoelectric stabilized sapphire resonator operating at 9.00000 GHz. With a Galani type stabilization scheme they have measured a reduced single sideband phase noise of about -124 dBc/Hz at 1 kHz with a f/sup -3/ dependence. The measurement was limited by the flicker noise of the phase detector in the feedback electronics. The frequency stability was also measured; at an integration time of 0.1 seconds a /spl delta/f/f of about 10/sup -11/ with a /spl tau//sup 0.7/ dependence was measured. The frequency drift strongly correlated with ambient temperature fluctuations. >

Paramagnetic susceptibility and permittivity measurements at microwave frequencies in cryogenic sapphire resonators

We present high-resolution measurements of the temperature-dependence of mode frequency for three monocrystalline microwave sapphire dielectric resonators at liquid helium temperatures. In two resonators the susceptibility is independent of frequency and displays a non-Curie law behaviour. This can be interpreted as arising from a van Vleck temperature-independent contribution to the paramagnetic susceptibility of the and ions involved. We also report measurements of the combined dependence of thermal expansion and permittivity on temperature in the range 2 - 20 K and show that this is about 50% larger in all three resonators than the value calculated from the presently accepted thermal expansion coefficient of sapphire.

High-resolution measurement of the temperature-dependence of the Q, coupling and resonant frequency of a microwave resonator

An automated system is described which facilitates fast high-resolution measurements of Q, coupling and resonant frequency of modes in a microwave resonator. We demonstrate measurements of Q and coupling with a resolution of and a fractional frequency measurement resolution of . The system is used to measure the temperature-dependence of the mode Q, coupling and resonant frequency for modes in two high-Q cryogenic sapphire resonators. Measurement of the temperature variation of Q is used to estimate the geometric factor, which is a measure of the mode energy confinement to the sapphire element distribution. Measurement of the mode frequency temperature-dependence can be used to determine the effect of paramagnetic impurities in the sapphire.

Very high Q microwave spectroscopy on trapped /sup 171/Yb/sup +/ ions: application as a frequency standard

A microwave frequency standard based on buffer-gas cooled /sup 171/Yb/sup +/ ions confined in a linear Paul trap has been demonstrated in prototype form. The standard exhibits a fractional frequency instability characterized by an Allan deviation /spl sigma//sub y/(/spl tau/)=3.7/spl times/10/sup -13//spl tau//sup -1/2/ for /spl tau/ >

A high stability atomic fountain clock using a cryogenic sapphire interrogation oscillator

We describe the operation of the cesium fountain clock in the quantum limited regime, yielding a frequency stability of 5 10/sup -14//spl tau/ /sup -1/2/, where /spl tau/ is the integration time in seconds. The measured frequency instability varies as 1//spl radic/N/sub at/ where N/sub at/ is the number of detected atoms, up to N/sub at/=6 10/sup 5/. Among the primary frequency standards, this is the best stability ever reported. The noise contribution of the fountain interrogation oscillator has been made negligible thanks to the ultra-low frequency noise in the 0.1-100 Hz Fourier frequency range of a cryogenic sapphire oscillator.