Digital control of residual amplitude modulation at the 10-7 level for ultra-stable lasers.

The stabilization of lasers on ultra-stable optical cavities by the Pound-Drever-Hall (PDH) technique is a widely used method. The PDH method relies on the phase-modulation of the laser, which is usually performed by an electro-optic modulator (EOM). When approaching the 10-16 fractional frequency stability level, this technology requires an active control of the residual amplitude modulation (RAM) generated by the EOM in order to bring the frequency stability of the laser down to the thermal noise limit of the ultra-stable cavity. In this article, we report on the development of an active system of RAM reduction based on a free space EOM, which is used to perform PDH-stabilization of a laser on a cryogenic silicon cavity. A minimum RAM instability of 1.4 × 10-7 is obtained by employing a digital servo that stabilizes the EOM DC electric field, the crystal temperature and the laser power. Considering an ultra-stable cavity with a finesse of 2.5 × 105, this RAM level would contribute to the fractional frequency instability at the level of about 5 × 10-19, well below the state of the art thermal noise limit of a few 10-17.

Digital Doppler-Cancellation Servo for Ultrastable Optical Frequency Dissemination Over Fiber.

Progress made in optical references, including ultrastable Fabry-Perot cavities, optical frequency combs, and optical atomic clocks, has driven the need for ultrastable optical fiber networks. Telecom-wavelength ultrapure optical signal transport has been demonstrated on distances ranging from the laboratory scale to the continental scale. In this article, we present a Doppler-cancellation setup based on a digital phase-locked loop (PLL) for ultrastable optical signal dissemination over fiber. The optical phase stabilization setup is based on a usual heterodyne Michelson-interferometer setup, while the software-defined radio (SDR) implementation of the PLL is based on a compact commercial board embedding a field-programmable gate array and analog-to-digital and digital-to-analog converters. Using three different configurations, including an undersampling method, we demonstrate a 20-m-long fiber link with residual fractional frequency instability as low as 10-18 at 1000 s and optical phase noise of -70 dBc/Hz at 1 Hz with a telecom frequency carrier.

Ultracompact reference ultralow expansion glass cavity.

We present the first experimental characterization of our ultracompact, ultrastable laser. The heart of the apparatus is an original Fabry-Perot cavity with 25 mm length and pyramidal geometry, equipped with highly reflective crystalline coatings. The cavity, along with its vacuum chamber and optical setup, fits inside a 30 L volume. We have measured the cavity's thermal and vibration sensitivities and present our first estimation of the cavity fractional frequency instability at σy(1 s)=7.5×10-15.

Author Correction: Photonic Generation of High Power, Ultrastable Microwave Signals by Vernier Effect in a Femtosecond Laser Frequency Comb.

A correction to this article has been published and is linked from the HTML and PDF versions of this paper. The error has been fixed in the paper.

Photonic Generation of High Power, Ultrastable Microwave Signals by Vernier Effect in a Femtosecond Laser Frequency Comb.

Optical frequency division of an ultrastable laser to the microwave frequency range by an optical frequency comb has allowed the generation of microwave signals with unprecedently high spectral purity and stability. However, the generated microwave signal will suffer from a very low power level if no external optical frequency comb repetition rate multiplication device is used. This paper reports theoretical and experimental studies on the beneficial use of the Vernier effect together with the spectral selective filtering in a double directional coupler add-drop optical fibre ring resonator to increase the comb repetition rate and generate high power microwaves. The studies are focused on two selective filtering aspects: the high rejection of undesirable optical modes of the frequency comb and the transmission of the desirable modes with the lowest possible loss. Moreover, the conservation of the frequency comb stability and linewidth at the resonator output is particularly considered. Accordingly, a fibre ring resonator is designed, fabricated, and characterized, and a technique to stabilize the resonator's resonance comb is proposed. A significant power gain is achieved for the photonically generated beat note at 10 GHz. Routes to highly improve the performances of such proof-of-concept device are also discussed.

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 1 s and below 2 ×10(-16) for [Formula: see text].

Frequency stability of a wavelength meter and applications to laser frequency stabilization.

Interferometric wavelength meters have attained frequency resolutions down to the megahertz range. In particular, Fizeau interferometers, which have no moving parts, are becoming a popular tool for laser characterization and stabilization. In this paper, we characterize such a wavelength meter using an ultrastable laser in terms of relative frequency instability σ(y)(τ) and demonstrate that it can achieve a short-term instability σ(y)(1s)≈2×10(-10) and a frequency drift of order 10 MHz/day. We use this apparatus to demonstrate frequency control of a near-infrared laser, where a frequency instability below 3×10(-10) from 1 to 2000 s is achieved. Such performance is, for example, adequate for ion trapping and atom cooling experiments.

New-generation of cryogenic sapphire microwave oscillators for space, metrology, and scientific applications.

This article reports on the characterization of cryogenic sapphire oscillators (CSOs), and on the first test of a CSO in a real field installation, where ultimate frequency stability and continuous operation are critical issues, with no survey. Thanks to low-vibration liquid-He cryocooler design, Internet monitoring, and a significant effort of engineering, these oscillators could bridge the gap from an experiment to a fully reliable machine. The cryocooler needs scheduled maintenance every 2 years, which is usual for these devices. The direct comparison of two CSOs demonstrates a frequency stability of 5 × 10(-16) for 30 s ≤ τ ≤ 300 s integration time, and 4.5 × 10(-15) at 1 day (1 × 10(-14) typical). Two prototypes are fully operational, codenamed ELISA and ULISS. ELISA has been permanently installed the new deep space antenna station of the European Space Agency in Malargüe, Argentina, in May 2012. ULISS is a transportable version of ELISA, modified to fit in a small van (8.5 m(2) footprint). Installation requires a few hours manpower and 1 day of operation to attain full stability. ULISS, intended for off-site experiments and as a technology demonstrator, and has successfully completed two long-distance travels.

Unprecedented long-term frequency stability with a microwave resonator oscillator.

This article reports on the long-term frequency stability characterization of a new type of cryogenic sapphire oscillator using an autonomous pulse-tube cryocooler as its cold source. This new design enables a relative frequency stability of better than 4.5 x 10(-15) over one day of integration. To the best of our knowledge, this represents the best long-term frequency stability ever obtained with a signal source based on a macroscopic resonator.

Advanced noise reduction techniques for ultra-low phase noise optical-to-microwave division with femtosecond fiber combs.

We report what we believe to be the lowest phase noise optical-to-microwave frequency division using fiber-based femtosecond optical frequency combs: a residual phase noise of -120 dBc/Hz at 1 Hz offset from an 11.55 GHz carrier frequency. Furthermore, we report a detailed investigation into the fundamental noise sources which affect the division process itself. Two frequency combs with quasi-identical configurations are referenced to a common ultrastable cavity laser source. To identify each of the limiting effects, we implement an ultra-low noise carrier-suppression measurement system, which avoids the detection and amplification noise of more conventional techniques. This technique suppresses these unwanted sources of noise to very low levels. In the Fourier frequency range of ∼200 Hz to 100 kHz, a feed-forward technique based on a voltage-controlled phase shifter delivers a further noise reduction of 10 dB. For lower Fourier frequencies, optical power stabilization is implemented to reduce the relative intensity noise which causes unwanted phase noise through power-to-phase conversion in the detector. We implement and compare two possible control schemes based on an acousto-optical modulator and comb pump current. We also present wideband measurements of the relative intensity noise of the fiber comb.

High-power solid-state sapphire whispering gallery mode maser.

We present new results on a cryogenic solid-state maser frequency standard, which relies on the excitation of whispering gallery (WG) modes within a doped monocrystalline sapphire resonator (alpha-Al2O3). Included substitutively within the highest purity HEMEX-grade sapphire crystal lattice are Fe2+ impurities at a concentration of parts per million, an unavoidable result of the manufacturing process. Mass conversion of Fe2+ to Fe3+ ions was achieved by thermally annealing the sapphire in air. Above-threshold maser oscillation was then excited in the resonator at zero applied DC magnetic field by pumping high-Q WG modes coincident in frequency with the electron spin resonance (ESR) energy levels of the Fe3+ spin population. A 2 stage annealing process was undertaken for a sapphire resonator with exceptionally low Fe3+ concentration, resulting in an improvement of 6 orders of magnitude in output power for this particular crystal, and exceeding the previous best implementation of our scheme in another crystal by nearly 20 dB. This represents an output signal 7 orders of magnitude more powerful than a typical commercial hydrogen maser. At this power level, we estimate a limit on the frequency stability of order 1 x 10(-17)/square root(tau) due to the Schawlow-Townes fundamental thermal noise limit.

Measurement of the fundamental thermal noise limit in a cryogenic sapphire frequency standard using bimodal maser oscillations.

We report observations of the Schawlow-Townes noise limit in a cryogenic sapphire secondary frequency standard. The effect causes a fundamental limit to the frequency stability, and was measured through the novel excitation of a bimodal maser oscillation of a Whispering Gallery doublet at 12.04 GHz. The beat frequency of 10 kHz between the oscillations enabled a sensitive probe for this measurement of fractional frequency instability of 10(-14) tau(-1/2) with only 0.5 pW of output power.

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.

Whispering-gallery mode technique applied to the measurement of the dielectric properties of Langasite between 4 K and 300 K.

We report new measurements of dielectric properties of Lanthanum gallium silicate (Langasite or LGS) conducted with the whispering-gallery mode technique at microwave frequencies and between 4.2 K and 300 K. The real part of the permittivity tensor of LGS presents two components having temperature coefficients of opposite sign. This unique property enables the design of a temperature compensated resonator that may be useful in building stable microwave oscillators or filters. We report also the first measurements of the two independent components of the imaginary part of the permittivity tensor. It appears LGS is a relatively high-loss dielectric material compared with sapphire or quartz.

Optimization of an ultra low-phase noise sapphire--SiGe HBT oscillator using nonlinear CAD.

In this paper, the electrical and noise performances of a 0.8 microm silicon germanium (SiGe) transistor optimized for the design of low phase-noise circuits are described. A nonlinear model developed for the transistor and its use for the design of a low-phase noise C band sapphire resonator oscillator are also reported. The best measured phase noise (at ambient temperature) is -138 dBc/Hz at 1 kHz offset from a 4.85 GHz carrier frequency, with a loaded QL factor of 75,000.

Cryogenic monolithic sapphire-rutile temperature compensated resonator oscillator.

We have tested a new temperature-compensated sapphire resonator as frequency determining element for high-stability microwave oscillator. Temperature compensation has been obtained by coating the sapphire resonator with a thin rutile film. A 2-microm rutile thickness is sufficient to reach turnover temperature higher than 40 K, and a 2 X 10(-12) short-term frequency stability has been obtained.