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International audience; In this paper, we present the current development status of a cavity stabilized laser at 1550 nm. The expected thermal noise limit of the silicon Fabry-Perot cavity is $3\times 10^{-17}$ at 17 K in terms of fractional frequency instability. We cooled it to its thermal expansion turning point, measured at 18.1 K, with a pulse-tube based cryocooler. Thanks to the thermal filtering and the temperature control of the cavity, the temperature induced fractional frequency instability is below the thermal noise up to 1000 s of integration time. We also discuss the vibration induced limitations, the thermal characterization of the cryocooler and the digital servo implementation and performances.

International audience; We report on the fully digital implementation of various locking schemes within the frame of microwave photonics systems such as Pound-Drever-Hall (PDH) for ultra-stable lasers based on Fabry-Perot cavities, heterodyne lockin amplifiers for fiber links, laser stabilization of optical clocks. We demonstrate similar performances over their analog counterparts, with a net gain on flexibility and reconfigurability.

International audience; This article introduces the counter, a frequency counter - i.e., a frequency-to-digital converter - based on the Linear Regression (LR) algorithm on time stamps. We discuss the noise of the electronics. We derive the statistical properties of the counter on rigorous mathematical basis, including the weighted measure and the frequency response. We describe an implementation based on a SoC, under test in our laboratory, and we compare the counter to the traditional and counters. The LR exhibits optimum rejection of white phase noise, superior to that of the and counters. White noise is the major practical problem of wideband digital electronics, both in the instrument internal circuits and in the fast processes which we may want to measure. With a measurement time , the variance is proportional to 1=2 for the counter, and to 1=3 for both the and counters. However, the counter has the smallest possible variance, 1.25 dB smaller than that of the counter. The counter finds a natural application in the measurement of the Parabolic Variance (PVAR), described in the companion article [1] IEEE Transact. UFFC vol. 63 no. 4 pp. 611-623, April 2016 (Special Issue on the 50th Anniversary of the Allan Variance).

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 m2 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.

Elisa is a cryocooled sapphire oscillator (CSO) intented for the new Deep Space Network ground station of the ESA. This oscillator is required to achieve a frequency stability σy (τ) ≤ 3 × 10−15 for τ ∈ [1 − 1000s] and a phase noise Sφ (1Hz) = −96dBc/Hz with scheduled maintenance of 2 years. This frequency standard must include a frequency synthesis with outputs at 10GHz, 100MHz and 5MHz showing identical CSO's stability. Elisa consists of a sapphire resonator (monocristal Al2 O3 puck) excited on whispering gallery modes (WG) and cooled down at 4.2K in a cryocooler. At this temperature unloaded Q-factors are around 1 × 109 . From our knowlege and the literature, W GH15,0,0 mode was chosen. Its resonant frequency was definied to simplify the frequency synthesis conception and to avoid frequency transitions of paramagnetic impurities. It was fixed at 10GHz - D where D is a confidence interval of 10MHz taking into account the manufactering tolerances. It can be easily compensated with the use of a Direct Digital Synthesizer (DDS) included in the frequency synthesis in order to reach 10GHz. The dimensions of the resonator were calculated by finite elements method. Different coupling methods were tested to achieve an efficient modal selection. Every component needed for constructing Elisa was analysed in detail. An original method of diode detector amplitude noise measurement, the design of low noise electronics, the principle of a frequency synthesis based on the use of a DDS and the description of two cryogenic technologies are shown. In the last case, we focused our study on the low mechanical vibration cryocooler. The performances demonstrated by Elisa achieve the specifications of the ESA. A frequency stability better than 3 × 10−15 for τ ∈ [1 − 1000s] was measured. A minimum value of 1.4 × 10−15 at τ = 20s was achieved. The phase noise measurement shows Sφ (1Hz) = −101dBc/Hz. Moreover, the frequency synthesis enables the transfer of the Elisa stability at 10GHz and 100MHz. The long term stability of 4.5 × 10−15 /day classifies Elisa at the state-of-the-art in the cryogenic sapphire oscillator category., Elisa est un oscillateur saphir cryogénique (CSO) dont la vocation est d'équiper la nouvelle station sol de l'ESA. Les performances requises sont une stabilité de fréquence σy (τ) ≤ 3 × 10−15 pour τ ∈ [1 − 1000 s] et un bruit de phase Sφ (1 Hz) = −93 dB.rad2 /Hz pour une autonomie de 2 ans. Cette référence de fréquence doit également possèder des sorties aux fréquences de 10 GHz, 100 MHz et 5 MHz pilotées par le CSO. Elisa intègre dans une boucle d'entretien un résonateur saphir (Al2 O3 ) excité sur des modes de galeries (WG) et refroidi à 4,2 K dans un cryogénérateur. A cette température, le facteur de qualité à vide peut atteindre 1 × 109 . Le mode opérationnel W GH15,0,0 a été choisi par rapport à notre savoir-faire et à la littérature. Sa fréquence de résonance a été fixée à 10GHz - D où D est un “intervalle de confiance” égal à 10 MHz. La fréquence de 10 GHz est suffisament éloignée des fréquences de transition des ions paramagnétiques présents dans le cristal de saphir et l'écart de fréquence D permet de faire face aux tolérances d'usinage. D peut être compensé par l'intermédiaire d'un “Direct Digital Synthesizer” intégré dans le chaîne de synthèse pour atteindre 10 GHz. Les dimensions du cylindre de saphir ont été calculées par la méthode des éléments finis. Après avoir validé les caractéristiques du résonateur, différentes méthodes de couplage ont été expérimentées dans le but d'atteindre une sélection modale performante. Tous les éléments nécessaire à la construction d'Elisa sont analysés en détails. Une méthode originale de mesure de bruit d'amplitude de détecteurs quadratiques, l'étude d'électroniques faibles bruits, le principe d'une chaîne de synthèse sur base d'un DDS et la description de deux technologies cryogéniques sont présentées. Pour ces dernières, nous avons focalisé notre étude sur un modèle de cryogénérateur à faible vibration mécanique. Les performances démontrées par Elisa satisfont le cahier des charges de l'ESA. Une stabilité de fréquence inférieure à 3 × 10−15 a été mesurée pour τ ∈ [1 − 1000 s]. Elle atteint 1, 4 × 10−15 à τ = 20 s. La mesure de bruit de phase montre Sφ (1 Hz) = −98 dB.rad2 /Hz. La chaîne de synthèse permet le tranfert des performances du CSO aux fréquences de 10 GHz et 100 MHz. La stabilité journalière de 4, 5 × 10−15 place Elisa à l'état-de-l'art.

The zero-field Fe3+:sapphire whispering-gallery-mode maser oscillator exhibits several alluring features: Its output is many orders of magnitude brighter than that of an active hydrogen maser and thus far less degraded by spontaneous-emission (Schawlow-Townes) and/or receiving-amplifier noise. Its oscillator loop is confined to a piece of mono-crystalline rock bolted into a metal can. Its quiet amplification combined with high resonator Q provide the ingredients for exceptionally low phase noise. We here concentrate on novelties addressing the fundamental conundrums and technical challenges that impede progress. (1) Roasting: The "mase-ability" of sapphire depends significantly on the chemical conditions under which it is grown and heat-treated. We provide some fresh details and nuances here. (2) Simplification: This paper obviates the need for a Ka-band synthesizer: it describes how a 31.3 GHz loop oscillator, operating on the preferred WG pump mode, incorporating Pound locking, was built from low-cost components. (3) "Dark Matter": A Siegman-level analysis of the experimental data determines the substitutional concentration of Fe3+ in HEMEX to be less than a part per billion prior to roasting and up to a few hundred ppb afterwards. Chemical assays, using different techniques (incl. glow discharge mass spectra spectroscopy and neutron activation analysis) consistently indicate, however, that HEMEX contains iron at concentrations of a few parts per million. Drawing from several forgotten-about/under-appreciated papers, this substantial discrepancy is addressed. (4) Excitons: Towards providing a new means of controlling the Fe3+:sapph. system, a cryogenic sapphire ring was illuminated, whilst masing, with UV light at wavelengths corresponding to known electronic and charge-transfer (thus valence-altering) transitions. Preliminary experiments are reported., pdf only; submitted to the proceedings of the 24th European Frequency and Time Forum, 13-15th April, 2010

B. Cretin, Professeur, ENSMM, Besançon P-A. Rolland, Professeur, Université des Sciences et Technologies de Lille, IEMN D. Cros, Professeur, IRCOM, Limoges M-E. Tobar, Professor, Frequency Standards and Metrology Research Group, UWA, Australia M. Oxborrow, Principal Research Scientist, Centre for Basic, Thermal and Length Metrology, NPL, United Kingdom V. Giordano, DR2, Institut FEMTO-ST, département LPMO, Besançon G. Santarelli, IR, SYRTE, Observatoire de Paris S. Merlet, Ingénieur BNM, Paris M. Chaubet, Ingénieur, CNES, Toulouse; This thesis is devoted to the realization and the characterization of a cryogenic microwave secondary frequency standard for metrological applications.\\ This standard is based on the excitation of a high-order electromagnetic mode, of the ``whispering-gallery'' type, within a cylindrically shaped piece of monocrystalline sapphire ($Al_2O_3$) maintained at a temperature near to that of liquid helium.\\ Such a resonator currently represents the best solution to realizing frequency stabilities of the order of $1\cdot 10^(-14)$.\\ Mode splitting is generally observed at cryogenic temperatures, which makes the adjustment of the coupling difficult. We present a simple model that successfully explains the observed degeneracy and lineshapes for each mode. Moreover, we solve the problem of spurious modes by placing the resonator in an open cavity.\\ Every component needed for constructing a frequency-stable microwave oscillator based around the cryogenic resonator is analysed in detail.\\ The experimental results we obtain are exceptional: the oscillator realizes a short-term fractional frequency instability of less than $7.5\cdot 10^(-15)$. Over the longer term, any frequency drift is clearly identifiable; the instability at one-day intervals lies below $2\cdot 10^(-14)$. This last result represents the state of the art for long-term secondary frequency standards. \\ Several other, related pieces of work are also presented: the measurement of the dielectric properties of a langasite crystal, the characterization of ultra-stable oscillators, a sapphire-rutile composite resonator oscillator, a synthesis chain, and the observation of a bistability phenomenon due to the accidental coincidence of a whispering gallery mode with the paramagnetic resonance of $Fe^(3+)$ ions within the sapphire crystal.; Ce mémoire présente l'élaboration et la caractérisation d'un étalon secondaire de fréquence à résonateur saphir cryogénique, dans la gamme des fréquences microondes.\\ Le monocristal de saphir ($Al_2O_3$), excité sur des modes électromagnétiques d'ordre élevé, les modes de galerie, et utilisé au voisinage de la température de l'hélium liquide, représente le meilleur candidat pour réaliser un oscillateur présentant une instabilité relative de fréquence de l'ordre de $1\cdot 10^(-14)$.\\ Une dégénérescence du mode généralement observée aux températures cryogéniques rend difficile l'ajustement des couplages. Nous présentons ici un modèle simple expliquant correctement la séparation du mode en fréquence et les formes d'onde observées expérimentalement.\\ D'autre part, le problème des modes parasites est résolu par la mise au point d'une structure résonante en cavité ouverte.\\ Tous les éléments nécessaires à la construction de cet oscillateur sont analysés en détails.\\ Les résultats obtenus sont tout à fait exceptionnels. Sur le court terme, l'instabilité relative de fréquence est inférieure à $7.5\cdot 10^(-15)$. Dans le domaine du long terme, aucune dérive n'est clairement identifiée. La stabilité sur 1 jour est $

B. Cretin, Professeur, ENSMM, Besançon P-A. Rolland, Professeur, Université des Sciences et Technologies de Lille, IEMN D. Cros, Professeur, IRCOM, Limoges M-E. Tobar, Professor, Frequency Standards and Metrology Research Group, UWA, Australia M. Oxborrow, Principal Research Scientist, Centre for Basic, Thermal and Length Metrology, NPL, United Kingdom V. Giordano, DR2, Institut FEMTO-ST, département LPMO, Besançon G. Santarelli, IR, SYRTE, Observatoire de Paris S. Merlet, Ingénieur BNM, Paris M. Chaubet, Ingénieur, CNES, Toulouse; This thesis is devoted to the realization and the characterization of a cryogenic microwave secondary frequency standard for metrological applications.\\ This standard is based on the excitation of a high-order electromagnetic mode, of the ``whispering-gallery'' type, within a cylindrically shaped piece of monocrystalline sapphire ($Al_2O_3$) maintained at a temperature near to that of liquid helium.\\ Such a resonator currently represents the best solution to realizing frequency stabilities of the order of $1\cdot 10^(-14)$.\\ Mode splitting is generally observed at cryogenic temperatures, which makes the adjustment of the coupling difficult. We present a simple model that successfully explains the observed degeneracy and lineshapes for each mode. Moreover, we solve the problem of spurious modes by placing the resonator in an open cavity.\\ Every component needed for constructing a frequency-stable microwave oscillator based around the cryogenic resonator is analysed in detail.\\ The experimental results we obtain are exceptional: the oscillator realizes a short-term fractional frequency instability of less than $7.5\cdot 10^(-15)$. Over the longer term, any frequency drift is clearly identifiable; the instability at one-day intervals lies below $2\cdot 10^(-14)$. This last result represents the state of the art for long-term secondary frequency standards. \\ Several other, related pieces of work are also presented: the measurement of the dielectric properties of a langasite crystal, the characterization of ultra-stable oscillators, a sapphire-rutile composite resonator oscillator, a synthesis chain, and the observation of a bistability phenomenon due to the accidental coincidence of a whispering gallery mode with the paramagnetic resonance of $Fe^(3+)$ ions within the sapphire crystal.; Ce mémoire présente l'élaboration et la caractérisation d'un étalon secondaire de fréquence à résonateur saphir cryogénique, dans la gamme des fréquences microondes.\\ Le monocristal de saphir ($Al_2O_3$), excité sur des modes électromagnétiques d'ordre élevé, les modes de galerie, et utilisé au voisinage de la température de l'hélium liquide, représente le meilleur candidat pour réaliser un oscillateur présentant une instabilité relative de fréquence de l'ordre de $1\cdot 10^(-14)$.\\ Une dégénérescence du mode généralement observée aux températures cryogéniques rend difficile l'ajustement des couplages. Nous présentons ici un modèle simple expliquant correctement la séparation du mode en fréquence et les formes d'onde observées expérimentalement.\\ D'autre part, le problème des modes parasites est résolu par la mise au point d'une structure résonante en cavité ouverte.\\ Tous les éléments nécessaires à la construction de cet oscillateur sont analysés en détails.\\ Les résultats obtenus sont tout à fait exceptionnels. Sur le court terme, l'instabilité relative de fréquence est inférieure à $7.5\cdot 10^(-15)$. Dans le domaine du long terme, aucune dérive n'est clairement identifiée. La stabilité sur 1 jour est $

International audience; We report on the recent progress in the development of digital implementation of Ultrastable Optical Frequency Controls, namely in the frame of experiments based on silicon cryogenic cavity, spherical Fabry-Pérot cavity, compact Ultra- Low Expansion (ULE) cavity and fiber link active compensation. With enhanced capabilities offered by the undersampling technique, we demonstrate similar performances but with a net gain in reconfigurability, flexibililty and dissemination over their analog counterpart.