Cs vapor cell atomic clocks

Contact: R. Boudot (rodolphe.boudot@femto-st.fr)

A/Overview

Our group is involved in the study and development of Cs vapor cell atomic clocks based on coherent population trapping (CPT). This domain involves optics, atomic physics, low-noise electronics (dc to microwaves), MEMS technologies and time and frequency metrology.

Our activities are divided into two main sections:

  1. Miniature Cs cell atomic clocks: With the help of MEMS techniques, VCSEL lasers and integrated electronics, we develop miniature atomic clocks aiming to combine a low power consumption (150 mW), a small volume (15 cm3) and a fractional frequency stability better than 10-11 at 1 hour and 1 day integration (1 μs per day), in a large temperature range (-40 to +85°C). Such “pocket-size” atomic frequency references are dedicated to be an alternative to quartz-crystal oscillators in numerous applications including satellite-based navigation and positioning systems, telecommunication systems, defense systems. These activities are performed in strong collaboration with FEMTO-ST MOEMS Group [http://projects.femto-st.fr/MOEMS-Group/fr].
  2. High-performance compact Cs cell atomic clocks: We aim to explore the ultimate performances that can be achieved using the CPT technique for atomic clocks applications. The goal is to demonstrate a CPT-based Cs cell atomic clock, with similar size and power consumption than commercially-available Cs beam clocks, but with a short-term frequency stability 10-50 times better. Our laboratory-prototype clock, combining an optimized CPT pumping scheme named push-pull optical pumping (proposed by Happer’s group in Princeton, in 2004) and a pulsed Ramsey-based interrogation protocol, has recently demonstrated a short-term frequency stability at the level of 2 10-13τ-1/2 up to 104 s. 

In CPT physics, atoms are trapped through a quantum interference process into a non-interacting coherent superposition of two long-lived ground state hyperfine levels. Under ideal conditions (isolated three-level Λ-scheme, no ground-state decoherence), a so-called dark state, obtained by simultaneous action of two resonant optical fields exactly frequency-split by the atomic ground-state hyperfine frequency (Raman resonance) fully decoupled from the excited state, is obtained. In this dark state, the transparency of the atomic medium is increased and a narrow CPT resonance is observed in the bottom of a broadened absorption line.  The CPT resonance line-width is ultimately limited by the microwave coherence relaxation time and can be measured to be of a few tens to hundreds of Hz.

Figure 1: CPT interaction in Cs atom represented by a 3- level Λ-scheme interacting with a bi-chromatic optical field. Both optical lines are frequency-split by 9.192 GHz (ground-state splitting), the CPT Cs clock transition. When the frequency difference between both optical lines exactly equals 9.192 GHz, atoms are optically-pumped in a coherent superposition of both ground states. In this so-called dark state, the transparency of the atomic vapor is increased, as shown on the right inset. The CPT resonance, with narrow line-width, can be used for the development of an atomic clock. In a CPT clock, the microwave interrogation signal is directly optically carried, preventing the use of a resonant cavity.

B/ Miniature Atomic clocks

The study and development of CPT-based miniature atomic clocks has started in FEMTO-ST in 2005 (supports from CNES, Région de Franche-Comté and ANR).

From 2008 to 2012, FEMTO-ST has piloted a European project called MAC-TFC (EC funding), combining the expertise of 10 industrial and academic partners (www.mac-tfc.eu). This project has led to the demonstration of a first European miniature atomic clock prototype. Main scientific achievements of this project were the development of custom-designed 894 nm (Cs D1 line at 894.6 nm) VCSEL diode lasers (Ulm University), the demonstration of 15-mW and low phase noise 4.596 GHz ASIC synthesizers devoted to be used as local oscillator (EPFL-IMT), and the development of an original Cs vapor microcell technology (FEMTO-ST/SAES/Wroclaw University).

This stimulating and successful project led in France to the beginning of new projects (supports from DGA, LabeX FIRST-TF, ANR, BPI). Since 2014, a French industrial-academic platform has been implemented in order to develop an industrial and commercially-available miniature atomic clock.

Basic blocks of a miniature atomic clock (MAC) are shown below on figure 2:

Figure 2: Schematic of CPT-based miniature Cs vapor cell atomic clock

The heart of a MAC is a micro-fabricated cell that contains alkali vapor, generally diluted with a pressure of buffer gas in order to slow down alkali atoms. Slight collisions between alkali atoms and buffer gas allow to increase the time for the atoms to reach the cell walls. This allows the detection of narrow CPT resonances (a few kHz line-width in mm-scale cell dimensions). The cell is typically heated at 80-95°C. A static magnetic field, parallel to the laser beam propagation direction, is applied to raise the Zeeman degeneracy. A magnetic shielding is used to prevent perturbations from the environment. Atoms in the cell interact with a laser beam coming from a VCSEL diode laser whose injection current is directly modulated at 4.596 GHz by a local oscillator to produce two first-order optical sidebands frequency-split by 9.192 GHz for CPT interaction. The laser beam is shaped, routed and polarized circularly with a quarter-wave plate. The light transmitted through the cell is detected by a photodiode. The output signal of the photodiode is used for various servo loops including in particular the laser frequency stabilization and the local oscillator frequency stabilization.

B.1/ Microcell technology

We have developed in FEMTO-ST an original Cs vapor microcell technology. These cells can be fabricated in parallel at the wafer level. This cell consists of a DRIE-etched silicon substrate sandwiched between two anodically-bonded glass wafers. The cell contains two cavities. The first cavity contains a pill Cs dispenser. The second cavity is the cavity in which CPT interaction takes place. Both cavities are connected by filtration channels. The originality of this cell technology is that the Cs vapor is generated after complete sealing of the cell by local laser activation of the Cs pill dispenser.

Figure 3 shows a photograph of Cs microfabricated cells developed in FEMTO-ST. This cell technology is called T-cell.

Figure 3: Photographs of Cs vapor microfabricated cells. The Cs dispenser is visible in the square cavity. Courtesy from FEMTO-ST MOEMS Group.

Figure 4: Example of a CPT resonance detected in a Cs-Ne microfabricated cell.

In 2015, we have demonstrated in FEMTO-ST an original architecture of micro-fabricated alkali vapor cell, named R-cell, designed for miniature atomic clocks. This cell combines diffraction gratings with anisotropically etched single-crystalline silicon sidewalls to route a normally-incident beam in a cavity oriented along the substrate plane.

Figure 5: Photograph of the R-cell architecture. Courtesy from FEMTO-ST MOEMS Group.

In 2017, we have proposed and reported a method for filling alkali vapor cells with cesium from a dispensing paste, compatible with collective deposition processes. This filling method could reduce the cost and the complexity of miniature cells fabrication. Optical linear spectroscopy was performed over one year on such cells, showing a stable atomic density. One of these cells has been implemented in a lab-prototype CPT clock. A fractional frequency aging rate of about –4.4 10-12 per day has been measured, compliant with typical objectives of MACs.

In 2018, we have reported, in collaboration with our industrial partner Tronics Microsystems, on the characterization of Cs vapor microcells based on pill dispensers and fabricated in a MEMS foundry, according to a process compatible with mass-production. More than three quarters of cells from 6-inch wafers are successfully filled with Cs vapor. Various cells of a given wafer have been characterized using CPT spectroscopy, demonstrating similar buffer gas (Ne) pressure with a standard deviation of about 2.5% and CPT resonances with similar line-width and contrast properties. In addition, frequency drifts mainly attributed to cell inner atmosphere variations have been investigated onto several cells over 250-500 hour measurements. The corresponding contribution at 1 day averaging time to the clock fractional frequency stability is estimated to be about 10-11 or lower. The fractional frequency stability of a clock prototype using such an industrial Cs-Ne microcell was measured to be 2.5 10-11 τ-1/2 up to 200 s averaging time, and better than 2 10-11 at 105 s. These performances tend to demonstrate that this vapor cell technology, compatible with mass-production, is suitable for industrial miniature quantum clocks or sensors.

 B.3/ MEMS-based oscillators

In general, the local oscillator of a MAC is a voltage controlled oscillator (VCO) phase locked to a 10 MHz quartz crystal oscillator using a fractional phase locked loop (PLL).

In this domain, as a possible alternative, we have investigated the development and characterization of MEMS-based oscillators using bulk acoustic wave (BAW) resonators, including solid mounted resonators (SMR) or high-overtone bulk acoustic wave resonators (HBAR). Such resonators exhibit high Q-f factors, low residual phase noise, miniaturized dimensions and low power consumption.

In 2011, we have demonstrated, in collaboration with IEMN and CEA-LETI, the development and the use of a SMR-based oscillator for miniature atomic clocks applications.

In 2014-2016, we have reported the characterization of 2.3 GHz AlN-Sapphire high-overtone bulk acoustic resonators (HBARs), with a typical loaded Q-factor of 25 000, 15–20 dB insertion loss, and resonances separated by about 10 MHz. The temperature coefficient of frequency of these HBARs was measured to be about -25 ppm/K. A significant distortion of the HBAR resonance line-shape, attributed to non-linear effects, has been observed at high input microwave power. The power-induced fractional frequency variation of the HBAR resonance was measured. The residual phase noise of a HBAR was measured in the range of -110 to -130  dBrad2/Hz at 1Hz Fourier frequency, yielding an ultimate HBAR-limited oscillator Allan deviation of about 7 10-12  at 1 s integration time. A HBAR resonator was used for the development of a low phase noise 2.3 GHz oscillator, yielding an absolute phase noise of -60, -120, and -145 dBrad2/Hz for offset frequencies of 10 Hz, 1 kHz, and 10 kHz, respectively, in excellent agreement with the Leeson effect. Such a HBAR oscillator has been used as a local oscillator in a microcell CPT-based atomic clock.

Figure 6: Photograph of a AlN-Sapphire HBAR resonator (designed by CEA-LETI).

Figure 7: Phase noise performances of a 2.3 GHz HBAR oscillator (in red). Performances compared to those of a conventional MAC LO or to state-of-the-art ideally frequency-multiplied 100 MHz OCXO.

B.4/ VCSELs.

VCSEL laser sources combine a low threshold current, low power consumption and high-modulation bandwidth capabilities and are well-adapted to be used in miniature atomic clocks. In the frame of the MAC-TFC project, in collaboration with Ulm University and LTF-UNINE, we have reported the metrological characterization of custom-designed 894nm VCSELs. We have also investigated the characterization of commercially-available 894 nm VCSELs.

B.5/ Laboratory-prototype clocks

Figure 8 shows a microcell-based compact atomic clock physics package developed in the frame of the MAC-TFC project. Figure 9 shows this physics package embedded onto the pilot electronics card (developed by EPFL).

Figure 8: Picture of the MAC-TFC clock physics package.

Figure 9: Picture of the MAC-TFC clock. The physics package is connected to electronics to operate the clock. Electronics were developed by EPFL-IMT.

We have recently developed a novel MAC prototype for lab works and graduate students. The clock physics package and electronics of the clock has been developed in FEMTO-ST. This prototype is used during EFTS seminars (http://efts.eu/dokuwiki/doku.php?id=current:01_program ).

Figure 10: Miniature clock prototype. Courtesy of J. Rutkowski and V. Maurice.

B.6/ Pulsed CPT spectroscopy in microfabricated cells.

Pulsed coherent population trapping (CPT) spectroscopy has been applied in buffer-gas filled Cs–Ne vapor micro-fabricated cells. Figure 11 depicts an example of Ramsey-CPT fringes detected in a Cs-Ne microcell. The properties of the Ramsey-CPT clock transition central fringe (line-width, signal amplitude, and contrast) were studied versus several experimental parameters, including the Ramsey sequence and the input laser intensity, and were compared to those obtained in the conventional continuous (CW) interrogation mode. In the pulsed case and for short Ramsey-free evolution times TR, the central fringe line-width is found to exhibit a small but visible power broadening and is measured to be narrower than the value of 1∕(2TR) that is reached for long TR. The microwave hyperfine coherence lifetime T2 in the Cs–Ne microcells is measured to be in the 50–500 μs range. Such studies could be interesting for the development of future chip-scale atomic clocks, operating in the pulsed regime.

Figure: Typical CPT resonance detected in the CW regime (black) and in the pulsed Ramsey-CPT regime (red), in a Cs-Ne MEMS cell.

C/ High-performance CPT-based Cs cell atomic clock

In 2011, in collaboration with LNE-SYRTE (S. Guérandel and E. de Clercq), we have started the development of a high-performance CPT-based Cs cell atomic clock. Funded in the beginning by LNE, these activities have been pursued from 2013 to 2016 in the frame of a European project called MClocks, funded by EURAMET, and piloted by INRIM (coordinator: S. Micalizio). This project has been supported since 2017 by LabeX FIRST-TF.

C.1/ A high-performance Cs cell atomic clock 

We have developed a high-performance Cs cell microwave CPT clock. This clock combines an optimized CPT pumping scheme, named  push-pull optical pumping (PPOP), pioneerly proposed by Y. Y. Jau et al. in 2004 (Happer's group, Princeton, Phys. Rev. Lett. 93, 16, 2004) and  a pulsed Ramsey-based interrogation protocol, yielding the detection of high-contrast Ramsey-CPT fringes. Our laboratory-prototype clock, using now a sophisticated Ramsey-based interrogation protocol named Auto-Balanced Ramsey (see C. Sanner et al., Phys. Rev. Lett. 2018) allowing to reduce drastically light-shift effects, has recently demonstrated a clock fractional frequency stability at the level of 2 10-13 τ-1/2 up to 104 s, reaching the level of 2.5 10-15 at 104 s.

Figure 12 shows the architecture of the CPT clock. It combines a DFB laser source tuned on the Cs D1 line, a fibered electro-optic modulator driven by a 4.596 GHz low noise microwave signal for generation of the CPT sidebands, an AOM for laser power stabilization and production of the Ramsey sequence and a Michelson delay-line system for the generation of the PPOP scheme. The light is sent into a 5-cm long and 2-cm diameter buffer-gas filled Cs cell. The light at the output of the cell is detected by a photodiode. The output signal is exploited by a FPGA-based digital electronics board (developed by C. Calosso, INRIM) that generates the Ramsey sequence pattern and manages different servo loops. The local oscillator is an ultra-low phase noise 100 MHz OCXO frequency-multiplied to 4.596 GHz. The output signal of the 100 MHZ OCXO is at the end compared to a hydrogen maser for stability measurements.

Figure 12: Schematic of the Ramsey-CPT clock

ramsey fringe

Figure 13: Example of Ramsey-CPT fringes. The line-width of the central fringe equals 1/(2T), with T the free-evolution time in the Ramsey-CPT sequence.

 C.2/ Low phase noise microwave frequency synthesizers

In collaboration with INRIM (C. Calosso/S. Micalizio), we have developed ultra-low phase noise microwave frequency synthesizers at 4.596 GHz or 9.192 GHz, dedicated to be used as local oscillators in high performance Cs (or Rb) vapor cell atomic clocks. Such microwave sources allow to reduce greatly the Dick effect contribution (3 10-14 at 1 s) to the short-term frequency stability of the atomic frequency standards. This level is comparable with the photon shot noise limit.

Figure 14: Photograph of a microwave frequency synthesizer developed by FEMTO-ST / INRIM [B. Francois, C. Calosso, R. Boudot].

Figure 15: Absolute phase noise performances of the microwave frequency synthesizer shown above. The pilot is a low noise 100 MHz OCXO (perfs in red at 100 MHz). The green data shows the absolute phase noise at 4.596 GHz. The green line is the phase noise at 4.596 GHz of the ideally frequency-multiplied 100 MHz OCXO.

 C.3/ Laser frequency stabilization with dual-frequency sub-Doppler spectroscopy

Saturated absorption technique is an elegant method widely-used in atomic and molecular physics, for high-resolution spectroscopy, laser frequency standards and metrology purposes. We have recently discovered that a saturated absorption scheme used with a dual-frequency laser can lead to a significant sign-reversal of the usual Doppler-free dip, yielding a deep enhanced-absorption spike. We have reported detailed experimental investigations of this phenomenon, together with a full in-depth theoretical description, thanks to the precious help of D. Brazhnikov (ILP, Novossibirsk) and E. de Clercq (LNE-SYRTE). It is shown that several physical effects can contribute or oppose to the formation of the high-contrast central spike in the absorption profile. These effects are the creation or destruction of dark states in the ground state and velocity selective optical pumping effects. Beyond their theoretical interest, results obtained in this manuscript are of great interest for laser spectroscopy, laser frequency stabilization purpose, with applications in laser cooling, matter-wave sensors, atomic clocks, quantum optics or optical frequency references.

Figure 16: Dual-frequency sub-Doppler spectroscopy setup.

The figure below reports high-contrast sub-Doppler absorption spikes in a hot atomic vapor cell exposed to a dual-frequency laser field.

Figure 17: High-contrast sub-Doppler absorption spikes in a hot atomic vapor cell exposed to a dual-frequency laser field.

This setup has allowed a significant improvement (one order of magnitude) of the laser frequency stabilization, compared to a conventional saturated absorption scheme setup.

C.4/ Reduction of light-shift effects with Auto-Balanced Ramsey (ABR) interrogation protocol

Vapor-cell atomic clocks are widely appreciated for their excellent short-term fractional frequency stability and their compactness. However, they are known to suffer on medium and long time scales from significant frequency instabilities, generally attributed to light-induced frequency-shift effects.

In order to tackle this limitation, we have investigated the application of the recently proposed Auto-Balanced Ramsey (ABR) interrogation protocol (see C. Sanner et al., Phys. Rev. Lett. 120, 053602 (2018)) onto our CPT-based pulsed hot-vapor Cs vapor-cell clock.

We have demonstrated that the ABR protocol, developed initially to probe the one-photon resonance of quantum optical clocks, can be successfully applied to a two-photon CPT resonance. The applied method, based on the alternation of two successive Ramsey-CPT sequences with unequal free-evolution times and the subsequent management of two interconnected phase and frequency servo loops, is found to allow a relevant reduction of the clock-frequency sensitivity to light-shift effects.

This ABR-CPT protocol, improved further later with symmetrization (SABR-CPT), has allowed a drastic reduction of the clock frequency sensitivity to laser power variations, by a factor 80 in comparison with the standard Ramsey-CPT regime. This technique has reduced the contribution of the laser power-shift effect on the clock frequency stability to the level of a few 10-16 at 104 s.

Figure 18: Symmetric ABR-CPT sequence. 

Figure 19 reports the Allan deviation of the clock in different conditions. The curve (a) shows the best performances ever obtained in the Ramsey-CPT regime. The curve (b) shows first results obtained in the ABR-CPT regime. The curve (c), extracted from a 5-days measurement, is obtained in the SABR-CPT regime, without compensation of the laser AM noise (explaining the degradation of the short-term stability). The curve (d), extracted from a 30 000 s data set with quiet experimental conditions, is obtained in the SABR-CPT regime, with additional compensation of the laser AM noise. In the last case, the clock demonstrates a clock fractional frequency stability of 2 10-13 τ-1/2, until almost 104 s, reaching the level of 2.5 10-15 at 104 s.

Figure 19: Allan deviation of the clock. (a) Ramsey-CPT, (b) First results obtained in the ABR-CPT regime, (c): SABR-CPT: extracted from a 5-days measurement, without compensation of the laser AM noise, (d): SABR-CPT, extracted from a 30 000 s data set with quiet experimental conditions, with additional compensation of the laser AM noise for improvement of the short-term stability. In the last case, the clock demonstrates a clock fractional frequency stability of 2 10-13 τ-1/2, until almost 104 s, reaching the level of 2.5 10-15 at 104 s.

 C.5/ Annex studies: Wall coated Cs vapor cells.

We have reported the realization and characterization using coherent population trapping (CPT) spectroscopy of octa-decyl-trichlorosilane (OTS)-coated centimeter-scale Cs vapor cells. The dual-structure of the resonance line-shape, with presence of a narrow structure line at the top of a Doppler-broadened structure, was clearly observed. The line-width of the narrow resonance was compared to the line-width of an evacuated Cs cell and of a buffer gas Cs cell of similar size. The Cs-OTS adsorption energy was measured to be (0.42+/-0.03) eV, with a clock frequency shift rate of 2.710-9/K in fractional unit. A hyperfine population lifetime, T1, and a microwave coherence lifetime, T2, of 1.6 and 0.5 ms were reported, corresponding to about 37 and 12 useful bounces, respectively.

Figure 20: Photograph an OTS-coated cell.

Figure 21: CPT resonance in a Cs-OTS cell (compared to a pure Cs cell of similar dimensions).

 Publications

    1. D. Miletic, P. Dziuban, R. Boudot, M. Hasegawa, R. K. Chutani, G. Mileti, V. Giordano and C. Gorecki, Electron. Lett. 46, 15, 1069-1071 (2010).
    2. R. Boudot, P. Dziuban, M. Hasegawa, R. Chutani, S. Galliou, V. Giordano and C. Gorecki, Journ. Appl. Phys. 109, 014912 (2011).
    3. M. Hasegawa, R. K. Chutani, C. Gorecki, R. Boudot, P. Dziuban, V. Giordano, S. Clatot, J. Dziuban and L. Mauri, Sensors Actuators A - Phys. 167, 594-601 (2011).
    4. R. Boudot, D. Miletic, P. Dziuban, P. Knapkiewicz, J. Dziuban, C. Affolderbach, G. Mileti, V. Giordano and C. Gorecki, Optics Express 19, 4, 3106-3114 (2011).
    5. R. Boudot, M. D. Li, V. Giordano, N. Rolland, P. A. Rolland, P. Vincent, Rev. Sci. Instr. 82, 034706 (2011).
    6. O. Kozlova, R. Boudot, S. Guerandel and E. De Clercq, IEEE Trans. Instrum. Meas. 60, 7, 2262-2266 (2011).
    7. D. Miletic, C. Affolderbach, M. Hasegawa, R. Boudot, C. Gorecki and G. Mileti, Appl. Phys. B: Lasers Opt. 109, 89–97 (2012).
    8. X. Liu and R. Boudot, IEEE Trans. Instr. Meas. 61, 10, 2852-2855 (2012).
    9. R. Boudot, X. Liu, P. Abbé, R. K. Chutani, N. Passilly, S. Galliou, C. Gorecki and V. Giordano, IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 59, 11, 2584-2587 (2012).
    10. R. Boudot and E. Rubiola, IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 59, 12, 2613-2624 (2012).
    11. X. Liu, J. M. Merolla, S. Guérandel, C. Gorecki, E. De Clercq and R. Boudot, Phys. Rev. A 87, 013416 (2013).
    12. F. Gruet, E. Kroemer, L. Bimboes, D. Miletic, C. Affolderbach, A. Al-Samaneh, D. Wahl, R. Boudot, G. Mileti and R. Michalzik, Optics Express 21, 5, 5781-5792 (2013).
    13. X. Liu, J.M. Merolla, S. Guérandel, E. De Clercq and R. Boudot, Optics Express 21, 10, 12451-12459 (2013).
    14. M. Hasegawa, R. K. Chutani, R. Boudot, L. Mauri, C. Gorecki, X. Liu and N. Passilly, J. Micromech. Microeng. 23, 055022 (2013).
    15. R. Salut, C. Gesset, G. Martin, B. Assouar, P. Bergonzo, R. Boudot, O. Elmazria and S. Ballandras, Elsevier, Microelectron. Eng. 112, 133-138 (2013).
    16. J. M. Friedt, R. Boudot, G. Martin and S. Ballandras, Rev. Sci. Instr. 85, 094704 (2014).
    17. B. François, J-M. Danet, C. E. Calosso and R. Boudot, Rev. Sci. Instr. 85, 094709 (2014).
    18. M. Abdel Hafiz, V. Maurice, R. Chutani, N. Passilly, C. Gorecki, S. Guérandel, E. De Clercq and R. Boudot, Journ. Appl. Phys. 117, 184901 (2015).
    19. E. Kroemer, M. Abdel Hafiz, V. Maurice, B. Fouilland, C. Gorecki and R. Boudot, Opt. Express 23, 14, 18373-18380 (2015).
    20. R. K. Chutani, V. Maurice, N. Passilly, C. Gorecki, R. Boudot, M. Abdel Hafiz, P. Abbé, S. Galliou, J. Y. Rauch and E. De Clercq, Nature Sci. Rep. 5, 14001 (2015).
    21. B. Francois, C. E. Calosso, M. Abdel Hafiz, S. Micalizio and R. Boudot, Rev. Sci. Instr. 86, 094707 (2015).
    22. M. Abdel Hafiz and R. Boudot, Journ. Appl. Phys. 118, 124903 (2015).
    23. T. Daugey, J. M. Friedt, G. Martin and R. Boudot, Rev. Sci. Instr. 86, 114703 (2015).
    24. M. Abdel Hafiz, G. Coget, E. De Clercq and R. Boudot, Opt. Lett. 41, 13, 2982-2985 (2016).
    25. M. Abdel Hafiz, X. Liu, S. Guérandel, E. De Clercq and R. Boudot, Journal of Physics: Conference Series, 723 (1), 012013 (2016).
    26. E. Kroemer, J. Rutkowski, V. Maurice, R. Vicarini, M. Abdel Hafiz, C. Gorecki and R. Boudot, Applied Optics 55, 31, 8839-8847 (2016).
    27. R. Boudot, G. Martin, J. M. Friedt and E. Rubiola, Journal of Applied Physics 120, 224903 (2016).
    28. P. Yun, F. Tricot, C. E. Calosso, S. Micalizio, B. Francois, R. Boudot, S. Guérandel and E. de Clercq, Phys. Rev. Applied7, 014018 (2017).
    29. M. Abdel Hafiz, G. Coget, P. Yun, S. Guérandel, E. De Clercq and R. Boudot, Journal of Applied Physics 121, 104903 (2017).
    30. V. Maurice, J. Rutkowski, E. Kroemer, S. Bargiel, N. Passilly, R. Boudot, C. Gorecki, L. Mauri and M. Moraja, Appl. Phys. Lett. 110, 164103 (2017).
    31. M. Abdel Hafiz, D. Brazhnikov, G. Coget, A. Taichenachev, V. I. Yudin, E. De Clercq and R. Boudot, New Journal of Physics 19, 073028 (2017).
    32. R. Boudot, V. Maurice, C. Gorecki and E. de Clercq, Journal of Optical Society America B 35, 5, 1004-1010 (2018).
    33. D. Brazhnikov, G. Coget, M. Abdel Hafiz, V. Maurice, C. Gorecki and R .Boudot, IEEE Transactions Ultrasonics Ferroelectrics Frequency Control 65, 6, 962-972 (2018).
    34. M. Abdel Hafiz, G. Coget, M. Petersen, C. Rocher, S. Guérandel, T. Zanon-Willette, E. de Clercq and R. Boudot, Physical Review Applied 9, 064002 (2018).
    35. M. Abdel Hafiz, G. Coget, M. Petersen, C. Calosso, S. Guérandel, E. de Clercq and R. Boudot, Applied Physics Letters 112, 244102 (2018).
    36. R. Vicarini, V. Maurice, M. Abdel Hafz, J. Rutkowski, C. Gorecki, N. Passilly, L. Ribetto, V. Gaff, V. Volant, S. Galliou and R. Boudot, Sensors Actuators, Phys. A 280, 99-106 (2018).
    37. V. I. Yudin, A. Taichenachev, M. Yu Basalaev, T. Zanon-Willette, T. E. Mehlstauber, R. Boudot, J. W. Pollock, M. Shuker, E. A. Donley and J. Kitching, New Journal of Physics 20, 123016 (2018).
    38. M. Shuker, J. W. Pollock, R. Boudot, V. I. Yudin, A. Taichenachev, J. Kitching and E. A. Donley, Physical Review Letters 122, 113601 (2019).
    39. M. Shuker, J. W. Pollock, R. Boudot, V. I. Yudin, A. Taichenachev, J. Kitching and E. A. Donley, Applied Physics Letters 114, 141106 (2019).
    40. D. Brazhnikov, M. Petersen, G. Coget, V. Maurice, N. Passilly, C. Gorecki and R. Boudot, Phys. Rev. A 99, 062508 (2019).