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Abstract
We introduce a simple and compact diode-pumped Pr:YLF-Cr:LiCAF laser, operating at 813.42 nm and providing a 130-mW, single-frequency output tunable over a 3-GHz range. The laser has a short-term intrinsic linewidth estimated to be 700 Hz (β-separation method), while exhibiting a free-running wavelength stability of below 1 pm in one hour. Using a feed-forward technique we demonstrate the integration of the laser output into a fully stabilized, 1-GHz Ti:sapphire laser frequency comb, resulting in a heterodyne beat note between the laser and the comb with a bandwidth of 65 kHz. Combining feed-forward control with a low-bandwidth servo feedback loop permits stable long-term locking with an rms beat note variation of 15 kHz over 2 minutes. This performance makes the laser a potential candidate for the lattice laser in a 87Sr optical lattice clock.
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1. Introduction
Atomic clocks operating at optical frequencies are an emerging technology which promises superior accuracy and precision to the existing primary standard based on transitions between the two hyperfine ground states of 133Cs atoms. Optical lattice clocks based on neutral 87Sr atoms have been shown to provide an Allan instability at least 100 times better than current frequency references such as the Cs standard [1,2], with an accuracy of 6.4 ${\times} $ 10−18 and a measurement time much faster than comparable single-ion optical clocks [1]. The neutral 87Sr atom clock scheme requires accurately tuned narrow-linewidth laser sources to cool, trap, re-pump and inspect the confined specimen. While the different stages of atom trapping pose different wavelength and stability requirements, the required transitions for 87Sr atoms are all located in the visible range from 461–813 nm, making them an ideal candidate for quantum sensors [3,4] and directly accessible to external-cavity diode lasers [5–14] and diode-pumped solid-state (DPSS) lasers [15,16]. The higher powers available directly from DPSS lasers make them of particular interest for use as 87Sr lattice lasers, with power in the several tens to several hundreds of mW being needed at the so-called “magic wavelength” of 813.42 nm, where large shifts in the clock levels caused by the strong electric field of the trapping lattice light are cancelled to first order. Suitable DPSS lasers should operate at a single, repeatable frequency, as well as having a size and power compatible with their integration into a typical trapping apparatus. Furthermore, a suitable laser should, in addition to excellent passive stability, be steerable towards a precise target frequency, within a given tuning range. In this work we report a new single-frequency Pr:YLF-Cr:LiCAF laser, operating at 813.42 nm with over 100 mW of output power and diode-pumped by a single InGaN blue laser diode. We present key performance data for this laser including stability and linewidth measurements, before demonstrating its integration into the spectrum of a 1-GHz Ti:sapphire frequency comb by using a high-bandwidth feed-forward phase lock.
Optical frequency combs provide a convenient route to prepare the frequencies of the multiple lasers needed in a lattice clock scheme, as well as enabling the stability of a single optical reference to be transferred to other frequencies in the optical and microwave domains [17–19]. A comb stabilized to an atomic standard can provide an absolute frequency reference for a narrow-line cw laser, which is routinely achieved by heterodyne beating between the cw laser and the comb modes in an open-loop configuration [20–22], in which precision and repeatability are limited by the inherently higher frequency noise in the cw laser. A typical approach to transfer the temporal coherence of the comb to the cw laser is to derive an error signal from a phase-frequency detector supplied by a stable reference frequency and the beat note between the cw and comb lasers, and to use this in a servo loop to control (via feedback) the cavity length or current of the cw laser [23–27]. Effective suppression of laser frequency noise using feedback to the cw laser therefore requires a fast, wide-bandwidth servo loop or a high-gain slow servo capture. The former poses a challenging task, involving careful design compromises and tuning of the servo loop, while the latter can lead to increased frequency jitter. Feed-forward approaches, of the kind we describe later in Section 3, typically offer higher bandwidths than servo feedback loops, and so represent an attractive option to achieve tight locking between a cw laser and a frequency comb.
An early example of acousto-optic feed-forward locking was in frequency comb synthesis [28], where the carrier-envelope offset frequency of a free-running mode-locked laser was subtracted through an acousto-optic frequency shifter (AOFS), bringing the comb offset to zero. This approach has successfully achieved attosecond level timing jitter without any servo lock feedback to the laser. Since then, owing to its simplicity, excellent noise reduction as well as its real-time frequency correcting ability, zero-offset combs using the feed-forward configuration have been demonstrated across different comb architectures [29–35]. The application of the feed-forward technique has also emerged in different fields of spectroscopy, such as dual-comb spectroscopy and cavity ring-down spectroscopy [36,37]. Another robust utilization is to phase-lock a cw laser to an optical frequency comb and vice versa, which was reported in 2012 by Gatti et al. [38]. With a fast response time of the order of several hundred nanoseconds, the feed-forward method has demonstrated effective transfer of the comb coherence properties to external cavity diode lasers (EDCL), distributed feedback diode (DFB) lasers and diode-pumped solid-state (DPSS) lasers [39–43]. With reported linewidth narrowing of between several hundred kHz and MHz levels, the feed-forward technique has been shown to be capable of producing stable cw laser beat notes comparable with the fundamental frequency comb mode linewidth. These previously reported examples of feed-forward phase-locking have been mostly in the telecom band, however extending this robust phase-locking technique into the visible region is beneficial not only for quantum clock applications but also for providing comb-referenced monochromatic light for use in astronomical spectrograph calibration [44].
In the remainder of this paper, we present a compact, two-stage cw laser based on Cr:LiCAF, which is capable of operating at the magic wavelength of 87Sr optical lattices (813.42 nm / 368.56 THz) [45,46]. We demonstrate that a feed-forward configuration can be implemented between the cw laser and an optical frequency comb, reducing the linewidth of their heterodyne beat note to 65 kHz. Combining slow servo feedback control with fast feed-forward correction enables long term stabilization to be achieved.
2. Diode-pumped, single-frequency Pr:YLF-Cr:LiCAF laser
The two main platforms emerging to accommodate the increasing demand for narrow-linewidth lasers for applications in atom cooling, metrology and sensing are DPSS lasers and external cavity diode lasers. In an earlier study [47] we compared the spectral purity of several commercial DPSS lasers and ECDLs and found that, due to the stronger suppression of side bands typically present in DPSS sources, the total output power within the specified linewidth of a DPSS laser can be considerably higher than in an ECDL, which can be explained by the greater contribution of spontaneous emission in an ECDL [48]. This observation motivates the development of new DPSS narrow-linewidth lasers, even at wavelengths where ECDL sources are already available.
When selecting a gain material for use in a DPSS single-frequency laser, colquiriite materials, such as Cr:LiSAF, Cr:LiCAF and Cr:LiSGaF, show good potential for efficient, tunable cw operation as a result of their relatively low saturation intensities when compared to conventional Ti:sapphire laser sources. Consequently, colquiriite lasers do not require high levels of pump power, which significantly reduces engineering complexities and hence the overall size and footprint of the laser head. Cr:LiCAF and Cr:LiSAF can both be pumped using a red light source, achieving a smaller quantum defect and lower thermal overhead than in Ti:sapphire lasers. Examples of previous work are summarized in [49] and include pumping by single-mode diodes [50], single-emitter multi-mode diodes [51] and tapered diodes [52]. Due to their broad gain bandwidth, Cr:colquiriite materials have been extensively studied for femtosecond pulse generation [53–55], however to our knowledge the results we present here are the first example of a Cr:LiCAF laser optimized for operation at the strontium magic wavelength of 813.42 nm. A clear advantage of choosing Cr:LiCAF over Cr:LiSAF is the mitigation of excited-state absorption (ESA) and upconversion related lifetime reduction at higher pump powers, which suggests the potential for good scalability [56].
Illustrated in Fig. 1, the laser employed a two-stage pumping arrangement in which a 6 W diode operating at 444 nm was used to pump a Pr:YLF crystal in a short cavity, resulting in over 2 W of 640 nm output. The excellent beam characteristics of this source (M2${\approx} $1.5 on both axes) enabled efficient beam delivery and pumping of a close-coupled Cr:LiCAF laser. The Cr:LiCAF crystal was 3% doped with dimensions of 3${\times} $1.5${\times} $6 mm3. Frequency selection was achieved using the combination of a commercially available single-wavelength reflective volume Bragg grating (OptiGrate Corp., Florida) and a solid intracavity etalon (2 mm, 25% reflectivity). A 2% output coupler was used to achieve over 130 mW of single-frequency output power, with a slope efficiency (laser output versus absorbed power) measured to be 29%. For peak single-frequency performance, 1.15 W of the 640 nm pump was absorbed. This pump power was generated using 4 W of incident 444-nm pump light, hence the overall optical efficiency of the system was 3.25%. No roll-over effects were experienced, which is mostly due to the low doping level of the Cr:LiCAF crystal, which leads to an absorption estimated to be 67%. The entire laser platform was one liter in volume on a 220${\times} $80 mm2 footprint.
Fig. 1. Single-frequency Pr:YLF-Cr:LiCAF laser, pumped by one 444-nm laser diode. A piezo-electric actuator (PZT) on the end mirror allows fine tuning of the output wavelength.
The laser frequency could be coarsely tuned using an intracavity oven over 50 GHz. Fine-tuning and frequency stabilization was achieved using a low-capacitance piezoelectric transducer (PZT) attached to the end mirror of the Cr:LiCAF laser cavity. The laser was tuned to the strontium magic wavelength and the free-running wavelength stability was measured on a High Finesse WS-8 wavemeter, presented in Fig. 2(a), showing a variation of <1 pm in over one hour.
Fig. 2. (a) Free-running wavelength stability measured on a High Finesse WS-8 wavemeter, showing a change of 900 fm in one hour. (b) Linewidth estimates using the $\beta $-separation method at various sampling speeds, recorded using a High Finesse LWA-1 k linewidth analyzer and indicating an instantaneous (100 kHz sampling rate) linewidth of 700 Hz.
The linewidth of the free-running system was estimated using the beta-separation method [57,58]. The measurements were done using a High Finesse linewidth analyzer (LWA-1k). This analyzer uses a high-speed digitizer with a noise frequency range of up to 10 MHz. The device samples the noise components for 100 ms; it can then estimate the linewidth of the laser at various sampling speeds by ignoring noise terms that are slower than the selected sampling speed. As such, the intrinsic linewidth of the laser was estimated to be 700 Hz, which is within the resolution of the device. The measurement was done at a 10-µs sampling time, and hence it considered frequency noise components >100 kHz. This was a useful indicator, as frequency noise components lower than this cut-off frequency can generally be compensated for in a feed-forward arrangement using a high-speed frequency shifter. Using the two-stage cavity structure and a relatively low saturation gain crystal, such as Cr:LiCAF, provides an efficient way of achieving the optical requirements of a strontium lattice laser. In fact, with added improvements in the frequency selection process and better utilization of the available 640-nm pump, a power level in the range of 1 W could be achieved using a single 444-nm diode and the 640-nm pump cavity. This power level would be sufficient for lattice applications, whilst optical amplification can also be considered, as demonstrated in previous work [5,8].
3. Feed-forward correction using an acousto-optic modulator
3.1 Concept
Feed-forward correction works by sampling a heterodyne beat note between a free-running laser and a stable optical frequency, which in our implementation is one comb tooth from a Ti:sapphire frequency comb. A replica output from the free-running laser can then be frequency shifted by an acousto-optic modulator (AOM) driven by a carrier derived from this beat note in such a way as to demodulate the frequency instability and maintain a phase lock with the reference frequency. Here, we present the details of our particular scheme, illustrated schematically in Fig. 3.
Fig. 3. Feed-forward correction scheme used to phase lock the cw laser to a single comb mode. See text for full details.
The free-running laser (frequency ${f_{cw}}$) is heterodyned with a lower-frequency comb mode (frequency ${f_{comb}}$) to yield a beat note with a frequency ${f_1}$. We manually adjust ${f_{cw}}$ to produce a beat note of approximately 40 MHz which is filtered and amplified before being summed with the output of a 40-MHz oscillator (${f_{osc}}$) in a double-balanced mixer to give an AOM drive frequency of ${f_1} + {f_{osc}} \approx $ 80 MHz. In this arrangement, a positive excursion in ${f_{cw}}$ also causes ${f_1}$ to increase, and the AOM drive frequency rises. A replica beam from the free-running laser diffracted by the AOM into the +1 Bragg order has this frequency excursion written onto it again, however light diffracted into the -1 order has this excursion removed, leaving the single-frequency laser locked to the comb mode with an offset of ${f_{osc}} = $ 40 MHz. This offset is not fundamentally necessary and is only incorporated to enable the feed-forward correction to be verified experimentally by observing a second heterodyne beat note at non-zero frequency.
3.2 Experiment
The optical frequency reference for the feed-forward correction was a 35-fs, Ti:sapphire laser (Novanta) which we configured as a fully-stabilized frequency comb by locking its repetition rate (${f_{rep}} = \; $999.931 MHz) and carrier-envelope-offset frequency (${f_{CEO}} = \; $30 MHz) to a Rb-referenced synthesizer. Around 20% of the laser power was used for the f-to-2f interferometer (Fig. 4(a), f-to-2f), while the rest of the power (∼1.5 W) was equally divided between two beat detection units (Fig. 4(a), BDU1 and BDU2). Both modules were configured in a similar manner, where the polarization-orthogonal cw and comb beams were each multiplexed in a polarizing beam splitter (PBS), with one difference in that the second cw beam passed through a traveling-wave AOM (bandwidth 80 MHz ${\pm} $ 7.5 MHz) before being combined with the comb beam in BDU2. Each BDU comprised a 1200 lines mm-1 diffraction grating, after which a narrow spectral portion around 813.4 nm was selected by a pinhole, projected into one polarization by a linear polarizer and focused onto an avalanche photodiode (APD).
Fig. 4. (a) Light from the 813.42 nm Cr:LiCAF laser is interfered with the output of a Ti:sapphire frequency comb in BDU1 to provide a beat note of frequency ${f_1}$ which is then conditioned to drive the AOM. The phase-stabilized $m ={-} 1$ Bragg order output of the AOM is interfered with the comb in BDU2 to evaluate the quality of the feed-forward correction by producing a second beat note of frequency ${f_2}$. The Ti:sapphire comb is locked by deriving its mode spacing (${f_{rep}})$ and carrier-envelope offset frequency (${f_{CEO}})$ by direct photodiode detection and f-to-2f interferometry respectively. PCF, photonic crystal fiber; P, polarizer. (b) Signal conditioning used to implement slow servo feedback control of the Cr:LiCAF laser frequency. COM, comparator; PFD, phase-frequency detector. (c) Feed-forward signal conditioning path.
The beat signal detected at BDU1, frequency ${f_1}$, was separated into signal paths, illustrated in Figs. 4(b) and 4(c). One path (Fig. 4(b)) was configured for slow servo feedback stabilization of the beat note to ${f_1} \approx $ 40 MHz by down-mixing it with a 30-MHz signal to 10 MHz and referencing the resulting frequency to a 10-MHz synthesizer by using a digital phase-frequency detector (PFD) [59]. The PFD output was conditioned by a proportional-integral (PI) servo-controller and then amplified before being used to actuate the end-mirror PZT in the Cr:LiCAF laser. A second signal path (Fig. 4(c)) implemented the feed-forward scheme already described in Section 3.1. The beat note from BDU1 was up-mixed with a 40-MHz oscillator (frequency, ${f_{osc}}$) then bandpass filtered to provide a frequency within the acceptance bandwidth of the AOM. This signal was sent to the AOM after suitable amplification in a radio-frequency power amplifier.
3.3 Results
In Fig. 5 we present power-spectrum and phase-noise characterizations of the radio-frequency (RF) beat in different free-running and phase-locked configurations. The power spectrum of the free-running beat (Fig. 5(a)) showed a -3-dB linewidth of 365 kHz, with excursions of several MHz over a few seconds. For longer term performance, a servo feedback loop was required to stabilize the first beat within an appropriate frequency range for AOM modulation. Due to the frequency jitter of the Cr:LiCAF laser, a high servo gain was needed, leading to a broadened beat-note bandwidth of 4.6 MHz, as shown in the power spectrum of Fig. 5(b). Implementing feed-forward control while the Cr:LiCAF laser was also servo stabilized achieved a considerable linewidth reduction, with a measured -3-dB value of 165 kHz (Fig. 5(c)). Finally, we implemented feed-forward control without servo feedback stabilization and achieved a -3-dB beat-note linewidth of 65 kHz, shown in Fig. 5(d).
Fig. 5. Power spectra (resolution bandwidth1 kHz; sweep time 15 ms) of the beat-note between the Ti:sapphire frequency comb and the cw Cr:LiCAF laser when (a) free-running, (b) PZT servo-feedback-stabilized, (c) PZT servo-feedback-stabilized with AOM feed-forward correction and (d) with only AOM feed-forward correction. (e) Phase-noise spectra for the signals represented in (b)–(d), recorded over 16 ms with a sampling rate of 1 GS/s.
In Fig. 5(e) we present phase-noise measurements which correspond to the power spectra in Figs. 5(b)–5(d). With only servo-feedback stabilization, the phase-noise properties of the beat are poor, reflecting the limited control of the cw laser frequency. Adding feed-forward control achieves a 40- to 50-dB reduction in phase noise at all frequencies below ${\approx} $2 MHz. The rise time of the AOM used in the feed-forward scheme (Gooch and Housego M080-1F-GH2) is 150 ns, corresponding to a bandwidth of several MHz, however the phase noise increases considerably above 1 MHz, suggesting that the modulation bandwidth is perhaps limited further by other components, for example the RF power amplifier used to supply the AOM.
Long-term stabilization was possible by combining servo-feedback with feed-forward control. In Fig. 6 we present the average beat frequencies recorded over a 140-second observation time using a frequency counter with a gate time of 500 ms. With no control, the direct beat between the Ti:sapphire comb and the Cr:LiCAF laser (Fig. 4, frequency ${f_1})$ varied over 20 MHz, with an rms fluctuation of 5.5 MHz. Adding servo-feedback stabilization considerably improved the frequency stability, constraining the average value of ${f_1}$ to 40 MHz ${\pm} $ 88 kHz. The further addition of feed-forward control produced a nearly six-fold improvement, with the beat note after the AOM, ${f_2}$, maintained at 40 MHz ${\pm} $ 15 kHz. Long term operation was not possible using only feed-forward control.
Fig. 6. Average beat frequencies between the Ti:sapphire frequency comb and the output of the Cr:LiCAF laser before (${f_1}$) and after (${f_2}$) feed-forward correction. Frequencies were measured by a frequency counter sampling at 1 Hz and with a gate time of 500 ms.
4. Conclusions
Feed-forward control provides a means of achieving high-bandwidth phase stabilization between independent coherent sources. In this work we have introduced a promising new Pr:YLF-Cr:LiCAF solid-state laser with potential applications in quantum technology, and have demonstrated how feed-forward stabilization can be used to tightly lock this laser to a second optical frequency reference, specifically a Ti:sapphire frequency comb. The upper-state lifetime of Cr:LiCAF is 170 µs [60], which limits direct pump-diode-current modulation of the laser to bandwidths of a few kHz, which are not sufficient to ensure tight phase locking and are similar to the bandwidth expected from the intracavity PZT element. Consequently, feed-forward control uniquely enables tight phase stabilization to an external optical reference, despite the absence of high-bandwidth actuators in the laser itself. In the future we expect that feed-forward control could be applied in a similar way to lock a Cr:LiCAF laser to an external reference cavity to directly achieve line narrowing of the laser output.
Funding
Science and Technology Facilities Council (ST/S001328/1, ST/V000403/1); Engineering and Physical Sciences Research Council (EP/L01596X/1, EP/R043922/1, LQT813).
Acknowledgments
The authors would also like to thank Dr. Richard A. McCracken, Dr. Toby Mitchell, and Dr. Hollie Wright for loaning of their equipment.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. B. J. Bloom, T. L. Nicholson, J. R. Williams, S. L. Campbell, M. Bishof, X. Zhang, W. Zhang, S. L. Bromley, and J. Ye, “An Optical Lattice Clock with Accuracy and Stability at the 10-18 Level,” Nature 506(7486), 71–75 (2014). [CrossRef]
2. L. Essen and J. Parry, “The caesium resonator as a standard of frequency and time,” Phil. Trans. R. Soc. Lond. A 250(973), 45–69 (1957). [CrossRef]
3. A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87(2), 637–701 (2015). [CrossRef]
4. O. Kock, W. He, D. Swierad, L. Smith, J. Hughes, K. Bongs, and Y. Singh, “Laser controlled atom source for optical clocks,” Sci. Rep. 6(1), 37321 (2016). [CrossRef]
5. K. Bongs, Y. Singh, L. Smith, W. He, O. Kock, D. Świerad, J. Hughes, S. Schiller, S. Alighanbari, S. Origlia, S. Vogt, U. Sterr, C. Lisdat, R. Le Targat, J. Lodewyck, D. Holleville, B. Venon, S. Bize, G. P. Barwood, P. Gill, I. R. Hill, Y. B. Ovchinnikov, N. Poli, G. M. Tino, J. Stuhler, and W. Kaenders, “Development of a strontium optical lattice clock for the SOC mission on the ISS,” C. R. Phys. 16(5), 553–564 (2015). [CrossRef]
6. L. Chen, L. Zhang, G. Xu, J. Liu, R. Dong, and T. Liu, “698-nm diode laser with 1-Hz linewidth,” Opt. Eng 56(1), 016101 (2017). [CrossRef]
7. S. Vogt, C. Lisdat, T. Legero, U. Sterr, I. Ernsting, A. Nevsky, and S. Schiller, “Demonstration of a transportable 1 Hz-linewidth laser,” Appl. Phys. B 104(4), 741–745 (2011). [CrossRef]
8. N. Poli, R. E. Drullinger, G. Ferrari, M. Prevedelli, F. Sorrentino, M. G. Tarallo, and G. M. Tino, “Prospect for a compact strontium optical lattice clock,” Proc. SPIE 6673, 66730F (2007). [CrossRef]
9. Y. Li, Y.-G. Lin, Q. Wang, S.-K. Wang, Y. Zhao, F. Meng, B.-K. Lin, J.-P. Cao, T.-C. Li, Z.-J. Fang, and E.-J. Zang, “A Hertz-Linewidth Ultrastable Diode Laser System for Clock Transition Detection of Strontium Atoms,” Chin. Phys. Lett. 31(2), 024207 (2014). [CrossRef]
10. W. Shao-Kai, W. Qiang, L. Yi-Ge, W. Min-Ming, L. Bai-Ke, Z. Er-Jun, L. Tian-Chu, and F. Zhan-Jun, “Cooling and Trapping 88Sr Atoms with 461 nm Laser,” Chin. Phys. Lett. 26(9), 093202 (2009). [CrossRef]
11. Q. Wang, B.-K. Lin, Y. Zhao, Y. Li, S.-K. Wang, M.-M. Wang, E.-J. Zang, T.-C. Li, and Z.-J. Fang, “Magneto-Optical Trapping of 88Sr atoms with 689 nm Laser,” Chin. Phys. Lett. 28(3), 033201 (2011). [CrossRef]
12. L. Zhang, J. Liu, L. Chen, G. Xu, T. Liu, and S. Zhang, “Development of Ultra-stable Clock Laser System for Space Applications,” 2019 Joint Conference of the IEEE International Frequency Control Symposium and European Frequency and Time Forum (EFTF/IFC) (2019).
13. E. M. Bridge, I. R. Hill, Y. B. Ovchinnikov, G. P. Barwood, E. A. Curtis, and P. Gill, “Progress towards a strontium optical lattice clock at NPL,” EFTF-2010 24th European Frequency and Time Forum (2010).
14. Y.-B. Wang, M.-J. Yin, J. Ren, Q.-F. Xu, B.-Q. Lu, J.-X. Han, Y. Guo, and H. Chang, “Strontium optical lattice clock at the National Time Service Center,” Chin. Phys. B 27(2), 023701 (2018). [CrossRef]
15. A. Sottile, E. Damiano, A. Di Lieto, and M. Tonelli, “Diode-pumped solid-state laser platform for compact and long-lasting strontium-based optical clocks,” Opt. Lett. 44(3), 594 (2019). [CrossRef]
16. A. D. Ludlow, “The Strontium Optical Lattice Clock: Optical Spectroscopy with Sub-Hertz Accuracy,” Ph.D. thesis, (Department of Physics, University of Colorado, 2008).
17. T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011). [CrossRef]
18. L. A. M. Johnson, P. Gill, and H. S. Margolis, “Evaluating the performance of the NPL femtosecond frequency combs: agreement at the 10(21 level),” Metrologia 52(1), 62–71 (2015). [CrossRef]
19. T. M. Fortier, A. Rolland, F. Quinlan, F. N. Baynes, A. J. Metcalf, A. Hati, A. D. Ludlow, N. Hinkley, M. Shimizu, T. Ishibashi, J. C. Campbell, and S. A. Diddams, “Optically referenced broadband electronic synthesizer with 15 digits of resolution,” Laser Photonics Rev. 10(5), 780–790 (2016). [CrossRef]
20. J. Jiang, A. Onae, H. Matsumoto, and F. L. Hong, “Frequency measurement of acetylene-stabilized lasers using a femtosecond optical comb without carrier-envelope offset frequency control,” Opt. Express 13(6), 1958 (2005). [CrossRef]
21. G. Galzerano, A. Gambetta, E. Fasci, A. Castrillo, M. Marangoni, P. Laporta, and L. Gianfrani, “Absolute frequency measurement of a water-stabilized diode laser at 1.384 µm by means of a fiber frequency comb,” Appl. Phys. B 102(4), 725–729 (2011). [CrossRef]
22. P. Balling, M. Fischer, P. Kubina, and R. Holzwarth, “Absolute frequency measurement of wavelength standard at 1542nm: acetylene stabilized DFB laser,” Opt. Express 13(23), 9196 (2005). [CrossRef]
23. J. D. Jost, J. L. Hall, and J. Ye, “Continuously tunable, precise, single frequency optical signal generator,” Opt. Express 10(12), 515–520 (2002). [CrossRef]
24. E. Benkler, F. Rohde, and H. R. Telle, “Robust interferometric frequency lock between cw lasers and optical frequency combs,” Opt. Lett. 38(4), 555–557 (2013). [CrossRef]
25. N. Beverini, M. Prevedelli, F. Sorrentino, B. Nyushkov, and A. Ruffini, “An analog + digital phase- frequency detector for phase locking of a diode laser to an optical frequency comb,” Quantum Electron. 34(6), 559–564 (2004). [CrossRef]
26. Q. Quraishi, M. Griebel, T. K. Ostmann, and R. Bratschitsch, “Generation of phase-locked and tunable continuous-wave radiation in the terahertz regime,” Opt. Lett. 30(23), 3231–3233 (2005). [CrossRef]
27. A. A. Mills, D. Gatti, J. Jiang, C. Mohr, W. Mefford, L. Gianfrani, M. Fermann, I. Hartl, and M. Marangoni, “Coherent phase lock of a 9 µm quantum cascade laser to a 2 µm thulium optical frequency comb,” Opt. Lett. 37(19), 4083–4085 (2012). [CrossRef]
28. S. Koke, C. Grebing, H. Frei, A. Anderson, A. Assion, and G. Steinmeyer, “Direct frequency comb synthesis with arbitrary offset and shot-noise-limited phase noise,” Nat. Photonics 4(7), 462–465 (2010). [CrossRef]
29. S. Koke, A. Anderson, H. Frei, A. Assion, and G. Steinmeyer, “Noise performance of a feed-forward scheme for carrier-envelope phase stabilization,” Appl. Phys. B 104(4), 799–804 (2011). [CrossRef]
30. R. A. McCracken, J. Sun, C. G. Leburn, and D. T. Reid, “Broadband phase coherence between an ultrafast laser and an OPO using lock-to-zero CEO stabilization,” Opt. Express 20(15), 16269–16274 (2012). [CrossRef]
31. F. Lücking, A. Assion, A. Apolonski, F. Krausz, and G. Steinmeyer, “Long-term carrier-envelope-phase-stable few-cycle pulses by use of the feed-forward method,” Opt. Lett. 37(11), 2076–2078 (2012). [CrossRef]
32. M. Yan, W. Li, K. Yang, H. Zhou, X. Shen, Q. Zhou, Q. Ru, D. Bai, and H. Zeng, “High-power Yb-fiber comb with feed-forward control of nonlinear-polarization-rotation mode-locking and large-mode-area fiber amplification,” Opt. Lett. 37(9), 1511–1513 (2012). [CrossRef]
33. R. T. Watts, S. G. Murdoch, and L. P. Barry, “Phase Noise Reduction of an Optical Frequency Comb Using a Feed-Forward Heterodyne Detection Scheme,” IEEE Photonics J. 8(1), 1–7 (2016). [CrossRef]
34. R. Lemons, W. Liu, I. F. de Fuentes, S. Droste, G. Steinmeyer, C. G. Durfee, and S. Carbajo, “Carrier-envelope phase stabilization of an Er:Yb:glass laser via a feed-forward technique,” Opt. Lett. 44(22), 5610–5613 (2019). [CrossRef]
35. K. Nakamura, S. Okubo, M. Schramm, K. Kashiwagi, and H. Inaba, “Offset-free all-fiber frequency comb with an acousto-optic modulator and two f–2f interferometers,” Appl. Phys. Express 10(7), 072501 (2017). [CrossRef]
36. Z. Chen, M. Yan, G. Mélen, T. W. Hänsch, and N. Picqué, “Feed-forward coherent dual-comb spectroscopy,” in Light, Energy and the Environment, OSA Technical Digest (online) (Optica Publishing Group, 2016), paper FTh3B.6.
37. R. Gotti, M. Prevedelli, S. Kassi, M. Marangoni, and D. Romanini, “Feed-forward coherent link from a comb to a diode laser: Application to widely tunable cavity ring-down spectroscopy,” J. Chem. Phys. 148(5), 054202 (2018). [CrossRef]
38. T. Sala, D. Gatti, A. Gambetta, N. Coluccelli, G. Galzerano, P. Laporta, and M. Marangoni, “Wide-bandwidth phase lock between a CW laser and a frequency comb based on a feed-forward configuration,” Opt. Lett. 37(13), 2592–2594 (2012). [CrossRef]
39. D. Gatti, T. Sala, A. Gambette, N. Coluccelli, G. N. Conti, G. Galzerano, P. Laporta, and M. Marangoni, “Analysis of the feed-forward method for the referencing of a CW laser to a frequency comb,” Opt. Express 20(22), 24880–24885 (2012). [CrossRef]
40. R. T. Watts, S. G. Murdoch, and L. P. Barry, “Spectral linewidth reduction of single-mode and mode-locked lasers using a feed-forward heterodyne detection scheme,” in CLEO: 2014, OSA Technical Digest (online) (Optica Publishing Group, 2014), paper STh3O.8.
41. M. O. Sahni, S. Trebaol, L. Bramerie, M. Joindot, SPÓ Dúill, S. G. Murdoch, L. P. Barry, and P. Besnard, “Frequency noise reduction performance of a feed-forward heterodyne technique: application to an actively mode-locked laser diode,” Opt. Lett. 42(19), 4000–4003 (2017). [CrossRef]
42. X. Shao, H. Han, Y. Su, H. Wang, Z. Zhang, S. Fang, G. Chang, and Z. Wei, “Locking CW laser to ultra-stable optical frequency comb by feed-forward method,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optica Publishing Group, 2019), paper JTh2A.104.
43. R. Yang, H. Lv, J. Luo, P. Hu, H. Yang, H. Fu, and J. Tan, “Ultrastable Offset-Locking Continuous Wave Laser to a Frequency Comb with a Compound Control Method for Precision Interferometry,” Sensors 20(5), 1248 (2020). [CrossRef]
44. A. Marconi, M. Abreu, V. Adibekyan, et al., “ANDES, the high resolution spectrograph for the ELT: science case, baseline design and path to construction,” Proc. SPIE 12184, 75 (2022). [CrossRef]
45. T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10-18 total uncertainty,” Nat. Commun. 6(1), 6896 (2015). [CrossRef]
46. Q. Wang, Y. G. Lin, F. Meng, Y. Li, B. K. Lin, E. J. Zang, T. C. Li, and Z. J. Fang, “Magic wavelength measurement of the 87Sr optical lattice clock at NIM,” Chin. Phys. Lett. 33(10), 103201 (2016). [CrossRef]
47. B. Szutor and F. Karpushko, “Spectral density contrast in DPSS and ECD lasers for quantum and other narrow-linewidth applications,” in W. A. Clarkson and R. K. Shori (eds.), Solid State Lasers XXIX: Technology and Devices., 112592D, Proceedings of SPIE, 11259, SPIE, SPIE LASE 2020, San Francisco, California, United States (2020).
48. C. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18(2), 259–264 (1982). [CrossRef]
49. U. Demirbas, “Cr:Colquiriite lasers: current status and challenges for further progress,” Prog. Quantum Electron. 68, 100227 (2019). [CrossRef]
50. U. Demirbas, S. Eggert, and A. Leitenstorfer, “Compact and efficient Cr:LiSAF lasers pumped by one single-spatial-mode diode: a minimal cost approach,” J. Opt. Soc. Am. B 29(8), 1894–1903 (2012). [CrossRef]
51. V. Kubecek, R. Quintero-Torres, and J.-C. M. Diels, “Ultra low pump- threshold laser diode pumped Cr:LiSAF laser,” in International Conference on Lasers, Applications, and Technologies 2002: Advanced Lasers and Systems, 5137, 43 (2003).
52. U. Demirbas, M. Schmalz, B. Sumpf, G. Erbert, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, F. X. Kärtner, and A. Leitenstorfer, “Femtosecond Cr:LiSAF and Cr:LiCAF lasers pumped by tapered diode lasers,” Opt. Express 19(21), 20444–20461 (2011). [CrossRef]
53. A. Miller, P. LiKamWa, B. H. T. Chai, and E. W. Van Stryland, “Generation of 150-fs tunable pulses in Cr:LiSrAlF6,” Opt. Lett. 17(3), 195–197 (1992). [CrossRef]
54. P. LiKamWa, B. H. T. Chai, and A. Miller, “Self-mode-locked Cr3+:LiCaAlF6 laser,” Opt. Lett. 17(20), 1438–1440 (1992). [CrossRef]
55. K. M. Gäbel, P. Rußbüldt, R. Lebert, and A. Valster, “Diode pumped Cr3+:LiCAF fs-laser,” Opt. Commun. 157(1-6), 327–334 (1998). [CrossRef]
56. P. Beaud, M. C. Richardson, Y. F. Chen, and B. H. T. Chai, “Optical amplification characteristics of Cr:LiSAF and Cr:LiCAF under flashlamp-pumping,” IEEE J. Quantum Electron. 30(5), 1259–1266 (1994). [CrossRef]
57. G. Di Domenico, S. Schilt, and P. Thomann, “Simple approach to the relation between laser frequency noise and laser line shape,” Appl. Opt. 49(25), 4801–4807 (2010). [CrossRef]
58. N. Bucalovic, V. Dolgovskiy, C. Schori, P. Thomann, G. Di Domenico, and S. Schilt, “Experimental validation of a simple approximation to determine the linewidth of a laser from its frequency noise spectrum,” Appl. Opt. 51(20), 4582–4588 (2012). [CrossRef]
59. M. Prevedelli, T. Freegarde, and T. W. Hänsch, “Phase locking of grating-tuned diode lasers,” Appl. Phys. B 60, S241–248 (1995).
60. S. A. Payne, L. L. Chase, H. W. Newkirk, L. K. Smith, and W. F. Krupke, “LiCaAlF6:Cr3+: a promising new solid-state laser material,” IEEE J. Quantum Electron. 24(11), 2243–2252 (1988). [CrossRef]
