Open Access
Add to BibSonomy
Abstract
The Extremely Large Telescope (ELT) will address an unprecedented optical wavelength range from 370 to 2400 nm, and its high-resolution spectrograph (HIRES) will require a laser frequency comb calibrator of comparable coverage. An architecture based around a Ti:sapphire master comb in principle enables wavelengths across this range to be obtained by a combination of second- and third-order nonlinear effects. In this scheme, near-infrared wavelength coverage can be addressed by downconversion of the comb to 1600 nm using an optical parametric oscillator (OPO), followed by broadband supercontinuum generation in highly nonlinear fiber. Here we present an example of this approach in the form of a 10 GHz astrocomb comprising a Fabry–Perot-filtered supercontinuum derived from a degenerate OPO and spanning 1.15–1.80 µm. We characterize the astrocomb using Fourier-transform spectroscopy, enabling the mode orders within the filtered comb to be identified.
Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
1. INTRODUCTION
The current minimum specification for the high-resolution spectrograph (HIRES) instrument in the Extremely Large Telescope (ELT) is simultaneous coverage from 400 to 1800 nm, with a goal of 350–2400 nm, and only one wavelength gap tolerated between 1360 and 1410 nm where high telluric absorption occurs [1]. Science cases supported by this instrument include the search for Earth-like exoplanets and the direct measurement of speculated variations in cosmological constants [2]. In addition to the requirement for wavelength coverage from the near-UV to the near-IR, the calibration unit for the ELT-HIRES spectrograph must provide both a wavelength precision and a stability of wavelength calibration accuracy from 500–1800 nm of better than 1 m s-1/day, expressed as a radial velocity specification. The sparsity, variable strength, and limited coverage of conventionally used emission lamps cannot meet these requirements, and so laser frequency combs (LFCs), which consist of a series of equally spaced laser modes in the frequency domain across the spectrum, are now considered the method of choice. Since the first on-sky demonstration of an LFC in 2007 [3], different approaches and systems architectures have been investigated [4] including the use of solid-state lasers [5–13], fiber lasers [3,14–18], microresonators [19,20], amplitude/ phase modulators [21–25], as well as four-wave mixing [26], while several astrocomb systems are already in place and have undergone testing in different telescopes worldwide [27,28].
ELT-HIRES is designed to have a spectral resolution of $R = 100{,}000$ and specifies a requirement for at least 2.5 pixels per spectral resolution element at wavelengths above 950 nm [1], which at 1600 nm implies a resolution of 1.9 GHz and a dispersion of 750 MHz/pixel. For LFC modes to be resolvable requires a mode spacing of at least a few times the spectrograph’s resolution, making a comb-mode spacing of 6–13 GHz suitable for calibrating the astronomical $ H $ and $ J $ bands (1170–1330 nm and 1490–1890 nm).
An LFC with the required bandwidth and mode spacing cannot be obtained directly from any existing laser oscillator, so instead the approach is to use a combination of wavelength extension and modal filtering to achieve the necessary specification. A Fabry–Perot cavity (FPC), adjusted to have a free-spectral range equal to an integer multiple of the laser repetition rate ${f_{{\rm rep}}}$, is commonly used as the mode-filtering element. Strong suppression of comb modes adjacent to those transmitted by the FPC requires a high-finesse design, but encounters a trade-off between finesse and operating bandwidth.
Fig. 1. Illustration of FPC filtering. In (a) denser source comb with mode spacing ${f_{{\rm rep},{\rm source}}}$ is filtered through a FPC, selecting a subset of comb modes with new spacing ${f_{{\rm rep},{\rm output}}}$, where ${f_{{\rm rep},{\rm output}}} = M{f_{{\rm rep},{\rm source}}}$. In this example ${M} = 4$, and each possible filtered subset is indicated by a different color. (b) Modeled transmission profile of the FP resonances with ${\rm wavelength} = 1600\;{\rm nm}$ as the cavity length is scanned. With only µm-level displacement, the output from the FPC can be any one of several neighboring subsets, and so uncertainty arises in the exact set of filtered modes.
This trade-off can be mitigated by using a master comb with an already wide mode spacing (e.g., 1 GHz) which, by permitting a lower finesse design, allows the reflectivities and group-delay characteristics of the FPC mirrors to be maintained over a wider wavelength range (see Section 2.C). The broad bandwidth of ELT-HIRES, together with the wider mode spacing requirements at shorter wavelengths, mean that multiple FPCs filtering different regions of the master comb are necessary. The wide operating bandwidth of ELT-HIRES already necessitates four separate grating spectrographs whose outputs are recorded on 10 different CCD cameras [2], so the requirement for multiple filter cavities is not unexpected.
As described in [29], a submicrometer (µm) adjustment of the length of a FPC is enough to select different modal subsets of the incident master comb. The desired subset can be selected by stabilizing the FPC to a cw laser pre-locked to one mode of the master comb [2] or by directly locking the FPC to a comb transmission peak [29]. Figure 1 schematically presents the behavior of a FPC of length $l$, showing the effect of a small length adjustment and illustrating the need for a way to resolve the potential ambiguity regarding which subset has been filtered from the master comb. How this issue can be addressed experimentally for the near-IR region is the subject of Section 3.C.
Previously, we presented an approach toward a fully stabilized broadband astrocomb, where a 1 GHz Ti:sapphire laser was used for supercontinuum generation, while simultaneously pumping a spectrally broadened phase coherent degenerate OPO [30]. This scheme provided a 1 GHz master comb with near-gap-free coverage from 0.5–2.2-µm. In this paper we now report the development of this work, leading to the demonstration of a 10 GHz astrocomb covering a wavelength range of 1.15–1.80 µm. Furthermore, we show how Fourier transform spectrometry can be used to determine with high accuracy the absolute mode numbers of the filtered comb modes.
2. EXPERIMENTAL ARRANGEMENT
A. Ti:sapphire Master Comb
As illustrated in Fig. 2, the system was based around a 1 GHz Ti:sapphire laser (Gigajet, Laser Quantum) centered at 806 nm and producing 30 fs pulses with an average power of 1 W. An 8:92 pellicle beamsplitter directed the majority of the laser power into a periodically poled potassium titanyl phosphate (PPKTP)-based degenerate OPO [31], while the rest was sampled by a GaAs photodiode for repetition rate (${f_{{\rm rep}}}$) detection. The signal was then mixed with a reference signal from a Rb-stabilized radio-frequency (RF) synthesizer (FSL-0010, Quicksyn Lite). The difference between the detected signal and the synthesized signal was minimized after using a feedback loop for cavity length control through adjustment of one of the intracavity laser mirrors mounted on a piezoelectric actuator. By using a servo controller (New Focus LB1005), the laser cavity length was locked to 7937 MHz, the eighth harmonic of ${f_{{\rm rep}}}$. Although ${f_{{\rm CEO}}}$ stabilization was not implemented, the laser has shown a passive ${f_{{\rm CEO}}}$ stability of 2.4 MHz/hour in previous measurements [11]. With more output power, an $f {\text -} {\rm to} {\text -} 2f$ system can be easily introduced.
Fig. 2. Experimental layout. The master source comb is an ${f_{{\rm rep}}}$ stabilized Ti:sapphire laser that then couples into (a) a PPKTP-based degenerate OPO, followed by (b) a spectrally broadening section with HNLF, and then (c) filtered by a dither-locked FPC unit. (d) The filtered comb then propagates into an FTS for modal analysis.
B. Synchronously Pumped Degenerate OPO
The pump beam was mode-matched into the OPO resonator with a 750 mm plano-convex lens and three silver mirrors. The design of the OPO was based on [31], employing a four-mirror folded ring cavity with a 1.0 mm quasi-phase-matched PPKTP crystal (Raicol Crystals). The crystal was Brewster cut with a domain period of 26.5 µm. The synchronously pumped cavity had a round-trip length of $\sim 300\;{\rm mm}$, matching that of the Ti:sapphire pump laser. The beam entered the cavity through a 1% output coupler and was focused by a curved silver mirror into the crystal. Both curved mirrors had radii of curvature of 20 mm, such that a ${1/}{e^2}$ radius of 14 µm was achieved in the crystal. The pump beam was mode matched to obtain a 10 µm focal radius in the crystal. To compensate for the astigmatism introduced by the Brewster-angled crystal, the two mirrors were set with a folding angle of 7.5°. A 100 µm piezoelectric translation stage mounted mirror on a plane cavity mirror was used to adjust the cavity length. A 25:75 pellicle beamsplitter was inserted inside the OPO cavity as the main output coupler. With the exception of the output coupler and pellicle, the rest of the OPO mirrors had a dielectric coating that transmitted the pump light and was highly reflective (${R}\gt {99.9}\%$) over the 1400–1800 nm region.
In a doubly resonant femtosecond OPO, oscillation is possible on multiple cavity lengths, each separated by a few hundred nanometers (nm), but only one of these typically corresponds to broadband and degenerate operation of the OPO. By using the recently demonstrated dither-free cavity stabilization approach [32], we locked the OPO for degenerate operation, achieving 120 mW, sub-50 fs pulses with a bandwidth of 100 nm centered at 1612 nm.
C. Spectral Broadening and Fabry–Perot Filtering
Around 90% of the OPO output power was focused through an aspheric lens into a 40 cm long highly nonlinear fiber (HNLF, Sumitomo Electric) for spectral broadening. The beam exited the fiber through a silver-coated off-axis parabolic reflector, which produced a 5 mm diameter beam across the full supercontinuum bandwidth. This beam was polarization multiplexed with the remaining OPO output using a broadband polarizing beamsplitter (PBS), following which two silver mirrors directed the orthogonally polarized beams into a plane-plane Fabry–Perot cavity (FPC).
The mirrors used in the FPC (Laseroptik) were a complementary pair, designed to have a combined group delay dispersion of close to zero from 1.3 to 1.9 µm and a reflectively of around 99% over the same range (Fig. 3), corresponding to a finesse of 200. The distance $l$ between the mirrors was set to 15 mm, corresponding a ${10} \times$ filtering factor from the 1 GHz master comb. The two beams leaving the FPC were separated by a second PBS, which guided the spectrally broadened output toward the Fourier transform spectrometer (FTS) while directing the OPO beam onto an InGaAs photodiode. One of the FPC mirrors was installed on a piezoelectric translation stage, allowing the mode resonances to be scanned using a 1 volt peak-to-peak triangular signal and the resonance condition to be optimized. With the other mirror mounted on a high-frequency sinusoidally driven piezoelectric actuator, the distance between the FPC mirrors was stabilized by dither locking on the InGaAs photodiode signal.
Fig. 3. (a) Individual (blue and green) and average (red) transmission and (b) group delay dispersion (GDD) curves of the FPC mirror pair.
D. Broadband Fourier Transform Spectrometer
The spectrally broadened OPO beam was multiplexed using a dichroic mirror with a 780.2 nm beam from a narrow-line cw diode laser (Vescent Photonics), and both beams were coupled into a broadband Fourier-transform spectrometer. The diode laser was dither locked to the ${^{87}}{\rm Rb}$ ${F} = 2$ to ${F} = 2,{{3}^\prime}$ transition [33], considered to correspond to a vacuum wavelength of ${\lambda _{{\rm Rb}}}$. As it is atomically referenced, once it is aligned to copropagate with the comb beam, it can be used as an optical reference for calibrating the path differences in the FTS, providing absolute frequency traceability for comb-mode positions. All the optics in the instrument were either silver-coated or had a broadband dielectric coating to ensure their performance over a broad wavelength range. The layout of the FTS was based on a Michelson interferometer as described in [34]. The FTS consisted of a pair of retroreflectors mounted back-to-back on a 10 cm long motorized stage (Fig. 4). The design enabled a fourfold increase in the optical path difference (OPD) between opposite arms of the interferometer, achieving an optical resolution of 750 MHz. At the exit of the FTS, the comb and Rb-reference beams were divided by a dichroic mirror before being detected by the InGaAs and Si photodiodes, respectively. The data were acquired with a USB oscilloscope (TiePie) with a sampling rate of 6.25 MS/s, corresponding to an acquisition time of 1.33 s per scan.
3. DATA ACQUISITION AND ANALYSIS
A. Path Difference Calibration
For every scan of the FTS, two sets of data were recorded: the fringes from the filtered OPO HNLF output and the interferograms from the Rb diode laser (Fig. 5). The data were filtered with a low-pass filter to remove any DC offset. With a 40 cm delay range, strong fringes at 780.2 nm were obtained across the full scan; 13 interferograms were observed with an extra two fringes at the extremes of the scan being visible and were attributed to parasitic reflections within the instrument. The OPD was characterized by a fringe-counting technique at 780.2 nm. With the interferogram centered at zero, the data points on both sides of the zero-crossing point of each fringe were found, and then linear interpolation used to determine the zero-crossing point of each fringe with subpixel accuracy. A further algorithm ensured only one zero-crossing point was counted per fringe. Each zero-crossing corresponded to a change in the physical path difference of $\lambda _{{\rm Rb}}^\prime = {\lambda _{{\rm Rb}}}/{n_{{\rm air}}}$ and an optical delay of ${\lambda _{{\rm Rb}}}/c$, allowing an accurate OPD scale to be constructed for the entire scan.
B. Interferogram Processing
With the OPD profile of the scan, the reference signal was linearly rescaled and apodized before obtaining the spectrum from a fast Fourier transform (FFT) of the data. Since the resolution of the instrument is not high enough to resolve the narrow-linewidth ($\sim{1}\;{\rm MHz}$) reference laser, the Fourier transformed data provided the characteristic instrument function of the FTS (Fig. 6). Triangular apodization was chosen, as it results in an all-positive ${{\rm sinc}^2}$ instrumental line shape. After apodization the full width at half-maximum (FWHM) instrumental linewidth was 1.35 GHz.
Fig. 6. FTS instrument line shape with a full width half-maximum value of 1.35 GHz, obtained from the reference laser data with the protocol described. A ${{\rm sinc}^2}$ instrument function can be observed.
Identical apodization was applied to the comb interferogram signal, along with noise rejection at delay positions far from each interferogram. The 1.35 GHz linewidth was sufficient to distinguish the 10 GHz spacing comb lines. The spectrum of the infrared comb is shown in Fig. 7, along with detail of individual comb modes in Fig. 8. The modulation between comb modes reflects the instrument line function of the FTS.
Fig. 7. Retrieved spectrum of the spectrally broadened degenerate OPO with substantial coverage of the astronomical $H$ band and partial coverage of the $J$ band.
Fig. 8. Representative filtered comb modes with shapes resulting from the line function of the spectrometer and with comb-mode numbers identified using the linear regression approach described in Section 3.C.
C. Frequency Axis and Comb Mode Identification
Accurate calibration of the OPD depends on having a reliable value for the effective calibration wavelength $\lambda _{{\rm Rb}}^\prime$, and this can be obtained by using the Ciddor relation [35], which provides the refractive index of air for given atmospheric conditions (temperature, humidity, pressure, and ${\rm CO}_2$ concentration). Even using an accurate value for $\lambda _{{\rm Rb}}^\prime$ obtained from atmospheric measurements in the lab, we found that the mode spacing returned by the FTS measurement differed by a small amount from the expected RF value. This discrepancy results from tiny microradian (µrad)-level misalignments between the comb and cw-laser beams as they propagate inside the interferometer, introducing a further small scaling factor into the OPD calibration.
This factor is easily determined by iteratively adjusting $\lambda _{{\rm Rb}}^\prime$ until the obtained mode spacing matches $10{f_{{\rm rep}}}$. In practice, the level of the correction needed is extremely small and is of an order similar to or less than that provided by correcting for air dispersion using the Ciddor relation ($\approx {10^{- 4}}$). The resulting spectrum is upsampled to better resolve the shapes of the comb lines.
The mode numbers of the comb modes contained in the FTS spectrum are determined in the following way. We select an intense region of the spectrum corresponding approximately to the full width at half-maximum bandwidth. Using a peak-finding algorithm, we identify the frequency of each comb mode across this bandwidth. These comb modes are spaced at $10{f_{{\rm rep}}}$, and their frequencies can be fitted to a line with the equation
to yield ${f_{{\rm CEO}}}$ and ${f_{{\rm rep}}}$ as the intercept and slope of the fitted line. Here $m$ is a set of consecutive integers representing the mode numbers of the comb, whose starting value is adjusted to ensure that the fit results in values of ${f_{{\rm CEO}}} \gt 0$ and ${f_{{\rm CEO}}} \lt {f_{{\rm rep}}}$, and $0 \le m_0 \le 9$ is an integer specifying the particular modal subset filtered by the FPC. We used the linear regression method described in [36] to provide the uncertainties in the intercept and gradient. Around one thousand comb-line positions were used for the fitting, which yielded ${f_{{\rm rep}}} = 992.1\;{\rm MHz} \pm 352\;{\rm Hz}$ and ${f_{{\rm CEO}}} = 565.7 \; {\rm MHz} \pm 64.3\;{\rm MHz} $. The fitted value for ${f_{{\rm rep}}}$ differed by 249 Hz from the value measured directly using a fast photodiode, which is within the uncertainty margin of the fit. By heterodyning the Rb-stabilized reference laser with the Ti:sapphire laser, we performed an independent check on the value of ${f_{{\rm CEO}}}$ yielded by the analysis. The Ti:sapphire pump laser is a comb described by the equationUsing the frequency for the Rb crossover transition to which the reference laser was stabilized [33], the beat frequency can be calculated, with associated uncertainties, to be ${164.3}\pm{187}\;{\rm MHz}$, which agreed within error to the beat frequency of 294 MHz recorded at the time of the FTS measurement.
4. CONCLUSION AND FUTURE DEVELOPMENT
We have demonstrated a mode-number-calibrated 10 GHz astrocomb from 1.15 to 1.8 µm, which is repetition rate stabilized to a Rb-referenced electronic oscillator. In combination with the previously reported broadband Ti:sapphire-OPO system [30], which spanned a wavelength of range of 500–2000 nm, the addition of broadband mode filtering in the infrared will allow the development of a flexible astrocomb system operating with mode spacings from a few gigahertz (GHz) to tens of GHz.
The mode-number identification method introduced here provides a route to obtain the comb-mode equation directly from the spectrometer measurement. Corroborating the comb offset obtained in this way with an independent $f {\text -} {\rm to} {\text -} 2f$ interferometer measurement of ${f_{{\rm CEO}}}$ remains available as a further test of the method.
Funding
Science and Technology Facilities Council (ST/N000625/1, ST/N006925/1, ST/S001328/1).
Acknowledgment
R. A. M. is supported by a Heriot-Watt University research fellowship.
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. ESO, “HIRES technical specification,” ESO Document Number ESO-332024 (2020).
2. A. Marconi, P. Di Marcantonio, V. D’Odorico, S. Cristiani, R. Maiolino, E. Oliva, L. Origlia, M. Riva, L. Valenziano, F. M. Zerbi, M. Abreu, V. Adibekyan, C. Allenda Prieto, P. J. Amado, W. Benz, I. Boisse, X. Bonfils, F. Bouchy, D. Buscher, A. Cabral, B. L. Canto Martins, A. Chiavassa, J. Coelho, E. Delgado, J. R. De Medeiros, I. Di Varano, P. Figueira, M. Fisher, J. P. U. Fynbo, A. C. H. Glasse, M. Haehnelt, C. Haniff, A. Hatzes, P. Huke, A. J. Korn, I. C. Leao, J. Liske, C. Lovis, I. Matute, R. A. McCracken, C. J. A. P. Martins, M. J. P. F. G. Monteiro, S. Morris, T. Morris, H. Nicklas, A. Niedzielski, N. Nunes, E. Palle, P. Parr-Burman, V. Parro, I. Parry, F. Pepe, N. Piskunov, D. Queloz, A. Quirrenbach, R. Rebolo Lopez, A. Reiners, D. T. Reid, N. Santos, W. Seifert, S. Sousa, H. C. Stempels, K. Strassmeier, X. Sun, S. Udry, M. Weber, and E. Zackrisson, “EELT-HIRES the high-resolution spectrograph for the E-ELT,” Proc. SPIE 9908, 990823 (2016). [CrossRef]
3. T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008). [CrossRef]
4. R. A. McCracken, J. M. Charsley, and D. T. Reid, “A decade of astrocombs: recent advances in frequency combs for astronomy [Invited],” Opt. Express 25, 15058–15078 (2017). [CrossRef]
5. D. A. Braje, M. S. Kirchner, S. Osterman, T. Fortier, and S. A. Diddams, “Astronomical spectrograph calibration with broad-spectrum frequency combs,” Eur. Phys. J. D 48, 57–66 (2008). [CrossRef]
6. C.-H. Li, A. G. Glenday, A. J. Benedick, G. Chang, L.-J. Chen, C. Cramer, P. Fendel, G. Furesz, F. X. Kärtner, S. Korzennik, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “In-situ determination of astro-comb calibrator lines to better than 10 cm s-1,” Opt. Express 18, 13239–13249 (2010). [CrossRef]
7. A. J. Benedick, G. Chang, J. R. Birge, L.-J. Chen, A. G. Glenday, C.-H. Li, D. F. Phillips, A. Szentgyorgyi, S. Korzennik, G. Furesz, R. L. Walsworth, and F. X. Kärtner, “Visible wavelength astro-comb,” Opt. Express 18, 19175–19184 (2010). [CrossRef]
8. D. F. Phillips, A. G. Glenday, C.-H. Li, C. Cramer, G. Furesz, G. Chang, A. Benedick, L.-J. Chen, F. X. Kartner, S. Korzennik, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “Calibration of an astrophysical spectrograph below 1 m/s using a laser frequency comb,” Opt. Express 20, 13711–13726 (2012). [CrossRef]
9. N. Langellier, C. H. Li, A. G. Glenday, G. Chang, H. W. Chen, J. Lim, G. Furesz, F. Kartner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. Walsworth, “Green astro-comb for HARPS-N,” Proc. SPIE 9147, 91478N (2014). [CrossRef]
10. A. G. Glenday, C.-H. Li, N. Langellier, G. Chang, L.-J. Chen, G. Furesz, A. A. Zibrov, F. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “Operation of a broadband visible-wavelength astro-comb with a high-resolution astrophysical spectrograph,” Optica 2, 250–254 (2015). [CrossRef]
11. R. A. McCracken, É. Depagne, R. B. Kuhn, N. Erasmus, L. A. Crause, and D. T. Reid, “Wavelength calibration of a high resolution spectrograph with a partially stabilized 15-GHz astrocomb from 550 to 890 nm,” Opt. Express 25, 6450–6460 (2017). [CrossRef]
12. K. Kashiwagi, T. Kurokawa, Y. Okuyama, T. Mori, Y. Tanaka, Y. Yamamoto, and M. Hirano, “Direct generation of 12.5-GHz-spaced optical frequency comb with ultrabroad coverage in near-infrared region by cascaded fiber configuration,” Opt. Express 24, 8120–8131 (2016). [CrossRef]
13. A. Ravi, D. F. Phillips, M. Beck, L. L. Martin, M. Cecconi, A. Ghedina, E. Molinari, A. Bartels, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “Astro-comb calibrator and spectrograph characterization using a turn-key laser frequency comb,” J. Astron. Telesc. Instrum. Syst. 3, 045003 (2017). [CrossRef]
14. T. Wilken, C. Lovis, A. Manescau, T. Steinmetz, L. Pasquini, G. Lo Curto, T. W. Hänsch, R. Holzwarth, T. Udem, G. Lo Curto, T. W. Hansch, R. Holzwarth, and T. Udem, “High-precision calibration of spectrographs,” Mon. Not. R. Astron. Soc. Lett. 405, L16–L20 (2010). [CrossRef]
15. F. Quinlan, G. Ycas, S. Osterman, and S. A. Diddams, “A 12.5 GHz-spaced optical frequency comb spanning >400 nm for near-infrared astronomical spectrograph calibration,” Rev. Sci. Instrum. 81, 063105 (2010). [CrossRef]
16. H. Doerr, T. J. Kentischer, T. Steinmetz, R. A. Probst, M. Franz, R. Holzwarth, T. Udem, T. W. Hänsch, and W. Schmidt, “Performance of a laser frequency comb calibration system with a high-resolution solar echelle spectrograph,” Proc. SPIE 8450, 84501G (2012). [CrossRef]
17. G. G. Ycas, F. Quinlan, S. A. Diddams, S. Osterman, S. Mahadevan, S. Redman, R. Terrien, L. Ramsey, C. F. Bender, B. Botzer, and S. Sigurdsson, “Demonstration of on-sky calibration of astronomical spectra using a 25 GHz near-IR laser frequency comb,” Opt. Express 20, 6631–6643 (2012). [CrossRef]
18. T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485, 611–614 (2012). [CrossRef]
19. M.-G. Suh, X. Yi, Y.-H. Lai, S. Leifer, I. S. Grudinin, G. Vasisht, E. C. Martin, M. P. Fitzgerald, G. Doppmann, J. Wang, D. Mawet, S. B. Papp, S. A. Diddams, C. Beichman, and K. Vahala, “Searching for exoplanets using a microresonator astrocomb,” Nat. Photonics 13, 25–30 (2019). [CrossRef]
20. E. Obrzud, M. Rainer, A. Harutyunyan, M. H. Anderson, J. Liu, M. Geiselmann, B. Chazelas, S. Kundermann, S. Lecomte, M. Cecconi, A. Ghedina, E. Molinari, F. Pepe, F. Wildi, F. Bouchy, T. J. Kippenberg, and T. Herr, “Amicrophotonic astrocomb,” Nat. Photonics 13, 31–35 (2019). [CrossRef]
21. X. Yi, K. Vahala, J. Li, S. Diddams, G. Ycas, P. Plavchan, S. Leifer, J. Sandhu, G. Vasisht, P. Chen, P. Gao, J. Gagne, E. Furlan, M. Bottom, E. C. Martin, M. P. Fitzgerald, G. Doppmann, and C. Beichman, “Demonstration of a near-IR line-referenced electro-optical laser frequency comb for precision radial velocity measurements in astronomy,” Nat. Commun. 7, 10436 (2016). [CrossRef]
22. E. Obrzud, M. Rainer, A. Harutyunyan, B. Chazelas, M. Cecconi, A. Ghedina, E. Molinari, S. Kundermann, S. Lecomte, F. Pepe, F. Wildi, F. Bouchy, and T. Herr, “Broadband near-infrared astronomical spectrometer calibration and on-sky validation with an electro-optic laser frequency comb,” Opt. Express 26, 34830–34841 (2018). [CrossRef]
23. A. J. Metcalf, T. Anderson, C. F. Bender, S. Blakeslee, W. Brand, D. R. Carlson, W. D. Cochran, S. A. Diddams, M. Endl, C. Fredrick, S. Halverson, D. D. Hickstein, F. Hearty, J. Jennings, S. Kanodia, K. F. Kaplan, E. Levi, E. Lubar, S. Mahadevan, A. Monson, J. P. Ninan, C. Nitroy, S. Osterman, S. B. Papp, F. Quinlan, L. Ramsey, P. Robertson, A. Roy, C. Schwab, S. Sigurdsson, K. Srinivasan, G. Stefansson, D. A. Sterner, R. Terrien, A. Wolszczan, J. T. Wright, and G. Ycas, “Stellar spectroscopy in the near-infrared with a laser frequency comb,” Optica 6, 233–239 (2019). [CrossRef]
24. A. J. Metcalf, C. D. Fredrick, R. C. Terrien, S. B. Papp, and S. A. Diddams, “30 GHz electro-optic frequency comb spanning 300thz in the near infrared and visible,” Opt. Lett. 44, 2673–2676 (2019). [CrossRef]
25. E. Obrzud, V. Brasch, T. Voumard, A. Stroganov, M. Geiselmann, F. Wildi, F. Pepe, S. Lecomte, and T. Herr, “Visible blue-to-red 10 GHz frequency comb via on-chip triple-sum-frequency generation,” Opt. Lett. 44, 5290–5293 (2019). [CrossRef]
26. J. M. Chavez Boggio, T. Fremberg, D. Bodenmuller, C. Sandin, M. Zajnulina, A. Kelz, D. Giannone, M. Rutowska, B. Moralejo, M. M. Roth, M. Wysmolek, and H. Sayinc, “Wavelength calibration with PMAS at 3.5 m Calar Alto Telescope using a tunable astrocomb,” Opt. Commun. 415, 186–193 (2018). [CrossRef]
27. Z. Hao, H. Ye, J. Han, Y. Wu, Y. Zhai, and D. Xiao, “Calibration tests of a 25-GHz mode-spacing broadband astro-comb on the fiber-fed high resolution spectrograph (HRS) of the Chinese 2.16-m telescope,” Publ. Astron. Soc. Pac. 130, 125001 (2018). [CrossRef]
28. R. A. Probst, D. Milaković, B. Toledo-Padron, G. L. Curto, G. Avila, A. Brucalassi, B. L. C. Martins, I. C. Leão, M. Esposito, J. I. G. Hernández, F. Grupp, T. W. Hänsch, H. Kellermann, F. Kerber, O. Mandel, A. Manescau, E. Pozna, R. Rebolo, J. R. de Medeiros, T. Steinmetz, A. Suárez Mascareño, T. Udem, J. Urrutia, Y. Wu, L. Pasquini, and R. Holzwarth, “A crucial test for astronomical spectrograph calibration with frequency combs,” Nat. Astron. 4, 603–608 (2020). [CrossRef]
29. Z. Zhang, K. Balskus, R. A. McCracken, and D. T. Reid, “Mode-resolved 10-GHz frequency comb from a femtosecond optical parametric oscillator,” Opt. Lett. 40, 2692–2695 (2015). [CrossRef]
30. Y. S. Cheng, D. Xiao, R. A. McCracken, and D. T. Reid, “Towards a visible to mid-infrared astrocomb for the extremely large telescope,” in Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference (CLEO/Europe-EQEC) (2019), paper ED-6.4.
31. R. A. McCracken and D. T. Reid, “Few-cycle near-infrared pulses from a degenerate 1 GHz optical parametric oscillator,” Opt. Lett. 40, 4102–4105 (2015). [CrossRef]
32. Y. S. Cheng, R. A. McCracken, and D. T. Reid, “Dither-free stabilization of a femtosecond doubly resonant OPO using parasitic sum-frequency mixing,” Opt. Lett. 45, 768–771 (2020). [CrossRef]
33. J. Ye, S. Swartz, P. Jungner, and J. L. Hall, “Hyperfine structure and absolute frequency of the (87)Rb 5P(3/2) state,” Opt. Lett. 21, 1280–1282 (1996). [CrossRef]
34. J. M. Charsley, R. A. McCracken, L. Reid, and D. T. Reid, “Broadband Fourier-transform spectrometer enabling modal subset identification in Fabry-Pérot-based astrocombs,” Opt. Express 25, 19251–19262 (2017). [CrossRef]
35. P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” Appl. Opt. 35, 1566–1573 (1996). [CrossRef]
36. D. York, N. Evensen, M. Martinez, and J. Delgado, “Unified equations for the slope,” Am. J. Phys. 72, 367–375 (2004). [CrossRef]
