SUPPLEMENTARY INFORMATION

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1 Frequency-agile dual-comb spectroscopy Guy Millot 1, Stéphane Pitois 1, Ming Yan 2,3, Tatevik Hovannysyan 1, Abdelkrim Bendahmane 1, Theodor W. Hänsch 2,3, Nathalie Picqué 2,3,4,* 1. Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 6303 CNRS - Univ. Bourgogne Franche- Comté, 9 Avenue A. Savary, F Dijon, France, EU 2. Ludwig-Maximilians-Universität München, Fakultät für Physik, Schellingstr. 4/III, D Munich, Germany 3. Max-Planck-Institut für Quantenoptik, Hans-Kopfermannstr. 1, D Garching, Germany 4. Institut des Sciences Moléculaires d Orsay (ISMO), CNRS, Univ. Paris-Sud, Université Paris- Saclay, F Orsay (France) * Corresponding author, Supplementary Figures NATURE PHOTONICS 1

2 Supplementary Figure 1. Temporal characterization of the light pulse intensity generated in the nonlinear fiber. All the measurements are digitized on an ultrafast oscilloscope (bandwidth 33 GHz, sampling rate samples.s -1.) a) Rectangular electric pulses of a duration of 50 ps (and, not shown in the figure, a repetition frequency of 300 MHz) are generated by a programmable pulse generator. They drive the radio-frequency amplifier of a LiNbO 3 Mach-Zehnder intensity modulator. b) Optical pulses at the output of the intensity modulator, monitored on a fast photodiode. The shape of the electric pulses is preserved. Such pulses seed the normal dispersion nonlinear fiber. Ten thousand traces are superimposed on the oscilloscope screen trace. c) Optical pulses at the output of the nonlinear fiber, monitored on a fast photodiode. The pulses are broadened to 162 ps. The oscilloscope is triggered by the electrical pulses. Ten thousand traces are superimposed on the oscilloscope screen trace, showing how small the timing jitter is. d) Zoom of c). The rising edge of the pulses shows a jitter with a standard deviation of 2.14 ps. 2 NATURE PHOTONICS

3 SUPPLEMENTARY INFORMATION Supplementary Figure 2. Radio-frequency characterization of the frequency combs generated by optical wave-breaking in a normally-dispersive fiber. a) Low-resolution radio-frequency spectrum of the signal generated by the optical frequency comb on a fast photodiode. The spectrum is composed of the beating signal between the comb modes (also called intermode beat signal) at the repetition frequency of 300 MHz and its harmonics. The decaying intensity of the harmonics is due to the limited bandwidth of the fast InGaAs photodiode. b,c) Intermode beat signal at the fundamental repetition frequency (300 MHz) of the comb b) at the input and c) at the output of the nonlinear fiber, respectively. The FWHM of the intermode beat signal at the fundamental repetition frequency of the comb, is limited to 1.0 Hz by the resolution of the radio-frequency spectrum analyzer. The intermode beat signal at the output of the fiber is similar to that at the input of the fiber. NATURE PHOTONICS 3

4 d,e) Beat note between a pair of optical lines of the two combs, resolved by a fast photodiode and a radio-frequency spectrum analyzer, d) at the input and e) at the output of the fiber, respectively. The lines are located thirty lines away from the continuous-wave laser carrier. It exhibits a FWHM of 2.5 Hz, demonstrating an excellent relative coherence time exceeding 400 ms. It is remarkable that the coherence between the two combs is satisfactorily maintained despite the kilometric length of the fiber. This is the consequence of the use of a single fiber for spectral broadening. With femtosecond oscillators, either free-running or stabilized against radio-frequency references, it is not possible to resolve individual comb lines (see e.g. [1]). 4 NATURE PHOTONICS

5 SUPPLEMENTARY INFORMATION Supplementary Figure 3. Influence of the line-width of the continuous-wave laser on the dual-comb spectra. a) Free-running beat notes between a narrow-line-width E15 Koheras laser (linewidth of 0.1 khz at 100 µs) and three different continuous-wave lasers (Blue: Yenista OSICS T , Red: Toptica, CTL1550 and Black: NKT Photonics, Koheras E15). The beat notes are recorded by a radio-frequency spectrum analyzer (FSV4, R&S), with a resolution bandwidth of 3 khz. b) The three continuous-wave lasers characterized in (a) are used as seed in the dualcomb set-up shown in Figure 1. The resulting three spectra are recorded in the region of 1,560 nm. The difference in comb repetition frequencies is set to 100 khz. The line spacing is 300 MHz. The spectra are averaged 100 times for a total measurement time of 52.4 ms. c) Expanded view of b). NATURE PHOTONICS 5

6 d) Zoom on a resolved comb line for comparison of the signal-to-noise ratio. For each spectrum, the width of the comb line is Fourier limited. The signal-to-noise is 730, 790 and 970, respectively for the Yenista, Toptica and NKT Photonics lasers, respectively. In other words, a change of three orders of magnitude in the continuouswave laser line-width only induces a change of 25% of the signal-to-noise ratio. This shows the efficiency of our scheme for compensating common-noise effects and for generating two mutually-coherent combs. See Supplementary Discussion for details. 6 NATURE PHOTONICS

7 SUPPLEMENTARY INFORMATION Supplementary Figure 4. Experimental set-up and spectrum used for an accurate line position measurement of the P(13) line of the ν 1 +ν 3 band of 12 C 2 H 2. a) Experimental set-up. The frequency of the continuous-wave laser diode is determined by measuring its beat note with the metrology comb. The repetition frequency and the carrier-envelope offset frequency of the commercial metrology comb are stabilized against the 10-MHz reference of an active hydrogen maser. In the dual-comb set-up, a filter is used after combination of the two comb beams. It narrows the spectral span to about 350 GHz and improves the signal-to-noise ratio compared to an unfiltered spectrum. b) Experimental spectrum of the P(13) line of the ν 1 +ν 3 band of acetylene ( 12 C 2 H 2 ) and fit of the line by a Voigt profile. The residuals observed fitted are plotted on a different intensity scale. The acetylene gas is sealed in a fiber-coupled cell with an absorption path length of 5.5 cm and a pressure of 6,666 Pa. The temperature is 296 K. NATURE PHOTONICS 7

8 Supplementary Discussion Comparison of different continuous-wave lasers. In laser spectroscopy, there is usually a trade-off between frequency agility over a large spectral span and laser line-width. In our experiments, a concern is that the convenient tuning capabilities may come at the expense of additional noise in the dual-comb spectra. We therefore characterize and test the robustness of our set-up by harnessing three continuous-wave lasers, of different free-running line-widths, and by comparing the resulting dual-comb spectra. The first laser is the system that we used for the spectroscopic measurements reported in this article. It is an extended-cavity laser diode tunable between 1,520 and 1,630 nm (OSICS T , Yenista). Its tuning speed is 10 nm.s -1 and its specified free-running line-width is 150 khz. The second laser is an extended-cavity laser diode tunable between 1,530 and 1,620 nm (CTL1550, Toptica). Its tuning speed is 10 nm.s -1 and its specified freerunning line-width is <100 khz at 5 µs. The third laser is a continuous-wave erbium doped fiber laser of very narrow linewidth (Koheras E15, NKT Photonics). Its central wavelength is 1, nm and it is tunable by temperature tuning of about 1 nm around this value. Its specified freerunning line-width is <0.1 khz at 100 µs, which is the reason why we chose to test this laser despite its lack of tunability. The wavelength of both extended-cavity lasers can be tuned either manually from the control panel or by using a computer software. The computer software makes it possible to straightforwardly program the tuning sequence. One can for instance keep the laser at a certain wavelength during a chosen time for a spectroscopic measurement and then quickly tune it to another selected wavelength for another spectroscopic measurement. During the spectroscopic measurements, the wavelength is not tuned. All the lasers are used free-running and they are set to an emission wavelength of about 1,560 nm. With each of these three laser systems, we implement the experimental configuration displayed in Figure 1, except that we beat a fraction of the continuous-wave laser used for frequency comb generation with another free-running narrow-line-width E15 Koheras laser (NKT Photonics). The beat note measurement is measured with a radio-frequency spectrum analyzer with a 3-kHz resolution bandwidth. It provides an upper limit of the line-width of our continuous-wave lasers. Supplementary Figure 3a displays the results: while the beat note involving the two NKT Photonics lasers has a full width of 3 khz at -3dB, the beats with the extendedcavity diode lasers broaden to more than 1 MHz. Remarkably, all the dual-comb spectra (Supplementary Figure 3b,c,d) exhibit a good signal-to-noise ratio and they show little sensitivity to the continuous-wave laser line-width. The displayed spectra average one hundred individual spectra, therefore the total measurement time is 52.4 ms. We checked that the signal-to-noise ratio increases with the square root of the number of averages, independently of the continuous-wave laser. The dips in the intensity of the comb lines are due to rovibrational lines of the 2ν 3 band of H 13 CN. In the zoom (Supplementary Figure 3d), the signal-to-noise ratio on the comb line is 730, 790 and 970, respectively for the Yenista, Toptica and NKT Photonics lasers, respectively. The decrease of about 25% 8 NATURE PHOTONICS

9 SUPPLEMENTARY INFORMATION in the signal-to-noise appears as a reasonable compromise to benefit from the versatility of the extended-cavity broadly-tunable frequency-agile laser diodes. Test of the accuracy of the frequency measurements of line positions We perform a dual-comb spectral measurement intended at calibrating the frequency of a Doppler-broadened acetylene line to a self-referenced Er-doped fiber frequency comb (called metrology comb below). This provides a stringent test of the suitability of our experimental set-up for accurate spectroscopic measurements. We use the set-up displayed in Supplementary Figure 4a. Compared to the set-up shown in Figure 1, we split the beam of the laser diode one more time in order to set up a beat measurement with the metrology comb. The metrology comb is referenced to an active, Global-Positioning-System (GPS) disciplined, hydrogen maser (Kvarz CH1-75A), with a specified frequency stability of at 1s. All the signal generators and counters used in this experiment are also synchronized to the 10-MHz reference signal of the hydrogen maser. The laser diode is free-running, like in the other measurements performed in this article, and we record its beat signal with one line of the metrology comb simultaneously to the recording of the interferogram. We set the wavelength of the laser diode around 1,533.4 nm. Only one comb interrogates an acetylene cell in the region of the P(13) line of the ν 1 +ν 3 band of 12 C 2 H 2, while the second comb serves as a local oscillator. The acetylene cell is a commercial cell, which reproduces the National Institute of Standard and Technology (NIST) Standard Reference Material (SRM) 2517a traceable gas cell recommendations [2]. We chose to investigate the P(13) line because it is one of the few lines characterized with higher accuracy in the NIST report [2]. In order to improve the signal-to-noise ratio, the interferometric signal is spectrally filtered to a span of about 350 GHz. We measure a continuous interferometric sequence of 52.4 ms, which we slice in one hundred parts of 524 µs. Each slice is Fourier transformed and the resulting spectra are averaged. We use the measurement of the continuous-wave laser frequency against the frequency comb and the setting of the line spacing of the interrogating comb (300 MHz) to calibrate the frequency scale of the optical spectrum. We extract the maxima of the individual comb lines and plot a portion of them in Supplementary Figure 4b, showing the P(13) line of the ν 1 +ν 3 band of 12 C 2 H 2. We adjust a Voigt profile (with a fixed Doppler full width at halfmaximum of 470 MHz) to the experimental line profile. The fitted profile and the residuals Observed Fitted are also displayed in Supplementary Figure 4b. The standard deviation of the adjustment is 0.4 %. We determine the experimental line position of the P(13) line of the ν 1 +ν 3 band of 12 C 2 H 2 to THz. We estimate the uncertainty of our measurement to about 5 MHz. It mostly originates from the drifts of the continuous-wave laser during the measurement, the line position determination statistical uncertainty in the fit and the uncertainty on the gas pressure in the commercial cell. The NIST recommended value [2] for SRM 2517a conditions (pressure: 6.7 kpa, absorption length: 5 cm) results from a low-pressure saturated-absorption measurement within an accuracy of 150 KHz [3] corrected by the experimentally-determined self-induced pressure shift [4]. It is 1, (10) nm, which converts into (12) THz. The agreement between our measurement and the NIST value is therefore better than 1 MHz. NATURE PHOTONICS 9

10 Considering that our measurement is performed over a very short time (52.4 ms), with a free-running continuous-wave laser, interrogating a Voigt profile, and considering the accuracy of the NIST standard, such excellent agreement fully validates the quality of our spectra. We estimate that, by using a continuous-wave laser stabilized against a molecular line or a Fabry-Pérot cavity of moderate finesse and by probing line profiles with a width induced by the Doppler-broadening only, we could improve our uncertainty to a few hundreds of khz. We note that commercially available Fizeau-type wavemeters have an accuracy of 10 MHz, they could therefore provide an easy-to-implement and significantly cheaper alternative to the metrology frequency comb. However, we did not have such wavemeter available in our laboratory. An advantage in favor of our technique is that the frequency calibration can be performed by the measurement of the continuous-wave laser frequency and of the comb line spacing, only. For most applications, a wavemeter will provide the required accuracy. This considerably simplifies the calibration compared to that with modelocked lasers, which would require two complex and expensive f-2f interferometers, to entirely determine the frequency of the comb lines. Most dual-comb implementations do not provide intrinsic self-calibration of the frequency scale: indeed, the frequency scale is usually calibrated against one or several molecular lines present in the spectrum and for which measurements are available in the literature. As dual-comb spectroscopy requires combs with little intensity variations and low intensity noise, most of the time, the direct output of a femtosecond oscillator is employed. In some cases, moderate spectral broadening with a normal dispersion fiber is performed. However, measuring the carrier-envelope offset frequency for calibration of the frequency scale requires two f-2f interferometers (one per comb). With optical parametric oscillators, a direct calibration would be even more complex. Therefore most researchers in the field of dual-comb spectroscopy have chosen not to develop such self-calibrated systems. To our knowledge, only a limited number of publications compare experimental line positions, measured with a self-calibrated dual-comb system, with line frequencies measured by other accurate techniques. Ref.[5] reports on a dual-comb system, where one line of each comb is stabilized against one Hz-linewidth continuous-wave laser and one other line to a combstabilized continuous-wave laser. The frequencies of the continuous-wave lasers are measured using a self-referenced comb and permit the calibration of the optical scale. The measurement of 47 lines of the 2ν 3 band of H 13 CN is compared with wavemeter measurements of a 1-MHz uncertainty [6]. The authors of [5] report a scatter of about 9 MHz around the values of [6]. They attribute such scatter to their experimental linewidth of 2.3 GHz and their signal-to-noise ratio. More recent measurements [7] by the same group involve an improved set-up where the combs are phase-locked to two Hzline-width stabilized continuous-wave lasers, and the frequency of the continuouswave lasers is measured with a third, self-referenced, comb. With narrower molecular line-widths limited by Doppler-broadening only and longer measurement times, they improve their uncertainty to 0.2 MHz and the measurement of 37 lines of ν1+ν3 band of C 2 H 2 agrees with the saturated-absorption measurements of [8] within a standard deviation of 0.45 MHz. The same group also reported line position measurements in 10 NATURE PHOTONICS

11 SUPPLEMENTARY INFORMATION the 3µm region, on the ν 3 band of methane [9]. With similar state-of-the-art techniques, they achieve a 300-kHz uncertainty. The comparison of 52 lines with the saturated-absorption measurements of [10] reveals an agreement within a standard deviation of 170 khz. Ref. [11] reports on a dual-comb system for near-infrared broadband absorption spectroscopy. For each comb, one comb line is locked to a cavity-stabilized sub-hzline-width continuous-wave laser, which is stabilized to an ultra-stable cavity. In addition, the carrier-envelop offset of each comb is detected with a f-2f interferometer and phase-locked to a radio-frequency reference from a H-maser. They calibrate their frequency scale with the frequency of the continuous-wave laser, the comb carrierenvelope offset frequencies, and the comb repetition frequencies. For four Dopplerbroadened lines of the ν 1 +ν 3 band of C 2 H 2, Ref.[11] reports an agreement within 2 MHz with the positions measured by sub-doppler spectroscopy of Ref.[3]. Ref [11] attributes the discrepancies to the signal-to-noise ratio in their spectrum and to residual fringes on the spectral baseline. In the THz region, an adaptive sampling scheme led to the measurement [12] of the position of a rotational transition in water vapor agreeing within 1 MHz with the JPL database [13]. As the precision of the measurements is fundamentally limited by the width of the Doppler-broadened lines and by the signal-to-noise ratio, the simplification in the frequency scale calibration, brought by our technique of dual-comb spectroscopy without mode-locked lasers, should benefit many applications. Supplementary references [1] Ideguchi, T. et al. Adaptive real-time dual-comb spectroscopy. Nat. Commun. 5:3375 doi: /ncomms4375 (2014). [2] Gilbert, S.L. & Swann, W.C. Acetylene 12 C 2 H 2 absorption reference for 1510 nm to 1540 nm wavelength calibration SRM 2517a, Natl. Inst. Stand. Technol. (US) Spec. Publ (National Institute of Standards and Technology, 2001). [3] Nakagawa, K., de Labachelerie, M., Awaji, Y. & Kourogi, M. Accurate optical frequency atlas of the 1.5 µm bands of acetylene. J. Opt. Soc. Am. B. 13, (1996). [4] Swann, W.C. & Gilbert, S.L. Pressure-induced shift and broadening of nm acetylene wavelength calibration lines. J. Opt. Soc. Am. B 17, (2000). [5] Coddington, I., Swann, W.C. & Newbury, N.R. Coherent multiheterodyne spectroscopy using stabilized optical frequency combs. Phys. Rev. Lett. 100, (2008). [6] Swann W.C., & Gilbert, S.L., Line centers, pressure shift, and pressure broadening of nm hydrogen cyanide wavelength calibration lines. J. Opt. Soc. Am. B 22, (2005). [7] Zolot, A.M., et al. Broad-band frequency references in the near-infrared: Accurate dual comb spectroscopy of methane and acetylene. J. Quant. Spectrosc. Radiat. Transfer 118, (2013). NATURE PHOTONICS 11

12 [8] Madej A.A, et al. Accurate absolute reference frequencies from 1511 to 1545 nm of the ν 1 +ν 3 band of 12 C 2 H 2 determined with laser frequency comb interval measurements, J. Opt. Soc. Am. B 23, (2006). [9] Baumann, E. et al. Spectroscopy of the methane ν 3 band with an accurate midinfrared coherent dual-comb spectrometer. Phys. Rev. A 84, (2011). [10] Okubo, S. et al. Absolute frequency list of the ν 3 -band transitions of methane at a relative uncertainty level of 10 11, Opt. Express 19, (2011). [11] Okubo, S. et al. Ultra-broadband dual-comb spectroscopy across µm, Appl. Phys. Express 8, (2015) [12] Yasui, T. et al. Adaptive sampling dual terahertz comb spectroscopy using dual free-running femtosecond lasers, Sci. Rep. 5, (2015) [13] Pickett, H.M. et al. Submillimeter, millimeter, and microwave spectral line catalog. J. Quant. Spectrosc. Radiat. Transf. 60, (1998). 12 NATURE PHOTONICS

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