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Abstract
Free-running dual-comb systems based on a single laser cavity are an attractive next generation technology for a wide variety of applications. The high average power achievable by dual-comb thin-disk laser (TDL) oscillators make this technology especially attractive for spectroscopy and sensing applications in the molecular fingerprint region enabled by nonlinear frequency conversion. However, the high noise levels of TDL oscillators, e.g., induced by the turbulent water-cooling of the disk, are a severe challenge for spectroscopic applications. In this contribution, we confirm for the first time the suitability of dual-comb TDLs for high-resolution spectroscopy. Based on the novel concept of polarization splitting inside a TDL, our oscillator generates two asynchronous pulse trains of 240-fs pulse duration at 6-W and 8-W average power per pulse train and ∼97-MHz repetition rate at a central wavelength of 1030 nm. In the first detailed noise investigation of such a system, we identify the repetition frequency as the dominant noise term and show that ∼85% of the frequency noise of the comb lines of both pulse trains is correlated (integrated from 200 Hz to 20 kHz). We detect the absorption spectrum of acetylene in free-running operation within a measurement time of 1 millisecond. Being highly suitable for nonlinear frequency conversion, we believe the here presented result is an important step towards simple yet powerful mid-infrared dual-comb systems for high-resolution spectroscopy.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Dual-comb multi-heterodyne spectroscopy is a powerful tool to retrieve high-resolution spectral information in very short measurement times, which has opened up numerous new opportunities for science and technology [1–3].The basic concept relies on the optical beating of two frequency combs with slightly different mode spacing, as e.g. generated by the output of two mode-locked lasers of slightly different repetition rate [4–13]. The achievable spectral resolution and accuracy of such a system then depends on the mutual frequency stability of both mode-locked lasers. One direction for improving the spectral resolution by allowing longer measurement times is based on active stabilization of the two lasers [6,9,12]. This, however, generally increases the complexity of the overall system. Another approach is the generation of the two required pulse trains directly from a single laser cavity. As most cavity components are shared, most of the frequency noise in both pulse trains is common and cancels out in the beating process which facilitates dual-comb spectroscopy in free-running operation. Various dual-comb systems based on a single mode-locked laser cavity have been successfully demonstrated, including Ti:sapphire [14], fiber [15–18], semiconductor [19,20], and recently diode-pumped bulk [21,22], as well as thin-disk [23] lasers. The different previously developed approaches can be divided into bi-directional [14,17,18], dual wavelength [15,16], spatial [23], and birefringent polarization multiplexing [19–22]. Whereas all these systems operate in the near-infrared spectral range, the molecular fingerprint region of interest for most spectroscopy applications lies in the mid-infrared [24]. To access these wavelengths by nonlinear frequency conversion processes, such as difference frequency generation [5,7,8,17] or using optical parametric oscillators [6,9–13], a sufficiently high pulse energy in combination with a high repetition rate for frequency comb application is an essential ingredient. From this perspective, ultrafast thin-disk laser (TDL) oscillators are very promising, since they deliver in combination of pulse energy (Ep) and repetition rate (frep) the highest average power (Pave = Ep · frep) of any laser oscillator technology.
Recently, Fritsch et al. [23] demonstrated the first dual-comb TDL achieving more than an order of magnitude higher average power compared to other dual-comb approaches. By spatial separation utilizing four cavity end mirrors, the Kerr lens mode-locked (KLM) Yb:YAG TDL generated two asynchronous pulse trains of 300-fs pulse duration and 12-W average power per pulse train at 61-MHz repetition rate and a central wavelength of 1030 nm. A proof-of-principle free-running dual-comb transmission measurement of an etalon confirmed a passive correlation between both pulse trains. However, a drawback of current TDLs is their high noise level compared to other laser technologies, which is mainly caused by the turbulent water-cooling of the disk. The resulting jitter of the comb lines might severely restrict their applicability.
Here, we show for the first time the suitability of dual-comb TDLs for high-resolution spectroscopy in free-running operation by detecting the absorption spectrum of acetylene within a measurement time of ∼1 millisecond. Our presented novel dual-comb approach is based on polarization splitting inside an ultrafast TDL oscillator. Our concept improves the passive noise correlation by supporting a closer propagation of both laser modes along the shared cavity components and by reducing the number of unshared cavity components compared to the spatial separation approach. We present the first detailed noise investigation of such a system and identify frep as the dominant noise term. In our system, ∼85% of the frequency noise contributing to the comb linewidth of both pulse trains according to the β-separation line approximation [25,26] is correlated (integration over Fourier frequencies ranging from 200 Hz to 20 kHz).
2. Experimental setup
Our dual-comb TDL [Fig. 1(a)] is based on a ∼100-μm-thick diamond-mounted Yb-doped disk (Trumpf GmbH). The disk is pumped at a wavelength of 969 nm with a volume-Bragg-grating-stabilized high-power fiber-coupled pump diode system (D4F6L22-969.(0,6)-300C-IS43.10 from Dilas Diodenlaser GmbH) on a spot diameter of 2.9 mm. A thin-film polarizer (TFP) placed at Brewster’s angle enables the polarization selection and the spatial separation of both laser modes. The TFP is a single-side-coated 2-mm-thick fused-silica plate that reflects the s-polarization and transmits the p-polarization into separate beam paths of ∼15-cm geometrical length. For pulse formation, the standard Kerr lens mode-locking scheme of TDLs is applied [27]. The cavity design follows the approach presented in Ref. [28]. Accordingly, an intracavity focus is created between two highly-reflective (HR) mirrors of 250-mm concave radius of curvature (RoC). A 6-mm-thick undoped anti-reflection-coated YAG plate acts as Kerr medium for both laser polarizations and is placed at normal incidence in the vicinity of the intracavity focus. Two copper plates with a round hole of about 1.7-mm diameter in front of each HR cavity end mirror act as hard apertures and suppress the onset of higher order modes. The position of the laser modes on the disk is adjusted individually by the corresponding cavity end mirror. The spatial separation of both laser modes on the disk is required to avoid gain competition, enabling stable mode-locked operation [inset Fig. 1(a)]. Along the shared cavity components, this spatial separation is smaller than 2 mm that makes the use of a separate hard aperture for each arm necessary. Overlapping both beams in mode-locked operation on the same position of the pump spot disturbed the mode-locking and resulted in a switch to continuous-wave lasing. Depending on their absolute overlap either of the two arms stopped lasing. Two dispersive mirrors introduce a total negative group delay dispersion of -8000 fs2 per cavity roundtrip. Both pulse trains share the same output coupler with a transmission of 7.4%. The difference in repetition rate between both pulse trains (Δfrep = | frep,1 – frep,2 |) is freely tunable from zero up to several hundred kHz by varying the position of one cavity end mirror. The optical coating of the TFP, the Kerr medium, as well as the dispersive and HR mirrors are designed in-house and grown using our ion-beam sputtering coating facility.
Fig. 1. (a) Schematic of the dual-comb thin-disk laser oscillator based on polarization splitting. A thin-film polarizer (TFP) in the cavity enables closing two cross-polarized laser cavities by the individual end mirrors. All other cavity mirrors as well as the thin disk are shared. (inset) Image of the pump spot on the disk with depleted areas by both laser modes. (b) Auto-correlation trace and (c) optical spectrum of both pulse trains with fit for sech2 soliton pulses. AR-KM: anti-reflection-coated Kerr medium; CM: curved mirror; DM: dispersive mirror; HA: hard aperture; HR: highly reflective mirror; OC: output coupler.
Pulse formation in both cavity arms is initialized by a gentle knock on the laser table. Two soliton pulse trains with a full-width at half-maximum (FWHM) pulse duration of 240 fs [Fig. 1(b)], centered at a wavelength of 1030 nm and with a FWHM spectral bandwidth of 5.5 nm [Fig. 1(c)], are generated at 97-MHz repetition rate. The average power amounts to 6 W and 8 W for the p- and s-polarized arm, respectively, corresponding to pulse energies of 60–80 nJ or peak powers of 220–300 kW. For a pump power of 150 W, the resulting overall optical-to-optical efficiency of 9% is reasonable as only a fraction of the total pumped area on the disk is being depleted by both laser modes [inset Fig. 1(a)]. The difference in the performance between both arms is attributed to the TFP. The mechanical stress induced by the single-sided coating causes a concave 20-m RoC of the 2-mm-thick substrate affecting the p-polarization in transmission and s-polarization in reflection.
3. Noise investigation
The frequency of an optical line (νN) generated by the output of a mode-locked laser is fully determined by the comb equation νN = N·frep + fCEO, where frep and fCEO are the repetition frequency and carrier-envelope offset (CEO) frequency, respectively. The width of an optical line is affected by the frequency noise contribution of the scaled repetition frequency (N·frep), with N being the corresponding mode number, and the noise contribution of the CEO frequency, as well as by their mutual correlation. Before investigating the frequency noise of all three terms of the comb equation [Fig. 2], the TDL has been experimentally optimized for low-noise operation. This includes the use of fixed (FMP1 from Thorlabs Inc.) as well as highly-stable mirror mounts (RD2-HS from Radiant Dyes Laser & Accessories GmbH) and the acoustical isolation of the laser against environmental noise. A low-pass RC-filter with a cut-off frequency of 7 Hz (see Ref. [29]) attenuates the noise imprinted by the high-current DC source onto the pump diode. The thin-disk head is mechanically isolated from the other cavity components on the breadboard and the water-flow on the disk is reduced to 0.6 l/min, since it was identified as the main source of mechanical noise in the 200-Hz to 2-kHz frequency range. Despite the comparably low water flow on the disk, the system operates stable over several hours after an overall warm-up time of about 20 minutes. However, the isolation of the head resulted in higher noise components in the lower frequency range below 200 Hz [Fig. 3(a)]. The reduction of these noise components will be the focus of future studies and could also be realized by active stabilization of the cavity lengths, e.g. for both arms together via a shared mirror or separately via the individual cavity end mirrors. As dual-comb spectroscopy measurements can be typically performed within a few millisecond-timescale these lower frequency noise components are not significant and they will not be considered in the following analysis.
Fig. 2. Setups for the frequency-noise investigation of (a) the repetition frequency (frep), (b) the carrier-envelope offset frequency (fCEO) and (c) an optical line (νN). The uncorrelated noise of νN and frep between the two pulse trains is accessed via difference frequency mixing of both individually detected radio-frequency (RF) signals as indicated in the dashed boxes. The phase-noise analyzer is a R&SFSWP26. AMP: RF amplifier; ATT: attenuator; BP: band-pass filter; LP: low-pass filter; PCF: photonic-crystal fiber; PD: photodiode; TFP: thin-film polarizer.
Fig. 3. Frequency noise power spectral density (FN-PSD) of (a) the individually comb frequencies and (b) the uncorrelated noise of N·frep and νN in comparison to the noise of the p-polarized comb frequencies. (c) FWHM linewidth of various comb components estimated by the β-separation line method [25,26]. (d) Timing jitter calculated from the FN-PSD of νN. Integration boundaries mentioned in the text are indicated as vertical dashed lines and labeled correspondingly.
Figure 2 shows the frequency-noise measurement schemes. The frequency noise of frep is determined at the 103rd harmonic (∼10 GHz) to increase the measurement sensitivity with respect to the shot-noise limit [Fig. 2(a)]. The Δfrep is set to 200 kHz in order to measure the uncorrelated frep noise at a mixed frequency fmix of ∼20 MHz after difference mixing both individually detected frep harmonics (fmix = | 103·frep,1−103·frep,2 |) [Fig. 2(a), dashed box]. In the difference mixing process, common frequency-noise cancels out and only noise components present in either of both arms are detected. The frequency noise of fCEO is investigated for the p-polarized arm only [Fig. 2(b)]. After temporally-compressing the pulses with a small fraction (∼200 mW) of the available average power and supercontinuum generation in a photonic crystal fiber, the fCEO beat note is detected in a common-path f-to-2f interferometer [30] (same fiber and interferometer as used in [29]) [Fig. 2(b)]. The νN noise is accessed by beating each pulse train with a frequency-stabilized single-longitudinal-mode continuous-wave (cw) laser [Fig. 2(c)]. The cw-laser is a CTL 1050 from TOPTICA Photonics AG which is stabilized to an optical reference from SILENTSYS SAS. The uncorrelated νN noise is assessed via difference frequency mixing of both individually-detected beat notes [Fig. 2(c), dashed box].
Figure 3(a) shows the individual components in terms of frequency noise power spectral density (FN-PSD). The N·frep noise curves are obtained by scaling the FN-PSD measured for frep by the square of a mode number N ≈ 3’000’000 corresponding to the central laser frequency. The N·frep noise curves of both pulse trains show an almost identical behavior up to the limiting shot-noise level of the photodiodes at ∼1 kHz. The peaks in the upper frequency range (>5 kHz) are detection artefacts attributed to the amplitude-to-phase noise coupling in the photodiodes. The measured fCEO noise is up to several orders of magnitude lower in comparison to the N·frep noise, thus, having negligible influence on the optical linewidth. It can be considered as an upper limit as additional frequency noise might have been introduced into the fCEO during the nonlinear pulse compression and supercontinuum generation. The dominant impact of the N·frep noise is confirmed by measuring the noise of the optical line νN, which almost exactly follows the N·frep curves up to their shot-noise limit at a frequency of 1 kHz.
The uncorrelated noise curves of frep and νN represent noise components being present only in one of both arms [Fig. 3(b)]. Their much lower values compared to the corresponding individual noise components indicate a high amount of correlation between both pulse trains. However, the measurement reveals two uncorrelated peaks present in either of both arms (in the range between 500 Hz to 1 kHz). These peaks cause a walk off between the comb lines of both frequency combs and limit the measurement time to 1 millisecond. Their origin is believed to be related to the water-cooling of the thin disk. The development of a low-noise cooling concept is expected to reduce the overall amount of the individual and the uncorrelated noise.
For better quantification of the noise in the system, the contribution of each noise component to the FWHM optical linewidth of the comb lines is estimated using the β-separation line approximation [25,26]. In this approximation, frequency noise components below the β-line [Fig. 3(a-b), black dashed line] do not contribute to the linewidth of the comb lines. The FN-PSD of N·frep and νN results in linewidths of ∼30 kHz and ∼28 kHz (integrated from 200 Hz to 1 kHz), respectively. In comparison, the corresponding fCEO linewidth of ∼3 kHz over the same integration range amounts to only 10% of the value calculated for N·frep. The noise correlation between both pulse trains is determined by comparing the estimated FWHM linewidth (integrated from 200 Hz to 20 kHz) obtained for the uncorrelated νN noise (∼4.6 kHz) with the value achieved of ∼32 kHz corresponding to the individual νN noise contributions. Thus, about ∼85% of the νN noise is correlated between both pulse trains.
For a comparable quantification of the noise correlation in the time domain, the timing jitter is calculated using the FN-PSD curves of νN which follow the frep curves but are not shot-noise limited [Fig. 3(d)]. While each pulse train jitters by about 28 fs, the relative jitter between both pulse trains amounts to <2 fs (integrated from 200 Hz to 20 kHz).
Overall, the noise investigation shows that the system is dominated by a highly correlated technical noise in the repetition rate. We expect that with an improved low-noise thin-disk cooling concept and a better isolation of the system against environmental perturbations these technical noise components can be strongly reduced especially in the lower frequency range and their passive correlation further improved. However, if the measurement time of the current system is limited in the order of ∼1 millisecond (i.e., integrating from 1 kHz to 20 kHz), optical linewidths of <2 kHz can be expected. The corresponding timing jitter of each pulse train remains less than 1 fs.
4. Dual-comb spectroscopy of acetylene
The outcome of the noise analysis is confirmed by a free-running dual-comb spectroscopy measurement of acetylene (C2H2). In the setup (depicted in Fig. 4), both pulse trains are overlapped in two polarizing beam splitters and spectrally narrowed to a detectable width of ∼1 nm by an etalon to avoid spectral aliasing (M·Δfrep ≤ frep/2, with M being the number of detected optical lines). A rotation of the etalon allows for tuning of the selected central wavelength. The overlapped beams are split between a reference arm, a sample arm containing the gas cell filled with 1’000 mbar pure C2H2, and an auxiliary cw-laser beat arm. Typical radio-frequency (RF) spectra are shown in the insets of Fig. 4 after Fourier transformation of the simultaneously recorded corresponding ∼1-ms time traces. The auxiliary cw-laser beat notes (fBN,cw1, fBN,cw2) facilitate the remapping of the detected RF beat notes into the optical domain. They enable to assign the optical frequency of the stabilized cw-laser (νcw) to its corresponding frequency in the RF spectrum (fcw = fBN,cw2 ± fBN,cw1, fcw ≙ νcw). The frequencies of the beat notes in the RF spectrum (fBN) can so be remapped into the optical domain by the scaling factor frep/Δfrep via νBN = νcw ± (fBN - fcw) · frep/Δfrep. The value of νcw is determined separately by a 771A Laser Spectrum Analyzer from Bristol Instruments with a spectral accuracy of ± 60 MHz (± 0.0002 nm).
Fig. 4. Schematic setup of the acetylene dual-comb spectroscopy. After attenuating and overlapping both cross-polarized pulse trains, the optical spectrum is narrowed by an etalon to a detectable spectral bandwidth of ∼1 nm (∼0.3 THz, ∼9 cm-1). The spectrally-narrowed pulse trains are then split into three arms of ∼1 mW of average power each and beat on separate photodiodes (DET10C/M from Thorlabs Inc.). The amplified (DHPCA-100 from Femto Messtechnik GmbH) and low-pass filtered time traces are detected simultaneously using a multi-channel sampling card at a sampling rate of 125 MS/s and 14-bit resolution (PicoScope 5444D MSO from Pico Technology Ltd). (insets) Typical RF spectra of the reference, sample, and cw-laser beat arm after Fourier transformation of a recorded 1-ms time trace shown for a Δfrep of 20 kHz. AMP: radio-frequency amplifier; LP: low-pass filter; PD: photodiode; PBS: polarizing beam splitter; λ/2: half-wave plate, Δfrep: difference in the repetition rate, fBN,cw1, fBN,cw2: auxiliary cw-laser beat notes.
Figure 5 shows a zoom into a typical burst recorded in the (a) reference and (b) sample arm. Fourier transformation of the recorded consecutive bursts results in resolving equally-spaced beat notes [Fig. 5(c-d)]. Here, they are shown for two different values of Δfrep with corresponding beat-note spacing. Their FWHM linewidth of ∼2 kHz is resolution-limited by the ∼1-ms measurement time but agrees with the value expected from the noise investigation. Finally, the acetylene absorption spectrum is obtained by normalizing the resolved beat notes of the sample arm by the reference arm and remapping the beat-note frequencies into the optical domain utilizing the cw-laser beat-note frequencies [Fig. 5(e)]. The measurement is in good agreement, both in position and relative transmission, with the reference spectrum calculated from the HITRAN database [31]. More advanced data post-processing to improve the signal-to-noise ratio can still be applied.
Fig. 5. Zoom into a typical burst recorded in the (a) reference and (b) sample arm (detected separately on a single channel of the sampling card with a sampling rate of 500 MS/s and 12-bit resolution). (c) and (d) are zooms into the RF spectra obtained by Fourier transformation of consecutive interferograms recorded in a time of about 1-ms for two different Δfrep (detected with 125 MS/s and 14-bit). (e) Experimental absorption spectrum of acetylene obtained by dual-comb spectroscopy (DCS) with a moving average over N datapoints in comparison to the reference spectrum calculated from the HITRAN database [31]. Δfrep: difference in the repetition rate; Δt: sampling time interval.
5. Conclusion
In conclusion, we have confirmed the suitability of free-running dual-comb thin-disk lasers for high-resolution spectroscopy by detecting the absorption spectrum of acetylene. A detailed noise study revealed frep as the dominant noise contribution and showed that ∼85% of the frequency noise contributing to the linewidth of the comb lines of both pulse trains is correlated (integrated from 200 Hz to 20 kHz). We expect that further reduction of the overall and uncorrelated noise is feasible by developing a low-noise thin-disk cooling concept.
We believe that the here presented power-scalable dual-comb TDL based on polarization splitting will soon operate at several tens of watt of average power per arm and a few hundred megahertz repetition rate [32]. We think these sources are highly attractive for driving nonlinear frequency conversion into the mid-infrared region and will become a versatile tool for dual-comb applications.
Funding
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (144970, 170772, 179146).
Acknowledgments
The authors thank U. Keller, C.R. Phillips and L.M. Krüger from the Ultrafast Laser Physics group (ETH Zürich) for lending the “CTL 1050” cw-laser to our research group.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are available in Ref. [33].
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