# Femtosecond optical parametric oscillators toward real-time dual-comb spectroscopy

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## Abstract

We demonstrate mid-infrared dual-comb spectroscopy with an optical parametric oscillator (OPO) toward real-time field measurement. A singly resonant OPO based on a MgO-doped periodically poled lithium niobate (PPLN) crystal is demonstrated. Chirped mirrors are used to compensate the dispersion caused by the optical cavity and the crystal. A low threshold of 17 mW has been achieved. The OPO source generates a tunable idler frequency comb between 2.7 and 4.7 μm. Dual-comb spectroscopy is achieved by coupling two identical Yb-fiber mode-locked lasers to this OPO with slightly different repetition frequencies. A measured absorption spectrum of methane is presented with a spectral bandwidth of \(300\,\hbox {cm}^{-1}\), giving an instrumental resolution of \(0.4\,\hbox {cm}^{-1}\). In addition, a second OPO containing two MgO-doped PPLN crystals in a singly resonant ring cavity is demonstrated. As such, this OPO generates two idler combs (average power up to 220 mW), covering a wavelength range between 2.7 and 4.2 μm, from which a mid-infrared dual-comb Fourier transform spectrometer is constructed. By detecting the heterodyned signal between the two idler combs, broadband spectra of molecular gases can be observed over a spectral bandwidth of more than \(350\,\hbox {cm}^{-1}\). This special cavity design allows the spectral resolution to be improved to \(0.2\,\hbox {cm}^{-1}\) without locking the OPO cavity, indicating that this OPO represents an ideal high-power broadband mid-infrared source for real-time gas sensing.

## Keywords

Optical Parametric Oscillator Group Velocity Dispersion Frequency Comb Periodically Pole Lithium Niobate Idle Beam## 1 Introduction

Laser absorption spectroscopy plays an important role in a variety of applications including industrial processing control, biomedical research, frequency metrology, and environmental monitoring. Due to the development of new laser sources and novel technologies, measurement performances continue to improve dramatically in terms of sensitivity, signal-to-noise ratio (SNR), spectrum bandwidth, frequency accuracy, and acquisition speed. Although the research on laser spectroscopy flourishes, it is still a challenge to achieve high-performance broadband measurements in a single experiment over a second timescale. Conventionally, Fourier transform spectroscopy (FTS) is the solution for such broadband measurements, from visible to far-infrared [1]. However, due to the moving mechanical part in the spectrometer and the low brightness of the light source, minutes to hours acquisition time is needed to reach a high spectral resolution and high SNR. On the other hand, wavelength modulation and frequency modulation spectroscopy based on continuous-wave (CW) lasers are typical techniques for sensitive trace gas detection with possible measurement time of 1 s. However, within these approaches, only a small portion of the wavelength region can be covered, limiting these methods for real-time applications of multi-gas detection [2]. Since its invention in the late 1990s, frequency combs have revolutionized optical frequency metrology [3], but also provide new opportunities for other applications, especially for gas detection based on laser absorption spectroscopy [4]. A single optical frequency comb source can be treated as a coherent superposition of hundreds of thousands of CW lasers, and it is noted to be an ideal source for laser spectroscopy in terms of high spectral power, broad spectral bandwidth, high coherence, and frequency accuracy [5]. Several demonstrations of direct frequency comb spectroscopy (DFCS) have been reported, employing a single frequency comb laser source combined with various detection methods [6, 7, 8, 9, 10, 11, 12, 13, 14, 15]. Among them, a quantum-noise-limited absorption sensitivity of \(1.7 \, \times 10^{-12}\,\hbox {cm}^{-1}\) per spectral element at 400 s of acquisition time is achieved, based on a cavity-enhanced DFCS combined with a fast-scanning Fourier transform spectrometer [8]. The development of dual-comb FTS overcomes the disadvantages caused by the moving mechanical part in a conventional FTS and gives an opportunity for simultaneous measurement of dispersion and absorption spectra of gas samples [16, 17, 18, 19, 20, 21, 22]. Due to the requirement of optical frequency stability, most experimental work on frequency comb sources has been performed in metrology laboratories. Although the operation of an optically coherent frequency comb outside the metrology laboratory has been demonstrated [23], it is still a long way before dual-comb spectroscopy could be used in realistic field measurements. One proposed solution is adaptive real-time dual-comb spectroscopy, which opens a door for real-time field measurement [24]. In this case, tight locking of both dual-comb sources is not needed due to the applied phase correction of the recorded interferogram and compensation for the jittering of the repetition frequencies. The advantage is that an alignment-free averaging process of the retrieved spectra is allowed and that the complexity of the signal processing is simplified, increasing the SNR dramatically. As such, most demonstrations of this technique have been done in near-infrared region.

Extension of the wavelength region of the optical frequency comb source is an ongoing research field for different applications both in industrial and in academic fields, as most commercial frequency comb sources cannot go beyond 2 μm. To date, frequency comb sources can be extended to the extreme ultraviolet [6], mid-infrared [25, 26, 27, 28, 29, 30, 31], and terahertz regions [32, 33]. Specifically, for trace gas sensing applications, the wavelength region between 2 and 20 μm is of great interest, as gases, liquids, and solids have unique absorption and dispersion features in this region, associated with their molecular rotational–vibrational transitions. For mid-infrared dual-comb spectroscopy, the light sources are mainly based on different frequency generation (DFG) and optical parametric oscillation [34, 35, 36]. The advantage of DFG sources is that the offset frequency of the comb is passively locked to zero and that only the stabilization of the repetition frequency needs to be considered for mid-infrared frequency comb generation. DFG-based dual-comb systems have provided accurate spectral measurements around 3.4 μm [34]. However, microwatt power levels and the relatively narrow spectral bandwidth of the DFG source can limit its spread in applications such as real-time multi-compound detection in complex gas mixtures. In addition, it is not possible to lock the DFG comb source to a cavity to increase the sensitivity.

In this paper, we demonstrate two different OPO-based dual-comb systems, both offering hundreds of milli-Watts of mid-infrared output power. Both systems have high potential to be integrated to a cavity-enhanced method, to increase the detection sensitivity [15, 37]. The two-crystal OPO cavity has shown to be a reliable source for rapid broadband, and mid-infrared absorption and dispersion measurements.

## 2 Theories

### 2.1 Dual-comb Fourier transform spectroscopy

### 2.2 Femtosecond optical parametric oscillator

Figure 3 gives a simplified representation on how the signal frequencies are generated and synchronized by the pump comb. For simplicity, only three successive comb lines (colored in black, red, and blue) from the pump are drawn. The signal frequencies for perfect phase-matching are presented as the dotted three comb lines, together with their parametric gain bandwidths. In practice, there are hundreds of thousands of signal comb lines and their parametric gain bandwidths which are overlapping. For femtosecond pump lasers, the duration of the pulse for which all combs lines are in phase is tens of femtoseconds, causing MW peak power of the pulse, which is needed for efficient nonlinear generation. In the frequency domain, all the depleted pump comb lines contribute to each individual signal comb line because all of the signal parametric gain bandwidths are overlapped. The free spectral range (FSR) of the OPO is equal to the FSR of the pump, as is the case for a synchronized OPO. The synchronization is inherently determined by the group velocity of the signal pulses, indicating that the signal frequencies can be tuned by changing the cavity length due to the fact that the group velocity is determined by the central wavelength of the signal light. One consequence of this is that a single OPO can be pumped by two mode-locked lasers with slightly different repetition frequencies, as long as the two signals have slightly different group velocities. This difference in group velocities is determined by the difference in central wavelengths between the two pump depletions; hence, it is possible to employ a single OPO for mid-infrared dual-comb spectroscopy. In the following two sections, we introduce two experimental setups with a single OPO for mid-infrared dual-comb spectroscopy.

## 3 Dual-comb FTS with a single-crystal OPO

### 3.1 Configuration of the single-crystal OPO

The spectral properties of the OPO are analyzed by a rapid-scanning Fourier transform spectrometer (Bruker Vertex 70), which offers a spectral resolution of \(0.16\,\hbox {cm}^{-1}\) (4.8 GHz). Idler spectra, recorded at a resolution of \(2\,\hbox {cm}^{-1}\), are illustrated in Fig. 5a, for the available seven poling periods of the PPLN crystal. The maximum spectral width of the idler is 300 nm (\(272\,\hbox {cm}^{-1}, \, 1/\hbox {e}\) value), centered at 3.3 μm. In the same panel, the OPO threshold for the different periods is shown. To achieve low threshold with narrow pulse duration, the crystal length and the intra-cavity dispersion management are crucial. The PPLN crystal has very large positive GVD in the signal wavelength region that causes prominent pulse-broadening effects. The GVD mismatch in the crystal between pump and signal pulses also causes a less efficient parametric process for this crystal length. With the 5-mm-long crystal, a very low threshold of 17 mW is obtained around 3.5 μm. With this crystal period and a maximum pump power of 1.6 W, the idler power reaches 250 mW, representing a pump-to-idler conversion efficiency of 16%. At longer wavelengths, the threshold increases, due to the reduced reflectivity of the cavity mirrors for the signal light and the increased absorption in the PPLN crystal [41, 42].

The fastest way to tune the wavelength of the OPO is to change the cavity length. The effect of the cavity length tuning on the optical spectrum is depicted in Fig. 5b. Each spectrum is the instantaneous laser emission for a given crystal period and given cavity length. As the OPO is synchronously pumped by a broadband source, while changing the cavity length over a few microns, the signal (and therefore also the idler) will shift in frequency to maintain the same round-trip time for the pulses in the cavity, corresponding to the repetition rate of the pump source. The variation in the shape of the spectrum has two origins: the variations in the mirror GVD across the tuning range and the lasing effect among various transverse modes within the OPO. Meanwhile, a variety of non-phase-matched, higher-order mixed waves between pump, signal, and idler are emitted along with the signal \((s)\) and idler \((i)\).

### 3.2 Experimental setup of the FTS

### 3.3 Results

## 4 Dual-comb FTS with a two-crystal OPO

### 4.1 Experimental setup

To solve the issues mentioned in the previous section, a two-crystal OPO within a ring cavity is introduced; more details of this OPO can be found in [36]. Within the OPO, two 5-mm-long PPLN crystals are used for optical frequency conversion to generate two idlers that are spatially separated. To establish the resonance of the signal pulses, a 3.4-m-long cavity composed of six chirped mirrors is designed to be synchronously pumped at 1,040 nm. The spectral range of the idler in this configuration extends from 2,300 to \(3,600 \,\hbox {cm}^{-1}\) by tuning the poling periods of the crystal. The spectral bandwidth for a single period is \(400 \,\hbox {cm}^{-1}\), centered at \(3,080\,\hbox {cm}^{-1}\); at this point, the full range of vibrational transitions of methane can be found.

The experimental setup of the dual-comb spectrometer is shown in Fig. 9. The implementation of the repetition frequency locking is for the sake of long-term frequency stability while the offset frequencies of the two combs are free-running. The repetition frequencies of the two pump lasers are both locked by synchronizing to a frequency synthesizer with a difference of 201.25 Hz between them. This locking scheme simplifies the signal processing as every two successive interferograms have a constant time delay. One idler beam (i1) transmits through a 15-cm-long cell and is recombined with the second idler beam (i2) at a beam splitter. The focused light can be detected by a Peltier-cooled fast infrared detector, giving the heterodyned signal for further Fourier analysis. A field-programmable gate array (FPGA) board is used for real-time digital signal processing and establishing a high throughput data streaming from the FPGA board to the computer storage for post-processing.

### 4.2 Results

Figure 11b presents the corresponding Fourier transform power spectrum of the interferogram with a RF resolution of 15 kHz. The FPGA board streams the digitized real-time signal to the computer during 0.1 s (25M samples at 16-bit amplitude resolution) for post-averaging. Concerning the spectral stability of the system, in the case of femtosecond fiber lasers, the line width of the free-running offset frequency is normally hundreds of kilohertz. For an OPO-based mid-infrared frequency comb, the stability of the free-running offset frequency is worse due to the optical resonator open to air fluctuations. This frequency instability causes troubles when the RF spectra need to be averaged to increase the SNR, as every RF component retrieved from the FFT calculation does not always represent the same optical frequencies due to the instability of the offset frequency. The consequences are the broadening effect of the absorption lines and a frequency shift of the retrieved RF spectrum. In our case, to process the data, the 20 spectra calculated by the interferograms within 0.1 s are averaged after the alignment of the absorption peaks. In Fig. 12, the upper panel shows the measured absorption spectrum (blue curve) with 0.1 s averaging after background removal, which is normalized to compare with the HITRAN database (red curve). The \(P\), \(Q\) , and \(R\) branches of the \(v_3\) vibrational transitions of methane can clearly be observed between 2,850 and \(3,200\,\hbox {cm}^{-1}\), giving a bandwidth of more than \(350\,\hbox {cm}^{-1}\) and a resolution of \(0.2\,\hbox {cm}^{-1}\). The noise equivalent absorption sensitivity (1 s averaging per spectral element) calculated from the absorption signal is \(6.2\times 10^{-6}\,\hbox {cm}^{-1}\,\hbox {Hz}^{-1/2}\) (\(5.3\times 10^{-7}\,\hbox {cm}^{-1}\,\hbox {Hz}^{-1/2}\) considering only the recording time). The achieved sensitivity is limited due to the usage of the short single-pass cell and the single infrared detector. The implementation of a cavity-enhanced technique and auto-balanced detector can dramatically increase the efficient optical pass length and the SNR. Quantum-noise-limited results were achieved in the case of direct frequency comb Fourier transform spectroscopy [8]. The difference in repetition frequencies, acquisition rate, and the amount of data points for FFT calculation determines the resolution of the retrieved spectra and the recording time. The lower panel of Fig. 12 shows the dispersion information retrieved from the same measurement, which is immune to the intensity fluctuations of the idler, as the intensity fluctuations do not affect the phase information within the two idlers combs. The spectral resolution can be improved by either increasing the difference between two repetition frequencies, or calculating more data points for each interferogram, but the trade-off is a lower SNR. To increase SNR, an auto-balanced detector is an option; otherwise, the spectra need to be averaged over time to improve the SNR.

### 4.3 Discussion

The proposed two-crystal OPO cavity has several advantages for dual-comb spectroscopy. Both generated idlers originate from the same OPO cavity experiencing identical disturbances, such as mirror vibrations and air or oven temperature fluctuations. As a consequence, the common OPO cavity cancels out much of the instability compared to using two separate OPOs as dual-comb sources. The frequency of idlers can be expressed by \(f^1_{\rm i} = f^1_{\rm p} - f^1_{\rm s}\) and \(f^2_{\rm i} = f^2_{\rm p} - f^2_{\rm s}\) for comb 1 and comb 2, respectively. The frequency of one beating note between two idlers can then be calculated as \(f^1_{\rm i} - f^2_{\rm i} = (f^1_{\rm p} - f^2_{\rm p})- (f^1_{\rm s} - f^2_{\rm s})\), which simplifies to \(\Delta f_{\rm i} = \Delta f_{\rm p} - \Delta f_{\rm s}\). As commercial pump lasers have good short-term stability, the instability of the radio frequency spectra is mainly due to the term of \(\Delta f_{\rm s}\). The cavity fluctuation affects the central wavelengths of two signal combs in a similar manner, offering a better frequency stability of \(\Delta f_{\rm s}\) than using two separate OPOs when the two offset frequencies are free-running. Moreover, the two signal beams resonating in the optical cavity are counter-propagating and do not affect the generation of the two idler beams. Besides, in comparison with an OPO cavity using a single PPLN crystal for dual-comb spectroscopy, the two-crystal OPO generates two idler beams which are spatially separated, offering an opportunity to measure both absorption and dispersion spectra of gas samples simultaneously. To improve the performance of the spectrometer and to allow a longer averaging time, the offset frequencies of both two combs need to be stabilized, which is a challenging work. A fully stabilized dual-comb system will make possible the realization of real-time, sensitive multi-gas detection. It is worth mentioning that the fast recording time of such mid-infrared spectrometer will be beneficial for observation of molecular interaction kinetics [44].

## 5 Conclusion

We have demonstrated for the first time broadband, mid-infrared dual-comb spectroscopy measuring absorption and dispersion spectra in gas phase simultaneously with a bandwidth of more than \(350\,\hbox {cm}^{-1}\) (2,850– \(3,200\,\hbox {cm}^{-1}\)) and a spectral resolution of \(0.2\,\hbox {cm}^{-1}\). Two different configurations of OPO are tested for dual-comb spectroscopy. The proposed two-crystal, ring cavity OPO exhibits a variety of advantages including access to the dispersion information of samples when compared with a single-crystal OPO. The 0.1-s-averaged results give a dramatic improvement in SNR over a single-shot experiment. The measurement of the optical phase shift due to the target gas sample can offer a variety of advantages over measurements based on absorption sensing. For instance, the linear relationship between the dispersion spectrum and the sample concentration is beneficial; on the contrary, the absorption saturates with increasing concentration [45, 46]. For dual-comb-based spectrometers, as well as for Michelson-based Fourier spectrometers, the dispersion signal is, to some extent, immune to the intensity fluctuations of the light sources and can provide more reliable and accurate background free data than measuring the absorption signal [43, 47]. This advantage is due to the fact that the intensity noise is related to the square of the amplitude of the laser light, while the phase noise is mainly dominated by the frequency stability of the lasers. For a fully stabilized system, the intensity noise dominates compared to the phase noise, indicating the advantages of dispersion measurement. These initial results presented in this paper give a promise for field measurement such as breath analysis and environmental monitoring with advantages of broad bandwidth, fast acquisition time, and high sensitivity.

## Notes

### Acknowledgments

This work is supported by the Technologiestichting STW Foundation (Project No. 11830) and the GO-EFRO “Ultragas-gas analysis system for quality control of agricultural products and medical diagnostics” (Project No. 2009-010034).

## References

- 1.J. Bates, Fourier transform infrared spectroscopy. Science
**191**, 31–37 (1976)CrossRefADSGoogle Scholar - 2.J.M. Supplee, E.A. Whittaker, W. Lenth, Theoretical description of frequency modulation and wavelength modulation spectroscopy. Appl. Opt.
**33**, 6294–6302 (1994)CrossRefADSGoogle Scholar - 3.T. Udem, R. Holzwarth, T.W. Hänsch, Optical frequency metrology. Nature
**416**, 233–237 (2002)CrossRefADSGoogle Scholar - 4.A. Schliesser, M. Brehm, F. Keilmann, D. van der Weide, Frequency-comb infrared spectrometer for rapid, remote chemical sensing. Opt. Expr.
**13**, 9029–9038 (2005)CrossRefADSGoogle Scholar - 5.J. Mandon, G. Guelachvili, N. Picqué, Fourier transform spectroscopy with a laser frequency comb. Nat. Photon.
**3**, 99–102 (2009)CrossRefADSGoogle Scholar - 6.A. Cingoz, D.C. Yost, T.K. Allison, A. Ruehl, M.E. Fermann, I. Hartl, J. Ye, Direct frequency comb spectroscopy in the extreme ultraviolet. Nature
**482**, 68–71 (2012)CrossRefADSGoogle Scholar - 7.S.A. Diddams, L. Hollberg, V. Mbele, Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb. Nature
**445**, 627–630 (2007)CrossRefGoogle Scholar - 8.A. Foltynowicz, T. Ban, P. Masłowski, F. Adler, J. Ye, Quantum-noise-limited optical frequency comb spectroscopy. Phys. Rev. Lett.
**107**, 233002 (2011)CrossRefADSGoogle Scholar - 9.C. Gohle, B. Stein, A. Schliesser, T. Udem, T.W. Hänsch, Frequency comb vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra. Phys. Rev. Lett.
**99**, 263902 (2007)CrossRefADSGoogle Scholar - 10.M.W. Haakestad, T.P. Lamour, N. Leindecker, A. Marandi, K.L. Vodopyanov, Intracavity trace molecular detection with a broadband Mid-IR frequency comb source. J. Opt. Soc. Am. B
**30**, 631–640 (2013)CrossRefADSGoogle Scholar - 11.L. Nugent-Glandorf, T. Neely, F. Adler, A.J. Fleisher, K.C. Cossel, B. Bjork, T. Dinneen, J. Ye, S.A. Diddams, Mid-infrared virtually imaged phased array spectrometer for rapid and broadband trace gas detection. Opt. Lett.
**37**, 3285–3287 (2012)CrossRefADSGoogle Scholar - 12.M.J. Thorpe, D. Balslev-Clausen, M.S. Kirchner, J. Ye, Cavity-enhanced optical frequency comb spectroscopy: application to human breath analysis. Opt. Expr.
**16**, 2387–2397 (2008)CrossRefADSGoogle Scholar - 13.M.J. Thorpe, J. Ye, Cavity-enhanced direct frequency comb spectroscopy. Appl. Phys. B
**91**, 397–414 (2008)CrossRefADSGoogle Scholar - 14.A.M. Zolot, F.R. Giorgetta, E. Baumann, J.W. Nicholson, W.C. Swann, I. Coddington, N.R. Newbury, Direct-comb molecular spectroscopy with accurate, resolved comb teeth over 43 THz. Opt. Lett.
**37**, 638–640 (2012)CrossRefADSGoogle Scholar - 15.A. Foltynowicz, P. Masłowski, A. Fleisher, B. Bjork, J. Ye, Cavity-enhanced optical frequency comb spectroscopy in the mid-infrared application to trace detection of hydrogen peroxide. Appl. Phys. B
**110**, 163–175 (2013)CrossRefADSGoogle Scholar - 16.S. Schiller, Spectrometry with frequency combs. Opt. Lett.
**27**, 766–768 (2002)CrossRefADSGoogle Scholar - 17.I. Coddington, W.C. Swann, N.R. Newbury, Coherent multiheterodyne spectroscopy using stabilized optical frequency combs. Phys. Rev. Lett.
**100**, 013902 (2008)CrossRefADSGoogle Scholar - 18.J. Roy, J.-D. Deschênes, S. Potvin, J. Genest, Continuous real-time correction and averaging for frequency comb interferometry. Opt. Expr.
**20**, 21932–21939 (2012)CrossRefADSGoogle Scholar - 19.F. Zhu, T. Mohamed, J. Strohaber, A.A. Kolomenskii, T. Udem, H.A. Schuessler, Real-time dual frequency comb spectroscopy in the near infrared. Appl. Phys. Lett.
**102**, 121116–4 (2013)CrossRefADSGoogle Scholar - 20.M. Cassinerio, A. Gambetta, N. Coluccelli, P. Laporta, G. Galzerano, Absolute dual-comb spectroscopy at 1.55 μm by free-running Er: fiber lasers. Appl. Phys. Lett.
**104**, 231102 (2014)CrossRefADSGoogle Scholar - 21.I. Coddington, W.C. Swann, N.R. Newbury, Coherent dual-comb spectroscopy at high signal-to-noise ratio. Phys. Rev. A
**82**, 043817 (2010)CrossRefADSGoogle Scholar - 22.F. Keilmann, C. Gohle, R. Holzwarth, Time-domain mid-infrared frequency-comb spectrometer. Opt. Lett.
**29**, 1542–1544 (2004)CrossRefADSGoogle Scholar - 23.L.C. Sinclair, I. Coddington, W.C. Swann, G.B. Rieker, A. Hati, K. Iwakuni, N.R. Newbury, Operation of an optically coherent frequency comb outside the metrology lab. Opt. Expr.
**22**, 6996–7006 (2014)CrossRefADSGoogle Scholar - 24.T. Ideguchi, A. Poisson, G. Guelachvili, N. Picqué, T.W. Hänsch, Adaptive real-time dual-comb spectroscopy. Nat. Commun.
**5**, 3375 (2014)CrossRefADSGoogle Scholar - 25.F. Adler, K.C. Cossel, M.J. Thorpe, I. Hartl, M.E. Fermann, J. Ye, Phase-stabilized, 1.5 W frequency comb at 2.8–4.8 μm. Opt. Lett.
**34**, 1330–1332 (2009)CrossRefADSGoogle Scholar - 26.Z. Zhang, X. Fang, T. Gardiner, D.T. Reid, High-power asynchronous midinfrared optical parametric oscillator frequency combs. Opt. Lett.
**38**, 2077–2079 (2013)CrossRefADSGoogle Scholar - 27.K.A. Ingold, A. Marandi, C.W. Rudy, K.L. Vodopyanov, R.L. Byer, Fractional-length sync-pumped degenerate optical parametric oscillator for 500-MHz 3-μm mid-infrared frequency comb generation. Opt. Lett.
**39**, 900–903 (2014)CrossRefGoogle Scholar - 28.F. Zhu, H. Hundertmark, A.A. Kolomenskii, J. Strohaber, R. Holzwarth, H.A. Schuessler, High-power mid-infrared frequency comb source based on a femtosecond Er: fiber oscillator. Opt. Lett.
**38**, 2360–2362 (2013)CrossRefADSGoogle Scholar - 29.A. Ruehl, A. Gambetta, I. Hartl, M.E. Fermann, K.S.E. Eikema, M. Marangoni, Widely-tunable mid-infrared frequency comb source based on difference frequency generation. Opt. Lett.
**37**, 2232–2234 (2012)CrossRefADSGoogle Scholar - 30.N. Leindecker, A. Marandi, R.L. Byer, K.L. Vodopyanov, Broadband degenerate OPO for mid-infrared frequency comb generation. Opt. Expr.
**19**, 6296–6302 (2011)CrossRefGoogle Scholar - 31.A. Marandi, N.C. Leindecker, V. Pervak, R.L. Byer, K.L. Vodopyanov, Coherence properties of a broadband femtosecond mid-ir optical parametric oscillator operating at degeneracy. Opt. Expr.
**20**, 7255–7262 (2012)CrossRefADSGoogle Scholar - 32.D. Burghoff, T.-Y. Kao, N. Han, C.W.I. Chan, X. Cai, Y. Yang, D.J. Hayton, J.-R. Gao, J.L. Reno, Q. Hu, Terahertz laser frequency combs. Nat. Photon.
**8**, 462–467 (2014)CrossRefADSGoogle Scholar - 33.T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, T. Araki, Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy. Appl. Phys. Lett.
**88**, 241104–3 (2006)CrossRefADSGoogle Scholar - 34.E. Baumann, F.R. Giorgetta, W.C. Swann, A.M. Zolot, I. Coddington, N.R. Newbury, Spectroscopy of the methane \(v_{3}\) band with an accurate midinfrared coherent dual-comb spectrometer. Phys. Rev. A
**84**, 062513 (2011)CrossRefADSGoogle Scholar - 35.Z. Zhang, T. Gardiner, D.T. Reid, Mid-infrared dual-comb spectroscopy with an optical parametric oscillator. Opti. Lett.
**38**, 3148–3150 (2013)CrossRefADSGoogle Scholar - 36.Y. Jin, S.M. Cristescu, F.J.M. Harren, J. Mandon, Two-crystal mid-infrared optical parametric oscillator for absorption and dispersion dual-comb spectroscopy. Opt. Lett.
**39**, 3270–3273 (2014)CrossRefGoogle Scholar - 37.B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T.W. Hänsch, N. Picqué, Cavity-enhanced dual-comb spectroscopy. Nat. Photon.
**4**, 55–57 (2010)CrossRefADSGoogle Scholar - 38.J.A. Armstrong, N. Bloembergen, J. Ducuing, P.S. Pershan, Interactions between light waves in a nonlinear dielectric. Phys. Rev.
**127**, 1918–1939 (1962)CrossRefADSGoogle Scholar - 39.L.E. Myers, R.C. Eckardt, M.M. Fejer, R.L. Byer, W.R. Bosenberg, J.W. Pierce, Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3. J. Opt. Soc. Am. B
**12**, 2102–2116 (1995)CrossRefADSGoogle Scholar - 40.L.E. Myers, W.R. Bosenberg, Periodically poled lithium niobate and quasi-phase-matched optical parametric oscillators. Quantum Electron. IEEE J.
**33**, 1663–1672 (1997)CrossRefADSGoogle Scholar - 41.M.M.J.W. van Herpen, S. Li, S.E. Bisson, F.J.M. Harren, Photoacoustic trace gas detection of ethane using a continuously tunable, continuous-wave optical parametric oscillator based on periodically poled lithium niobate. Appl. Phys. Lett.
**81**, 1157–1159 (2002)CrossRefADSGoogle Scholar - 42.M.M.J.W. van Herpen, A.K.Y. Ngai, S.E. Bisson, J.H.P. Hackstein, E.J. Woltering, F.J.M. Harren, Optical parametric oscillator-based photoacoustic detection of \(\hbox {CO}_2\) at 4.23 μm allows real-time monitoring of the respiration of small insects. Appl. Phys. B
**82**, 665–669 (2006)CrossRefADSGoogle Scholar - 43.J.A. de Haseth, P. Griffiths,
*Fourier Transform Infrared Spectrometry*(Wiley, London, 2007)Google Scholar - 44.A. Fleisher, B. Bjork, T. Bui, K. Cossel, M. Okumura, J. Ye, Mid-infrared time-resolved frequency comb spectroscopy of transient free radicals. J. Phys. Chem. Lett.
**5**, 2241 (2014)CrossRefGoogle Scholar - 45.G. Wysocki, D. Weidmann, Molecular dispersion spectroscopy for chemical sensing using chirped mid-infrared quantum cascade laser. Opt. Expr.
**18**, 26123–26140 (2010)CrossRefADSGoogle Scholar - 46.M. Nikodem, G. Wysocki, Molecular dispersion spectroscopy new capabilities in laser chemical sensing. Ann. N. Y. Acad. Sci.
**1260**, 101–111 (2012)CrossRefADSGoogle Scholar - 47.J. Kauppinen, J. Partanen,
*Fourier Transforms in Spectroscopy*(Wiley, London, 2001)CrossRefzbMATHGoogle Scholar

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