Abstract

This work presents a very simple yet effective way to obtain direct referencing of a quantum-cascade-laser at 4.3 μm to a near-IR frequency-comb. Precise tuning of the comb repetition-rate allows the quantum-cascade-laser to be scanned across absorption lines of a CO2 gaseous sample and line profiles to be acquired with extreme reproducibility and accuracy. By averaging over 50 acquisitions, line-centre frequencies are retrieved with an uncertainty of 30 kHz in a linear interaction regime. The extension of this methodology to other lines and molecules, by the use of widely tunable extended-cavity quantum-cascade-lasers, paves the way to a wide availability of high-quality and traceable spectroscopic data in the most crucial region for molecular detection and interrogation.

©2011 Optical Society of America

1. Introduction

The past two decades have witnessed the advent of two of the most exciting spectroscopic tools ever realized. On one side frequency combs have revolutionized the way optical frequencies are measured, making it much more simple and accurate than ever [13]. On the other side quantum-cascade-lasers (QCLs) have enabled laser-assisted spectroscopy in the fingerprint region from 4 to 11 μm with high sensitivity and versatility [46]. The idea at the basis of this work is to combine these two technologies to obtain a system capable of measuring molecular spectra with an unprecedented level of accuracy, in the mid-infrared (MIR) region from 3 to 12 μm.

For a number of reasons – near-infrared (NIR) emission wavelengths of the commercial optical frequency comb synthesizers, spectroscopic interest for the ultraviolet (UV) region, efficiency of nonlinear up-conversion processes - most comb-assisted spectroscopy experiments have been so far focused on the spectral region between the UV and the NIR. In the MIR region very few results have been reported, the most representative examples being the investigation of a two-photon line [7] of SF6 and of single lines of molecules [8,9] such as CH4 and CO2.

A first critical issue coming into play when a MIR frequency is to be measured against a NIR frequency-comb is the availability of a tunable narrow-linewidth probing laser in the MIR. Quantum-cascade-lasers definitely represent the most promising candidates thanks to their intrinsically narrow emission line-width [10], high output power, broad tunability [6], and emission wavelengths spanning the whole fingerprint region [5]. In such region, however, direct referencing of a QCL to a NIR comb has been so far demonstrated at 4.4 μm only, by making use of a rather cumbersome apparatus where two additional cw lasers were used as intermediate oscillators to enhance the beat-note signals [11].

A second issue of MIR comb-assisted spectroscopy is the realization of an efficient nonlinear frequency-mixing scheme to relate the frequency of the probing laser to that of the NIR comb. Two approaches have been mostly pursued so far, namely the down-conversion of the comb [12-13] or the up-conversion of the probing laser [14-15], as schematically represented in Fig. 1 , respectively. Panel (a) refers to the case of a difference-frequency-generation (DFG) process between a pair of phase-coherent pulse trains whose spectral distance matches the frequency to be measured. Since the two pulse trains share the same carrier-envelope-offset frequency, the DFG between them results in a harmonic MIR comb without any offset frequency. Such scheme has been successfully implemented to reach wavelengths from 3.2 to 12 μm with power levels in the 100 μW-10 mW range and rep-rate of ~100 MHz, starting either from a Ti:sapphire oscillator [13] or by Erbium/Ytterbium-doped fiber oscillators [1618]. The main drawback of such approach is that the comb and the probing laser lye in the MIR region, where low-noise high-speed detectors are difficult to be found. As an alternative scheme – (b) panel - the MIR probing laser can be summed (or subtracted) to the NIR comb to get a frequency-shifted comb. The overlap between this comb and a spectrally-broadened replica of the initial NIR comb produces a number of phase-coherent beating signals whose low-frequency note can be used to refer the MIR laser to an integer number of the comb repetition frequency.

 figure: Fig. 1

Fig. 1 Nonlinear schemes for comb-referencing of a MIR cw laser. (a) Down-conversion of the near-IR comb through difference-frequency-generation (DFG). (b) Up-conversion of the probing laser through sum-frequency-generation (SFG). Comb 1 and comb2 represent a pair of phase-coherent NIR frequency combs.

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In this work we have followed the second approach to obtain a robust phase-locking of a DFB-QCL operating at 4.3 μm to a NIR Er-based frequency comb. By scanning the repetition rate of the comb over a range corresponding to tens of gigahertz in the optical domain, highly repeatable acquisitions of several absorption lines of a CO2 gas sample were obtained, with signal-to-noise-ratios that can exceed 1500 by averaging over 5 acquisitions only. This implies line centre frequencies to be retrieved within few minutes with an accuracy that is more than two orders of magnitude higher than that reported in HITRAN, without recurring to any nonlinear spectroscopic regime such as saturated-absorption spectroscopy and without any stabilization of the carrier-envelope-offset frequency of the comb. The proposed scheme is likely to represent a new methodology for the determination of spectroscopic parameters of molecular compounds in the gas phase, featuring unprecedented accuracy, a simple and compact apparatus, and the full coverage of the fingerprint region, which is of utmost importance for detection and identification of gases of environmental interest.

2. The frequency referencing scheme

The scheme used to obtain referencing of the QCL to the comb relies on the versatility offered by a two-branch Er:fiber femtosecond oscillator. This laser features two phase-coherent outputs [19] resulting from the amplification of two identical replicas of the oscillator pulse train. One of the outputs is spectrally centred at 1.55 μm and carries an average optical power of 250 mW at 100 MHz rep-rate. The second output is coupled to a highly nonlinear fiber and produces a supercontinuum (SC) whose spectral extension can be easily tailored by modification of the chirp of the pulses injected into the fiber itself [20]. Figure 2(a) reports the spectrum of the 1.55 μm output and a sequence of spectra of the short-wavelength part of the SC, tunable from 1.05 to 1.4 μm. The presence of the two independent branches as well as the reconfigurability of the SC output offer exceptionally favourable conditions for frequency measurements in the fingerprint region: i) the powerful 1.55 μm output can be made to interact with the 3-12 μm probing laser to produce, by sum-frequency-generation, an intense frequency-shifted comb lying in the 1.05-1.4 μm region; ii) for any frequency of the probing laser and thus for any position of the shifted comb, strong beating signals can be obtained with the SC output provided that its spectral density is optimized accordingly. As highlighted by the horizontal arrows and by the optical-frequency markers on top of them, the frequency separation between the main output and the SC output essentially covers the whole fingerprint frequency range, from 25 THz (12 μm) to 100 THz (3 μm). Other recently proposed schemes based on electro-optical-sampling, even if already successfully implemented with QCLs [21], do not represent a viable alternative for frequencies higher than 40 THz [22].

 figure: Fig. 2

Fig. 2 Experimental spectra involved in comb-referencing of a MIR cw laser. (a) Examples of phase-coherent spectra achievable from a dual-branch Er-fiber laser: main output at 1.55 μm (red line) and SC output (coloured lines at shorter wavelengths), together with their frequency difference (horizontal arrows and corresponding labels). (b) Spectrum (light blue) resulting from SFG between QCL (not reported in the figure) and main oscillator output (red line), together with the SC spectrum used for the beating (dark blue), as situated 70 THz far apart the main Erbium output.

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The experimental apparatus used to obtain referencing of the QCL to the comb is particularly compact and sketched in Fig. 3 . The QCL is a cw liquid-nitrogen cooled DFB laser from Alpes driven by a commercial power supply (LDC-3744B model, from ILX Lightwave) providing single longitudinal mode operation and an optical power up to 20 mW, with a threshold of 90 mA and a slope of 170 μW/mA. It can be tuned around 4.33 μm by roughly 120 GHz with a sensitivity of ~370 MHz/mA. After proper beams spatial and temporal matching, the two outputs of the Er:fiber laser are collinearly recombined with eachother and then with the QCL by means of dichroic mirrors. The three beams are focused in a 4-mm long PPLN crystal providing the up-conversion of the QCL to the 1.14 μm spectral region used for the beating (power levels inside the crystals amount to 770 μW for the QCL and 150 mW for the 1.55-μm comb). The spectrum of the sum-frequency beam spans roughly 10 nm and it is compared in Fig. 2(b) with the spectrum of the SC when tuned to the same 1.14 μm central wavelength. After spectral filtering of the broader SC, the beating-note between the two signals – 50 μW for the SC and ~5 nW for the sum frequency–is extracted by a 125 MHz InGaAs detector. As already shown elsewhere [21], such scheme allows the QCL frequency to be directly referred to the repetition frequency of the comb without any contribution from the carrier-envelope-offset frequency.

 figure: Fig. 3

Fig. 3 Experimental apparatus. D: diaphragm, DM: dichroic mirror, PAR: 90° off-axis parabolic mirror, PPLN: periodically-poled lithium niobate, P: prism, PC: personal computer, PD: amplified InGaAs photo-detector, MCT: Peltier.cooled mercury-cadmium-telluride detector, TCO2: cell transmittance; frep = variable laser repetition frequency, as set by PC, frep’ = actual laser rep-rate, as made to coincide with frep by frep-Servo, fbeat: offset frequency used for stabilization of the beating note.

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Figure 4 shows the beating signal between the QCL and the NIR comb, as acquired with an electrical spectrum analyzer. The QCL line-width – nearly 7 MHz – was found to be a factor of two larger than reported elsewhere [11], as a result of the rather high rms noise of the current driver (10 μA within a bandwidth of nearly 1 MHz). On the other hand, the free-running drift of the beat-note was rather slow - of the order of one megahertz per second - even without active stabilization of the QCL temperature. The signal-to-noise-ratio was at the best 26 dB with a resolution bandwidth of 300 kHz. The QCL frequency was stabilized against the nearest comb mode with a frequency offset of 15 MHz and a servo-loop bandwidth of 2 kHz, as limited by the external analog modulation port of the current driver. In such conditions the line-width remained almost unchanged, but it is worth noting that with a less noisy and faster driver, line narrowing of the QCL would have been possible, as recently demonstrated in Ref. 21 with a 2.7-THz QCL.

 figure: Fig. 4

Fig. 4 Electrical spectrum of the beat-note between comb and QCL. Main panel: phase-locked conditions, 300 kHz resolution bandwidth, 10 kHz video-bandwidth and 20-spectra averaging. Inset: free-running beating, 300 kHz resolution bandwidth, 300 kHz video-bandwidth and 3-spectra averaging.

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3. Comb-assisted frequency scan of CO2 absorption lines

Tuning of the repetition-rate allowed comb-assisted frequency scans (CAFS) of the QCL throughout absorption lines of a CO2 gas sample filling a 12-cm-long stainless-steel cell. With a maximum rep-rate scanning range of 29 kHz, an optical frequency range of nearly 20 GHz was covered, which was sufficiently wide to observe and precisely identify a manifold of rovibrational lines of CO2 and its isotopologues. Figure 5(a) shows two examples of absorption profiles acquired as a function of the laser repetition rate with two different scans lasting 7 minutes each (scanning speed of 4 kHz/min) at a pressure of 7.3 Torr. The reproducibility and linearity of the frequency axis is remarkably high, allowing several scans to be acquired and averaged together to increase the signal-to-noise-ratio. The (b) panel shows the absorption profile of the P15f rovibrational line of the main CO2 isotopologue resulting from a narrow laser scan, together with its least-squares fitting to a Voigt convolution. The analysis of residuals shows the absence of any systematic error and a signal-to-noise ratio (SNR) as high as 1500 after 5 scans. This is sufficient to appreciate even slight deviations from the commonly used Voigt profile, as originated by, e.g., Dicke narrowing effects [23]. This is clearly highlighted in the figure by the W-shaped structure of the residuals around the line-centre frequency. Even without entering into a detailed discussion of the topic, it is evident that CAFS represents a formidable tool for a deep investigation of collisional processes in molecular samples in the gas phase, as well as for the accurate determination of a wealth of molecular parameters.

 figure: Fig. 5

Fig. 5 Absorption profiles and line-centre frequencies of a CO2 gas sample. (a) CO2 absorption spectra at a pressure of 7.3 Torr, resulting from a wide scan of the laser rep-rate (bottom scale) and thus of the QCL absolute frequency. The violet and red lines represent two independent measurements, to be referred to the left and right vertical scale, respectively. Dots represent line-centre frequencies and transmitted signals calculated from the HITRAN database for the observed transitions. (b) 5-fold averaged absorption profile of the P15f line of the main CO2 isotopologue (blue line), as obtained from repeated narrower scans (4-kHz wide with 4000 points). The fitting curve (yellow line) was calculated with a Voigt convolution. The residuals of the fitting are highlighted in the bottom part of the panel. (c) Table giving the line-centre frequencies of all investigated lines, from HITRAN and from a multi-line least-squares fitting procedure of the entire CAFS experimental absorption spectrum. Only the significant digits, that is the ones falling within the uncertainty range, are reported for the two sets. For the HITRAN frequencies this range is ± 30 MHz, corresponding to ± 0.001 cm−1, while for the measured set it scales from a minimum of ± 227 kHz (~ ± 0.000007 cm−1) for the most intense lines (~91% absorption) to about 11 MHz (~ ± 0.0004 cm−1) for the less intense ones (<1.8% absorption).

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To obtain an absolute frequency calibration of the spectroscopic data, both the 15-MHz frequency offset and the repetition-rate of the Erbium laser were referred to a GPS-disciplined Rb oscillator. The correct ratio between radiofrequencies and optical frequencies was unambiguously assessed by taking advantage of the considerable spectral coverage of the scan and of the 30-MHz accuracy given by HITRAN for most of the investigated absorption lines. With such scaling factor the assignment of absolute centre-frequency values to the observed transitions was readily achieved. The new determinations, as reported in a table format in Fig. 5(c) together with the corresponding HITRAN values, were obtained by a multi-line least-squares fitting procedure of the entire experimental absorption spectrum. The uncertainty of the reported values changes according to the signal-to-noise-ratio and thus to the absorption strength, this being the reason why the number of significant digits is not constant for all observed lines. In order to have a calibration of the uncertainty level, we repeated 50 independent measurements on one of the most intense lines, namely the P15f of the main CO2 isotopologue at a pressure of 7.3 Torr - see Fig. 5(b). For each acquisition we performed a least-square fitting with a Voigt convolution and extracted a line-centre frequency value. The ensemble of frequencies is reported in Fig. 6 . The average deviation from HITRAN amounts to < 1.7 MHz, thus well within the 30 MHz uncertainty range of HITRAN, while the standard deviation is 227 kHz, corresponding to a relative precision of 3.2⋅10−9 with respect to the line-centre frequency, and of 2⋅10−3 with respect to the ~115 MHz HWHM of the profile. In the absence of sources of significant systematic errors, the 227-kHz precision level can be considered as a reliable estimate of the frequency accuracy of the single determination. An improvement by a factor of 100 would be obtained in a non-linear regime of interaction (i.e., saturated absorption spectroscopy) making use of a sufficiently high power level, which can be easily achievable in the whole fingerprint region with currently available QCLs [24].

 figure: Fig. 6

Fig. 6 Dispersion of the retrieved line-centre frequencies. Each point identifies one out of the 50 independent measurements on the P15f line of the main CO2 isotopologue at a pressure of 7.3 Torr.

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Another step towards higher precisions would be obtained by a wide-bandwidth phase-lock between QCL and comb, leading to significant QCL line-narrowing.

4. Conclusions

In conclusion, the joint use of a two-branch Er:fiber femtosecond oscillator and of a quantum-cascade-laser at 4.3 μm was shown to be an extremely compact yet effective solution to measure with unprecedented accuracy and versatility molecular absorption profiles. When combined to highly-sensitive spectroscopic detection schemes, such as cavity ring-down spectroscopy, this approach would provide a new strategy to measure isotope abundance ratios for rare isotopologues. Similarly, it could be exploited to address the problem of absolute determinations of amount of substances at trace levels. Furthermore, thanks to the extremely linear, predictable and reproducible frequency-scale, molecular parameters such as line-centre frequencies, line-strengths, pressure-shift and pressure-broadening coefficients can be straightforwardly retrieved with a strongly enhanced level of accuracy over the existing data. The commercial availability of widely tunable and powerful quantum-cascade-lasers with emission wavelengths spanning the whole fingerprint region makes such an approach easily extendable to other lines and molecules. Such an extension would produce a huge amount of spectroscopic data of crucial interest for molecular fingerprinting, molecular traceability, as well as for obtaining a deeper insight into the full comprehension of molecular spectra.

Acknowledgments

The authors acknowledge support by the EU FP7 FET project CROSS TRAP (Contract No. ICT-244068) and the financial contribution from Polo di Lecco – Politecnico di Milano.

References and links

1. Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002). [CrossRef]   [PubMed]  

2. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–640 (2000). [CrossRef]   [PubMed]  

3. Th. Udem, R. Holzwarth, and T. W. Hansch, “Femtosecond optical frequency combs,” Eur. Phys. J. Spec. Top. 172(1), 69–79 (2009). [CrossRef]  

4. J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994). [CrossRef]   [PubMed]  

5. M. Beck, D. Hofstetter, T. Aellen, J. Faist, U. Oesterle, M. Ilegems, E. Gini, and H. Melchior, “Continuous Wave Operation of a Mid-Infrared Semiconductor Laser at Room Temperature,” Science 295(5553), 301–305 (2002). [CrossRef]   [PubMed]  

6. A. Hugi, R. Maulini, and J. Faist, “External cavity quantum cascade laser,” Semicond. Sci. Technol. 25(8), 083001 (2010). [CrossRef]  

7. A. Amy-Klein, A. Goncharov, C. Daussy, C. Grain, O. Lopez, G. Santarelli, and C. Chardonnet, “Absolute frequency measurement in the 28-THz spectral region with a femtosecond laser comb and a long-distance optical link to a primary standard,” Appl. Phys. B 78(1), 25–30 (2004). [CrossRef]  

8. P. Malara, P. Maddaloni, G. Gagliardi, and P. De Natale, “Absolute frequency measurement of molecular transitions by a direct link to a comb generated around 3-microm,” Opt. Express 16(11), 8242–8249 (2008). [CrossRef]   [PubMed]  

9. D. Mazzotti, P. Cancio, G. Giusfredi, P. De Natale, and M. Prevedelli, “Frequency-comb-based absolute frequency measurements in the mid-infrared with a difference-frequency spectrometer,” Opt. Lett. 30(9), 997–999 (2005). [CrossRef]   [PubMed]  

10. S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. De Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104(8), 083904 (2010). [CrossRef]   [PubMed]  

11. S. Bartalini, P. Cancio, G. Giusfredi, D. Mazzotti, P. De Natale, S. Borri, I. Galli, T. Leveque, and L. Gianfrani, “Frequency-comb-referenced quantum-cascade laser at 4.4 microm,” Opt. Lett. 32(8), 988–990 (2007). [CrossRef]   [PubMed]  

12. M. Zimmermann, C. Gohle, R. Holzwarth, Th. Udem, and T. W. Hansch, “Optical clockwork with an offset-free difference-frequency comb: accuracy of sum- and difference-frequency generation,” Opt. Lett. 29(3), 310–312 (2004). [CrossRef]   [PubMed]  

13. S. M. Foreman, A. Marian, J. Ye, E. A. Petrukhin, M. A. Gubin, O. D. Mücke, F. N. C. Wong, E. P. Ippen, and F. X. Kärtner, “Demonstration of a HeNe/CH4-based optical molecular clock,” Opt. Lett. 30(5), 570–572 (2005). [CrossRef]   [PubMed]  

14. A. Amy-Klein, A. Goncharov, M. Guinet, C. Daussy, O. Lopez, A. Shelkovnikov, and C. Chardonnet, “Absolute frequency measurement of a SF6 two-photon line by use of a femtosecond optical comb and sum-frequency generation,” Opt. Lett. 30(24), 3320–3322 (2005). [CrossRef]   [PubMed]  

15. J. Jiang, A. Onae, H. Matsumoto, and F. L. Hong, “Frequency measurement of acetylene-stabilized lasers using a femtosecond optical comb without carrier-envelope offset frequency control,” Opt. Express 13(6), 1958–1965 (2005). [CrossRef]   [PubMed]  

16. C. Erny, K. Moutzouris, J. Biegert, D. Kühlke, F. Adler, A. Leitenstorfer, and U. Keller, “Mid-infrared difference-frequency generation of ultrashort pulses tunable between 3.2 and 4.8 microm from a compact fiber source,” Opt. Lett. 32(9), 1138–1140 (2007). [CrossRef]   [PubMed]  

17. A. Gambetta, R. Ramponi, and M. Marangoni, “Mid-infrared optical combs from a compact amplified Er-doped fiber oscillator,” Opt. Lett. 33(22), 2671–2673 (2008). [CrossRef]   [PubMed]  

18. T. A. Johnson and S. A. Diddams, “Mid-IR Frequency Comb Upconversion Spectroscopy”, in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CPDB11.

19. F. Adler, A. Sell, F. Sotier, R. Huber, and A. Leitenstorfer, “Attosecond relative timing jitter and 13 fs tunable pulses from a two-branch Er:fiber laser,” Opt. Lett. 32(24), 3504–3506 (2007). [CrossRef]   [PubMed]  

20. F. Tauser, F. Adler, and A. Leitenstorfer, “Widely tunable sub-30-fs pulses from a compact erbium-doped fiber source,” Opt. Lett. 29(5), 516–518 (2004). [CrossRef]   [PubMed]  

21. S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4(9), 636–640 (2010). [CrossRef]  

22. P. Gaal, M. B. Raschke, K. Reimann, and M. Woerner, “Measuring optical frequencies in the 0–40 THz range with non-synchronized electro–optic sampling,” Nat. Photonics 1(10), 577–580 (2007). [CrossRef]  

23. G. Casa, D. A. Parretta, A. Castrillo, R. Wehr, and L. Gianfrani, “Highly accurate determinations of CO2 line strengths using intensity-stabilized diode laser absorption spectrometry,” J. Chem. Phys. 127(8), 084311 (2007). [CrossRef]   [PubMed]  

24. A. Castrillo, E. De Tommasi, L. Gianfrani, L. Sirigu, and J. Faist, “Doppler-free saturated-absorption spectroscopy of CO2 at 4.3 microm by means of a distributed feedback quantum cascade laser,” Opt. Lett. 31(20), 3040–3042 (2006). [CrossRef]   [PubMed]  

References

  • View by:

  1. Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
    [Crossref] [PubMed]
  2. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–640 (2000).
    [Crossref] [PubMed]
  3. Th. Udem, R. Holzwarth, and T. W. Hansch, “Femtosecond optical frequency combs,” Eur. Phys. J. Spec. Top. 172(1), 69–79 (2009).
    [Crossref]
  4. J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
    [Crossref] [PubMed]
  5. M. Beck, D. Hofstetter, T. Aellen, J. Faist, U. Oesterle, M. Ilegems, E. Gini, and H. Melchior, “Continuous Wave Operation of a Mid-Infrared Semiconductor Laser at Room Temperature,” Science 295(5553), 301–305 (2002).
    [Crossref] [PubMed]
  6. A. Hugi, R. Maulini, and J. Faist, “External cavity quantum cascade laser,” Semicond. Sci. Technol. 25(8), 083001 (2010).
    [Crossref]
  7. A. Amy-Klein, A. Goncharov, C. Daussy, C. Grain, O. Lopez, G. Santarelli, and C. Chardonnet, “Absolute frequency measurement in the 28-THz spectral region with a femtosecond laser comb and a long-distance optical link to a primary standard,” Appl. Phys. B 78(1), 25–30 (2004).
    [Crossref]
  8. P. Malara, P. Maddaloni, G. Gagliardi, and P. De Natale, “Absolute frequency measurement of molecular transitions by a direct link to a comb generated around 3-microm,” Opt. Express 16(11), 8242–8249 (2008).
    [Crossref] [PubMed]
  9. D. Mazzotti, P. Cancio, G. Giusfredi, P. De Natale, and M. Prevedelli, “Frequency-comb-based absolute frequency measurements in the mid-infrared with a difference-frequency spectrometer,” Opt. Lett. 30(9), 997–999 (2005).
    [Crossref] [PubMed]
  10. S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. De Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104(8), 083904 (2010).
    [Crossref] [PubMed]
  11. S. Bartalini, P. Cancio, G. Giusfredi, D. Mazzotti, P. De Natale, S. Borri, I. Galli, T. Leveque, and L. Gianfrani, “Frequency-comb-referenced quantum-cascade laser at 4.4 microm,” Opt. Lett. 32(8), 988–990 (2007).
    [Crossref] [PubMed]
  12. M. Zimmermann, C. Gohle, R. Holzwarth, Th. Udem, and T. W. Hansch, “Optical clockwork with an offset-free difference-frequency comb: accuracy of sum- and difference-frequency generation,” Opt. Lett. 29(3), 310–312 (2004).
    [Crossref] [PubMed]
  13. S. M. Foreman, A. Marian, J. Ye, E. A. Petrukhin, M. A. Gubin, O. D. Mücke, F. N. C. Wong, E. P. Ippen, and F. X. Kärtner, “Demonstration of a HeNe/CH4-based optical molecular clock,” Opt. Lett. 30(5), 570–572 (2005).
    [Crossref] [PubMed]
  14. A. Amy-Klein, A. Goncharov, M. Guinet, C. Daussy, O. Lopez, A. Shelkovnikov, and C. Chardonnet, “Absolute frequency measurement of a SF6 two-photon line by use of a femtosecond optical comb and sum-frequency generation,” Opt. Lett. 30(24), 3320–3322 (2005).
    [Crossref] [PubMed]
  15. J. Jiang, A. Onae, H. Matsumoto, and F. L. Hong, “Frequency measurement of acetylene-stabilized lasers using a femtosecond optical comb without carrier-envelope offset frequency control,” Opt. Express 13(6), 1958–1965 (2005).
    [Crossref] [PubMed]
  16. C. Erny, K. Moutzouris, J. Biegert, D. Kühlke, F. Adler, A. Leitenstorfer, and U. Keller, “Mid-infrared difference-frequency generation of ultrashort pulses tunable between 3.2 and 4.8 microm from a compact fiber source,” Opt. Lett. 32(9), 1138–1140 (2007).
    [Crossref] [PubMed]
  17. A. Gambetta, R. Ramponi, and M. Marangoni, “Mid-infrared optical combs from a compact amplified Er-doped fiber oscillator,” Opt. Lett. 33(22), 2671–2673 (2008).
    [Crossref] [PubMed]
  18. T. A. Johnson and S. A. Diddams, “Mid-IR Frequency Comb Upconversion Spectroscopy”, in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CPDB11.
  19. F. Adler, A. Sell, F. Sotier, R. Huber, and A. Leitenstorfer, “Attosecond relative timing jitter and 13 fs tunable pulses from a two-branch Er:fiber laser,” Opt. Lett. 32(24), 3504–3506 (2007).
    [Crossref] [PubMed]
  20. F. Tauser, F. Adler, and A. Leitenstorfer, “Widely tunable sub-30-fs pulses from a compact erbium-doped fiber source,” Opt. Lett. 29(5), 516–518 (2004).
    [Crossref] [PubMed]
  21. S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4(9), 636–640 (2010).
    [Crossref]
  22. P. Gaal, M. B. Raschke, K. Reimann, and M. Woerner, “Measuring optical frequencies in the 0–40 THz range with non-synchronized electro–optic sampling,” Nat. Photonics 1(10), 577–580 (2007).
    [Crossref]
  23. G. Casa, D. A. Parretta, A. Castrillo, R. Wehr, and L. Gianfrani, “Highly accurate determinations of CO2 line strengths using intensity-stabilized diode laser absorption spectrometry,” J. Chem. Phys. 127(8), 084311 (2007).
    [Crossref] [PubMed]
  24. A. Castrillo, E. De Tommasi, L. Gianfrani, L. Sirigu, and J. Faist, “Doppler-free saturated-absorption spectroscopy of CO2 at 4.3 microm by means of a distributed feedback quantum cascade laser,” Opt. Lett. 31(20), 3040–3042 (2006).
    [Crossref] [PubMed]

2010 (3)

A. Hugi, R. Maulini, and J. Faist, “External cavity quantum cascade laser,” Semicond. Sci. Technol. 25(8), 083001 (2010).
[Crossref]

S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. De Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104(8), 083904 (2010).
[Crossref] [PubMed]

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4(9), 636–640 (2010).
[Crossref]

2009 (1)

Th. Udem, R. Holzwarth, and T. W. Hansch, “Femtosecond optical frequency combs,” Eur. Phys. J. Spec. Top. 172(1), 69–79 (2009).
[Crossref]

2008 (2)

2007 (5)

2006 (1)

2005 (4)

2004 (3)

2002 (2)

M. Beck, D. Hofstetter, T. Aellen, J. Faist, U. Oesterle, M. Ilegems, E. Gini, and H. Melchior, “Continuous Wave Operation of a Mid-Infrared Semiconductor Laser at Room Temperature,” Science 295(5553), 301–305 (2002).
[Crossref] [PubMed]

Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[Crossref] [PubMed]

2000 (1)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–640 (2000).
[Crossref] [PubMed]

1994 (1)

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[Crossref] [PubMed]

Adler, F.

Aellen, T.

M. Beck, D. Hofstetter, T. Aellen, J. Faist, U. Oesterle, M. Ilegems, E. Gini, and H. Melchior, “Continuous Wave Operation of a Mid-Infrared Semiconductor Laser at Room Temperature,” Science 295(5553), 301–305 (2002).
[Crossref] [PubMed]

Amy-Klein, A.

A. Amy-Klein, A. Goncharov, M. Guinet, C. Daussy, O. Lopez, A. Shelkovnikov, and C. Chardonnet, “Absolute frequency measurement of a SF6 two-photon line by use of a femtosecond optical comb and sum-frequency generation,” Opt. Lett. 30(24), 3320–3322 (2005).
[Crossref] [PubMed]

A. Amy-Klein, A. Goncharov, C. Daussy, C. Grain, O. Lopez, G. Santarelli, and C. Chardonnet, “Absolute frequency measurement in the 28-THz spectral region with a femtosecond laser comb and a long-distance optical link to a primary standard,” Appl. Phys. B 78(1), 25–30 (2004).
[Crossref]

Barbieri, S.

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4(9), 636–640 (2010).
[Crossref]

Bartalini, S.

S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. De Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104(8), 083904 (2010).
[Crossref] [PubMed]

S. Bartalini, P. Cancio, G. Giusfredi, D. Mazzotti, P. De Natale, S. Borri, I. Galli, T. Leveque, and L. Gianfrani, “Frequency-comb-referenced quantum-cascade laser at 4.4 microm,” Opt. Lett. 32(8), 988–990 (2007).
[Crossref] [PubMed]

Beck, M.

M. Beck, D. Hofstetter, T. Aellen, J. Faist, U. Oesterle, M. Ilegems, E. Gini, and H. Melchior, “Continuous Wave Operation of a Mid-Infrared Semiconductor Laser at Room Temperature,” Science 295(5553), 301–305 (2002).
[Crossref] [PubMed]

Beere, H.

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4(9), 636–640 (2010).
[Crossref]

Biegert, J.

Borri, S.

S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. De Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104(8), 083904 (2010).
[Crossref] [PubMed]

S. Bartalini, P. Cancio, G. Giusfredi, D. Mazzotti, P. De Natale, S. Borri, I. Galli, T. Leveque, and L. Gianfrani, “Frequency-comb-referenced quantum-cascade laser at 4.4 microm,” Opt. Lett. 32(8), 988–990 (2007).
[Crossref] [PubMed]

Cancio, P.

Capasso, F.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[Crossref] [PubMed]

Casa, G.

G. Casa, D. A. Parretta, A. Castrillo, R. Wehr, and L. Gianfrani, “Highly accurate determinations of CO2 line strengths using intensity-stabilized diode laser absorption spectrometry,” J. Chem. Phys. 127(8), 084311 (2007).
[Crossref] [PubMed]

Castrillo, A.

S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. De Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104(8), 083904 (2010).
[Crossref] [PubMed]

G. Casa, D. A. Parretta, A. Castrillo, R. Wehr, and L. Gianfrani, “Highly accurate determinations of CO2 line strengths using intensity-stabilized diode laser absorption spectrometry,” J. Chem. Phys. 127(8), 084311 (2007).
[Crossref] [PubMed]

A. Castrillo, E. De Tommasi, L. Gianfrani, L. Sirigu, and J. Faist, “Doppler-free saturated-absorption spectroscopy of CO2 at 4.3 microm by means of a distributed feedback quantum cascade laser,” Opt. Lett. 31(20), 3040–3042 (2006).
[Crossref] [PubMed]

Chardonnet, C.

A. Amy-Klein, A. Goncharov, M. Guinet, C. Daussy, O. Lopez, A. Shelkovnikov, and C. Chardonnet, “Absolute frequency measurement of a SF6 two-photon line by use of a femtosecond optical comb and sum-frequency generation,” Opt. Lett. 30(24), 3320–3322 (2005).
[Crossref] [PubMed]

A. Amy-Klein, A. Goncharov, C. Daussy, C. Grain, O. Lopez, G. Santarelli, and C. Chardonnet, “Absolute frequency measurement in the 28-THz spectral region with a femtosecond laser comb and a long-distance optical link to a primary standard,” Appl. Phys. B 78(1), 25–30 (2004).
[Crossref]

Cho, A. Y.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[Crossref] [PubMed]

Colombelli, R.

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4(9), 636–640 (2010).
[Crossref]

Cundiff, S. T.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–640 (2000).
[Crossref] [PubMed]

Daussy, C.

A. Amy-Klein, A. Goncharov, M. Guinet, C. Daussy, O. Lopez, A. Shelkovnikov, and C. Chardonnet, “Absolute frequency measurement of a SF6 two-photon line by use of a femtosecond optical comb and sum-frequency generation,” Opt. Lett. 30(24), 3320–3322 (2005).
[Crossref] [PubMed]

A. Amy-Klein, A. Goncharov, C. Daussy, C. Grain, O. Lopez, G. Santarelli, and C. Chardonnet, “Absolute frequency measurement in the 28-THz spectral region with a femtosecond laser comb and a long-distance optical link to a primary standard,” Appl. Phys. B 78(1), 25–30 (2004).
[Crossref]

De Natale, P.

De Tommasi, E.

Diddams, S. A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–640 (2000).
[Crossref] [PubMed]

Ding, L.

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4(9), 636–640 (2010).
[Crossref]

Erny, C.

Faist, J.

A. Hugi, R. Maulini, and J. Faist, “External cavity quantum cascade laser,” Semicond. Sci. Technol. 25(8), 083001 (2010).
[Crossref]

A. Castrillo, E. De Tommasi, L. Gianfrani, L. Sirigu, and J. Faist, “Doppler-free saturated-absorption spectroscopy of CO2 at 4.3 microm by means of a distributed feedback quantum cascade laser,” Opt. Lett. 31(20), 3040–3042 (2006).
[Crossref] [PubMed]

M. Beck, D. Hofstetter, T. Aellen, J. Faist, U. Oesterle, M. Ilegems, E. Gini, and H. Melchior, “Continuous Wave Operation of a Mid-Infrared Semiconductor Laser at Room Temperature,” Science 295(5553), 301–305 (2002).
[Crossref] [PubMed]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[Crossref] [PubMed]

Foreman, S. M.

Gaal, P.

P. Gaal, M. B. Raschke, K. Reimann, and M. Woerner, “Measuring optical frequencies in the 0–40 THz range with non-synchronized electro–optic sampling,” Nat. Photonics 1(10), 577–580 (2007).
[Crossref]

Gagliardi, G.

Galli, I.

S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. De Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104(8), 083904 (2010).
[Crossref] [PubMed]

S. Bartalini, P. Cancio, G. Giusfredi, D. Mazzotti, P. De Natale, S. Borri, I. Galli, T. Leveque, and L. Gianfrani, “Frequency-comb-referenced quantum-cascade laser at 4.4 microm,” Opt. Lett. 32(8), 988–990 (2007).
[Crossref] [PubMed]

Gambetta, A.

Gellie, P.

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4(9), 636–640 (2010).
[Crossref]

Gianfrani, L.

S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. De Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104(8), 083904 (2010).
[Crossref] [PubMed]

S. Bartalini, P. Cancio, G. Giusfredi, D. Mazzotti, P. De Natale, S. Borri, I. Galli, T. Leveque, and L. Gianfrani, “Frequency-comb-referenced quantum-cascade laser at 4.4 microm,” Opt. Lett. 32(8), 988–990 (2007).
[Crossref] [PubMed]

G. Casa, D. A. Parretta, A. Castrillo, R. Wehr, and L. Gianfrani, “Highly accurate determinations of CO2 line strengths using intensity-stabilized diode laser absorption spectrometry,” J. Chem. Phys. 127(8), 084311 (2007).
[Crossref] [PubMed]

A. Castrillo, E. De Tommasi, L. Gianfrani, L. Sirigu, and J. Faist, “Doppler-free saturated-absorption spectroscopy of CO2 at 4.3 microm by means of a distributed feedback quantum cascade laser,” Opt. Lett. 31(20), 3040–3042 (2006).
[Crossref] [PubMed]

Gini, E.

M. Beck, D. Hofstetter, T. Aellen, J. Faist, U. Oesterle, M. Ilegems, E. Gini, and H. Melchior, “Continuous Wave Operation of a Mid-Infrared Semiconductor Laser at Room Temperature,” Science 295(5553), 301–305 (2002).
[Crossref] [PubMed]

Giusfredi, G.

Gohle, C.

Goncharov, A.

A. Amy-Klein, A. Goncharov, M. Guinet, C. Daussy, O. Lopez, A. Shelkovnikov, and C. Chardonnet, “Absolute frequency measurement of a SF6 two-photon line by use of a femtosecond optical comb and sum-frequency generation,” Opt. Lett. 30(24), 3320–3322 (2005).
[Crossref] [PubMed]

A. Amy-Klein, A. Goncharov, C. Daussy, C. Grain, O. Lopez, G. Santarelli, and C. Chardonnet, “Absolute frequency measurement in the 28-THz spectral region with a femtosecond laser comb and a long-distance optical link to a primary standard,” Appl. Phys. B 78(1), 25–30 (2004).
[Crossref]

Grain, C.

A. Amy-Klein, A. Goncharov, C. Daussy, C. Grain, O. Lopez, G. Santarelli, and C. Chardonnet, “Absolute frequency measurement in the 28-THz spectral region with a femtosecond laser comb and a long-distance optical link to a primary standard,” Appl. Phys. B 78(1), 25–30 (2004).
[Crossref]

Gubin, M. A.

Guinet, M.

Hall, J. L.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–640 (2000).
[Crossref] [PubMed]

Hansch, T. W.

Hänsch, T. W.

Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[Crossref] [PubMed]

Hofstetter, D.

M. Beck, D. Hofstetter, T. Aellen, J. Faist, U. Oesterle, M. Ilegems, E. Gini, and H. Melchior, “Continuous Wave Operation of a Mid-Infrared Semiconductor Laser at Room Temperature,” Science 295(5553), 301–305 (2002).
[Crossref] [PubMed]

Holzwarth, R.

Th. Udem, R. Holzwarth, and T. W. Hansch, “Femtosecond optical frequency combs,” Eur. Phys. J. Spec. Top. 172(1), 69–79 (2009).
[Crossref]

M. Zimmermann, C. Gohle, R. Holzwarth, Th. Udem, and T. W. Hansch, “Optical clockwork with an offset-free difference-frequency comb: accuracy of sum- and difference-frequency generation,” Opt. Lett. 29(3), 310–312 (2004).
[Crossref] [PubMed]

Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[Crossref] [PubMed]

Hong, F. L.

Huber, R.

Hugi, A.

A. Hugi, R. Maulini, and J. Faist, “External cavity quantum cascade laser,” Semicond. Sci. Technol. 25(8), 083001 (2010).
[Crossref]

Hutchinson, A. L.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[Crossref] [PubMed]

Ilegems, M.

M. Beck, D. Hofstetter, T. Aellen, J. Faist, U. Oesterle, M. Ilegems, E. Gini, and H. Melchior, “Continuous Wave Operation of a Mid-Infrared Semiconductor Laser at Room Temperature,” Science 295(5553), 301–305 (2002).
[Crossref] [PubMed]

Ippen, E. P.

Jiang, J.

Jones, D. J.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–640 (2000).
[Crossref] [PubMed]

Kärtner, F. X.

Keller, U.

Kühlke, D.

Leitenstorfer, A.

Leveque, T.

Lopez, O.

A. Amy-Klein, A. Goncharov, M. Guinet, C. Daussy, O. Lopez, A. Shelkovnikov, and C. Chardonnet, “Absolute frequency measurement of a SF6 two-photon line by use of a femtosecond optical comb and sum-frequency generation,” Opt. Lett. 30(24), 3320–3322 (2005).
[Crossref] [PubMed]

A. Amy-Klein, A. Goncharov, C. Daussy, C. Grain, O. Lopez, G. Santarelli, and C. Chardonnet, “Absolute frequency measurement in the 28-THz spectral region with a femtosecond laser comb and a long-distance optical link to a primary standard,” Appl. Phys. B 78(1), 25–30 (2004).
[Crossref]

Maddaloni, P.

Maineult, W.

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4(9), 636–640 (2010).
[Crossref]

Malara, P.

Marangoni, M.

Marian, A.

Matsumoto, H.

Maulini, R.

A. Hugi, R. Maulini, and J. Faist, “External cavity quantum cascade laser,” Semicond. Sci. Technol. 25(8), 083001 (2010).
[Crossref]

Mazzotti, D.

Melchior, H.

M. Beck, D. Hofstetter, T. Aellen, J. Faist, U. Oesterle, M. Ilegems, E. Gini, and H. Melchior, “Continuous Wave Operation of a Mid-Infrared Semiconductor Laser at Room Temperature,” Science 295(5553), 301–305 (2002).
[Crossref] [PubMed]

Moutzouris, K.

Mücke, O. D.

Oesterle, U.

M. Beck, D. Hofstetter, T. Aellen, J. Faist, U. Oesterle, M. Ilegems, E. Gini, and H. Melchior, “Continuous Wave Operation of a Mid-Infrared Semiconductor Laser at Room Temperature,” Science 295(5553), 301–305 (2002).
[Crossref] [PubMed]

Onae, A.

Parretta, D. A.

G. Casa, D. A. Parretta, A. Castrillo, R. Wehr, and L. Gianfrani, “Highly accurate determinations of CO2 line strengths using intensity-stabilized diode laser absorption spectrometry,” J. Chem. Phys. 127(8), 084311 (2007).
[Crossref] [PubMed]

Petrukhin, E. A.

Prevedelli, M.

Ramponi, R.

Ranka, J. K.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–640 (2000).
[Crossref] [PubMed]

Raschke, M. B.

P. Gaal, M. B. Raschke, K. Reimann, and M. Woerner, “Measuring optical frequencies in the 0–40 THz range with non-synchronized electro–optic sampling,” Nat. Photonics 1(10), 577–580 (2007).
[Crossref]

Reimann, K.

P. Gaal, M. B. Raschke, K. Reimann, and M. Woerner, “Measuring optical frequencies in the 0–40 THz range with non-synchronized electro–optic sampling,” Nat. Photonics 1(10), 577–580 (2007).
[Crossref]

Ritchie, D.

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4(9), 636–640 (2010).
[Crossref]

Santarelli, G.

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4(9), 636–640 (2010).
[Crossref]

A. Amy-Klein, A. Goncharov, C. Daussy, C. Grain, O. Lopez, G. Santarelli, and C. Chardonnet, “Absolute frequency measurement in the 28-THz spectral region with a femtosecond laser comb and a long-distance optical link to a primary standard,” Appl. Phys. B 78(1), 25–30 (2004).
[Crossref]

Sell, A.

Shelkovnikov, A.

Sirigu, L.

Sirtori, C.

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4(9), 636–640 (2010).
[Crossref]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[Crossref] [PubMed]

Sivco, D. L.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[Crossref] [PubMed]

Sotier, F.

Stentz, A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–640 (2000).
[Crossref] [PubMed]

Tauser, F.

Udem, Th.

Th. Udem, R. Holzwarth, and T. W. Hansch, “Femtosecond optical frequency combs,” Eur. Phys. J. Spec. Top. 172(1), 69–79 (2009).
[Crossref]

M. Zimmermann, C. Gohle, R. Holzwarth, Th. Udem, and T. W. Hansch, “Optical clockwork with an offset-free difference-frequency comb: accuracy of sum- and difference-frequency generation,” Opt. Lett. 29(3), 310–312 (2004).
[Crossref] [PubMed]

Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[Crossref] [PubMed]

Wehr, R.

G. Casa, D. A. Parretta, A. Castrillo, R. Wehr, and L. Gianfrani, “Highly accurate determinations of CO2 line strengths using intensity-stabilized diode laser absorption spectrometry,” J. Chem. Phys. 127(8), 084311 (2007).
[Crossref] [PubMed]

Windeler, R. S.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–640 (2000).
[Crossref] [PubMed]

Woerner, M.

P. Gaal, M. B. Raschke, K. Reimann, and M. Woerner, “Measuring optical frequencies in the 0–40 THz range with non-synchronized electro–optic sampling,” Nat. Photonics 1(10), 577–580 (2007).
[Crossref]

Wong, F. N. C.

Ye, J.

Zimmermann, M.

Appl. Phys. B (1)

A. Amy-Klein, A. Goncharov, C. Daussy, C. Grain, O. Lopez, G. Santarelli, and C. Chardonnet, “Absolute frequency measurement in the 28-THz spectral region with a femtosecond laser comb and a long-distance optical link to a primary standard,” Appl. Phys. B 78(1), 25–30 (2004).
[Crossref]

Eur. Phys. J. Spec. Top. (1)

Th. Udem, R. Holzwarth, and T. W. Hansch, “Femtosecond optical frequency combs,” Eur. Phys. J. Spec. Top. 172(1), 69–79 (2009).
[Crossref]

J. Chem. Phys. (1)

G. Casa, D. A. Parretta, A. Castrillo, R. Wehr, and L. Gianfrani, “Highly accurate determinations of CO2 line strengths using intensity-stabilized diode laser absorption spectrometry,” J. Chem. Phys. 127(8), 084311 (2007).
[Crossref] [PubMed]

Nat. Photonics (2)

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4(9), 636–640 (2010).
[Crossref]

P. Gaal, M. B. Raschke, K. Reimann, and M. Woerner, “Measuring optical frequencies in the 0–40 THz range with non-synchronized electro–optic sampling,” Nat. Photonics 1(10), 577–580 (2007).
[Crossref]

Nature (1)

Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (10)

C. Erny, K. Moutzouris, J. Biegert, D. Kühlke, F. Adler, A. Leitenstorfer, and U. Keller, “Mid-infrared difference-frequency generation of ultrashort pulses tunable between 3.2 and 4.8 microm from a compact fiber source,” Opt. Lett. 32(9), 1138–1140 (2007).
[Crossref] [PubMed]

A. Gambetta, R. Ramponi, and M. Marangoni, “Mid-infrared optical combs from a compact amplified Er-doped fiber oscillator,” Opt. Lett. 33(22), 2671–2673 (2008).
[Crossref] [PubMed]

S. Bartalini, P. Cancio, G. Giusfredi, D. Mazzotti, P. De Natale, S. Borri, I. Galli, T. Leveque, and L. Gianfrani, “Frequency-comb-referenced quantum-cascade laser at 4.4 microm,” Opt. Lett. 32(8), 988–990 (2007).
[Crossref] [PubMed]

M. Zimmermann, C. Gohle, R. Holzwarth, Th. Udem, and T. W. Hansch, “Optical clockwork with an offset-free difference-frequency comb: accuracy of sum- and difference-frequency generation,” Opt. Lett. 29(3), 310–312 (2004).
[Crossref] [PubMed]

S. M. Foreman, A. Marian, J. Ye, E. A. Petrukhin, M. A. Gubin, O. D. Mücke, F. N. C. Wong, E. P. Ippen, and F. X. Kärtner, “Demonstration of a HeNe/CH4-based optical molecular clock,” Opt. Lett. 30(5), 570–572 (2005).
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A. Amy-Klein, A. Goncharov, M. Guinet, C. Daussy, O. Lopez, A. Shelkovnikov, and C. Chardonnet, “Absolute frequency measurement of a SF6 two-photon line by use of a femtosecond optical comb and sum-frequency generation,” Opt. Lett. 30(24), 3320–3322 (2005).
[Crossref] [PubMed]

D. Mazzotti, P. Cancio, G. Giusfredi, P. De Natale, and M. Prevedelli, “Frequency-comb-based absolute frequency measurements in the mid-infrared with a difference-frequency spectrometer,” Opt. Lett. 30(9), 997–999 (2005).
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F. Adler, A. Sell, F. Sotier, R. Huber, and A. Leitenstorfer, “Attosecond relative timing jitter and 13 fs tunable pulses from a two-branch Er:fiber laser,” Opt. Lett. 32(24), 3504–3506 (2007).
[Crossref] [PubMed]

F. Tauser, F. Adler, and A. Leitenstorfer, “Widely tunable sub-30-fs pulses from a compact erbium-doped fiber source,” Opt. Lett. 29(5), 516–518 (2004).
[Crossref] [PubMed]

A. Castrillo, E. De Tommasi, L. Gianfrani, L. Sirigu, and J. Faist, “Doppler-free saturated-absorption spectroscopy of CO2 at 4.3 microm by means of a distributed feedback quantum cascade laser,” Opt. Lett. 31(20), 3040–3042 (2006).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. De Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104(8), 083904 (2010).
[Crossref] [PubMed]

Science (3)

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
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M. Beck, D. Hofstetter, T. Aellen, J. Faist, U. Oesterle, M. Ilegems, E. Gini, and H. Melchior, “Continuous Wave Operation of a Mid-Infrared Semiconductor Laser at Room Temperature,” Science 295(5553), 301–305 (2002).
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D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–640 (2000).
[Crossref] [PubMed]

Semicond. Sci. Technol. (1)

A. Hugi, R. Maulini, and J. Faist, “External cavity quantum cascade laser,” Semicond. Sci. Technol. 25(8), 083001 (2010).
[Crossref]

Other (1)

T. A. Johnson and S. A. Diddams, “Mid-IR Frequency Comb Upconversion Spectroscopy”, in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CPDB11.

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Figures (6)

Fig. 1
Fig. 1 Nonlinear schemes for comb-referencing of a MIR cw laser. (a) Down-conversion of the near-IR comb through difference-frequency-generation (DFG). (b) Up-conversion of the probing laser through sum-frequency-generation (SFG). Comb 1 and comb2 represent a pair of phase-coherent NIR frequency combs.
Fig. 2
Fig. 2 Experimental spectra involved in comb-referencing of a MIR cw laser. (a) Examples of phase-coherent spectra achievable from a dual-branch Er-fiber laser: main output at 1.55 μm (red line) and SC output (coloured lines at shorter wavelengths), together with their frequency difference (horizontal arrows and corresponding labels). (b) Spectrum (light blue) resulting from SFG between QCL (not reported in the figure) and main oscillator output (red line), together with the SC spectrum used for the beating (dark blue), as situated 70 THz far apart the main Erbium output.
Fig. 3
Fig. 3 Experimental apparatus. D: diaphragm, DM: dichroic mirror, PAR: 90° off-axis parabolic mirror, PPLN: periodically-poled lithium niobate, P: prism, PC: personal computer, PD: amplified InGaAs photo-detector, MCT: Peltier.cooled mercury-cadmium-telluride detector, TCO2: cell transmittance; frep = variable laser repetition frequency, as set by PC, frep’ = actual laser rep-rate, as made to coincide with frep by frep-Servo, fbeat: offset frequency used for stabilization of the beating note.
Fig. 4
Fig. 4 Electrical spectrum of the beat-note between comb and QCL. Main panel: phase-locked conditions, 300 kHz resolution bandwidth, 10 kHz video-bandwidth and 20-spectra averaging. Inset: free-running beating, 300 kHz resolution bandwidth, 300 kHz video-bandwidth and 3-spectra averaging.
Fig. 5
Fig. 5 Absorption profiles and line-centre frequencies of a CO2 gas sample. (a) CO2 absorption spectra at a pressure of 7.3 Torr, resulting from a wide scan of the laser rep-rate (bottom scale) and thus of the QCL absolute frequency. The violet and red lines represent two independent measurements, to be referred to the left and right vertical scale, respectively. Dots represent line-centre frequencies and transmitted signals calculated from the HITRAN database for the observed transitions. (b) 5-fold averaged absorption profile of the P15f line of the main CO2 isotopologue (blue line), as obtained from repeated narrower scans (4-kHz wide with 4000 points). The fitting curve (yellow line) was calculated with a Voigt convolution. The residuals of the fitting are highlighted in the bottom part of the panel. (c) Table giving the line-centre frequencies of all investigated lines, from HITRAN and from a multi-line least-squares fitting procedure of the entire CAFS experimental absorption spectrum. Only the significant digits, that is the ones falling within the uncertainty range, are reported for the two sets. For the HITRAN frequencies this range is ± 30 MHz, corresponding to ± 0.001 cm−1, while for the measured set it scales from a minimum of ± 227 kHz (~ ± 0.000007 cm−1) for the most intense lines (~91% absorption) to about 11 MHz (~ ± 0.0004 cm−1) for the less intense ones (<1.8% absorption).
Fig. 6
Fig. 6 Dispersion of the retrieved line-centre frequencies. Each point identifies one out of the 50 independent measurements on the P15f line of the main CO2 isotopologue at a pressure of 7.3 Torr.

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