MOLECULAR SPECTROSCOPY WITH LASER FREQUENCY COMBS NATHALIE PICQUÉ 1,2,3 and THEODOR W. HÄNSCH 1,2 1. Max Planck Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany 2. Ludwig-Maximilians-Universität München, Fakultät für Physik, Schellingstrasse 4/III, 80799 München, Germany 3. Institut des Sciences Moléculaires d Orsay, C.N.R.S, Bâtiment 350, Université Paris-Sud, 91405 Orsay, France Abstract The millions of precisely controlled laser comb lines produced with a train of ultrashort laser pulses can harnessed for highly-multiplexed molecular spectroscopy. Dual-comb spectroscopy is emerging as a powerful new tool. Proof-of-principle experiments already report a million-fold improvement in the recording time, the resolution and the sensitivity of broad spectral bandwidth linear absorption spectroscopy. 1 Introduction Introduced in the late 1990s, laser frequency combs [1,2] have revolutionized precise measurements of frequency and time. The regular pulse train of a mode-locked femtosecond laser can give rise to a regular comb spectrum of millions of laser modes with a spacing precisely equal to the pulse repetition frequency. Optical frequency combs have enabled the development of new ultra-precise optical atomic clocks and commercially available combs have quickly matured to routine instruments for precise optical spectroscopy. Frequency combs are now becoming enabling tools for an increasing number of applications, from the calibration of astronomical spectrographs to molecular spectroscopy. The broad spectral bandwidth and the high-resolution structure of a frequency comb indeed make it an attractive tool for broadband direct absorption molecular spectroscopy and fingerprinting. As for precision spectroscopy of simple atomic systems, in molecular spectroscopy the comb may serve as a frequency ruler against which the frequency of a continuous-wave laser used to probe the sample is calibrated. However in recent years, novel techniques have been developed in which the comb directly interrogates the sample. Direct absorption frequency comb spectroscopy results in short measurement time and high accuracy over a broad spectral bandwidth. Such advances have been demonstrated with Michelson-based Fourier transform (FT) [3-6], dispersive [7-10] and dual-comb based Fourier transform spectrometers [11-21]. Michelson-based Fourier spectrometers record the 1
spectroscopic signal on a single photodetector and therefore present the advantage of an almost unlimited spectral span in any spectral region with Doppler limited resolution. The moving mirror of such scanning time-domain interferometers however inherently limits the measurement time and resolution. The sensitivity for weak absorption may additionally be significantly improved with the coherent coupling of a laser frequency comb to a high finesse-cavity containing the sample. Cavity-enhanced and cavity-ring-down spectroscopies are widely used for ultrasensitive spectroscopic absorption measurements and they have led for long to remarkable progress [22] in fundamental spectroscopy and non-intrusive trace-gas sensing when practiced with tunable narrow bandwidth lasers. In one approach to cavity-enhanced frequency comb spectroscopy, the spectral analysis of the light transmitted through the cavity is performed with a dispersive spectrometer, usually equipped with a detector array. This results [8] in the massively parallel recording of spectra typically spanning 10 nm with GHz resolution and ms acquisition time. Although dispersive spectrometers do not generally allow to directly resolve the comb lines in a motionless short measurement, scanning [9] the comb and cavity modes and implementing Vernier techniques [10] proved successful in improving the resolution, at the price of longer and sequential recordings. However, large detector arrays are not conveniently available in the mid-infrared molecular fingerprint spectral region, where most molecules have intense rovibrational signatures. Recent experiments of multi-heterodyne frequency comb Fourier transform spectroscopy (also called dual-comb spectroscopy) have demonstrated that the precisely spaced spectral lines of a laser frequency comb can be harnessed for the rapid and sensitive acquisition of highly multiplexed spectra of molecules. This approach to frequency comb spectroscopy can work in any spectral region because it uses a single photodetector, and it provides extremely short measurement times. This article discusses some of the distinguishing features of dual-comb spectroscopy. 1 Dual comb spectroscopy principle In a typical implementation of dual-comb spectroscopy (Fig. 1), an absorbing sample is interrogated by a frequency comb laser source. The information encoded by this interrogating comb needs then to be retrieved by a spectrometer. This is achieved by heterodyning the interrogating comb with a second comb, which serves as a reference. It provides simultaneous and accurate access to a broad spectral bandwidth within a short measurement time and can physically be equally understood in terms of time domain interference, multi-heterodyne detection, optical free induction decay, linear optical sampling or cross-correlation between two electric fields. In practice, the light transmitted by the sample is superimposed on a second frequency comb with slightly different repetition frequency. A single fast photodetector then produces an output signal with a comb of radio frequencies due to interference between pairs of optical comb lines. In the frequency domain (Fig.2a), the optical spectrum is thus effectively mapped into the radio frequency region, where it becomes accessible to fast digital signal processing. In the time domain (Fig. 2b), the pulse train of the interrogating comb excites the absorbing sample at regular time intervals. A second pulse train of different repetition frequency 2
Figure 1: Two frequency combs, 1 and 2, have slightly different line spacing. One of these combs, 1, is transmitted through the cell and heterodyned against the second comb, yielding a down-converted radio-frequency comb containing information on the absorption and dispersion experienced by each line of the comb 1. Other implementations allow the two combs to interrogate the sample. a) b) Figure 2: Physical principle of dual-comb spectroscopy. The repetition frequency of the two lasers is respectively f r1 and f r2 and they differ by Δf r<< f r1 The technique requires to keep constant the differences f r1- f r2 and f 01- f 02 during the measurement or to monitor their variations so to make a posteriori corrections a) In the frequency domain, the reference comb 2 with f r2 line spacing acts as a highly multiplexed heterodyne receiver to generate a radio-frequency comb b) In the time domain, the reference comb FC2 pulse train slowly walks through the interrogating pulses from FC1 to generate a measurement I(t) of the interrogating electric field. 3
samples the transient response or free induction decay of the medium, akin to an optical sampling oscilloscope. Here the phase correlations between successive laser pulses are crucial for reproducible sampling, even if the free induction decay happens on a time scale that is short compared to the time interval between two laser pulses. The first low-resolution proof-of-principle experiment was performed [16] in 2004 with unstabilized mode-locked lasers and a few groups have been contributing [11-21] since in the THz, infrared or visible regions. These firsts implementations have demonstrated a very intriguing potential of dual-comb spectroscopy without moving parts for ultra-rapid and ultra-sensitive recording of complex molecular spectra [11]. Compared to conventional Michelson-based Fourier transform spectroscopy, recording times could be shortened from seconds to microseconds [12,13,15], with interesting prospects for spectroscopy of short lived transient species. The resolution improves proportionally to the measurement time. Therefore longer recordings allow high resolution spectroscopy of molecules with extreme precision [14,15], since the absolute frequency of each laser comb line can be known with the accuracy of an atomic clock. Selected experimental examples from our group illustrate these features in the next paragraphs. 2 Real-time broad spectral bandwidth absorption spectroscopy An experiment carried out in the telecommunication region may first be used to highlight an important benefit of dual-comb spectroscopy: the extremely short acquisition times [12,13,15]. Two 1550-nm Er-doped fiber lasers emit ~90 fs pulses at a repetition frequency of the order of 100 MHz and 20 mw average output power. The difference between the repetition rates of the two combs is set to a value ranging between 10 Hz and 20 khz. The combs are actively stabilized. The available spectral domain is limited by the Er:doped fiber oscillators to about 120 nm. A single comb interrogates the cell, which is filled with acetylene. The two comb beams are recombined with a 50-50 beam-mixer. They beat on a fast InGaAs photodiode and the electric signal is amplified and digitized. The upper part of Figure 3 shows an experimental interferogram. Due to the slight mismatch between the constant repetition frequencies of the pulses of the two combs, the interferogram repeats itself at a period, which is the inverse of the difference in the repetition frequencies of the two lasers. Strong bursts occur when pulses from the two lasers overlap. On one side of these bursts, the modulation of the interferogram, zoomed on in the second row of Figure 3, is due to the molecular signatures. When a single comb interrogates the sample, the resulting interferometer can indeed be viewed as the equivalent of a dispersive Fourier transform Michelson interferometer, in which the sample is placed in one arm of the spectrometer. The Fourier transform of a small part of the interferogram time sequence reveals the spectrum (lower part of Fig.3). A spectrum of acetylene in the region of the ν 1 +ν 3 overtone band spans 120 nm and is measured within a single recording of 42 µs, which brings an unapodized resolution of 3 GHz. For comparison, recording such a spectrum with a conventional Fourier transform spectrometer requires more than 10 seconds. The method indeed demonstrates when compared to Michelson-based FT spectroscopy, a million-fold improvement in recording times at identical signal-to-noise ratio. 4
Figure 3: The upper part of the figure displays a typical interferogram. It reproduces periodically, with a period equal to 1/Δf r. Depending on the desired optical resolution, the Fourier Transform (FT) of only a portion of this sequence is calculated. For instance, the FT of an interferogram of 42 µs duration is enough to resolve the Doppler-broadened profiles of the molecular sample, as shown on the lower part of the figure. The entire emission domain of the Erbium-fiber lasers is represented. The last row of the figure shows a zoom on the ν 1+ν 3 band of acetylene, at 3 GHz unapodized resolution, resulting from a 42 µs measurement without averaging. Furthermore, due to the periodic structure of the interferogram, one can analyze spectral information at rates above 200 Hz for spectral resolutions at best equal to the comb line spacing. Techniques [17] to increase the refresh rate by changing the difference in repetition frequencies of the two lasers have been proposed, resulting in an intriguing potential for time-resolved spectroscopy of single events. The sensitivity [11] of molecular fingerprinting with dual-comb spectroscopy is dramatically improved when the absorbing sample is placed in a high-finesse optical cavity, because the effective path length is increased. When the equidistant lines from a laser frequency comb are simultaneously injected over a large spectral range into the cavity holding the gas sample, multiple trace gases may be identified within a few tens of microseconds. The cavity finesse determines the enhancement factor for the intracavity absorption signal. Using femtosecond Yb-doped femtosecond fiber lasers that emit around 1.0 µm (Figure 4), weak overtone molecular transitions could be probed with high sensitivity. As an experimental demonstration, the rovibrational spectrum of ammonia, a molecule of astrophysical and environmental interests, is recorded in the region of the 3ν 1 band. The cavity finesse F > 1200 enhances the effective absorption length to 880 m. In Fig. 5, the cavity transmission spans about 20 nm and the spectrum consisting of 1500 spectral elements, with 4.5 GHz resolution and a signal-to-noise ratio of 380, is measured within 18 µs. The weak overtone transitions of the 3ν 1 band are rotationally resolved for the first time, to our knowledge. The minimum-detectable-absorption coefficient α min and the 5
noise-equivalent absorption coefficient at 1s-time averaging are 3 10-8 cm -1 and 1 10-10 cm - 1 Hz -1/2, respectively. This proof-of-principle experiment [11] already demonstrates, with a 100-fold shorter measurement time, a α min coefficient, which is 20-fold better than the one reported in [8]. The spectral bandwidth is presently limited by the Ytterbium amplifier. However, special mirror design managing dispersion has demonstrated [8] to overlap the cavity modes and the comb components across 100 nm simultaneously and the multiplex spectrometer principle allows for the measurement of multi-octave spanning spectra. Therefore a bandwidth of 100 nm should easily achievable by the spectral broadening of the combs with highly nonlinear optical fibers. Figure 4: The interrogating comb pulses are amplified and coupled to a resonant high finesse cavity, which has a free spectral range of 130 MHz and which holds the absorbing sample. The comb is locked to the cavity with a Pound-Drever-Hall scheme. The light leaking out of the cavity beats with the reference comb on a fast photodiode and the electric signal is digitized with a high resolution acquisition board. The Fourier transform of the time domain interference signal reveals the absorption spectrum. Figure 5: Cavity-enhanced dual-comb spectrum of the crowded region of the 3ν 1 overtone band of ammonia. 3 Towards precision dual-comb spectroscopy Frequency combs proved a revolutionary tool for frequency metrology. In dualcomb spectroscopy, increasing the measurement time and including in the Fourier transform calculation a sequence that comprises more than two bursts (upper part of Figure 3) enables to resolve the individual comb lines. The resulting spectra [13] are sampled by 6
Figure 6 : Dual-comb spectrum spanning 105 nm with 420 khz apodised optical resolution. The Fourier transform of an interferogram made of 536 millions samples recorded in 3.35 s is successively zoomed to display very well resolved comb lines and a single experimental comb line profile drawn on such a frequency scale that the entire spectrum would need a 90 km-wide page. Figure 7: Spectrum of resolved comb lines with KHz width in the optical domain in a 536 Megasamples dualcomb spectrum measured within 6 s. a, 1-nm wide spectrum revealing several acetylene profiles shaping the discrete comb line intensities. b, Zoom on the P e(27) line of the ν 1+ν 3 band. c, Zoom on one single comb line illustrating the 2,300 Hz apodised optical resolution. combs of 100-MHz line-spacing that may cover domains of tens of nm (Figure 6) with comb lines exhibiting khz optical linewidth (Figure 7). A dense grid of accurate frequency markers therefore allows for precise self-calibration of the frequency scale. However the molecular spectra are sampled by the comb line spacing, with a step equal to the repetition frequency. As the comb repetition frequency most often lies between 50 MHz and 200 MHz, most of molecular profiles at room temperature in the gas phase are appropriately sampled by the line spacing of the comb. In case better resolutions would be needed, interleaving techniques [13,15] may sample the spectra down to the ultimate optical 7
resolution imposed by the width of the comb lines. 4 Adaptive dual-comb spectroscopy The recording of distorsion-free spectra requires demanding servo-control [13-15] of the laser combs or computer-based a posteriori corrections [20]: typically the timing jitter from the subsequent interfering pulses has to be of the order of 1 to 10 attoseconds. When this is not achieved, chromatic distortions, called phase errors, cannot be accounted for a posteriori and produce artifacts, which may totally scramble the spectral information. Most of the potential applications of dual-comb spectroscopy require the recording of broadband spectra without sharp features, as they are e.g. encountered in the gas phase with Doppler-broadened transitions or in the liquid phase. Simple instrumental schemes that would keep the very fast recording times of dual-comb spectroscopy are therefore desirable. An adaptive sampling technique that allows recording such distorsion-free spectra with free-running femtosecond lasers has been developed and it has been demonstrated with commercial fiber lasers emitting around 1.0 µm. Adaptive sampling [22] allows for fluctuations in the repetition frequency and pulse-to-pulse phase shift of the femtosecond lasers and produces a clock signal synchronous to these fluctuations that triggers the sampling of the interference pattern generated by the two combs. This adaptive sampling uses the reference signal of the beat between one pair of lines of the two combs. This reference signal is then electronically multiplied to meet the Nyquist criterion, producing a clock for data acquisition, which compensates for the optical delay fluctuations of the interferogram, so that sampling occurs at even optical delays, leading to distortion-less spectra. In an implementation of the adaptive sampling scheme, free-running commercial Ytterbium femtosecond lasers are used with a repetition frequency of 100 MHz and a difference in repetition frequency of about 121 Hz. The lasers are placed in a basic laboratory environment, without air-conditioning system, vibration isolation or dust protection. Each laser beats with a continuous-wave 1040 nm ytterbium fiber laser. Mixing the beating signal generates a 20 MHz reference that is frequency-multiplied four-fold to produce a 80 MHz clock signal which is connected to the external clock input of the data acquisition board. The two femtosecond lasers beams are also combined on a beam mixer and interrogate a Fabry-Pérot resonator with a free spectral range of 49.1 GHz and a finesse of 22.3. The time-domain interference pattern of the Fabry-Pérot transmission is sampled by the data acquisition board at the clock frequency. An interferogram with 131072 samples measured within 1.6 ms is Fourier transformed to uncover a spectrum with 489 MHz resolution displayed in Figure 8. Figure 8a shows the full spectral span. Figure 8b compares a small portion of the spectrum resulting of an interferogram with adaptive sampling and that of an interferogram sampled with internal clock of the data. Without the adaptive sampling, not only the transmission function of the resonator is spectrally strongly scrambled but also successive acquisitions dramatically differ so that averaging spectra is impossible. 8
a) b) Figure 8: a. Fabry-Pérot transmission spectra taken with the adaptive sampling technique over the full emission range of Yb fs lasers. The red line marked cw indicates the frequency of the continuous-wave laser used to isolate the beating signal between one line of each comb. The correction for the relative comb fluctuations is better in the vicinity of this frequency. b. Comparison between spectra measured with free running lasers and a) the adaptive clock, b) the internal clock of the data acquisition board. Five sequential spectra (N=1-5) and their average are shown. 4 Conclusion The spectral structure of sharp lines of a laser comb proves very useful even in the recording of broadband spectra without sharp features, as they are e.g. encountered for molecular gases or in the liquid phase. Dual-comb spectroscopy demonstrates a millionfold improvement in the recording time, the resolution and the sensitivity of broad spectral bandwidth linear absorption spectroscopy. A similar improvement in the accuracy may come into reach with Doppler-free spectra. Laser combs in combination with other advancing tools of laser science, nonlinear optics, photonics, and electronic signal processing may vastly enhance the range and capabilities of molecular laser spectroscopy. Molecular physics with laser frequency combs is however still in its infancy. Several challenging issues, like the development of suitable comb sources in the molecular fingerprint mid-infrared and ultraviolet regions, still need to be overcome before the full potential of such techniques can be realized. The interdisciplinary scientific outcomes of comb-based spectroscopic tools will mostly depend on the instrumental characteristics that will be achieved, but frequency comb spectroscopy might establish the basis of groundbreaking spectroscopic tools and open up new insights in the understanding of the structure of matter as well as new horizons in advanced diagnostics instruments, for instance in chemistry or biomedicine. Acknowledgements Research conducted in the scope of the European Associated Laboratory European Laboratory for Frequency Comb Spectroscopy. Support by the Max Planck Foundation, the Munich Center for Advanced Photonics, the Triangle de la Physique, the E.A.D.S Foundation, the Conseil Général de l Essonne and the Agence Nationale de la Recherche is gratefully acknowledged. Guy Guelachvili, Birgitta Bernhardt, Patrick Jacquet, Takuro Ideguchi, Julien Mandon and Antonin Poisson are warmly acknowledged for their contribution to the work reported here. 9
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