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Techniques developed to control a train of ultrashort pulses in the frequency domain have led to rapid advancements not only in ultrahigh-precision metrology1 but also in the generation of attosecond pulses for time-resolved studies15. This close relationship between time and frequency techniques continues with the development of the extreme-ultraviolet (XUV) frequency combs, in which high-harmonic generation (HHG), a standard technique in attosecond physics, is used to produce phase-coherent XUV radiation. In conventional HHG, a single infrared pulse generates a burst of attosecond pulses separated by half cycles of the driving laser field, resulting in an odd-harmonic spectrum (Fig. 1). By contrast, in intracavity HHG, a phase-coherent infrared pulse train is used to produce a train of such bursts that repeat at the repetition frequency of the fundamental comb. This new temporal structure is responsible for the much finer frequency comb at each harmonic order. We anticipate that the XUV frequency comb will allow high-precision characterization of the HHG process and provide further insights into attosecond physics.

Figure 1: Intracavity high-harmonic generation.
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An infrared frequency comb is passively amplified in a power build-up cavity with a mirror/diffraction grating hybrid output coupler for the XUV range26. Xenon gas is introduced at the tight focus of the cavity. The resultant HHG spectrum (top inset) from a single infrared pulse consists of odd harmonics of the infrared carrier frequency, ν0. By using an infinite train of pulses, we create a new comb structure in every harmonic at the repetition frequency (frep) of the pulse train (lower insets). This comb structure is stabilized using a continuous-wave laser (frequency, νYAG) and slowly scanned over an argon transition (frequency, νAr) at 82 nm. νXUV and νNIR respectively represent frequencies in the XUV and near-infrared spectral regions.

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The existence of the XUV comb structure is critically dependent on the phase coherence of the HHG process. The temporal coherence of HHG in an isolated pulse has been studied extensively16,17, but the requirements are more stringent for XUV comb generation, where the phase coherence must be maintained over many consecutive pulses. This issue has been a topic of investigation since the first demonstrations of intracavity HHG3,4, in which only the phase coherence of the third harmonic was verified. In subsequent work, pulse-to-pulse temporal coherence of the seventh harmonic at 152 nm, below the ionization threshold, was demonstrated interferometrically18. The pulse-to-pulse phase coherence of above-threshold harmonics in the XUV range was first demonstrated in ref. 8. This coherence was critical for two-pulse Ramsey spectroscopy of helium at 51 nm with a systematic uncertainty of 6 MHz (ref. 8) in a widely tunable system19. We note that this approach differs fundamentally from the work presented here. The two-pulse Ramsey sequence is a phase measurement and, as a result, is susceptible to systematic phase errors between the two pulses. These errors lead to apparent frequency shifts. Thus, all sources of phase error must be considered and characterized before an absolute frequency measurement can be made. By contrast, a frequency comb consisting of an infinite pulse train is an optical frequency synthesizer with equally spaced frequency comb teeth, defined by only two numbers: the repetition frequency (frep) of the pulse train and the carrier envelope offset frequency (fceo). Thus, the phase instabilities can lead to broadening of the comb teeth, but the absolute frequencies of the XUV comb remain simply and robustly determined. It is precisely this characteristic that led to the recent frequency comb revolution in metrology even though multipulse Ramsey spectroscopy in the visible and infrared spectral regions has existed since the late 1970s20. In this Letter, we demonstrate the extension of frequency comb spectroscopy to the XUV spectral region, which will lead to many applications in short-wavelength metrology.

In intracavity HHG, a high-average-power infrared frequency comb5 is coupled to a dispersion-controlled optical cavity (Fig. 1), which allows for passive coherent pulse build-up at the full repetition rate of 154 MHz (Supplementary Information). The high repetition rate of intracavity HHG should in principle provide increased average flux relative to conventional single-pass HHG systems, which typically use lasers with repetition frequencies and average powers that are smaller by orders of magnitude. However, until now the presence of the optical cavity has presented challenges to matching the average flux of these systems, owing to optical damage problems associated with the large average intracavity power and to the nonlinear-response of the HHG medium. At the high intensities and gas densities required to optimize the XUV flux, the plasma density at the intracavity focus reaches levels that can lead to various nonlinearities such as optical bistability, self-phase modulation and pulse distortion. Recently, these effects have been studied in detail with both simulations and experiments21,22. These effects, amplified by the narrow cavity linewidth, clamp the achievable intracavity peak power and lead to instabilities in the lock between the comb and the cavity, limiting the attainable XUV flux and coherence time. Thus, a robust means of mitigating these effects is to decrease the finesse. However, this requires that a more powerful laser be used to excite the enhancement cavity to keep the intracavity pulse energy high. This obstacle has been overcome by recent advances in high-repetition-rate, high-average-power chirped-pulse amplified Yb:fibre lasers5,23,24,25.

Our ability to reach high intracavity pulse energies while minimizing the deleterious effects of a large plasma density has resulted in the generation of unprecedented power in high harmonics spectrally separated for spectroscopy. We measure the power in the fifteenth harmonic to be 21 μW with xenon as the target gas (Fig. 2), which corresponds to more than 200 μW per harmonic produced in the cavity. This is an increase of more than an order of magnitude over previous intracavity HHG results26,27. Similar outcoupled power (not spectrally separated) was recently reported28. We have also observed shorter-wavelength radiation by using krypton as the target gas for HHG. Owing to the higher ionization potential of krypton, we were able to detect the twenty-fifth and twenty-seventh harmonic orders with 8 kW of intracavity power (peak intensity of 9 × 1013 W cm−2) (Fig. 2c), extending intracavity HHG to photon energies above 30 eV. As shown in Fig. 2d, there are only modest improvements in power for most harmonics as the intracavity infrared power is increased above 5.5 kW. As the plasma density increases, depletion of the on-axis neutral atomic density and a decrease in phase matching cause the XUV power clamp. These results show that future gains in harmonic power in a similar system will most probably be achieved by increasing the focal area at the interaction region.

Figure 2: Power scaling results.
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a, Characteristic image of the harmonics in xenon dispersed on a plate coated with fluorescent material. The threshold of the image was adjusted for the twenty-third harmonic to make it more visible. b, c, Vertically integrated intensity from a charge-coupled-device (CCD) image for xenon (b) and krypton (c) target gas, and corresponding integrated harmonic powers (Methods Summary). The observed widths of the harmonic orders are given by the instrument wavelength resolution. The photon flux has been normalized by the spectral bandwidth. d, Harmonic powers generated in xenon as functions of infrared intracavity power, showing saturation at powers greater than 5.5 kW. The oscillations visible for some harmonics are due to quantum path interference18.

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To demonstrate the comb structure of XUV radiation, we have spectrally resolved the 3s23p6 J =  0 → 3s23p55d J = 1 electric dipole (E1) transition in argon with an upper-state energy of 121,932.8 cm−1 (corresponding to a wavelength of ∼82 nm) and the 2s22p6 J =  0 → 2s22p54s J =  1 E1 transition in neon with an upper-state energy of 159,534.6 cm−1 (∼63 nm) by means of resonance fluorescence spectroscopy. These transitions lie within the thirteenth and seventeenth harmonic bandwidths of our source, respectively. To reduce the Doppler width of the transition below the repetition frequency of the comb, we use pulsed supersonic atomic beams propagating orthogonally to the XUV beam. The average harmonic power available for spectroscopy is ∼1 μW owing to a single reflection from a mirror to steer the XUV beam into the interaction region and several pinholes to isolate the central part of the beam that contains the phase-coherent short trajectories18. Moreover, owing to the electric dipole nature of these transitions, only a single comb tooth with ∼10−5 of the total power, 10 pW, contributes to the signal. Nevertheless, we have achieved a ratio of signal to scattered photon background in the range of 0.5–1 using a photomultiplier tube to detect directly the XUV spontaneous emission to the ground state.

The fundamental infrared comb is controlled by phase-locking a comb tooth to a continuous-wave neodymium-doped yttrium aluminium garnet (Nd:YAG) laser by feedback onto the laser cavity length2. The Nd:YAG laser frequency (νYAG) is referenced to a molecular iodine transition and serves as an absolute optical frequency marker with an uncertainty of 5 kHz (ref. 29). The comb offset frequency, fceo, has a free-running linewidth of 15 kHz (ref. 5) and is adjusted to optimize intracavity power, but is otherwise unlocked. Its value is deduced from the knowledge of νYAG and frep, which we measure against the hydrogen maser at the US National Institute of Standards and Technology (Supplementary Information). Figure 3 shows the fluorescence signal as the phase-locked-loop offset frequency, δ, is slowly changed and XUV comb teeth are scanned across the atomic resonance for two different collimation angles of the atomic beam. With the scattered photon background subtracted, the signal contrast is 100%, confirming the sharp comb structure. Least-squares fits for the argon data reveal respective Gaussian full-widths at half-maximum of 47 ± 5 and 11 ± 1 MHz for the two angles. These results are consistent with what would be expected from the geometric collimation. Thus, the observed linewidth places only an upper bound on the comb teeth linewidth, and this bound is less than 10 MHz. The statistical uncertainty in the determination of the line centre for the narrower line shape is 500 kHz, demonstrating an unprecedented fractional frequency precision of better than 2 × 10−10 in the XUV range.

Figure 3: Atomic fluorescence signal.
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a, b, Photomultiplier signals as functions of an XUV comb tooth frequency for argon beam collimation angles of ∼4 mrad (a) and ∼1 mrad (b). The signal is normalized to the incident XUV power and the scattered photon background is subtracted (Methods Summary). Error bars (1 s.d.) are determined from the shot noise of counted fluorescence photons. The red curves are least-squares fits to a Gaussian model. c, Signal for the neon transition with a collimation angle of ∼4 mrad. The contrast and signal-to-noise ratio are lower owing to the increased Doppler width and the smaller absorption cross-section, respectively.

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To determine the absolute frequency of the argon transition, it is necessary to determine the comb tooth number in addition to frep and fceo. This requires making several measurements at different values of frep and keeping track of the change in the comb tooth number (Supplementary Information). Figure 4 shows the results of ten measurements at different values of frep chosen to provide absolute comb mode determination. The data analysis is carried out by noting that the fixed point of the infrared comb (comb tooth phase locked to the Nd:YAG laser) is multiplied by the HHG process to create corresponding fixed points for every harmonic comb. These fixed points are offset from qνYAG by Δ = qδ(modulo frep), where q is the harmonic order. Thus, the argon transition frequency is

where n is the absolute comb tooth number and m is the difference in comb tooth number between the thirteenth harmonic fixed point and the actual comb tooth probing the argon transition. This point of view not only makes the analysis independent of drifts in fceo, but also highlights the direct frequency link between the infrared and the higher-harmonic combs.

Figure 4: Absolute frequency determination.
figure 4

Measurement of the resonance centre frequency at ten different values of frep parameterized by the offset, Δ, of the thirteenth harmonic fixed point from 13νYAG. The top part of the figure schematically illustrates two different measurements at frep1 and frep2, with corresponding respective offsets of Δ1 and Δ2. The short black lines represent the locations of individual frequency comb teeth. In the main plot, the solid red lines show the expected locations of the resonance centres for the extracted comb tooth number, m, and the pairs of blue dashed lines show the expected locations for m ± 1. Inset, magnified version of a measurement, demonstrating that the comb tooth number is unambiguously determined.

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Once m is determined, we correct the final value for residual Doppler shifts arising from imperfect orthogonal alignment of the laser and the atomic beam. This is done by comparing the measured transition frequency of a pure argon beam (velocity of 520 ± 20 m s−1) with that of a helium–argon mixture (5:1 ratio of partial pressures; velocity of 740 ± 60 m s−1) and translating the collimation slit until the two measured frequencies match, ensuring orthogonality between the laser and the atomic beams. Owing to the small fractional change in the velocity of the two beams, the uncertainty in the procedure is ∼3 MHz. All other systematic shifts such as recoil, density and Stark shifts, as well as the contribution due to the uncertainty in νYAG, are estimated to be smaller than 1 MHz. We have also binned our data for different laser operation conditions and find no systematic shifts at the 2-MHz level for a 30% change in xenon backing pressure or a 20% change in the intracavity power for HHG, again highlighting the robustness of the XUV comb for frequency measurements. The final absolute frequency for this transition is 3,655,454,073 ± 3 MHz, which agrees well with previous measurements that have an uncertainty of 2.3 GHz (ref. 30).

Now that the XUV frequency comb has been developed into a robust tool, it is imperative to determine its ultimate coherence. The current upper bound on the thirteenth harmonic comb linewidth is less than 10 MHz, limited by the atomic thermal motion. We plan to implement a heterodyne beat measurement between two intracavity HHG sources to overcome this limitation, improving the phase noise characterization by orders of magnitude. With these developments, ultrahigh-precision spectroscopy in the XUV range is firmly within our grasp, enabling a wide range of applications.

Methods Summary

The Yb:fibre comb delivers 120-fs pulses at a 154-MHz repetition frequency with a maximum average power of 80 W (ref. 5). For the studies presented here, we run the laser at ∼30 W. Target gas is injected at the intracavity focus using a glass nozzle with a 100-μm aperture and a backing pressure of ∼2 atm. The XUV light is coupled out of the cavity using an intracavity diffraction grating with 10% efficiency26.

The power of the thirteenth harmonic is measured with an XUV photodiode. The power in the other harmonics is determined using a plate coated with sodium salicylate, which fluoresces at 420 nm when excited by XUV radiation, with uniform quantum efficiency between 40 and 100 nm (ref. 18). The fluorescence is imaged using a CCD camera and calibrated using the thirteenth harmonic, which can be measured with either the photodiode or the CCD. The estimated calibration uncertainty is 20–30%.

The supersonic argon source consists of a pulsed valve nozzle (0.5-mm diameter), a 0.5-mm-diameter skimmer and a secondary slit located 33 cm from the skimmer. Both the slit width and slit position can be adjusted to study the Doppler width and shifts. The valve generates 500-μs-long pulses at a repetition rate of 20 Hz with a backing pressure of 0.5 atm.

The fluorescence is detected with a photomultiplier tube and pulse counter. The counter has two gates: one coincident with the argon pulse arrival time, to measure the signal; and another located between argon pulses, to measure the background. Most of the laser light passes through the interaction region unimpeded and is detected with a second XUV photodiode, which provides the normalization signal. Individual frequency scans take ∼150 s. Results presented in Fig. 3 are averages of 3–10 scans with an acquisition time of 8–25 min.