Previous work has shown that use of a passive enhancement cavity designed for ultrashort pulses can enable the up-conversion of the fs frequency comb into the extreme ultraviolet (XUV) spectral region utilizing the highly nonlinear process of high harmonic generation. This promising approach for an efficient source of highly coherent light in this difficult to reach spectral region promises to be a unique tool for precision spectroscopy and temporally resolved measurements. Yet to date, this approach has not been extensively utilized due in part to the low powers so far achieved and in part due to the challenges in directly probing electronic transitions with the frequency comb itself. We report on a dramatically improved XUV frequency comb producing record power levels to date in the 50–150nm spectral region based on intracavity high harmonic generation. We measure up to 77 μW at the 11th harmonic of the fundamental (72nm) with μW levels down to the 15th harmonic (53nm). Phase-matching and related design considerations unique to intracavity high harmonic generation are discussed, guided by numerical simulations which provide insight into the role played by intracavity ionization dynamics. We further propose and analyze dual-comb spectroscopy in the XUV and show that the power levels reported here permit this approach for the first time. Dual-comb spectroscopy in this physically rich spectral region promises to enable the study of a significantly broader range of atomic and molecular spectra with unprecedented precision and accuracy.
© 2011 OSA
The fs frequency comb has had a profound impact on both precision spectroscopy and ultrafast science, enabling significant advances across both fields. By providing a coherent link between optical and microwave frequencies, the frequency comb has dramatically accelerated the development of optically based atomic clocks  and advanced the frontiers of spectroscopic tests of fundamental physical laws . However, many atomic, molecular, and even nuclear transitions [3, 4] of great physical interest are located in the vacuum (VUV) and extreme ultraviolet (XUV) spectral region, remaining relatively inaccessible to the precision and accuracy enabled by the fs frequency comb. Recent work by several groups has focused on improving the spectral resolution in the XUV utilizing, for example, Fourier transform spectroscopy with synchrotron sources [5, 6], or through multi-pulse Ramsey spectroscopy with sources based on high-harmonic generation (HHG) of visible laser systems[7, 8]. Although powerful tools for many studies, the precision and accuracy of these approaches is orders of magnitude less than what is possible with the fs frequency comb.
Work initially demonstrated in 2005 [9, 10] showed that the fs frequency comb can be up-converted to the XUV utilizing fs enhancement cavities (fsEC’s) [11, 12] designed to support ultrashort pulses and increase the intracavity pulse energy to levels suitable for HHG. This approach offers the potential for a highly efficient and extremely coherent table-top source of VUV to XUV radiation suitable for precision spectroscopy as well as for time resolved experiments at high repetition rates. Subsequent work improved upon the generated XUV power levels and cavity designs [13, 14, 15] and provided an understanding of the dynamic interplay between the intracavity pulse evolution and ionization of the gas target [16, 17].
We report here on a significantly improved XUV frequency comb based on a novel high power Ti:sapphire-based laser system and optimized fsEC design. The demonstrated power levels of 10–77 μW in the 50–150 nm spectral region promises to establish the XUV frequency comb as a powerful tool enabling precision spectroscopy in the VUV to XUV. Although such higher power sources are needed, the complex and varied spectra of atomic and molecular transitions combined with the dense spacing of the fs comb structure makes implementing precision spectroscopy in this spectral region challenging and highly dependent on the system being studied. Recent results have demonstrated for the first time the direct measurement of a single-photon transition in argon at 82 nm using a gas jet and a continuous XUV frequency comb. This initial result confirms the coherent structure of the XUV comb, yet such direct spectroscopic approaches are limited to investigation of narrow and well isolated transitions. We propose and analyze in the last section the use of dual-comb spectroscopy [18, 19] to address these challenges and enable a robust approach to precision spectroscopy in this physically rich spectral region, enabling broad spectral coverage without compromising precision or accuracy. We discuss estimates of signal-to-noise ratios (SNR) that can be achieved given the power levels of our current system that demonstrates the feasibility of this approach.
2. Experimental setup
High power laser sources based on fiber technology have been pursued by several groups in an effort to improve the overall performance and power of the XUV frequency comb [20, 21, 22]. Ti:sapphire based frequency combs, however, offer greater wavelength tunability useful for spectroscopy, and operate at shorter wavelengths which can improve overall HHG conversion efficiency. A drawback, however, is the challenge in scaling the average power of the frequency comb in such bulk solid-state laser systems compared to fiber based sources. In previous work, our group achieved very high efficiency in amplification of a solid-state Ti:sapphire fs frequency comb to a record 7 Watts average power based on our demonstration of injection locking a fs amplification cavity (fsAC) . Here, we utilize a fs frequency comb and fsAC operating at 50 MHz to generate 80 fs pulses with up to 6 Watts average power. This high power frequency comb source provides over 100 nJ’s per pulse incident on the fsEC for HHG.
A schematic of the experimental system is shown in Fig. 1. The 600 mW pulse train from a standard homebuilt Ti:sapphire fs frequency comb is stretched to ≈ 4 ps in SF10 glass to reduce the peak power per pulse before amplification. The stretched pulse train is actively stabilized to a second Ti:sapphire cavity using a small modulation of the cavity length to generate an error signal. This fsAC is pumped with 18.5 Watts (532 nm) where it regeneratively amplifies the injected pulse train up to 6 Watts. The input coupling to the fsAC is 40%. Without being seeded by the fs frequency comb, the fsAC does not mode-lock and operates in a quasi-cw mode on multiple frequencies. In previous work we verified that when sufficiently injection locked the fsAC preserves the coherence of the original fs comb . The amplified pulse train is compressed back to its original Fourier-transform limit of ≈ 80 fs using a pair of SF11 prisms with ≈4 meters separation and then spatially mode-matched to the fsEC where the incident pulse energy is enhanced from 100 to 200 times (depending on the input coupler used). This results in an 80 fs intracavity pulse with up to 25 μJ pulse energy. Depending on the fsEC design, the intracavity intensity can reach > 1×1014 W/cm2. In recent work , we showed that the plasma resulting from the ionization of a xenon gas target near the intracavity focus (see Fig. 1) can prevent stable locking to the fsEC due to the dynamic phase shift imparted on the pulse. This fundamental limit to pulse enhancement requires that we limit the intracavity peak intensity to < 1014W/cm2 in our fsEC design. For the results presented here, a 1% input coupler was used to generate up to 15μJ pulses with an intracavity beam waist of 2×wo ≈ 30μm. The larger input coupling compared to previous work [9, 10] minimizes the spectral filtering of the fsEC due to linear dispersion and likewise reduces its sensitivity to the nonlinear response of the generated plasma. The increased beam waist, as we will discuss, greatly minimizes the Gouy phase mismatch between the fundamental and harmonic light  in addition to increasing the overall interaction volume.
Xenon gas is introduced at the intracavity focus using a nozzle with a 1mm inner diameter and a 100μm×300μm rectangular slit at the end which is positioned above the region of the cavity beam waist. In this way we can switch between two different interaction lengths defined approximately by the orientation of the slit with respect to the optical axis. The actual interaction length and pressure at the focal region depends strongly on the position of the nozzle due to the effusive expansion of the gas into the vacuum chamber. Based on fluid flow simulations  we estimate the actual pressure may be an order of magnitude less than the backing pressure used, while the actual interaction length may vary up to twice the length of the slit. Fluid flow simulations also predict that the use of the rectangular slit compared to a circular aperture can be advantageous in maximizing the actual gas pressure within the focal volume for a given backing pressure . The fsEC utilizes a 250 μm sapphire plate placed at Brewster’s angle for the fundamental beam to couple out the intracavity high harmonics generated as the intense intracavity pulse ionizes the injected xenon gas, as has been done in previous designs [9, 10]. The reduced thickness of the sapphire plate compared to previous designs helps minimize the Kerr nonlinearity which can degrade the power enhancement and pulse spectrum  and minimizes the amount of dispersion compensation required from the fsEC mirrors. To compensate for the sapphire plate group delay dispersion, the center wavelength of the laser spectrum is shifted from that of the center wavelength of the low loss mirrors (whose group delay dispersion varies with wavelength). This results in near zero group delay dispersion for the intracavity pulse.
3. Experimental results
The generated harmonics reflected from the sapphire plate are separated with a Pt coated concave grating (2400 g/mm) and imaged onto a sodium salycilate phosphor screen. The grating is designed for a peak diffraction efficiency at 80nm, with a rapidly decreasing efficiency below 60nm (see Fig. 2a). The fluorescence spectrum from the screen is imaged onto a ccd camera located outside the vacuum chamber for analysis. Figure 2 shows the recorded high harmonic spectrum when using a 300 μm interaction length and ≈500 Torr backing pressure. Figure 2b shows the image of the phosphor screen from the ccd camera. The intracavity power was ≈ 600 Watts (12 μJ pulse energy). Harmonics are observed down to the 15th of the laser fundamental (53nm), potentially limited by the grating efficiency. We calculate the 15th harmonic as the cutoff harmonic given our intracavity intensity. To carefully measure the absolute power in the XUV, the phosphor screen was replaced with a calibrated silicon photodiode with a 150 nm thick integrated aluminum filter (AXUV100Al from International Radiation Detectors). This detector has an independently calibrated responsivity (performed at NIST) at wavelengths near 72 nm while providing approximately 5 orders of magnitude suppression of the fundamental light at 800 nm. Using a slit immediately in front of the photodiode we isolated the 11th harmonic and monitored the average power coupled out of the fsEC. We found this combination of grating and filtered photodiode necessary to eliminate stray light and spurious signals and provide reliable power measurements.
Table 1 shows the estimated power of 77 (±15)μW for the 11th harmonic. The ±20% uncertainty in the estimated power takes into account uncertainties in the detector responsivity and grating efficiency (the latter based on the manufacturer’s theoretical estimates of groove uniformity). The power in the remaining harmonics is calculated based on the relative power levels from the lineout of the ccd image as shown in Fig. 2a. Due to the unconfirmed linearity of the phosphor image, our results are most accurate for the 11th harmonic alone. These power levels are the highest yet achieved for a frequency comb operating in this wavelength region, and make the XUV source a powerful tool for many applications including precision spectroscopy, time resolved experiments operating at high repetition rates, and angle-resolved photoemission spectroscopy to name a few. The results are more than an order of magnitude greater than previously demonstrated [14, 13] with the exception of very recent work in which > 20μW was generated near 71 nm based on a high power fiber laser system .
These results establish intracavity HHG utilizing a fsEC as a powerful source of highly coherent light for future experiments in the VUV and XUV. We note, however, that at these power levels damage to the sapphire plate from the generated harmonics currently limits the continuous operation of the system, requiring periodic translation of its surface to recover full power. This limitation is in addition to nonlinear damage of the dielectric mirrors that can occur due to the high intensity of the fundamental beam, as described in previous work . Damage of optical components under continuous VUV and/or XUV irradiation in a vacuum environment is a well known and problematic phenomena, often attributed to the single photon ionization of contaminants such as hydrocarbons that can enable secondary chemical reactions on the surface of the sapphire substrate . We are currently investigating ways to mitigate such limitations beyond just a cleaner vacuum environment, including the possible rotation of the sapphire substrate itself or utilizing alternative output coupling methods (e.g. [28, 13, 29]). However, we observe significantly increased operation times when the XUV power level is kept below ≈40 μW. For example, when using the 100 μm xenon interaction length (by rotating the gas jet aperture), the maximum power in the 11th harmonic is reduced to ≈37 μW but the system reliability is improved. As damage is less severe at these power levels, we utilize results taken with the 100μm nozzle orientation in the following discussions on intracavity high harmonic generation.
The XUV power levels demonstrated here are due in large part to the improved Ti:sapphire-based high power frequency comb seeding the fsEC, which enables: (1) a larger input coupling to reduce the cavity finesse and (2) a larger intracavity beam waist, while still reaching intensities necessary for ionization of the gas target. The lower cavity finesse minimizes the restrictive spectral filtering of the fsEC due to linear dispersion  and enables robust active stabilization of the frequency comb to the cavity. Furthermore, the sensitivity of the system to plasma-induced phase shifts [16, 17] is greatly minimized compared to higher finesse cavities (as we discuss shortly with the aid of numerical simulations). The larger beam waist not only increases the interaction volume but significantly improves the macroscopic phase-matching between the fundamental and the generated harmonics. With intracavity pulse energies of 10–20 μJ per pulse in such experiments, tight focusing to a small beam waist is typically required to reach intensities needed for sufficient ionization of xenon (> 5 × 1013W/cm2) as compared to more traditional free-space single-pass experiments in which >100 μJ pulse energies are available from low repetition rate amplified laser systems. As a result, minimizing the Gouy phase mismatch between the driving laser field and the generated XUV harmonics becomes an important factor in optimizing the overall HHG efficiency inside the fsEC. In our experiments, we note a significant increase of the harmonic yield when making a seemingly modest change to the intracavity beam waist from ≈ 20μm to 30μm.
To highlight the affect of the beam waist on the phase-matching conditions typically found in such intracavity HHG experiments, we limit the discussion for the moment to the low intensity limit in which contributions from the intrinsic atomic phase  are negligible and the ionization fraction is small. (Recent work has also taken into consideration the role of the intrinsic atomic phase on the intracavity harmonic yield [31, 32].) Fig. 3a shows the calculated absorption (labs) and coherence (lc) lengths of the 11th harmonic for different intracavity beam sizes as a function of pressure. We estimate that achievable target gas pressures in our current vacuum chamber design remain less than 100 Torr. The coherence length determines the length scale at which the harmonic field can coherently grow and is defined as lc = π/Δk, where the total wavevector mismatch Δk = δkm + δkGouy. Here, δkm accounts for the phase mismatch between the fundamental beam and the generated harmonic arising from the positive neutral gas dispersion and the negative dispersion of the generated plasma, while δkGouy represents the negative phase mismatch due to the differing Gouy phase shift of each field (which goes as ). For this example we assume a constant ionization level of ≈ 7% based on our numerical simulations (discussed shortly). We note that the sign of the phase mismatch due to the generated plasma is the same as that from δkGouy, and therefore high ionization levels would be detrimental to the overall phase-matching conditions. For the generated harmonic field to coherently grow, the coherence length must be sufficiently long compared to the interaction length defined by the gas target (lmed). Figure 3a demonstrates the significant increase in the coherence length with increasing beam size due to the reduction in δkGouy. In the wavelength region of interest here (50–100 nm), reabsorption will ultimately limit the generated harmonic yield at sufficiently high pressures provided lmed is much longer than labs as discussed in . In Fig 3b. we compare the predicted yield for the 11th harmonic versus pressure for various beam waists based on the analytic expression obtained in :Figure 3b demonstrates how a small increase to the intracavity beam waist can significantly improve the phase-matching conditions and therefore the generated harmonic power. The improved phase-matching in our current fsEC design contributes to the higher XUV power levels reported here. In principal, the phase mismatch from δkGouy can be compensated by increasing the gas pressure, and therefore increasing δkm, so long as the ionization fraction remains low. In practice, however, the pressures required for this are often difficult to realize in such tight-focusing geometries. A practical limitation to further increasing the beam waist relates to the corresponding decrease of the cavity mode size on the intracavity dielectric focusing mirrors and the resulting increased likelihood for nonlinear damage. Proposed alternative cavity geometries may enable an increased beam waist without increasing the cavity mode on the mirrors . This would allow for higher intracavity pulse energies and further improve the overall XUV power levels.
Figure 4 shows the experimentally measured power in the 11th harmonic as a function of backing pressure using the 100μm nozzle orientation. We consistently observe a roll-off in the power of the 11th harmonic around 600 Torr of backing pressure in our system. The apparent saturation of the harmonic yield with pressure is in part due to the changing phase matching conditions and increased absorption as previously discussed. However, the calculated saturation pressure (≈ 100 Torr) is greater than the anticipated pressures that can be achieved in the current experiment. To better understand the roll-off of the harmonic power additional constraints unique to the intracavity experiments must also be considered. The primary reason for this is easily seen in the observed decrease of intracavity pulse energy with increasing pressure also shown in Fig. 4. Unlike a single-pass free-space experiment in which the incident energy remains constant, the increasing target pressure here results in a decreased intracavity pulse energy which therefore contributes to the roll-off in harmonic power.
The origin of the decreasing intracavity pulse energy with increasing backing pressure is due to the nonlinear temporal chirp acquired by the pulse while ionizing the gas target . In the presence of the generated plasma, the position of the fsEC resonance can be shifted due to the plasma-induced intracavity phase shift. Active stabilization of the fsEC length can ideally compensate for the overall average nonlinear phase shift to maintain optimal resonance with the incident pulse train. It should be noted that active stabilization to the peak of the nonlinear cavity resonance is not guaranteed due to the bistability of the system, though small shifts to the error signal locking position can help mitigate locking instabilities as recently pointed out in . However, even if active cavity length stabilization is able to maintain resonance, the quickly changing phase across the duration of the pulse (chirp) due to the dynamic ionization of the gas ultimately reduces the constructive interference with the incident pulse train and therefore the final steady-state pulse energy. This fundamental limitation to pulse enhancement in a fsEC designed for HHG is described in greater detail in our recent work  as well as in . In the following, we apply the numerical simulations described in  to the current fsEC design to demonstrate the observed dependence of the intracavity pulse energy on target gas pressure, as well as to highlight the advantages of using a lower fsEC finesse to mitigate limitations due to plasma formation.
Figure 5a shows the numerically simulated intracavity pulse energy versus pressure for two different fsEC designs and incident pulse energies. In these simulations we assume active stabilization of the fsEC length will keep the incident pulse train locked to the peak of the (nonlinear) cavity resonance. The dispersion of the cavity mirrors, considered in the simulations in reference , is left out of the simulations for this comparison. The curve for the 1% input coupling case assumes 0.7% intracavity loss and an incident 80 fs pulse train with 100 nJ per pulse, similar to the current experimental setup. In the absence of the gas target the intracavity pulse energy reaches 12μJ. As the gas pressure is increased, the simulated intracavity pulse energy decreases in a manner consistent with that observed experimentally. Figure 5b shows the steady-state pulse profile given a target pressure of 20 Torr (6.4×1023m−3) as well as for the case without gas present (nearly indistinguishable). Also shown is the plasma density profile which changes rapidly across the pulse duration, reaching a maximum ionization level of ≈7% and resulting in a nonlinear temporal chirp on the pulse. Due to the finite lifetime of the plasma, a residual background level of plasma remains after one pulse round trip. This is indicated by the ≈2.8% plasma density that immediately precedes the pulse in Fig. 5b. We note that this static plasma density is detrimental to intracavity HHG in several ways. First, as the phase-mismatch is dominated by δkGouy, this static plasma density level will only worsen the phase-matching conditions since it has the same sign as the contribution from δkGouy. It is therefore important, in such tight-focusing geometries, to keep the ionization levels inside the fsEC as low as possible to improve the phase-matching conditions. Secondly, the static plasma level simultaneously reduces the available neutral atoms each round trip which contribute to the generated harmonic power. From our simulations we note a strong dependence of this residual background level on the maximum intracavity intensity, the actual decay rate of the plasma, and the pulse round trip time inside the fsEC. For systems with significantly higher repetition rates, the static intracavity plasma levels can also be expected to be higher. A better understanding of the plasma decay mechanisms and potential methods to mitigate this effect will be of interest to optimize future designs.
It is useful to compare these results with those obtained using a higher finesse cavity. For example, when using a standard Ti:sapphire frequency comb as in the original demonstrations [9, 10], typical pulse train energies of ≈12 nJ require a significantly higher cavity finesse to reach similar intracavity pulse energies as used in this work. In Fig. 5 we show simulation results for such pulse energies utilizing a fsEC with a 0.1% input coupler and 0.08% intracavity loss. Due to the higher cavity finesse, the intracavity power drops more abruptly compared to the 1% case as the pressure (and therefore plasma density) is increased. Figure 5c shows the resulting intracavity pulse intensity profile and plasma density at a gas pressure of 20 Torr. In addition to the decreased pulse intensity, the figure also shows that the corresponding change in the ionization level from the pulse each round trip is greatly reduced compared to the 1% input coupling case. It is the coherent recombination of these generated electrons with their parent ions that give rise to the atomic dipole response [35, 36] and therefore the overall harmonic power. The reduction of the single pass ionization fraction indicated in Fig. 5c compared to 5b will therefore result in decreased powers. In addition, active stabilization with the higher cavity finesse will be more difficult or prohibited due to the increased bistability in the system . This comparison demonstrates the advantages of utilizing a higher power frequency comb source coupled with a low finesse fsEC to mitigate the limitations inherent in intracavity HHG.
5. Towards direct frequency comb spectroscopy in the VUV and XUV
The higher powers now accessible with the XUV frequency comb opens the door to significant advances in precision spectroscopy in the VUV and XUV spectral regions, where many simple atomic and molecular transitions of fundamental interest can be directly interrogated. There are, however, many complications in probing an atomic or molecular system directly with the frequency comb. For example, the unambiguous measurement of an electronic transition requires that it’s linewidth be less than the mode-spacing of the frequency comb, fr. Additionally, the entire spectral region of interest must fall between two frequency comb components, making, for example, complex molecular spectra nearly impossible to unambiguously identify. At visible and IR wavelengths, it is possible to eliminate these problems by isolating individual components of the frequency comb using resonant optical filter cavities combined with a grating or other high dispersion optical systems [37, 38, 39]. These methods will not work, however, at VUV and XUV wavelengths due to the obvious absorption in such optical components. One can in principal measure isolated transitions in the VUV/XUV that have sufficiently narrow linewidths by utilizing fluorescence or ionization techniques for detection of a single comb component [40, 41]. However, the transitions that can be investigated are restricted, making direct frequency comb spectroscopy (DFCS) in the VUV and XUV with a single source very challenging.
A novel method to enable detection and identification of individual frequency comb components without spatially separating them was originally suggested by Schiller . The idea is to simply use a second phase coherent frequency comb with a slightly different repetition rate as a local oscillator. If the two combs are overlapped on a photodiode, the generated pho-tocurrent can be filtered to yield unique rf heterodyne beatnotes (fj) between pairs of frequency components from each comb. The phase and amplitude of each comb component can then be monitored by detection of its unique rf beatnote fj. With this approach one can directly and unambiguously measure atomic or molecular absorption spectra by sending a probe comb through a sample and mixing it with the local oscillator comb. This method has been utilized by several groups to demonstrate spectroscopy of complex molecular spectra in the visible and IR (e.g. [42, 19]). The method takes advantage of the broadband nature of the frequency comb, and can simultaneously provide high resolution and absolute frequency referencing.
To extend dual-comb DFCS to the VUV/XUV regime requires detection of high fidelity rf heterodyne beatnotes (fj). Limitations to the achievable SNR are determined by the usual contributions from residual intensity noise, detection noise, and shot noise. For absorption spectroscopy, sufficient power is needed from individual comb components to generate heterodyne signals (fj) above the detector noise floor. A more restrictive limit to the SNR in dual-comb DFCS which ultimately determines its sensitivity is due to the large shot noise level present when simultaneously detecting such large numbers of heterodyne signals in parallel, as pointed by the authors in . To demonstrate the feasibility of extending this approach to the VUV/XUV regime, we make a simple estimate of the SNR that can be obtained for the 11th harmonic given the XUV powers now accessible. For simplicity, we assume a white noise frequency spectrum dominated by contributions from shot noise and the detector noise floor. This is a reasonable assumption given we are operating with low optical power and assuming the heterodyne frequencies fj are sufficiently large that 1/f noise is negligible. The SNR of the detected photocurrent for a particular heterodyne frequency fj can then be expressed as:
The extension of the fs frequency comb into the VUV and XUV spectral region has the potential to impact a broad range of scientific studies. The average powers reported here are a significant step forward in making such sources practical in future experiments. We have presented a novel Ti:sapphire-based system which enables significant improvements to the fsEC cavity design and discussed the importance of phase-matching considerations and intracavity ionization dynamics to the overall performance of the system. We plan to utilize the relatively high average powers now available to extend dual-comb DFCS into the VUV and XUV spectral region.
We gratefully acknowlege Ewan Wright for insightful discussions and contributions to the numerical simulations. This work was funded in part by the National Science Foundation (NSF) and the Defense Advanced Research Projects Agency (DARPA).
References and links
1. S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hansch, “Direct link between microwave and optical frequencies with a 300 thz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102 (2000). [CrossRef] [PubMed]
2. M. Fischer, N. Kolachevsky, M. Zimmermann, R. Holzwarth, T. Udem, T. W. Hansch, M. Abgrall, J. Grunert, I. Maksimovic, S. Bize, H. Marion, F. P. Dos Santos, P. Lemonde, G. Santarelli, P. Laurent, A. Clairon, C. Salomon, M. Haas, U. D. Jentschura, and C. H. Keitel, “New limits on the drift of fundamental constants from laboratory measurements,” Phys. Rev. Lett. 92 (2004). [CrossRef] [PubMed]
3. W. G. Rellergert, D. DeMille, R. R. Greco, M. P. Hehlen, J. R. Torgerson, and E. R. Hudson, “Constraining the evolution of the fundamental constants with a solid-state optical frequency reference based on the th-229 nucleus,” Phys. Rev. Lett. 104, 4 (2010). [CrossRef]
4. B. R. Beck, J. A. Becker, P. Beiersdorfer, G. V. Brown, K. J. Moody, J. B. Wilhelmy, F. S. Porter, C. A. Kilbourne, and R. L. Kelley, “Energy splitting of the ground-state doublet in the nucleus th-229,” Phys. Rev. Lett. 98, 4 (2007). [CrossRef]
5. M. Agaker, J. Andersson, J. C. Englund, J. Rausch, J. E. Rubensson, and J. Nordgren, “Spectroscopy in the vacuum-ultraviolet,” Nature Photon. 5, 248 (2011).
6. N. de Oliveira, M. Roudjane, D. Joyeux, D. Phalippou, J. C. Rodier, and L. Nahon, “High-resolution broad-bandwidth fourier-transform absorption spectroscopy in the vuv range down to 40 nm,” Nature Photon. 5, 149 (2011). [CrossRef]
7. R. Eramo, S. Cavalieri, C. Corsi, I. Liontos, and M. Bellini, “Method for high-resolution frequency measurements in the extreme ultraviolet regime: Random-sampling ramsey spectroscopy,” Phys. Rev. Lett. 106, 213003 (2011). [CrossRef] [PubMed]
8. D. Z. Kandula, C. Gohle, T. J. Pinkert, W. Ubachs, and K. S. E. Eikema, “Extreme ultraviolet frequency comb metrology,” Phys. Rev. Lett. 105, 4 (2010). [CrossRef]
9. R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett. 94, 193201 (2005). [CrossRef] [PubMed]
10. C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hansch, “A frequency comb in the extreme ultraviolet,” Nature 436, 234 (2005). [CrossRef] [PubMed]
11. R. J. Jones and J. Ye, “Femtosecond pulse amplification by coherent addition in a passive optical cavity,” Opt. Lett. 27, 1848 (2002).
14. A. Ozawa, J. Rauschenberger, C. Gohle, M. Herrmann, D. R. Walker, V. Pervak, A. Fernandez, R. Graf, A. Apolonski, R. Holzwarth, F. Krausz, T. W. Hansch, and T. Udem, “High harmonic frequency combs for high resolution spectroscopy,” Phys. Rev. Lett. 100, 253901 (2008). [CrossRef] [PubMed]
15. A. Cingöz, D. C. Yost, T. K. Allison, A. Ruehl, M. Fermann, I. Hartl, and J. Ye, “Direct Frequency Comb Spectroscopy in the Extreme Ultraviolet,” arXiv:1109.1871v1 (2011).
17. T. Allison, A. Cingöz, D. C. Yost, and J. Ye, “Cavity extreme nonlinear optics,” arXiv:1105.4195v1 (2011).
18. S. Schiller, “Spectrometry with frequency combs,” Optics Letters 27, 766 (2002). [CrossRef]
20. I. Pupeza, T. Eidam, J. Rauschenberger, B. Bernhardt, A. Ozawa, E. Fill, A. Apolonski, T. Udem, J. Limpert, Z. A. Alahmed, A. M. Azzeer, A. Tunnermann, T. W. Hansch, and F. Krausz, “Power scaling of a high-repetition-rate enhancement cavity,” Opt. Lett. 35, 2052 (2010). [CrossRef] [PubMed]
21. T. R. Schibli, I. Hartl, D. C. Yost, M. J. Martin, A. Marcinkevicius, M. E. Fermann, and J. Ye, “Optical frequency comb with submillihertz linewidth and more than 10 W average power,” Nature Photon.s 2, 355 (2008). [CrossRef]
23. J. Paul, J. Johnson, J. Lee, and R. J. Jones, “Generation of high-power frequency combs from injection-locked femtosecond amplification cavities,” Optics Letters 33, 2482 (2008). [CrossRef] [PubMed]
24. A. L’Huillier, X. Li, and L. L.A., “Propagation effects in high-order harmonic generation,” J. Opt. Soc. B 7 (1990).
25. Fluid flow simulations provided by David Jones and TJ Hammond of University of British Columbia. .
27. A. Gatto, N. Kaiser, S. Gunster, D. Ristau, F. Sarto, M. Trovo’, and M. Danailov, “Synchrotron radiation induced damages in optical materials,” SPIE 4932, 366 (2003). [CrossRef]
29. A. Ozawa, A. Vernaleken, W. Schneider, I. Gotlibovych, T. Udem, and T. W. Hansch, “Non-collinear high harmonic generation: a promising outcoupling method for cavity-assisted xuv generation,” Optics Express 16, 6233 (2008). [CrossRef] [PubMed]
31. D. C. Yost, T. R. Schibli, J. Ye, J. L. Tate, J. Hostetter, M. B. Gaarde, and K. J. Schafer, “Vacuum-ultraviolet frequency combs from below-threshold harmonics,” Nature Physics 5, 815 (2009). [CrossRef]
32. T. Hammond, A. K. Mills, and D. J. Jones, “Near-threshold harmonics from a femtosecond enhancement cavity-based euv source: Effects of multiple quantum pathways on spatial profile and yield,” (Submitted for publication).
33. E. Constant, D. Garzella, P. Breger, E. Mevel, C. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: Model and experiment,” Phys. Rev. Lett. 82, 1668 (1999). [CrossRef]
34. J. Weitenberg, P. Russbuldt, T. Eidam, and I. Pupeza, “Transverse mode tailoring in a quasi-imaging high-finesse femtosecond enhancement cavity,” Optics Express 19, 9551 (2011). [CrossRef] [PubMed]
37. C. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hansch, “Frequency comb vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra,” Phys. Rev. Lett. 99, 263902 (2007). [CrossRef]
39. M. J. Thorpe and J. Ye, “Cavity-enhanced direct frequency comb spectroscopy,” Applied Physics B-Lasers and Optics 91, 397 (2008). [CrossRef]
40. E. E. Eyler, D. E. Chieda, M. C. Stowe, M. J. Thorpe, T. R. Schibli, and J. Ye, “Prospects for precision measurements of atomic helium using direct frequency comb spectroscopy,” European Physical Journal D 48, 43 (2008). [CrossRef]
41. M. Herrmann, M. Haas, U. D. Jentschura, F. Kottmann, D. Leibfried, G. Saathoff, C. Gohle, A. Ozawa, V. Batteiger, S. Knunz, N. Kolachevsky, H. A. Schussler, T. W. Hansch, and T. Udem, “Feasibility of coherent xuv spectroscopy on the 1s–2s transition in singly ionized helium,” Physical Review A 79, 15 (2009). [CrossRef]
42. B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hansch, and N. Picque, “Cavity-enhanced dual-comb spectroscopy,” Nature Photon. 4, 55 (2010). [CrossRef]