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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 23 — Nov. 7, 2011
  • pp: 23315–23326
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Optimizing intracavity high harmonic generation for XUV fs frequency combs

Jane Lee, David R. Carlson, and R. Jason Jones  »View Author Affiliations


Optics Express, Vol. 19, Issue 23, pp. 23315-23326 (2011)
http://dx.doi.org/10.1364/OE.19.023315


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Abstract

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

1. Introduction

Work initially demonstrated in 2005 [9

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

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]

] showed that the fs frequency comb can be up-converted to the XUV utilizing fs enhancement cavities (fsEC’s) [11

11. R. J. Jones and J. Ye, “Femtosecond pulse amplification by coherent addition in a passive optical cavity,” Opt. Lett. 27, 1848 (2002).

, 12

12. R. J. Jones and J. Ye, “High-repetition-rate coherent femtosecond pulse amplification with an external passive optical cavity,” Opt. Lett. 29, 2812 (2004). [CrossRef] [PubMed]

] 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

13. D. C. Yost, T. R. Schibli, and J. Ye, “Efficient output coupling of intracavity high-harmonic generation,” Opt. Lett. 33, 1099 (2008). [CrossRef] [PubMed]

, 14

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

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).

] and provided an understanding of the dynamic interplay between the intracavity pulse evolution and ionization of the gas target [16

16. D. Carlson, J. Lee, J. Mongelli, E. Wright, and R. Jones, “Intracavity ionization and pulse formation in femtosecond enhancement cavities,” Optics Letters 36, 2991 (2011). [CrossRef] [PubMed]

, 17

17. T. Allison, A. Cingöz, D. C. Yost, and J. Ye, “Cavity extreme nonlinear optics,” arXiv:1105.4195v1 (2011).

].

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[15

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).

]. 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

18. S. Schiller, “Spectrometry with frequency combs,” Optics Letters 27, 766 (2002). [CrossRef]

, 19

19. I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett. 100, 013902, (2008). [CrossRef] [PubMed]

] 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

Fig. 1 Schematic of experimental setup for generating XUV frequency comb. fsAC: fs amplification cavity; fsEC: fs enhancement cavity.

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.

Fig. 2 Detected high harmonic spectrum. (a) Theoretical grating efficiency and recorded harmonic power taken from (b) ccd image of phosphor screen.

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

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]

, 13

13. D. C. Yost, T. R. Schibli, and J. Ye, “Efficient output coupling of intracavity high-harmonic generation,” Opt. Lett. 33, 1099 (2008). [CrossRef] [PubMed]

] with the exception of very recent work in which > 20μW was generated near 71 nm based on a high power fiber laser system [15

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).

].

Table 1. Estimated harmonic power coupled out of the fsEC. Stated error range due to uncertainty in detector responsivity and grating efficiency.

table-icon
View This Table

4. Discussion

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 [11

11. R. J. Jones and J. Ye, “Femtosecond pulse amplification by coherent addition in a passive optical cavity,” Opt. Lett. 27, 1848 (2002).

] and enables robust active stabilization of the frequency comb to the cavity. Furthermore, the sensitivity of the system to plasma-induced phase shifts [16

16. D. Carlson, J. Lee, J. Mongelli, E. Wright, and R. Jones, “Intracavity ionization and pulse formation in femtosecond enhancement cavities,” Optics Letters 36, 2991 (2011). [CrossRef] [PubMed]

, 17

17. T. Allison, A. Cingöz, D. C. Yost, and J. Ye, “Cavity extreme nonlinear optics,” arXiv:1105.4195v1 (2011).

] 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 [30

30. P. Balcou and A. Lhuillier, “Phase-matching effects in strong-field harmonic-generation,” Physical Review A 47, 1447 (1993). [CrossRef] [PubMed]

] 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

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

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).

].) 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 = πk, 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 1/wo2). 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 [33

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]

]. 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 [33

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]

]:
IqAq2labs2ρ21+4π2[labs2/lc2]×[1+elmedlabs2cos(πlmedlcoh)elmed2labs],
(1)
where Aq2 is the atomic dipole amplitude for the qth harmonic, ρ is the gas density and lmed ≈200μm for this example. This expression relates the on-axis relative harmonic yield to the 3 characteristic length scales lc, labs, and lmed. 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 [34

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]

]. This would allow for higher intracavity pulse energies and further improve the overall XUV power levels.

Fig. 3 Comparison of phase-matching and harmonic yield dependence on intracavity beam size. (a) Coherence (solid curves) and absorption (dashed curve) lengths versus pressure. (b) Relative on-axis power versus pressure.

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.

Fig. 4 Measured power of the 11th harmonic and corresponding intracavity energy of the fundamental pulse versus backing pressure.

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 [16

16. D. Carlson, J. Lee, J. Mongelli, E. Wright, and R. Jones, “Intracavity ionization and pulse formation in femtosecond enhancement cavities,” Optics Letters 36, 2991 (2011). [CrossRef] [PubMed]

]. 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 [17

17. T. Allison, A. Cingöz, D. C. Yost, and J. Ye, “Cavity extreme nonlinear optics,” arXiv:1105.4195v1 (2011).

]. 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 [16

16. D. Carlson, J. Lee, J. Mongelli, E. Wright, and R. Jones, “Intracavity ionization and pulse formation in femtosecond enhancement cavities,” Optics Letters 36, 2991 (2011). [CrossRef] [PubMed]

] as well as in [17

17. T. Allison, A. Cingöz, D. C. Yost, and J. Ye, “Cavity extreme nonlinear optics,” arXiv:1105.4195v1 (2011).

]. In the following, we apply the numerical simulations described in [16

16. D. Carlson, J. Lee, J. Mongelli, E. Wright, and R. Jones, “Intracavity ionization and pulse formation in femtosecond enhancement cavities,” Optics Letters 36, 2991 (2011). [CrossRef] [PubMed]

] 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 [16

16. D. Carlson, J. Lee, J. Mongelli, E. Wright, and R. Jones, “Intracavity ionization and pulse formation in femtosecond enhancement cavities,” Optics Letters 36, 2991 (2011). [CrossRef] [PubMed]

], 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.

Fig. 5 (a) Simulated intracavity power for two fsEC designs with different finesse and incident pulse energies. Steady-state profile and plasma density for (b) 1% input coupling fsEC versus (c) 0.1% input coupling fsEC given a gas target pressure of 20 Torr.

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

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

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]

], 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

35. P. B. Corkum, “Plasma perspective on strong-field multiphoton ionization,” Phys. Rev. Lett. 71, 1994 (1993). [CrossRef] [PubMed]

, 36

36. M. Lewenstein, P. Balcou, M. Y. Ivanov, A. Lhuillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Physical Review A 49, 2117 (1994). [CrossRef] [PubMed]

] 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 [15

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).

]. 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

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]

, 38

38. S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb,” Nature 445, 627 (2007). [CrossRef] [PubMed]

, 39

39. M. J. Thorpe and J. Ye, “Cavity-enhanced direct frequency comb spectroscopy,” Applied Physics B-Lasers and Optics 91, 397 (2008). [CrossRef]

]. 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

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

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]

]. 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 [18

18. S. Schiller, “Spectrometry with frequency combs,” Optics Letters 27, 766 (2002). [CrossRef]

]. 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

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]

, 19

19. I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett. 100, 013902, (2008). [CrossRef] [PubMed]

]). 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 [43

43. N. R. Newbury, I. Coddington, and W. Swann, “Sensitivity of coherent dual-comb spectroscopy,” Opt. Express 18, 7929 (2010). [CrossRef] [PubMed]

]. 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:
SNRpmNEP2+4hνP/ητ
(2)
where τ is the averaging time, pm is the optical power in a single frequency comb component, P is the total power in the each comb incident on the photodiode, and η is the detector quantum efficiency. Noise in the detection system is expressed in terms of its noise equivalent power (NEP). We assume in this expression that the probe and local oscillator combs have approximately the same power. Silicon photodiodes with sufficient bandwidth suitable for such measurements are commercially available with η ∼ 1 at these wavelengths. We estimate a NEP for the detection system of 1pW/Hz in this example based on specifications of commerically available photodiodes. For wavelengths above the CaF2 fluoride cut-off wavelength of ≈120 nm, overlapping the probe comb beam with the local oscillator comb will be straight forward. At shorter wavelengths, diffractive optics will be required for beam combining resulting in increased power loss. Here we use ≈ 10μW as an estimate for the usable power in the 11th harmonic, and pm ≈ 10pW (which assumes ≈ 1 nm spectral bandwidth for the 10th harmonic). To reduce the shot noise contribution from off-resonant comb frequencies, a VUV spectrometer can be used to reduced the total detected spectral bandwidth to ≈ 0.1nm, resulting in P ≈ 1μW. Such a system would enable detection of individual comb components in the XUV with a SNR of 3τ, reaching ∼10 after 100 seconds. Much longer integration times are completely feasbile to improve the absorption sensitivty of the detection system. The use of dual-comb DFCS from the VUV to XUV spectral regions is therefore quite feasible and should enable a broader range of precision spectrocopic studies in the near future.

6. Conclusion

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.

Acknowledgments

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).

12.

R. J. Jones and J. Ye, “High-repetition-rate coherent femtosecond pulse amplification with an external passive optical cavity,” Opt. Lett. 29, 2812 (2004). [CrossRef] [PubMed]

13.

D. C. Yost, T. R. Schibli, and J. Ye, “Efficient output coupling of intracavity high-harmonic generation,” Opt. Lett. 33, 1099 (2008). [CrossRef] [PubMed]

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).

16.

D. Carlson, J. Lee, J. Mongelli, E. Wright, and R. Jones, “Intracavity ionization and pulse formation in femtosecond enhancement cavities,” Optics Letters 36, 2991 (2011). [CrossRef] [PubMed]

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]

19.

I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett. 100, 013902, (2008). [CrossRef] [PubMed]

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]

22.

A. Ruehl, A. Marcinkevicius, M. E. Fermann, and I. Hartl, “80 W, 120 fs Yb-fiber frequency comb,” Opt. Lett. 35, 3015 (2010). [CrossRef] [PubMed]

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. .

26.

K. D. Moll, R. J. Jones, and J. Ye, “Nonlinear dynamics inside femtosecond enhancement cavities,” Optics Express 13, 1672 (2005). 1094–4087. [CrossRef] [PubMed]

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]

28.

K. D. Moll, R. J. Jones, and J. Ye, “Output coupling methods for cavity-based high-harmonic generation,” Optics Express 14, 8189 (2006). [CrossRef] [PubMed]

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]

30.

P. Balcou and A. Lhuillier, “Phase-matching effects in strong-field harmonic-generation,” Physical Review A 47, 1447 (1993). [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]

35.

P. B. Corkum, “Plasma perspective on strong-field multiphoton ionization,” Phys. Rev. Lett. 71, 1994 (1993). [CrossRef] [PubMed]

36.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. Lhuillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Physical Review A 49, 2117 (1994). [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]

38.

S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb,” Nature 445, 627 (2007). [CrossRef] [PubMed]

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]

43.

N. R. Newbury, I. Coddington, and W. Swann, “Sensitivity of coherent dual-comb spectroscopy,” Opt. Express 18, 7929 (2010). [CrossRef] [PubMed]

OCIS Codes
(190.7110) Nonlinear optics : Ultrafast nonlinear optics
(300.6540) Spectroscopy : Spectroscopy, ultraviolet

ToC Category:
Nonlinear Optics

Citation
Jane Lee, David R. Carlson, and R. Jason Jones, "Optimizing intracavity high harmonic generation for XUV fs frequency combs," Opt. Express 19, 23315-23326 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-23-23315


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References

  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,” Nature436, 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).
  12. R. J. Jones and J. Ye, “High-repetition-rate coherent femtosecond pulse amplification with an external passive optical cavity,” Opt. Lett.29, 2812 (2004). [CrossRef] [PubMed]
  13. D. C. Yost, T. R. Schibli, and J. Ye, “Efficient output coupling of intracavity high-harmonic generation,” Opt. Lett.33, 1099 (2008). [CrossRef] [PubMed]
  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).
  16. D. Carlson, J. Lee, J. Mongelli, E. Wright, and R. Jones, “Intracavity ionization and pulse formation in femtosecond enhancement cavities,” Optics Letters36, 2991 (2011). [CrossRef] [PubMed]
  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 Letters27, 766 (2002). [CrossRef]
  19. I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett.100, 013902, (2008). [CrossRef] [PubMed]
  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.s2, 355 (2008). [CrossRef]
  22. A. Ruehl, A. Marcinkevicius, M. E. Fermann, and I. Hartl, “80 W, 120 fs Yb-fiber frequency comb,” Opt. Lett.35, 3015 (2010). [CrossRef] [PubMed]
  23. J. Paul, J. Johnson, J. Lee, and R. J. Jones, “Generation of high-power frequency combs from injection-locked femtosecond amplification cavities,” Optics Letters33, 2482 (2008). [CrossRef] [PubMed]
  24. A. L’Huillier, X. Li, and L. L.A., “Propagation effects in high-order harmonic generation,” J. Opt. Soc. B7 (1990).
  25. Fluid flow simulations provided by David Jones and TJ Hammond of University of British Columbia. .
  26. K. D. Moll, R. J. Jones, and J. Ye, “Nonlinear dynamics inside femtosecond enhancement cavities,” Optics Express13, 1672 (2005). 1094–4087. [CrossRef] [PubMed]
  27. A. Gatto, N. Kaiser, S. Gunster, D. Ristau, F. Sarto, M. Trovo’, and M. Danailov, “Synchrotron radiation induced damages in optical materials,” SPIE4932, 366 (2003). [CrossRef]
  28. K. D. Moll, R. J. Jones, and J. Ye, “Output coupling methods for cavity-based high-harmonic generation,” Optics Express14, 8189 (2006). [CrossRef] [PubMed]
  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 Express16, 6233 (2008). [CrossRef] [PubMed]
  30. P. Balcou and A. Lhuillier, “Phase-matching effects in strong-field harmonic-generation,” Physical Review A47, 1447 (1993). [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 Physics5, 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 Express19, 9551 (2011). [CrossRef] [PubMed]
  35. P. B. Corkum, “Plasma perspective on strong-field multiphoton ionization,” Phys. Rev. Lett.71, 1994 (1993). [CrossRef] [PubMed]
  36. M. Lewenstein, P. Balcou, M. Y. Ivanov, A. Lhuillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Physical Review A49, 2117 (1994). [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]
  38. S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb,” Nature445, 627 (2007). [CrossRef] [PubMed]
  39. M. J. Thorpe and J. Ye, “Cavity-enhanced direct frequency comb spectroscopy,” Applied Physics B-Lasers and Optics91, 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 D48, 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 A79, 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]
  43. N. R. Newbury, I. Coddington, and W. Swann, “Sensitivity of coherent dual-comb spectroscopy,” Opt. Express18, 7929 (2010). [CrossRef] [PubMed]

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