Abstract

Vacuum-ultraviolet (VUV) light is critical for the study of molecules and materials, but the generation of femtosecond pulses in the VUV region at high repetition rates has proven difficult. Here we demonstrate the efficient generation of VUV light at megahertz repetition rates using highly cascaded four-wave mixing processes in a negative-curvature hollow-core fiber. Both even- and odd-order harmonics are generated up to the 15th harmonic (69 nm, 18.0 eV), with high energy resolution of ${\sim}{{40}}\;{\rm{meV}}$. In contrast to direct high harmonic generation, this highly cascaded harmonic generation process requires lower peak intensity and therefore can operate at higher repetition rates, driven by a robust ${\sim}{{10}}\;{\rm{W}}$ fiber-laser system in a compact setup. Additionally, we present numerical simulations that explore the fundamental capabilities and spatiotemporal dynamics of highly cascaded harmonic generation. This VUV source can enhance the capabilities of spectroscopies of molecular and quantum materials, such as photoionization mass spectrometry and time-, angle-, and spin-resolved photoemission.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

The vacuum-ultraviolet (VUV) spectral region, covering approximately 6–15 eV, has a unique ability to probe physical and chemical processes. For example, the bond energies of all molecules and the ionization energies of most materials lie in this energy range. Consequently, VUV light sources are used as an ionization source in angle-resolved photoelectron spectroscopy (ARPES) [15] and photoionization mass spectrometry (PIMS) [612], or to initiate chemical reactions relevant to atmospheric science in a controlled environment [1315]. However, this science is limited by the lack of bright VUV light sources, especially coherent (laser) sources. While low-flux sources, such as deuterium lamps, can satisfy some applications [16], many experiments require higher flux to overcome shot noise in a reasonable amount of time. Single-wavelength sources, such as the ninth harmonic of a Nd:YAG laser (118.2 nm, 10.49 eV) [17], are not tunable, limiting the scope of experiments for which they can be used. Tunable deep-ultraviolet light has been produced from phase-matched four-wave mixing schemes [18,19], but extending this strategy into the VUV has typically provided very limited or no tunability [2022]. Synchrotrons and free-electron lasers are currently the only sources of fully tunable, high-flux VUV light [8]; however, these facility-scale sources have limited access and time resolution.

Direct high harmonic generation (HHG) driven by intense femtosecond laser pulses can generate multiple harmonic orders throughout the VUV, extreme UV (EUV), and soft X-ray (SXR) spectral regions when very high intensities (${\gt}1{0^{13}}\;{\rm{W}}/{\rm{cm}}^2$) are available. However, scaling to higher repetition rates with lower pulse energy is not as simple as focusing tighter to reach the same peak intensities. In a free-focus geometry, small focal spot sizes correspond to impractically short lengths and high gas pressures [23], while for HHG in a hollow capillary waveguide, the confinement loss scales with the inverse cube of the core diameter [24]. HHG using solid [25,26] and liquid [27] targets has recently been investigated with good success. However, only a few papers [27,28] have demonstrated generation into the VUV, and the path to scaling the flux and efficiency to enable applications is still unclear.

Negative curvature antiresonant hollow-core fibers offer an attractive alternative to a simple hollow capillary waveguide, as they use microstructures in the core region to induce interference effects that confine light to a small diameter with minimal propagation loss [2931]. Notably, HHG has been demonstrated in a similar antiresonant photonic crystal fiber at 1 kHz repetition rate [32]. Nevertheless, using megahertz (MHz)-repetition-rate fiber lasers, it is still impractical to achieve peak intensities high enough for efficient conversion using direct HHG, without rapid damage to the core microstructures.

Here we utilize a new highly cascaded harmonic generation (HCHG) process to enable the simultaneous production of 13 UV/VUV spectral lines using driving laser intensities well below the threshold required for HHG [33,34]. By focusing two colors (the fundamental and second harmonic of a 10 W average power Yb:fiber laser) into a xenon-filled negative curvature hollow-core fiber, and tuning the xenon pressure to provide optimal phase matching, both even and odd harmonic orders are generated ranging from the 3rd to the 15th harmonic order. We use a peak intensity of approximately ${{2}} \times 1{0^{12}}\;{\rm{W}}/{\rm{cm}}^2$, which is significantly lower than the ${\sim}1 \times 1{0^{14}}\;{\rm{W}}/{\rm{cm}}^2$ typically required for efficient HHG [35]. Indeed, at the intensity used in our experiments, the ponderomotive energy of the electron is only 0.1 eV, and the single-atom, single-color ionization probability [36,37] is less than $1{0^{- 12}}$—far below the typical HHG regime. As expected for a perturbative cascaded interaction, the flux at each harmonic decreases with increasing harmonic order, but at ${\sim}10^{14}{-} 10^{17}\;{\rm{ph}}/{\rm{s}}$ it rivals synchrotron flux levels [8] for photon energies up to 10.8 eV. Using a model that only includes the third-order nonlinearity (${\chi ^{(3)}}$), we confirm our hypothesis regarding the cascaded mechanism for harmonic generation and gain a deeper understanding of the physics of HCHG.

2. EXPERIMENT

We start with a prototype ultrafast ytterbium-doped fiber laser producing 10 µJ, 160 fs pulses at 1035 nm with a repetition rate of 1 MHz. The output is then frequency doubled to 518 nm [beta- barium borate (BBO), Eksma Optics] with about 50% efficiency. The 1035 and 518 nm pulses are overlapped in time using a delay stage and focused into a 30 µm diameter negative-curvature fiber (Glo-Photonics PMC-500/700) filled with ${\sim}{{1000}}\;{\rm{Torr}}$ (20 psia) of xenon gas [Fig. 1(a)]. With 4 W of 1035 nm light and 3 W of 518 nm light entering the fiber (parallel linear polarization), we generate about 200 mW of third harmonic (345 nm) through a degenerate four-wave-mixing process—here two photons of the second harmonic are combined to produce one photon each of the fundamental and the third harmonic. This third-harmonic light can then combine with the fundamental and second-harmonic light to drive additional four-wave-mixing processes in a cascaded series [Fig. 1(b)]. Such cascaded processes have been studied previously, but past studies [3840] have used Ti:sapphire lasers with shorter pulses, order-of-magnitude-higher pulse energies, and larger-diameter capillary waveguides. In contrast, we employ a compact fiber laser and a small diameter negative-curvature waveguide to produce harmonics up to the 15th harmonic.

 figure: Fig. 1.

Fig. 1. Highly cascaded harmonic generation (HCHG). (a) In our experiment, a 1035 nm laser is frequency doubled, and both fundamental and second-harmonic beams are focused into a xenon-filled, 30 µm core diameter, hollow-core negative-curvature fiber to drive the HCHG process. The resulting VUV light is then spectrally selected by a grating-based monochromator. (b) The HCHG process is the result of numerous four-wave-mixing steps, each combining three photons to generate a higher-energy photon. We note that the photon combinations for H4 and higher represent just one possible route to each harmonic.

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After generation, the VUV light passes through an in-vacuum monochromator in order to select a single wavelength for transmission to the sample. In these experiments, we employed three different monochromator designs. (1) First, we used a prism monochromator to measure the flux of harmonic orders 3–9. In this setup, the VUV beam was collimated using a concave collimating mirror (${\rm{R}} = {{500}}\;{\rm{mm}}$), diffracted through a ${\rm{Mg}}{{\rm{F}}_2}$ prism (60° apex), reflected by a flat wavelength-tuning mirror, and focused (${\rm{R}} = {{400}}\;{\rm{mm}}$) through a 1 mm exit slit, before reaching one of several detectors. All reflective optics were coated with ${\rm{Mg}}{{\rm{F}}_2}$-protected aluminum optimized for 120 nm (Acton Optics and Coatings). The powers of harmonic orders 3–5 were measured on a thermal power meter (Newport), while the power of the ninth harmonic was measured on a calibrated ${\rm{A}}{{\rm{l}}_2}{{\rm{O}}_3}$ photodiode (NIST). The relative power of orders 5–9 was measured by replacing the detector with a Ce:YAG crystal (1 mm thick) imaged onto a camera (Edmund Optics). The powers of orders 6–8 were estimated by calibrating the relative power measurement (camera) to the absolute power measurement (photodiode) of the ninth harmonic. Using this method, the estimated flux of the fifth harmonic agreed to within a factor of 2 with the power meter measurement, suggesting that our flux estimates for orders 6–8 are also accurate to within a factor of 2. (2) For measuring a high-resolution spectrum of the eighth and ninth harmonics, we replaced the prism and rotating flat mirror with a reflective diffraction grating (Richardson Grating Lab, 1200 g/mm, ${\rm{Mg}}{{\rm{F}}_2}$ coating), which could be rotated to tune the wavelength. We used a 50 µm exit slit and the ${\rm{A}}{{\rm{l}}_2}{{\rm{O}}_3}$ detector. This 90° Czerny–Turner monochromator has an estimated resolution of 10 meV. (3) Finally, for harmonic orders 9–15, we eliminated the focusing optic after the diffraction grating in the Czerny–Turner design, instead using a single (${\rm{R}} = {{250}}\;{\rm{mm}}$, Acton 120 nm coating) optic to refocus the beam onto the 1 mm exit slit, with a converging beam incident on the grating [Wadsworth monochromator, Fig. 1(a)]. A bare aluminum grating (Richardson Grating Lab, 1200 g/mm) was used to increase reflectivity at wavelengths beyond the ${\rm{Mg}}{{\rm{F}}_2}$ absorption edge near 110 nm. We also included a rejector mirror (angle of incidence 72°) in the beam, placed immediately after the exit of the hollow fiber. This dielectric mirror was designed to transmit most of the 1035, 517, and 345 nm light while reflecting all shorter wavelengths. This mirror greatly reduces the heat load on the more sensitive ${\rm{Al}} + {\rm{Mg}}{{\rm{F}}_2}$-coated optics. This also allowed us to direct the 1035, 517, and 345 nm beams outside the vacuum chamber to monitor for optimal fiber coupling and temporal overlap.

Tables Icon

Table 1. Observed and Estimated Source Photon Flux for Each Harmonica

 figure: Fig. 2.

Fig. 2. Spectrum and calibrated photon flux observed for each harmonic. (a) VUV spectra acquired using the high-throughput (purple, log scale) and high-resolution (red, linear scale) monochromator configurations. Harmonics up to H14 are clearly visible. The high-resolution monochromator reveals an intrinsic spectral resolution of 40 meV (${{E}}/\Delta {{{E}}_{{\rm{FWHM}}}} \approx {{250}}$ for H8 and H9). (b) Observed photon flux for each harmonic, measured using the prism monochromator (4–10 eV, blue) and the Wadsworth monochromator (10–18 eV, purple). Above 11 eV, the beamline optics have substantially reduced efficiency.

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3. RESULTS AND DISCUSSION

Using highly cascaded harmonic generation, we simultaneously generate bright even and odd harmonic orders 3–15 of the bichromatic 1035 and 517 nm driving laser. The measured radiant flux (radiant power) and the corresponding photon flux of each harmonic are recorded in Table 1 and shown in Fig. 2. High-resolution spectra of the eighth and ninth harmonics [Fig. 2(a), shown in red] reveal bandwidths of 40 meV (full width at half-maximum), which is somewhat more bandwidth than the 8 meV bandwidth of the driving laser, indicating that the HCHG process likely produces shorter pulses, or pulses that can be compressed to be shorter, than the driving pulses. This type of temporal shortening is often seen with nonlinear optical processes such as HHG [41].

The HCHG process demonstrated here is a cascaded four-wave-mixing process. This is distinct from HHG, where each harmonic is generated directly from the driving laser using high-order nonlinearities. The perturbative approach here uses the lowest-order isotropic nonlinear polarizability term of xenon, ${\chi ^{(3)}}$, to generate all observed harmonics. The first step of our harmonic generation process is the generation of the third harmonic from the second harmonic and fundamental beams [Fig. 1(b)]. The energy conservation is described by

$${{\omega _3} = {\omega _2} + {\omega _2} - {\omega _1},}$$
where ${\omega _n}$ is the angular frequency of the $n$th harmonic, ${\omega _n} = n{\omega _1}$, and ${\omega _1}$ is the frequency of the driving laser $({\hbar {{{\omega}}_1} = 1.2\;{\rm{eV}}})$. The phase mismatch in a gas-filled hollow waveguide [42] is given by
$$\begin{split}{\Delta k \equiv {k_1} + {k_3} - 2{k_2}} &= {2\pi\! N\left({\frac{{{\delta _3}}}{{{\lambda _3}}} + \frac{{{\delta _1}}}{{{\lambda _1}}} - \frac{{2{\delta _2}}}{{{\lambda _2}}}} \right)}\\[-3pt]&\quad -{ \frac{u}{{4\pi\! {a^2}}}\left({{\lambda _3} + {\lambda _1} - 2{\lambda _2}} \right)},\end{split}$$
where ${\lambda _n}$ is the $n$th harmonic wavelength, ${{{k}}_n}$ is the corresponding wavevector, ${{N}}$ is the number density of the gas, ${\delta _n}$ is the gas dispersion (related to the refractive index by $n - 1 = N\delta$) for the $n$th harmonic, ${{u}}$ is a mode-dependent constant (2.405 for the lowest-order mode used here [42]), and $a$ is the diameter of the waveguide. The xenon refractive index has been measured [43] for wavelengths longer than 140 nm. The first term on the right side of Eq. (2) is the pressure-dependent contribution from the gas, and the second term is the pressure-independent term from the waveguide confinement. Typically, there is some pressure that will eliminate the phase mismatch, allowing the third-harmonic generation to be phase matched.

Once the third harmonic is produced, this wavelength can lead to the generation of higher harmonics by the same process. Beyond the fourth harmonic, multiple pathways can lead to the production of each harmonic, for example:

$$\begin{split}&{\omega _4} = {\omega _3} + {\omega _2} - {\omega _1}, \\[-4pt]& {\omega _4} = {\omega _3} + {\omega _3} - {\omega _2}, \\[-4pt]& {\omega _5} = {\omega _4} + {\omega _2} - {\omega _1}, \\[-4pt]& {\omega _5} = {\omega _3} + {\omega _3} - {\omega _1}, \\[-4pt]& {\omega _6} = {\omega _5} + {\omega _2} - {\omega _1}, \\[-4pt]& {{\omega _6} = {\omega _4} + {\omega _3} - {\omega _1}}, \\[-4pt]& {\omega _7} = {\omega _6} + {\omega _2} - {\omega _1}, \\[-4pt]& {\omega _7} = {\omega _5} + {\omega _3} - {\omega _1}, \\[-4pt]& {\omega _7} = {\omega _4} + {\omega _4} - {\omega _1}, \\[-4pt]&\qquad\quad\; \ldots \end{split}$$

Each of these processes has an optimal phase-matching condition, and most of these processes are phase matched for some xenon pressure below that needed to phase match third-harmonic generation, which is the first step in the cascaded process. Because we apply pressure only to the front of the 100 mm fiber (around 1000 Torr, tuned to optimize harmonic production) and allow the gas to flow through the fiber into a vacuum, we have a gradient of pressure along the length of the fiber [Figs. 3(a) and 3(b)], estimated from a finite element calculation employing a pressure-dependent conductance. The range of xenon pressures in our fiber allows many of the relevant phase-matching and quasi-phase-matching conditions to be met at some point along the fiber. However, more complicated situations are possible—past work [38,39] indicates that quasi-phase-matching conditions arising from the periodic buildup and decay of intermediate harmonics could be more important than true phase matching for cascaded processes.

 figure: Fig. 3.

Fig. 3. Simulation of HCHG. (a) The xenon is supplied to the front of the fiber so that the pressure in the fiber decreases to vacuum along the length of the fiber. (b) A finite element simulation of the pressure in the fiber shows that the pressure decreases most rapidly at the end of the fiber, as the flow transitions from viscous flow to molecular flow. (c) Using the pressure profile from (b), numerical simulations using the nonlinear Schrödinger equation (NLSE) confirm the generation of numerous harmonics in the UV and VUV spectral region. (d) Each harmonic is generated throughout the length of the fiber, rather than within a small phase-matched region.

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To provide a more complete picture of the HCHG process, we perform numerical calculations using the nonlinear Schrödinger equation (NLSE) and implemented in the PyNLO package [44,45]. In these simulations, the pulses are modeled with a ${\rm sech}^2$ temporal profile with a full width at half-maximum of 160 fs and a pulse energy of 2 µJ each. The pressure-dependent nonlinear index of xenon is assumed to be ${1.1} \times 1{0^{- 22}}\;{{\rm{m}}^2}/({\rm{W}}\,{\rm{bar}})$ [46,47]. The calculations predict output fluxes [Fig. 3(c)] roughly comparable to what we measure (Fig. 2), confirming that our experimental results are consistent with a ${\chi ^{(3)}}$-driven cascaded mixing process. These calculations reveal that the harmonics are produced all along the length of the fiber [Fig. 3(d)], indicating that quasi-phase matching is likely important in the production of bright harmonics. The pressure profile used here was chosen primarily for experimental convenience and may not be ideal for harmonic generation. Further experimentation and more advanced calculations are needed to determine the ideal pressure profile for HCHG.

One advantage of direct HHG is the ability to generate wavelengths extending far beyond the ionization energy of the nonlinear medium where absorption is very high. In contrast, the cascaded harmonic generation shown here could reasonably be expected to cut off at the first harmonic that is strongly absorbed by the medium. However, an additional calculation shown in Fig. 4 reveals that attenuation of harmonics beyond 3ω have only a small effect on the flux of higher harmonics. Moreover, the experimental results shown in Fig. 2 also indicate that absorption of a higher harmonic does not prevent the generation of higher harmonics. The ionization energy of xenon is 12.13 eV, with a high density of Rydberg states in the vicinity of our 10th harmonic at 12.0 eV. As shown in Fig. 2, we observe a lower intensity at this wavelength, yet harmonics up to the 15th are observed. We therefore conclude that the HCHG process has some ability to generate harmonics beyond absorption bands in the medium. Furthermore, in HCHG, we can effectively drive the nonlinear optical process with relatively long-duration pulses, giving us the opportunity to generate harmonics with spectral bandwidth significantly narrower than is typical for HHG.

 figure: Fig. 4.

Fig. 4. Simulated harmonic flux when one harmonic is severely attenuated. Attenuation of the third harmonic (red) leads to all higher harmonics being severely attenuated. In contrast, attenuation of the fourth harmonic (blue) has only a small effect on the higher harmonic fluxes. This result indicates that multiple pathways can produce each harmonic above the fourth order.

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The HCHG process is a powerful tool for bringing high-flux VUV light to tabletop experiments. To our knowledge, this is the smallest, most energy-efficient source of femtosecond pulses of vacuum-ultraviolet light in the 7–11 eV spectral range. The total energy consumption of all electronics and power supplies used for this source is approximately 1 kW (an additional ${\sim}1\;{\rm{kW}}$ is used by water chillers). Nevertheless, our flux for our harmonics in the 6–10 eV spectral range meets or exceeds that of the Advanced Light Source synchrotron (${{2}} \times 1{0^{13}}\;{\rm{photons}}/{\rm{s}}$ for similar bandwidth). [48] Thus, bright multispectral VUV light can be implemented in individual labs, and synchrotron facilities can then be used more efficiently for experiments requiring fully tunable VUV light or high fluxes at higher photon energies.

The VUV light produced by this source is linearly polarized, which is a valuable feature that broadens the scope of possible applications [49]. Any linear polarization for the VUV can be produced, as the polarization of the driving lasers is conserved. Additionally, the use of circularly polarized driving lasers may allow circularly polarized light to be generated directly. Circularly polarized harmonics have been produced from both HHG (counter-rotating fields) [50] and four-wave mixing (seed co-rotating with a single pump) [51]. Since HCHG is simply a cascade of multiple four-wave-mixing steps, it should also produce circularly polarized light when co-rotating fields are used. Future studies will be required to experimentally verify this capability.

This source could enable major advancements in important scientific applications such as time-, spin-, and/or angle-resolved photoemission spectroscopy [15,5254] as well as PIMS [68,12]. For example, the high repetition rate of this laser is well suited for ARPES experiments that can suffer from a loss of energy resolution due to space charge effects. Moreover, the tunability of this VUV source is currently being used for PIMS experiments, where it has demonstrated the ability to differentiate between different molecules that have the same mass [55].

4. CONCLUSION

We have demonstrated the generation of high-flux vacuum-ultraviolet light using highly cascaded harmonic generation. Numerical simulations show that the harmonic generation is driven by cascaded four-wave-mixing processes. The observed spectral bandwidths of ${\sim}{{40}}\;{\rm{meV}}$ are ideal for many scientific applications, and narrower spectra down to 1 meV can be obtained using moderately sized monochromators. The process of highly cascaded harmonic generation can bring bright, high-repetition-rate, multispectral VUV light, previously available only at large facilities, to laboratory tabletops.

Funding

Basic Energy Sciences (DE-FG02-99ER14982); Air Force Office of Scientific Research (FA9550-16-1-0121); Defense Advanced Research Projects Agency (W31P4Q-13-1-0015); National Science Foundation (DGE-1650115).

Acknowledgment

Current affiliations: DEC: Sandia National Laboratories. SJB, MSK, SRD, JJR: Thorlabs Inc. DGW: Lockheed Martin.

Disclosures

DDH, SJB, DGW, MSK, SRD, JJR, HCK: KMLabs (E,P).

MMM, HCK, SJB: KMLabs (I).

KMLabs uses this HCHG technology to build VUV laser systems.

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32. O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369–373 (2009). [CrossRef]  

33. D. Winters, S. Backus, M. Kirchner, C. Durfee, M. Murnane, and H. Kapteyn, “1 MHz ultrafast cascaded VUV generation in negative curvature hollow fibers,” in Conference on Lasers and Electro-Optics (OSA, 2018).

34. J. Ramirez, D. Hickstein, D. Couch, M. Kirchner, M. Murnane, H. Kapteyn, and S. Backus, “1 MHz ultrafast high order cascaded VUV generation in negative curvature hollow fibers,” in Conference on Lasers and Electro-Optics (OSA, 2019).

35. C. G. Durfee III, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high-order harmonics in hollow waveguides,” Phys. Rev. Lett. 83, 2187–2190 (1999). [CrossRef]  

36. X. M. Tong and C. D. Lin, “Empirical formula for static field ionization rates of atoms and molecules by lasers in the barrier-suppression regime,” J. Phys. B 38, 2593–2600 (2005). [CrossRef]  

37. M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).

38. L. Misoguti, S. Backus, C. G. Durfee, R. Bartels, M. M. Murnane, and H. C. Kapteyn, “Generation of broadband VUV light using third-order cascaded processes,” Phys. Rev. Lett. 87, 013601 (2001). [CrossRef]  

39. C. G. Durfee, L. Misoguti, S. Backus, H. C. Kapteyn, and M. M. Murnane, “Phase matching in cascaded third-order processes,” J. Opt. Soc. Am. B 19, 822–831 (2002). [CrossRef]  

40. L. Misoguti, I. P. Christov, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Nonlinear wave-mixing processes in the extreme ultraviolet,” Phys. Rev. A 72, 063803 (2005). [CrossRef]  

41. E. Gagnon, P. Ranitovic, X.-M. Tong, C. L. Cocke, M. M. Murnane, H. C. Kapteyn, and A. S. Sandhu, “Soft X-ray-driven femtosecond molecular dynamics,” Science 317, 1374–1378 (2007). [CrossRef]  

42. C. G. Durfee Iii, A. Rundquist, S. Backus, Z. Chang, C. Herne, H. C. Kapteyn, and M. M. Murnane, “Guided-wave phase-matching of ultrashort-pulse light,” J. Nonlinear Opt. Phys. Mater. 08, 211–234 (1999). [CrossRef]  

43. A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Measurement of refractive indices of neon, argon, krypton and xenon in the 253.7–140.4 nm wavelength range. Dispersion relations and estimated oscillator strengths of the resonance lines,” J. Quant. Spectrosc. Radiat. Transf. 25, 395–402 (1981). [CrossRef]  

44. J. Hult, “A fourth-order Runge–Kutta in the interaction picture method for simulating supercontinuum generation in optical fibers,” J. Light. Technol. 25, 3770–3775 (2007). [CrossRef]  

45. G. Ycas, D. Maser, and D. D. Hickstein, PyNLO—Python Package for Nonlinear Optics (GitHub Repository, 2018), https://Github.Com/PyNLO/PyNLO.

46. D. P. Shelton, “Nonlinear-optical susceptibilities of gases measured at 1064 and 1319 nm,” Phys. Rev. A 42, 2578–2592 (1990). [CrossRef]  

47. A. Couairon, H. S. Chakraborty, and M. B. Gaarde, “From single-cycle self-compressed filaments to isolated attosecond pulses in noble gases,” Phys. Rev. A 77, 053814 (2008). [CrossRef]  

48. B. Bandyopadhyay, O. Kostko, Y. Fang, and M. Ahmed, “Probing methanol cluster growth by vacuum ultraviolet ionization,” J. Phys. Chem. A 119, 4083–4092 (2015). [CrossRef]  

49. Z.-F. Sun, C. K. Bishwakarma, L. Song, A. van der Avoird, M. C. van Hemert, A. G. Suits, G. C. McBane, and D. H. Parker, “Imaging inelastic scattering of CO with argon: polarization dependent differential cross sections,” Phys. Chem. Chem. Phys. 21, 9200–9211 (2019). [CrossRef]  

50. O. Kfir, P. Grychtol, E. Turgut, R. Knut, D. Zusin, D. Popmintchev, T. Popmintchev, H. Nembach, J. M. Shaw, A. Fleischer, H. Kapteyn, M. Murnane, and O. Cohen, “Generation of bright phase-matched circularly-polarized extreme ultraviolet high harmonics,” Nat. Photonics 9, 99–105 (2015). [CrossRef]  

51. A. Lekosiotis, F. Belli, C. Brahms, and J. C. Travers, “Generation of broadband circularly polarized deep-ultraviolet pulses in hollow capillary fibers,” in Conference on Lasers and Electro-Optics (OSA, 2020).

52. X. Shi, W. You, Y. Zhang, Z. Tao, P. M. Oppeneer, X. Wu, R. Thomale, K. Rossnagel, M. Bauer, H. Kapteyn, and M. Murnane, “Ultrafast electron calorimetry uncovers a new long-lived metastable state in 1T-TaSe2 mediated by mode-selective electron-phonon coupling,” Sci. Adv. 5, eaav4449 (2019). [CrossRef]  

53. M. Bauer, C. Lei, K. Read, R. Tobey, J. Gland, M. M. Murnane, and H. C. Kapteyn, “Direct observation of surface chemistry using ultrafast soft-X-ray pulses,” Phys. Rev. Lett. 87, 025501 (2001). [CrossRef]  

54. W. You, P. Tengdin, C. Chen, X. Shi, D. Zusin, Y. Zhang, C. Gentry, A. Blonsky, M. Keller, P. M. Oppeneer, H. Kapteyn, Z. Tao, and M. Murnane, “Revealing the nature of the ultrafast magnetic phase transition in Ni by correlating extreme ultraviolet magneto-optic and photoemission spectroscopies,” Phys. Rev. Lett. 121, 077204 (2018). [CrossRef]  

55. D. E. Couch, Q. L. Nguyen, D. D. Hickstein, A. Liu, H. C. Kapteyn, M. M. Murnane, and N. J. Labbe, “Detection of the Keto-Enol tautomerization in acetaldehyde, acetone, cyclohexanone, and methyl vinyl ketone with a novel VUV light source,” Proc. Combust. Inst.38,(2021), to be published.

References

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    [Crossref]
  40. L. Misoguti, I. P. Christov, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Nonlinear wave-mixing processes in the extreme ultraviolet,” Phys. Rev. A 72, 063803 (2005).
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  41. E. Gagnon, P. Ranitovic, X.-M. Tong, C. L. Cocke, M. M. Murnane, H. C. Kapteyn, and A. S. Sandhu, “Soft X-ray-driven femtosecond molecular dynamics,” Science 317, 1374–1378 (2007).
    [Crossref]
  42. C. G. Durfee Iii, A. Rundquist, S. Backus, Z. Chang, C. Herne, H. C. Kapteyn, and M. M. Murnane, “Guided-wave phase-matching of ultrashort-pulse light,” J. Nonlinear Opt. Phys. Mater. 08, 211–234 (1999).
    [Crossref]
  43. A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Measurement of refractive indices of neon, argon, krypton and xenon in the 253.7–140.4 nm wavelength range. Dispersion relations and estimated oscillator strengths of the resonance lines,” J. Quant. Spectrosc. Radiat. Transf. 25, 395–402 (1981).
    [Crossref]
  44. J. Hult, “A fourth-order Runge–Kutta in the interaction picture method for simulating supercontinuum generation in optical fibers,” J. Light. Technol. 25, 3770–3775 (2007).
    [Crossref]
  45. G. Ycas, D. Maser, and D. D. Hickstein, PyNLO—Python Package for Nonlinear Optics (GitHub Repository, 2018), https://Github.Com/PyNLO/PyNLO .
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    [Crossref]
  47. A. Couairon, H. S. Chakraborty, and M. B. Gaarde, “From single-cycle self-compressed filaments to isolated attosecond pulses in noble gases,” Phys. Rev. A 77, 053814 (2008).
    [Crossref]
  48. B. Bandyopadhyay, O. Kostko, Y. Fang, and M. Ahmed, “Probing methanol cluster growth by vacuum ultraviolet ionization,” J. Phys. Chem. A 119, 4083–4092 (2015).
    [Crossref]
  49. Z.-F. Sun, C. K. Bishwakarma, L. Song, A. van der Avoird, M. C. van Hemert, A. G. Suits, G. C. McBane, and D. H. Parker, “Imaging inelastic scattering of CO with argon: polarization dependent differential cross sections,” Phys. Chem. Chem. Phys. 21, 9200–9211 (2019).
    [Crossref]
  50. O. Kfir, P. Grychtol, E. Turgut, R. Knut, D. Zusin, D. Popmintchev, T. Popmintchev, H. Nembach, J. M. Shaw, A. Fleischer, H. Kapteyn, M. Murnane, and O. Cohen, “Generation of bright phase-matched circularly-polarized extreme ultraviolet high harmonics,” Nat. Photonics 9, 99–105 (2015).
    [Crossref]
  51. A. Lekosiotis, F. Belli, C. Brahms, and J. C. Travers, “Generation of broadband circularly polarized deep-ultraviolet pulses in hollow capillary fibers,” in Conference on Lasers and Electro-Optics (OSA, 2020).
  52. X. Shi, W. You, Y. Zhang, Z. Tao, P. M. Oppeneer, X. Wu, R. Thomale, K. Rossnagel, M. Bauer, H. Kapteyn, and M. Murnane, “Ultrafast electron calorimetry uncovers a new long-lived metastable state in 1T-TaSe2 mediated by mode-selective electron-phonon coupling,” Sci. Adv. 5, eaav4449 (2019).
    [Crossref]
  53. M. Bauer, C. Lei, K. Read, R. Tobey, J. Gland, M. M. Murnane, and H. C. Kapteyn, “Direct observation of surface chemistry using ultrafast soft-X-ray pulses,” Phys. Rev. Lett. 87, 025501 (2001).
    [Crossref]
  54. W. You, P. Tengdin, C. Chen, X. Shi, D. Zusin, Y. Zhang, C. Gentry, A. Blonsky, M. Keller, P. M. Oppeneer, H. Kapteyn, Z. Tao, and M. Murnane, “Revealing the nature of the ultrafast magnetic phase transition in Ni by correlating extreme ultraviolet magneto-optic and photoemission spectroscopies,” Phys. Rev. Lett. 121, 077204 (2018).
    [Crossref]
  55. D. E. Couch, Q. L. Nguyen, D. D. Hickstein, A. Liu, H. C. Kapteyn, M. M. Murnane, and N. J. Labbe, “Detection of the Keto-Enol tautomerization in acetaldehyde, acetone, cyclohexanone, and methyl vinyl ketone with a novel VUV light source,” Proc. Combust. Inst.38,(2021), to be published.

2019 (5)

L. Sheps, I. Antonov, and K. Au, “Sensitive mass spectrometer for time-resolved gas-phase chemistry studies at high pressures,” J. Phys. Chem. A 123, 10804–10814 (2019).
[Crossref]

H. Jin, J. Yang, L. Xing, J. Hao, Y. Zhang, C. Cao, Y. Pan, and A. Farooq, “An experimental study of indene pyrolysis with synchrotron vacuum ultraviolet photoionization mass spectrometry,” Phys. Chem. Chem. Phys. 21, 5510–5520 (2019).
[Crossref]

S. Ickert, S. Beck, M. W. Linscheid, and J. Riedel, “VUV photodissociation induced by a deuterium lamp in an ion trap,” J. Am. Soc. Mass Spectrom. 30, 2114–2122 (2019).
[Crossref]

Z.-F. Sun, C. K. Bishwakarma, L. Song, A. van der Avoird, M. C. van Hemert, A. G. Suits, G. C. McBane, and D. H. Parker, “Imaging inelastic scattering of CO with argon: polarization dependent differential cross sections,” Phys. Chem. Chem. Phys. 21, 9200–9211 (2019).
[Crossref]

X. Shi, W. You, Y. Zhang, Z. Tao, P. M. Oppeneer, X. Wu, R. Thomale, K. Rossnagel, M. Bauer, H. Kapteyn, and M. Murnane, “Ultrafast electron calorimetry uncovers a new long-lived metastable state in 1T-TaSe2 mediated by mode-selective electron-phonon coupling,” Sci. Adv. 5, eaav4449 (2019).
[Crossref]

2018 (6)

W. You, P. Tengdin, C. Chen, X. Shi, D. Zusin, Y. Zhang, C. Gentry, A. Blonsky, M. Keller, P. M. Oppeneer, H. Kapteyn, Z. Tao, and M. Murnane, “Revealing the nature of the ultrafast magnetic phase transition in Ni by correlating extreme ultraviolet magneto-optic and photoemission spectroscopies,” Phys. Rev. Lett. 121, 077204 (2018).
[Crossref]

T. Kobayashi, “Development of ultrashort pulse lasers for ultrafast spectroscopy,” Photonics 5, 19 (2018).
[Crossref]

O. Venot, Y. Bénilan, N. Fray, M.-C. Gazeau, F. Lefèvre, Et. Es-sebbar, E. Hébrard, M. Schwell, C. Bahrini, F. Montmessin, M. Lefèvre, and I. P. Waldmann, “VUV-absorption cross section of carbon dioxide from 150 to 800 K and applications to warm exoplanetary atmospheres,” Astron. Astrophys. 609, A34 (2018).
[Crossref]

H. Zhang, J. Shu, B. Yang, P. Zhang, and P. Ma, “A rapid detection method for policy-sensitive amines real-time supervision,” Talanta 178, 636–643 (2018).
[Crossref]

T. T. Luu, Z. Yin, A. Jain, T. Gaumnitz, Y. Pertot, J. Ma, and H. J. Wörner, “Extreme–ultraviolet high–harmonic generation in liquids,” Nat. Commun. 9, 3723 (2018).
[Crossref]

J. Seres, E. Seres, C. Serrat, and T. Schumm, “Non-perturbative generation of DUV/VUV harmonics from crystal surfaces at 108 MHz repetition rate,” Opt. Express 26, 21900 (2018).
[Crossref]

2017 (1)

S. Gholam-Mirzaei, J. Beetar, and M. Chini, “High harmonic generation in ZnO with a high-power mid-IR OPA,” Appl. Phys. Lett. 110, 061101 (2017).
[Crossref]

2016 (3)

Y. He, I. M. Vishik, M. Yi, S. Yang, Z. Liu, J. J. Lee, S. Chen, S. N. Rebec, D. Leuenberger, A. Zong, C. M. Jefferson, R. G. Moore, P. S. Kirchmann, A. J. Merriam, and Z.-X. Shen, “Invited article: high resolution angle resolved photoemission with tabletop 11 eV laser,” Rev. Sci. Instrum. 87, 011301 (2016).
[Crossref]

H. Huang, H. Lu, H. Huang, L. Wang, J. Zhang, and D. Y. C. Leung, “Recent development of VUV-based processes for air pollutant degradation,” Front. Environ. Sci. 4, 17 (2016).
[Crossref]

G. T. Buckingham, J. P. Porterfield, O. Kostko, T. P. Troy, M. Ahmed, D. J. Robichaud, M. R. Nimlos, J. W. Daily, and G. B. Ellison, “The thermal decomposition of the benzyl radical in a heated micro-reactor. II. Pyrolysis of the tropyl radical,” J. Chem. Phys. 145, 014305 (2016).
[Crossref]

2015 (3)

A. Hartung, J. Kobelke, A. Schwuchow, J. Bierlich, J. Popp, M. A. Schmidt, and T. Frosch, “Low-loss single-mode guidance in large-core antiresonant hollow-core fibers,” Opt. Lett. 40, 3432–3435 (2015).
[Crossref]

B. Bandyopadhyay, O. Kostko, Y. Fang, and M. Ahmed, “Probing methanol cluster growth by vacuum ultraviolet ionization,” J. Phys. Chem. A 119, 4083–4092 (2015).
[Crossref]

O. Kfir, P. Grychtol, E. Turgut, R. Knut, D. Zusin, D. Popmintchev, T. Popmintchev, H. Nembach, J. M. Shaw, A. Fleischer, H. Kapteyn, M. Murnane, and O. Cohen, “Generation of bright phase-matched circularly-polarized extreme ultraviolet high harmonics,” Nat. Photonics 9, 99–105 (2015).
[Crossref]

2014 (4)

J. Rothhardt, M. Krebs, S. Hädrich, S. Demmler, J. Limpert, and A. Tünnermann, “Absorption-limited and phase-matched high harmonic generation in the tight focusing regime,” New J. Phys. 16, 033022 (2014).
[Crossref]

W. Belardi and J. C. Knight, “Hollow antiresonant fibers with low bending loss,” Opt. Express 22, 10091 (2014).
[Crossref]

V. N. Strocov, M. Kobayashi, X. Wang, L. L. Lev, J. Krempasky, V. V. Rogalev, T. Schmitt, C. Cancellieri, and M. L. Reinle-Schmitt, “Soft-X-ray ARPES at the Swiss Light Source: from 3D materials to buried interfaces and impurities,” Synchrotron Radiat. News 27(2), 31–40 (2014).
[Crossref]

S. Eich, A. Stange, A. V. Carr, J. Urbancic, T. Popmintchev, M. Wiesenmayer, K. Jansen, A. Ruffing, S. Jakobs, T. Rohwer, S. Hellmann, C. Chen, P. Matyba, L. Kipp, K. Rossnagel, M. Bauer, M. M. Murnane, H. C. Kapteyn, S. Mathias, and M. Aeschlimann, “Time- and angle-resolved photoemission spectroscopy with optimized high-harmonic pulses using frequency-doubled Ti:sapphire lasers,” J. Electron Spectrosc. Relat. Phenom. 195, 231–236 (2014).
[Crossref]

2012 (1)

R. Carley, K. Döbrich, B. Frietsch, C. Gahl, M. Teichmann, O. Schwarzkopf, P. Wernet, and M. Weinelt, “Femtosecond laser excitation drives ferromagnetic gadolinium out of magnetic equilibrium,” Phys. Rev. Lett. 109, 057401 (2012).
[Crossref]

2011 (1)

S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7, 138–141 (2011).
[Crossref]

2009 (2)

S. Février, F. Gérôme, A. Labruyère, B. Beaudou, G. Humbert, and J.-L. Auguste, “Ultraviolet guiding hollow-core photonic crystal fiber,” Opt. Lett. 34, 2888–2890 (2009).
[Crossref]

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369–373 (2009).
[Crossref]

2008 (3)

C. A. Taatjes, N. Hansen, D. L. Osborn, K. Kohse-Höinghaus, T. A. Cool, and P. R. Westmoreland, “‘Imaging’ combustion chemistry via multiplexed synchrotron-photoionization mass spectrometry,” Phys. Chem. Chem. Phys. 10, 20–34 (2008).
[Crossref]

D. L. Osborn, P. Zou, H. Johnsen, C. C. Hayden, C. A. Taatjes, V. D. Knyazev, S. W. North, D. S. Peterka, M. Ahmed, and S. R. Leone, “The multiplexed chemical kinetic photoionization mass spectrometer: a new approach to isomer-resolved chemical kinetics,” Rev. Sci. Instrum. 79, 104103 (2008).
[Crossref]

A. Couairon, H. S. Chakraborty, and M. B. Gaarde, “From single-cycle self-compressed filaments to isolated attosecond pulses in noble gases,” Phys. Rev. A 77, 053814 (2008).
[Crossref]

2007 (3)

E. Gagnon, P. Ranitovic, X.-M. Tong, C. L. Cocke, M. M. Murnane, H. C. Kapteyn, and A. S. Sandhu, “Soft X-ray-driven femtosecond molecular dynamics,” Science 317, 1374–1378 (2007).
[Crossref]

J. Hult, “A fourth-order Runge–Kutta in the interaction picture method for simulating supercontinuum generation in optical fibers,” J. Light. Technol. 25, 3770–3775 (2007).
[Crossref]

S. Mathias, L. Miaja-Avila, M. M. Murnane, H. Kapteyn, M. Aeschlimann, and M. Bauer, “Angle-resolved photoemission spectroscopy with a femtosecond high harmonic light source using a two-dimensional imaging electron analyzer,” Rev. Sci. Instrum. 78, 083105 (2007).
[Crossref]

2005 (3)

X. M. Tong and C. D. Lin, “Empirical formula for static field ionization rates of atoms and molecules by lasers in the barrier-suppression regime,” J. Phys. B 38, 2593–2600 (2005).
[Crossref]

A. E. Jailaubekov and S. E. Bradforth, “Tunable 30-femtosecond pulses across the deep ultraviolet,” Appl. Phys. Lett. 87, 021107 (2005).
[Crossref]

L. Misoguti, I. P. Christov, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Nonlinear wave-mixing processes in the extreme ultraviolet,” Phys. Rev. A 72, 063803 (2005).
[Crossref]

2002 (1)

2001 (2)

L. Misoguti, S. Backus, C. G. Durfee, R. Bartels, M. M. Murnane, and H. C. Kapteyn, “Generation of broadband VUV light using third-order cascaded processes,” Phys. Rev. Lett. 87, 013601 (2001).
[Crossref]

M. Bauer, C. Lei, K. Read, R. Tobey, J. Gland, M. M. Murnane, and H. C. Kapteyn, “Direct observation of surface chemistry using ultrafast soft-X-ray pulses,” Phys. Rev. Lett. 87, 025501 (2001).
[Crossref]

2000 (1)

P. Farmanara, V. Stert, and W. Radloff, “Ultrafast photodissociation dynamics of acetone excited by femtosecond 155 nm laser pulses,” Chem. Phys. Lett. 320, 697–702 (2000).
[Crossref]

1999 (2)

C. G. Durfee, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high-order harmonics in hollow waveguides,” Phys. Rev. Lett. 83, 2187–2190 (1999).
[Crossref]

C. G. Durfee Iii, A. Rundquist, S. Backus, Z. Chang, C. Herne, H. C. Kapteyn, and M. M. Murnane, “Guided-wave phase-matching of ultrashort-pulse light,” J. Nonlinear Opt. Phys. Mater. 08, 211–234 (1999).
[Crossref]

1997 (1)

N. P. Lockyer and J. C. Vickerman, “Single photon ionisation mass spectrometry using laser-generated vacuum ultraviolet photons,” Laser Chem. 17, 139–159 (1997).
[Crossref]

1994 (2)

1990 (1)

D. P. Shelton, “Nonlinear-optical susceptibilities of gases measured at 1064 and 1319 nm,” Phys. Rev. A 42, 2578–2592 (1990).
[Crossref]

1986 (1)

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).

1981 (1)

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Measurement of refractive indices of neon, argon, krypton and xenon in the 253.7–140.4 nm wavelength range. Dispersion relations and estimated oscillator strengths of the resonance lines,” J. Quant. Spectrosc. Radiat. Transf. 25, 395–402 (1981).
[Crossref]

1964 (1)

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783–1809 (1964).
[Crossref]

Abjean, R.

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Measurement of refractive indices of neon, argon, krypton and xenon in the 253.7–140.4 nm wavelength range. Dispersion relations and estimated oscillator strengths of the resonance lines,” J. Quant. Spectrosc. Radiat. Transf. 25, 395–402 (1981).
[Crossref]

Aeschlimann, M.

S. Eich, A. Stange, A. V. Carr, J. Urbancic, T. Popmintchev, M. Wiesenmayer, K. Jansen, A. Ruffing, S. Jakobs, T. Rohwer, S. Hellmann, C. Chen, P. Matyba, L. Kipp, K. Rossnagel, M. Bauer, M. M. Murnane, H. C. Kapteyn, S. Mathias, and M. Aeschlimann, “Time- and angle-resolved photoemission spectroscopy with optimized high-harmonic pulses using frequency-doubled Ti:sapphire lasers,” J. Electron Spectrosc. Relat. Phenom. 195, 231–236 (2014).
[Crossref]

S. Mathias, L. Miaja-Avila, M. M. Murnane, H. Kapteyn, M. Aeschlimann, and M. Bauer, “Angle-resolved photoemission spectroscopy with a femtosecond high harmonic light source using a two-dimensional imaging electron analyzer,” Rev. Sci. Instrum. 78, 083105 (2007).
[Crossref]

Agostini, P.

S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7, 138–141 (2011).
[Crossref]

Ahmed, M.

G. T. Buckingham, J. P. Porterfield, O. Kostko, T. P. Troy, M. Ahmed, D. J. Robichaud, M. R. Nimlos, J. W. Daily, and G. B. Ellison, “The thermal decomposition of the benzyl radical in a heated micro-reactor. II. Pyrolysis of the tropyl radical,” J. Chem. Phys. 145, 014305 (2016).
[Crossref]

B. Bandyopadhyay, O. Kostko, Y. Fang, and M. Ahmed, “Probing methanol cluster growth by vacuum ultraviolet ionization,” J. Phys. Chem. A 119, 4083–4092 (2015).
[Crossref]

D. L. Osborn, P. Zou, H. Johnsen, C. C. Hayden, C. A. Taatjes, V. D. Knyazev, S. W. North, D. S. Peterka, M. Ahmed, and S. R. Leone, “The multiplexed chemical kinetic photoionization mass spectrometer: a new approach to isomer-resolved chemical kinetics,” Rev. Sci. Instrum. 79, 104103 (2008).
[Crossref]

Ammosov, M. V.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).

Antonov, I.

L. Sheps, I. Antonov, and K. Au, “Sensitive mass spectrometer for time-resolved gas-phase chemistry studies at high pressures,” J. Phys. Chem. A 123, 10804–10814 (2019).
[Crossref]

Au, K.

L. Sheps, I. Antonov, and K. Au, “Sensitive mass spectrometer for time-resolved gas-phase chemistry studies at high pressures,” J. Phys. Chem. A 123, 10804–10814 (2019).
[Crossref]

Auguste, J.-L.

Backus, S.

L. Misoguti, I. P. Christov, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Nonlinear wave-mixing processes in the extreme ultraviolet,” Phys. Rev. A 72, 063803 (2005).
[Crossref]

C. G. Durfee, L. Misoguti, S. Backus, H. C. Kapteyn, and M. M. Murnane, “Phase matching in cascaded third-order processes,” J. Opt. Soc. Am. B 19, 822–831 (2002).
[Crossref]

L. Misoguti, S. Backus, C. G. Durfee, R. Bartels, M. M. Murnane, and H. C. Kapteyn, “Generation of broadband VUV light using third-order cascaded processes,” Phys. Rev. Lett. 87, 013601 (2001).
[Crossref]

C. G. Durfee Iii, A. Rundquist, S. Backus, Z. Chang, C. Herne, H. C. Kapteyn, and M. M. Murnane, “Guided-wave phase-matching of ultrashort-pulse light,” J. Nonlinear Opt. Phys. Mater. 08, 211–234 (1999).
[Crossref]

C. G. Durfee, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high-order harmonics in hollow waveguides,” Phys. Rev. Lett. 83, 2187–2190 (1999).
[Crossref]

J. Ramirez, D. Hickstein, D. Couch, M. Kirchner, M. Murnane, H. Kapteyn, and S. Backus, “1 MHz ultrafast high order cascaded VUV generation in negative curvature hollow fibers,” in Conference on Lasers and Electro-Optics (OSA, 2019).

D. Winters, S. Backus, M. Kirchner, C. Durfee, M. Murnane, and H. Kapteyn, “1 MHz ultrafast cascaded VUV generation in negative curvature hollow fibers,” in Conference on Lasers and Electro-Optics (OSA, 2018).

Baer, C. R. E.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369–373 (2009).
[Crossref]

Bahrini, C.

O. Venot, Y. Bénilan, N. Fray, M.-C. Gazeau, F. Lefèvre, Et. Es-sebbar, E. Hébrard, M. Schwell, C. Bahrini, F. Montmessin, M. Lefèvre, and I. P. Waldmann, “VUV-absorption cross section of carbon dioxide from 150 to 800 K and applications to warm exoplanetary atmospheres,” Astron. Astrophys. 609, A34 (2018).
[Crossref]

Bandyopadhyay, B.

B. Bandyopadhyay, O. Kostko, Y. Fang, and M. Ahmed, “Probing methanol cluster growth by vacuum ultraviolet ionization,” J. Phys. Chem. A 119, 4083–4092 (2015).
[Crossref]

Bartels, R.

L. Misoguti, S. Backus, C. G. Durfee, R. Bartels, M. M. Murnane, and H. C. Kapteyn, “Generation of broadband VUV light using third-order cascaded processes,” Phys. Rev. Lett. 87, 013601 (2001).
[Crossref]

Bauer, M.

X. Shi, W. You, Y. Zhang, Z. Tao, P. M. Oppeneer, X. Wu, R. Thomale, K. Rossnagel, M. Bauer, H. Kapteyn, and M. Murnane, “Ultrafast electron calorimetry uncovers a new long-lived metastable state in 1T-TaSe2 mediated by mode-selective electron-phonon coupling,” Sci. Adv. 5, eaav4449 (2019).
[Crossref]

S. Eich, A. Stange, A. V. Carr, J. Urbancic, T. Popmintchev, M. Wiesenmayer, K. Jansen, A. Ruffing, S. Jakobs, T. Rohwer, S. Hellmann, C. Chen, P. Matyba, L. Kipp, K. Rossnagel, M. Bauer, M. M. Murnane, H. C. Kapteyn, S. Mathias, and M. Aeschlimann, “Time- and angle-resolved photoemission spectroscopy with optimized high-harmonic pulses using frequency-doubled Ti:sapphire lasers,” J. Electron Spectrosc. Relat. Phenom. 195, 231–236 (2014).
[Crossref]

S. Mathias, L. Miaja-Avila, M. M. Murnane, H. Kapteyn, M. Aeschlimann, and M. Bauer, “Angle-resolved photoemission spectroscopy with a femtosecond high harmonic light source using a two-dimensional imaging electron analyzer,” Rev. Sci. Instrum. 78, 083105 (2007).
[Crossref]

M. Bauer, C. Lei, K. Read, R. Tobey, J. Gland, M. M. Murnane, and H. C. Kapteyn, “Direct observation of surface chemistry using ultrafast soft-X-ray pulses,” Phys. Rev. Lett. 87, 025501 (2001).
[Crossref]

Beaudou, B.

Beck, S.

S. Ickert, S. Beck, M. W. Linscheid, and J. Riedel, “VUV photodissociation induced by a deuterium lamp in an ion trap,” J. Am. Soc. Mass Spectrom. 30, 2114–2122 (2019).
[Crossref]

Beetar, J.

S. Gholam-Mirzaei, J. Beetar, and M. Chini, “High harmonic generation in ZnO with a high-power mid-IR OPA,” Appl. Phys. Lett. 110, 061101 (2017).
[Crossref]

Belardi, W.

Belli, F.

A. Lekosiotis, F. Belli, C. Brahms, and J. C. Travers, “Generation of broadband circularly polarized deep-ultraviolet pulses in hollow capillary fibers,” in Conference on Lasers and Electro-Optics (OSA, 2020).

Benabid, F.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369–373 (2009).
[Crossref]

Bénilan, Y.

O. Venot, Y. Bénilan, N. Fray, M.-C. Gazeau, F. Lefèvre, Et. Es-sebbar, E. Hébrard, M. Schwell, C. Bahrini, F. Montmessin, M. Lefèvre, and I. P. Waldmann, “VUV-absorption cross section of carbon dioxide from 150 to 800 K and applications to warm exoplanetary atmospheres,” Astron. Astrophys. 609, A34 (2018).
[Crossref]

Bideau-Mehu, A.

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Measurement of refractive indices of neon, argon, krypton and xenon in the 253.7–140.4 nm wavelength range. Dispersion relations and estimated oscillator strengths of the resonance lines,” J. Quant. Spectrosc. Radiat. Transf. 25, 395–402 (1981).
[Crossref]

Bierlich, J.

Bishwakarma, C. K.

Z.-F. Sun, C. K. Bishwakarma, L. Song, A. van der Avoird, M. C. van Hemert, A. G. Suits, G. C. McBane, and D. H. Parker, “Imaging inelastic scattering of CO with argon: polarization dependent differential cross sections,” Phys. Chem. Chem. Phys. 21, 9200–9211 (2019).
[Crossref]

Blonsky, A.

W. You, P. Tengdin, C. Chen, X. Shi, D. Zusin, Y. Zhang, C. Gentry, A. Blonsky, M. Keller, P. M. Oppeneer, H. Kapteyn, Z. Tao, and M. Murnane, “Revealing the nature of the ultrafast magnetic phase transition in Ni by correlating extreme ultraviolet magneto-optic and photoemission spectroscopies,” Phys. Rev. Lett. 121, 077204 (2018).
[Crossref]

Bradforth, S. E.

A. E. Jailaubekov and S. E. Bradforth, “Tunable 30-femtosecond pulses across the deep ultraviolet,” Appl. Phys. Lett. 87, 021107 (2005).
[Crossref]

Brahms, C.

A. Lekosiotis, F. Belli, C. Brahms, and J. C. Travers, “Generation of broadband circularly polarized deep-ultraviolet pulses in hollow capillary fibers,” in Conference on Lasers and Electro-Optics (OSA, 2020).

Buckingham, G. T.

G. T. Buckingham, J. P. Porterfield, O. Kostko, T. P. Troy, M. Ahmed, D. J. Robichaud, M. R. Nimlos, J. W. Daily, and G. B. Ellison, “The thermal decomposition of the benzyl radical in a heated micro-reactor. II. Pyrolysis of the tropyl radical,” J. Chem. Phys. 145, 014305 (2016).
[Crossref]

Cancellieri, C.

V. N. Strocov, M. Kobayashi, X. Wang, L. L. Lev, J. Krempasky, V. V. Rogalev, T. Schmitt, C. Cancellieri, and M. L. Reinle-Schmitt, “Soft-X-ray ARPES at the Swiss Light Source: from 3D materials to buried interfaces and impurities,” Synchrotron Radiat. News 27(2), 31–40 (2014).
[Crossref]

Cao, C.

H. Jin, J. Yang, L. Xing, J. Hao, Y. Zhang, C. Cao, Y. Pan, and A. Farooq, “An experimental study of indene pyrolysis with synchrotron vacuum ultraviolet photoionization mass spectrometry,” Phys. Chem. Chem. Phys. 21, 5510–5520 (2019).
[Crossref]

Carley, R.

R. Carley, K. Döbrich, B. Frietsch, C. Gahl, M. Teichmann, O. Schwarzkopf, P. Wernet, and M. Weinelt, “Femtosecond laser excitation drives ferromagnetic gadolinium out of magnetic equilibrium,” Phys. Rev. Lett. 109, 057401 (2012).
[Crossref]

Carr, A. V.

S. Eich, A. Stange, A. V. Carr, J. Urbancic, T. Popmintchev, M. Wiesenmayer, K. Jansen, A. Ruffing, S. Jakobs, T. Rohwer, S. Hellmann, C. Chen, P. Matyba, L. Kipp, K. Rossnagel, M. Bauer, M. M. Murnane, H. C. Kapteyn, S. Mathias, and M. Aeschlimann, “Time- and angle-resolved photoemission spectroscopy with optimized high-harmonic pulses using frequency-doubled Ti:sapphire lasers,” J. Electron Spectrosc. Relat. Phenom. 195, 231–236 (2014).
[Crossref]

Chakraborty, H. S.

A. Couairon, H. S. Chakraborty, and M. B. Gaarde, “From single-cycle self-compressed filaments to isolated attosecond pulses in noble gases,” Phys. Rev. A 77, 053814 (2008).
[Crossref]

Chang, Z.

C. G. Durfee Iii, A. Rundquist, S. Backus, Z. Chang, C. Herne, H. C. Kapteyn, and M. M. Murnane, “Guided-wave phase-matching of ultrashort-pulse light,” J. Nonlinear Opt. Phys. Mater. 08, 211–234 (1999).
[Crossref]

Chen, C.

W. You, P. Tengdin, C. Chen, X. Shi, D. Zusin, Y. Zhang, C. Gentry, A. Blonsky, M. Keller, P. M. Oppeneer, H. Kapteyn, Z. Tao, and M. Murnane, “Revealing the nature of the ultrafast magnetic phase transition in Ni by correlating extreme ultraviolet magneto-optic and photoemission spectroscopies,” Phys. Rev. Lett. 121, 077204 (2018).
[Crossref]

S. Eich, A. Stange, A. V. Carr, J. Urbancic, T. Popmintchev, M. Wiesenmayer, K. Jansen, A. Ruffing, S. Jakobs, T. Rohwer, S. Hellmann, C. Chen, P. Matyba, L. Kipp, K. Rossnagel, M. Bauer, M. M. Murnane, H. C. Kapteyn, S. Mathias, and M. Aeschlimann, “Time- and angle-resolved photoemission spectroscopy with optimized high-harmonic pulses using frequency-doubled Ti:sapphire lasers,” J. Electron Spectrosc. Relat. Phenom. 195, 231–236 (2014).
[Crossref]

Chen, S.

Y. He, I. M. Vishik, M. Yi, S. Yang, Z. Liu, J. J. Lee, S. Chen, S. N. Rebec, D. Leuenberger, A. Zong, C. M. Jefferson, R. G. Moore, P. S. Kirchmann, A. J. Merriam, and Z.-X. Shen, “Invited article: high resolution angle resolved photoemission with tabletop 11 eV laser,” Rev. Sci. Instrum. 87, 011301 (2016).
[Crossref]

Chini, M.

S. Gholam-Mirzaei, J. Beetar, and M. Chini, “High harmonic generation in ZnO with a high-power mid-IR OPA,” Appl. Phys. Lett. 110, 061101 (2017).
[Crossref]

Christov, I. P.

L. Misoguti, I. P. Christov, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Nonlinear wave-mixing processes in the extreme ultraviolet,” Phys. Rev. A 72, 063803 (2005).
[Crossref]

Cocke, C. L.

E. Gagnon, P. Ranitovic, X.-M. Tong, C. L. Cocke, M. M. Murnane, H. C. Kapteyn, and A. S. Sandhu, “Soft X-ray-driven femtosecond molecular dynamics,” Science 317, 1374–1378 (2007).
[Crossref]

Cohen, O.

O. Kfir, P. Grychtol, E. Turgut, R. Knut, D. Zusin, D. Popmintchev, T. Popmintchev, H. Nembach, J. M. Shaw, A. Fleischer, H. Kapteyn, M. Murnane, and O. Cohen, “Generation of bright phase-matched circularly-polarized extreme ultraviolet high harmonics,” Nat. Photonics 9, 99–105 (2015).
[Crossref]

Cool, T. A.

C. A. Taatjes, N. Hansen, D. L. Osborn, K. Kohse-Höinghaus, T. A. Cool, and P. R. Westmoreland, “‘Imaging’ combustion chemistry via multiplexed synchrotron-photoionization mass spectrometry,” Phys. Chem. Chem. Phys. 10, 20–34 (2008).
[Crossref]

Couairon, A.

A. Couairon, H. S. Chakraborty, and M. B. Gaarde, “From single-cycle self-compressed filaments to isolated attosecond pulses in noble gases,” Phys. Rev. A 77, 053814 (2008).
[Crossref]

Couch, D.

J. Ramirez, D. Hickstein, D. Couch, M. Kirchner, M. Murnane, H. Kapteyn, and S. Backus, “1 MHz ultrafast high order cascaded VUV generation in negative curvature hollow fibers,” in Conference on Lasers and Electro-Optics (OSA, 2019).

Couch, D. E.

D. E. Couch, Q. L. Nguyen, D. D. Hickstein, A. Liu, H. C. Kapteyn, M. M. Murnane, and N. J. Labbe, “Detection of the Keto-Enol tautomerization in acetaldehyde, acetone, cyclohexanone, and methyl vinyl ketone with a novel VUV light source,” Proc. Combust. Inst.38,(2021), to be published.

Couny, F.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369–373 (2009).
[Crossref]

Daily, J. W.

G. T. Buckingham, J. P. Porterfield, O. Kostko, T. P. Troy, M. Ahmed, D. J. Robichaud, M. R. Nimlos, J. W. Daily, and G. B. Ellison, “The thermal decomposition of the benzyl radical in a heated micro-reactor. II. Pyrolysis of the tropyl radical,” J. Chem. Phys. 145, 014305 (2016).
[Crossref]

Delone, N. B.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).

Demmler, S.

J. Rothhardt, M. Krebs, S. Hädrich, S. Demmler, J. Limpert, and A. Tünnermann, “Absorption-limited and phase-matched high harmonic generation in the tight focusing regime,” New J. Phys. 16, 033022 (2014).
[Crossref]

DiChiara, A. D.

S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7, 138–141 (2011).
[Crossref]

DiMauro, L. F.

S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7, 138–141 (2011).
[Crossref]

Döbrich, K.

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D. Winters, S. Backus, M. Kirchner, C. Durfee, M. Murnane, and H. Kapteyn, “1 MHz ultrafast cascaded VUV generation in negative curvature hollow fibers,” in Conference on Lasers and Electro-Optics (OSA, 2018).

Durfee, C. G.

C. G. Durfee, L. Misoguti, S. Backus, H. C. Kapteyn, and M. M. Murnane, “Phase matching in cascaded third-order processes,” J. Opt. Soc. Am. B 19, 822–831 (2002).
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L. Misoguti, S. Backus, C. G. Durfee, R. Bartels, M. M. Murnane, and H. C. Kapteyn, “Generation of broadband VUV light using third-order cascaded processes,” Phys. Rev. Lett. 87, 013601 (2001).
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C. G. Durfee, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high-order harmonics in hollow waveguides,” Phys. Rev. Lett. 83, 2187–2190 (1999).
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C. G. Durfee Iii, A. Rundquist, S. Backus, Z. Chang, C. Herne, H. C. Kapteyn, and M. M. Murnane, “Guided-wave phase-matching of ultrashort-pulse light,” J. Nonlinear Opt. Phys. Mater. 08, 211–234 (1999).
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S. Eich, A. Stange, A. V. Carr, J. Urbancic, T. Popmintchev, M. Wiesenmayer, K. Jansen, A. Ruffing, S. Jakobs, T. Rohwer, S. Hellmann, C. Chen, P. Matyba, L. Kipp, K. Rossnagel, M. Bauer, M. M. Murnane, H. C. Kapteyn, S. Mathias, and M. Aeschlimann, “Time- and angle-resolved photoemission spectroscopy with optimized high-harmonic pulses using frequency-doubled Ti:sapphire lasers,” J. Electron Spectrosc. Relat. Phenom. 195, 231–236 (2014).
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H. Jin, J. Yang, L. Xing, J. Hao, Y. Zhang, C. Cao, Y. Pan, and A. Farooq, “An experimental study of indene pyrolysis with synchrotron vacuum ultraviolet photoionization mass spectrometry,” Phys. Chem. Chem. Phys. 21, 5510–5520 (2019).
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Février, S.

Fleischer, A.

O. Kfir, P. Grychtol, E. Turgut, R. Knut, D. Zusin, D. Popmintchev, T. Popmintchev, H. Nembach, J. M. Shaw, A. Fleischer, H. Kapteyn, M. Murnane, and O. Cohen, “Generation of bright phase-matched circularly-polarized extreme ultraviolet high harmonics,” Nat. Photonics 9, 99–105 (2015).
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O. Venot, Y. Bénilan, N. Fray, M.-C. Gazeau, F. Lefèvre, Et. Es-sebbar, E. Hébrard, M. Schwell, C. Bahrini, F. Montmessin, M. Lefèvre, and I. P. Waldmann, “VUV-absorption cross section of carbon dioxide from 150 to 800 K and applications to warm exoplanetary atmospheres,” Astron. Astrophys. 609, A34 (2018).
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R. Carley, K. Döbrich, B. Frietsch, C. Gahl, M. Teichmann, O. Schwarzkopf, P. Wernet, and M. Weinelt, “Femtosecond laser excitation drives ferromagnetic gadolinium out of magnetic equilibrium,” Phys. Rev. Lett. 109, 057401 (2012).
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E. Gagnon, P. Ranitovic, X.-M. Tong, C. L. Cocke, M. M. Murnane, H. C. Kapteyn, and A. S. Sandhu, “Soft X-ray-driven femtosecond molecular dynamics,” Science 317, 1374–1378 (2007).
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Gahl, C.

R. Carley, K. Döbrich, B. Frietsch, C. Gahl, M. Teichmann, O. Schwarzkopf, P. Wernet, and M. Weinelt, “Femtosecond laser excitation drives ferromagnetic gadolinium out of magnetic equilibrium,” Phys. Rev. Lett. 109, 057401 (2012).
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T. T. Luu, Z. Yin, A. Jain, T. Gaumnitz, Y. Pertot, J. Ma, and H. J. Wörner, “Extreme–ultraviolet high–harmonic generation in liquids,” Nat. Commun. 9, 3723 (2018).
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O. Venot, Y. Bénilan, N. Fray, M.-C. Gazeau, F. Lefèvre, Et. Es-sebbar, E. Hébrard, M. Schwell, C. Bahrini, F. Montmessin, M. Lefèvre, and I. P. Waldmann, “VUV-absorption cross section of carbon dioxide from 150 to 800 K and applications to warm exoplanetary atmospheres,” Astron. Astrophys. 609, A34 (2018).
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W. You, P. Tengdin, C. Chen, X. Shi, D. Zusin, Y. Zhang, C. Gentry, A. Blonsky, M. Keller, P. M. Oppeneer, H. Kapteyn, Z. Tao, and M. Murnane, “Revealing the nature of the ultrafast magnetic phase transition in Ni by correlating extreme ultraviolet magneto-optic and photoemission spectroscopies,” Phys. Rev. Lett. 121, 077204 (2018).
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Gérôme, F.

Ghimire, S.

S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7, 138–141 (2011).
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Gland, J.

M. Bauer, C. Lei, K. Read, R. Tobey, J. Gland, M. M. Murnane, and H. C. Kapteyn, “Direct observation of surface chemistry using ultrafast soft-X-ray pulses,” Phys. Rev. Lett. 87, 025501 (2001).
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Glownia, J. H.

Gnass, D. R.

Grychtol, P.

O. Kfir, P. Grychtol, E. Turgut, R. Knut, D. Zusin, D. Popmintchev, T. Popmintchev, H. Nembach, J. M. Shaw, A. Fleischer, H. Kapteyn, M. Murnane, and O. Cohen, “Generation of bright phase-matched circularly-polarized extreme ultraviolet high harmonics,” Nat. Photonics 9, 99–105 (2015).
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Guern, Y.

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Measurement of refractive indices of neon, argon, krypton and xenon in the 253.7–140.4 nm wavelength range. Dispersion relations and estimated oscillator strengths of the resonance lines,” J. Quant. Spectrosc. Radiat. Transf. 25, 395–402 (1981).
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J. Rothhardt, M. Krebs, S. Hädrich, S. Demmler, J. Limpert, and A. Tünnermann, “Absorption-limited and phase-matched high harmonic generation in the tight focusing regime,” New J. Phys. 16, 033022 (2014).
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C. A. Taatjes, N. Hansen, D. L. Osborn, K. Kohse-Höinghaus, T. A. Cool, and P. R. Westmoreland, “‘Imaging’ combustion chemistry via multiplexed synchrotron-photoionization mass spectrometry,” Phys. Chem. Chem. Phys. 10, 20–34 (2008).
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Hao, J.

H. Jin, J. Yang, L. Xing, J. Hao, Y. Zhang, C. Cao, Y. Pan, and A. Farooq, “An experimental study of indene pyrolysis with synchrotron vacuum ultraviolet photoionization mass spectrometry,” Phys. Chem. Chem. Phys. 21, 5510–5520 (2019).
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Hartung, A.

Hayden, C. C.

D. L. Osborn, P. Zou, H. Johnsen, C. C. Hayden, C. A. Taatjes, V. D. Knyazev, S. W. North, D. S. Peterka, M. Ahmed, and S. R. Leone, “The multiplexed chemical kinetic photoionization mass spectrometer: a new approach to isomer-resolved chemical kinetics,” Rev. Sci. Instrum. 79, 104103 (2008).
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Y. He, I. M. Vishik, M. Yi, S. Yang, Z. Liu, J. J. Lee, S. Chen, S. N. Rebec, D. Leuenberger, A. Zong, C. M. Jefferson, R. G. Moore, P. S. Kirchmann, A. J. Merriam, and Z.-X. Shen, “Invited article: high resolution angle resolved photoemission with tabletop 11 eV laser,” Rev. Sci. Instrum. 87, 011301 (2016).
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Hébrard, E.

O. Venot, Y. Bénilan, N. Fray, M.-C. Gazeau, F. Lefèvre, Et. Es-sebbar, E. Hébrard, M. Schwell, C. Bahrini, F. Montmessin, M. Lefèvre, and I. P. Waldmann, “VUV-absorption cross section of carbon dioxide from 150 to 800 K and applications to warm exoplanetary atmospheres,” Astron. Astrophys. 609, A34 (2018).
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O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369–373 (2009).
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Hellmann, S.

S. Eich, A. Stange, A. V. Carr, J. Urbancic, T. Popmintchev, M. Wiesenmayer, K. Jansen, A. Ruffing, S. Jakobs, T. Rohwer, S. Hellmann, C. Chen, P. Matyba, L. Kipp, K. Rossnagel, M. Bauer, M. M. Murnane, H. C. Kapteyn, S. Mathias, and M. Aeschlimann, “Time- and angle-resolved photoemission spectroscopy with optimized high-harmonic pulses using frequency-doubled Ti:sapphire lasers,” J. Electron Spectrosc. Relat. Phenom. 195, 231–236 (2014).
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Herne, C.

C. G. Durfee, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high-order harmonics in hollow waveguides,” Phys. Rev. Lett. 83, 2187–2190 (1999).
[Crossref]

C. G. Durfee Iii, A. Rundquist, S. Backus, Z. Chang, C. Herne, H. C. Kapteyn, and M. M. Murnane, “Guided-wave phase-matching of ultrashort-pulse light,” J. Nonlinear Opt. Phys. Mater. 08, 211–234 (1999).
[Crossref]

Hickstein, D.

J. Ramirez, D. Hickstein, D. Couch, M. Kirchner, M. Murnane, H. Kapteyn, and S. Backus, “1 MHz ultrafast high order cascaded VUV generation in negative curvature hollow fibers,” in Conference on Lasers and Electro-Optics (OSA, 2019).

Hickstein, D. D.

D. E. Couch, Q. L. Nguyen, D. D. Hickstein, A. Liu, H. C. Kapteyn, M. M. Murnane, and N. J. Labbe, “Detection of the Keto-Enol tautomerization in acetaldehyde, acetone, cyclohexanone, and methyl vinyl ketone with a novel VUV light source,” Proc. Combust. Inst.38,(2021), to be published.

Holler, M.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369–373 (2009).
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H. Huang, H. Lu, H. Huang, L. Wang, J. Zhang, and D. Y. C. Leung, “Recent development of VUV-based processes for air pollutant degradation,” Front. Environ. Sci. 4, 17 (2016).
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H. Huang, H. Lu, H. Huang, L. Wang, J. Zhang, and D. Y. C. Leung, “Recent development of VUV-based processes for air pollutant degradation,” Front. Environ. Sci. 4, 17 (2016).
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S. Ickert, S. Beck, M. W. Linscheid, and J. Riedel, “VUV photodissociation induced by a deuterium lamp in an ion trap,” J. Am. Soc. Mass Spectrom. 30, 2114–2122 (2019).
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A. E. Jailaubekov and S. E. Bradforth, “Tunable 30-femtosecond pulses across the deep ultraviolet,” Appl. Phys. Lett. 87, 021107 (2005).
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Jain, A.

T. T. Luu, Z. Yin, A. Jain, T. Gaumnitz, Y. Pertot, J. Ma, and H. J. Wörner, “Extreme–ultraviolet high–harmonic generation in liquids,” Nat. Commun. 9, 3723 (2018).
[Crossref]

Jakobs, S.

S. Eich, A. Stange, A. V. Carr, J. Urbancic, T. Popmintchev, M. Wiesenmayer, K. Jansen, A. Ruffing, S. Jakobs, T. Rohwer, S. Hellmann, C. Chen, P. Matyba, L. Kipp, K. Rossnagel, M. Bauer, M. M. Murnane, H. C. Kapteyn, S. Mathias, and M. Aeschlimann, “Time- and angle-resolved photoemission spectroscopy with optimized high-harmonic pulses using frequency-doubled Ti:sapphire lasers,” J. Electron Spectrosc. Relat. Phenom. 195, 231–236 (2014).
[Crossref]

Jansen, K.

S. Eich, A. Stange, A. V. Carr, J. Urbancic, T. Popmintchev, M. Wiesenmayer, K. Jansen, A. Ruffing, S. Jakobs, T. Rohwer, S. Hellmann, C. Chen, P. Matyba, L. Kipp, K. Rossnagel, M. Bauer, M. M. Murnane, H. C. Kapteyn, S. Mathias, and M. Aeschlimann, “Time- and angle-resolved photoemission spectroscopy with optimized high-harmonic pulses using frequency-doubled Ti:sapphire lasers,” J. Electron Spectrosc. Relat. Phenom. 195, 231–236 (2014).
[Crossref]

Jefferson, C. M.

Y. He, I. M. Vishik, M. Yi, S. Yang, Z. Liu, J. J. Lee, S. Chen, S. N. Rebec, D. Leuenberger, A. Zong, C. M. Jefferson, R. G. Moore, P. S. Kirchmann, A. J. Merriam, and Z.-X. Shen, “Invited article: high resolution angle resolved photoemission with tabletop 11 eV laser,” Rev. Sci. Instrum. 87, 011301 (2016).
[Crossref]

Jin, H.

H. Jin, J. Yang, L. Xing, J. Hao, Y. Zhang, C. Cao, Y. Pan, and A. Farooq, “An experimental study of indene pyrolysis with synchrotron vacuum ultraviolet photoionization mass spectrometry,” Phys. Chem. Chem. Phys. 21, 5510–5520 (2019).
[Crossref]

Johannin-Gilles, A.

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Measurement of refractive indices of neon, argon, krypton and xenon in the 253.7–140.4 nm wavelength range. Dispersion relations and estimated oscillator strengths of the resonance lines,” J. Quant. Spectrosc. Radiat. Transf. 25, 395–402 (1981).
[Crossref]

Johnsen, H.

D. L. Osborn, P. Zou, H. Johnsen, C. C. Hayden, C. A. Taatjes, V. D. Knyazev, S. W. North, D. S. Peterka, M. Ahmed, and S. R. Leone, “The multiplexed chemical kinetic photoionization mass spectrometer: a new approach to isomer-resolved chemical kinetics,” Rev. Sci. Instrum. 79, 104103 (2008).
[Crossref]

Kapteyn, H.

X. Shi, W. You, Y. Zhang, Z. Tao, P. M. Oppeneer, X. Wu, R. Thomale, K. Rossnagel, M. Bauer, H. Kapteyn, and M. Murnane, “Ultrafast electron calorimetry uncovers a new long-lived metastable state in 1T-TaSe2 mediated by mode-selective electron-phonon coupling,” Sci. Adv. 5, eaav4449 (2019).
[Crossref]

W. You, P. Tengdin, C. Chen, X. Shi, D. Zusin, Y. Zhang, C. Gentry, A. Blonsky, M. Keller, P. M. Oppeneer, H. Kapteyn, Z. Tao, and M. Murnane, “Revealing the nature of the ultrafast magnetic phase transition in Ni by correlating extreme ultraviolet magneto-optic and photoemission spectroscopies,” Phys. Rev. Lett. 121, 077204 (2018).
[Crossref]

O. Kfir, P. Grychtol, E. Turgut, R. Knut, D. Zusin, D. Popmintchev, T. Popmintchev, H. Nembach, J. M. Shaw, A. Fleischer, H. Kapteyn, M. Murnane, and O. Cohen, “Generation of bright phase-matched circularly-polarized extreme ultraviolet high harmonics,” Nat. Photonics 9, 99–105 (2015).
[Crossref]

S. Mathias, L. Miaja-Avila, M. M. Murnane, H. Kapteyn, M. Aeschlimann, and M. Bauer, “Angle-resolved photoemission spectroscopy with a femtosecond high harmonic light source using a two-dimensional imaging electron analyzer,” Rev. Sci. Instrum. 78, 083105 (2007).
[Crossref]

J. Ramirez, D. Hickstein, D. Couch, M. Kirchner, M. Murnane, H. Kapteyn, and S. Backus, “1 MHz ultrafast high order cascaded VUV generation in negative curvature hollow fibers,” in Conference on Lasers and Electro-Optics (OSA, 2019).

D. Winters, S. Backus, M. Kirchner, C. Durfee, M. Murnane, and H. Kapteyn, “1 MHz ultrafast cascaded VUV generation in negative curvature hollow fibers,” in Conference on Lasers and Electro-Optics (OSA, 2018).

Kapteyn, H. C.

S. Eich, A. Stange, A. V. Carr, J. Urbancic, T. Popmintchev, M. Wiesenmayer, K. Jansen, A. Ruffing, S. Jakobs, T. Rohwer, S. Hellmann, C. Chen, P. Matyba, L. Kipp, K. Rossnagel, M. Bauer, M. M. Murnane, H. C. Kapteyn, S. Mathias, and M. Aeschlimann, “Time- and angle-resolved photoemission spectroscopy with optimized high-harmonic pulses using frequency-doubled Ti:sapphire lasers,” J. Electron Spectrosc. Relat. Phenom. 195, 231–236 (2014).
[Crossref]

E. Gagnon, P. Ranitovic, X.-M. Tong, C. L. Cocke, M. M. Murnane, H. C. Kapteyn, and A. S. Sandhu, “Soft X-ray-driven femtosecond molecular dynamics,” Science 317, 1374–1378 (2007).
[Crossref]

L. Misoguti, I. P. Christov, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Nonlinear wave-mixing processes in the extreme ultraviolet,” Phys. Rev. A 72, 063803 (2005).
[Crossref]

C. G. Durfee, L. Misoguti, S. Backus, H. C. Kapteyn, and M. M. Murnane, “Phase matching in cascaded third-order processes,” J. Opt. Soc. Am. B 19, 822–831 (2002).
[Crossref]

L. Misoguti, S. Backus, C. G. Durfee, R. Bartels, M. M. Murnane, and H. C. Kapteyn, “Generation of broadband VUV light using third-order cascaded processes,” Phys. Rev. Lett. 87, 013601 (2001).
[Crossref]

M. Bauer, C. Lei, K. Read, R. Tobey, J. Gland, M. M. Murnane, and H. C. Kapteyn, “Direct observation of surface chemistry using ultrafast soft-X-ray pulses,” Phys. Rev. Lett. 87, 025501 (2001).
[Crossref]

C. G. Durfee Iii, A. Rundquist, S. Backus, Z. Chang, C. Herne, H. C. Kapteyn, and M. M. Murnane, “Guided-wave phase-matching of ultrashort-pulse light,” J. Nonlinear Opt. Phys. Mater. 08, 211–234 (1999).
[Crossref]

C. G. Durfee, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high-order harmonics in hollow waveguides,” Phys. Rev. Lett. 83, 2187–2190 (1999).
[Crossref]

D. E. Couch, Q. L. Nguyen, D. D. Hickstein, A. Liu, H. C. Kapteyn, M. M. Murnane, and N. J. Labbe, “Detection of the Keto-Enol tautomerization in acetaldehyde, acetone, cyclohexanone, and methyl vinyl ketone with a novel VUV light source,” Proc. Combust. Inst.38,(2021), to be published.

Keller, M.

W. You, P. Tengdin, C. Chen, X. Shi, D. Zusin, Y. Zhang, C. Gentry, A. Blonsky, M. Keller, P. M. Oppeneer, H. Kapteyn, Z. Tao, and M. Murnane, “Revealing the nature of the ultrafast magnetic phase transition in Ni by correlating extreme ultraviolet magneto-optic and photoemission spectroscopies,” Phys. Rev. Lett. 121, 077204 (2018).
[Crossref]

Keller, U.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369–373 (2009).
[Crossref]

Kfir, O.

O. Kfir, P. Grychtol, E. Turgut, R. Knut, D. Zusin, D. Popmintchev, T. Popmintchev, H. Nembach, J. M. Shaw, A. Fleischer, H. Kapteyn, M. Murnane, and O. Cohen, “Generation of bright phase-matched circularly-polarized extreme ultraviolet high harmonics,” Nat. Photonics 9, 99–105 (2015).
[Crossref]

Kipp, L.

S. Eich, A. Stange, A. V. Carr, J. Urbancic, T. Popmintchev, M. Wiesenmayer, K. Jansen, A. Ruffing, S. Jakobs, T. Rohwer, S. Hellmann, C. Chen, P. Matyba, L. Kipp, K. Rossnagel, M. Bauer, M. M. Murnane, H. C. Kapteyn, S. Mathias, and M. Aeschlimann, “Time- and angle-resolved photoemission spectroscopy with optimized high-harmonic pulses using frequency-doubled Ti:sapphire lasers,” J. Electron Spectrosc. Relat. Phenom. 195, 231–236 (2014).
[Crossref]

Kirchmann, P. S.

Y. He, I. M. Vishik, M. Yi, S. Yang, Z. Liu, J. J. Lee, S. Chen, S. N. Rebec, D. Leuenberger, A. Zong, C. M. Jefferson, R. G. Moore, P. S. Kirchmann, A. J. Merriam, and Z.-X. Shen, “Invited article: high resolution angle resolved photoemission with tabletop 11 eV laser,” Rev. Sci. Instrum. 87, 011301 (2016).
[Crossref]

Kirchner, M.

D. Winters, S. Backus, M. Kirchner, C. Durfee, M. Murnane, and H. Kapteyn, “1 MHz ultrafast cascaded VUV generation in negative curvature hollow fibers,” in Conference on Lasers and Electro-Optics (OSA, 2018).

J. Ramirez, D. Hickstein, D. Couch, M. Kirchner, M. Murnane, H. Kapteyn, and S. Backus, “1 MHz ultrafast high order cascaded VUV generation in negative curvature hollow fibers,” in Conference on Lasers and Electro-Optics (OSA, 2019).

Knight, J. C.

Knut, R.

O. Kfir, P. Grychtol, E. Turgut, R. Knut, D. Zusin, D. Popmintchev, T. Popmintchev, H. Nembach, J. M. Shaw, A. Fleischer, H. Kapteyn, M. Murnane, and O. Cohen, “Generation of bright phase-matched circularly-polarized extreme ultraviolet high harmonics,” Nat. Photonics 9, 99–105 (2015).
[Crossref]

Knyazev, V. D.

D. L. Osborn, P. Zou, H. Johnsen, C. C. Hayden, C. A. Taatjes, V. D. Knyazev, S. W. North, D. S. Peterka, M. Ahmed, and S. R. Leone, “The multiplexed chemical kinetic photoionization mass spectrometer: a new approach to isomer-resolved chemical kinetics,” Rev. Sci. Instrum. 79, 104103 (2008).
[Crossref]

Kobayashi, M.

V. N. Strocov, M. Kobayashi, X. Wang, L. L. Lev, J. Krempasky, V. V. Rogalev, T. Schmitt, C. Cancellieri, and M. L. Reinle-Schmitt, “Soft-X-ray ARPES at the Swiss Light Source: from 3D materials to buried interfaces and impurities,” Synchrotron Radiat. News 27(2), 31–40 (2014).
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C. G. Durfee, L. Misoguti, S. Backus, H. C. Kapteyn, and M. M. Murnane, “Phase matching in cascaded third-order processes,” J. Opt. Soc. Am. B 19, 822–831 (2002).
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W. You, P. Tengdin, C. Chen, X. Shi, D. Zusin, Y. Zhang, C. Gentry, A. Blonsky, M. Keller, P. M. Oppeneer, H. Kapteyn, Z. Tao, and M. Murnane, “Revealing the nature of the ultrafast magnetic phase transition in Ni by correlating extreme ultraviolet magneto-optic and photoemission spectroscopies,” Phys. Rev. Lett. 121, 077204 (2018).
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D. Winters, S. Backus, M. Kirchner, C. Durfee, M. Murnane, and H. Kapteyn, “1 MHz ultrafast cascaded VUV generation in negative curvature hollow fibers,” in Conference on Lasers and Electro-Optics (OSA, 2018).

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S. Eich, A. Stange, A. V. Carr, J. Urbancic, T. Popmintchev, M. Wiesenmayer, K. Jansen, A. Ruffing, S. Jakobs, T. Rohwer, S. Hellmann, C. Chen, P. Matyba, L. Kipp, K. Rossnagel, M. Bauer, M. M. Murnane, H. C. Kapteyn, S. Mathias, and M. Aeschlimann, “Time- and angle-resolved photoemission spectroscopy with optimized high-harmonic pulses using frequency-doubled Ti:sapphire lasers,” J. Electron Spectrosc. Relat. Phenom. 195, 231–236 (2014).
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M. Bauer, C. Lei, K. Read, R. Tobey, J. Gland, M. M. Murnane, and H. C. Kapteyn, “Direct observation of surface chemistry using ultrafast soft-X-ray pulses,” Phys. Rev. Lett. 87, 025501 (2001).
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C. G. Durfee, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high-order harmonics in hollow waveguides,” Phys. Rev. Lett. 83, 2187–2190 (1999).
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Nembach, H.

O. Kfir, P. Grychtol, E. Turgut, R. Knut, D. Zusin, D. Popmintchev, T. Popmintchev, H. Nembach, J. M. Shaw, A. Fleischer, H. Kapteyn, M. Murnane, and O. Cohen, “Generation of bright phase-matched circularly-polarized extreme ultraviolet high harmonics,” Nat. Photonics 9, 99–105 (2015).
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D. E. Couch, Q. L. Nguyen, D. D. Hickstein, A. Liu, H. C. Kapteyn, M. M. Murnane, and N. J. Labbe, “Detection of the Keto-Enol tautomerization in acetaldehyde, acetone, cyclohexanone, and methyl vinyl ketone with a novel VUV light source,” Proc. Combust. Inst.38,(2021), to be published.

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G. T. Buckingham, J. P. Porterfield, O. Kostko, T. P. Troy, M. Ahmed, D. J. Robichaud, M. R. Nimlos, J. W. Daily, and G. B. Ellison, “The thermal decomposition of the benzyl radical in a heated micro-reactor. II. Pyrolysis of the tropyl radical,” J. Chem. Phys. 145, 014305 (2016).
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X. Shi, W. You, Y. Zhang, Z. Tao, P. M. Oppeneer, X. Wu, R. Thomale, K. Rossnagel, M. Bauer, H. Kapteyn, and M. Murnane, “Ultrafast electron calorimetry uncovers a new long-lived metastable state in 1T-TaSe2 mediated by mode-selective electron-phonon coupling,” Sci. Adv. 5, eaav4449 (2019).
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C. A. Taatjes, N. Hansen, D. L. Osborn, K. Kohse-Höinghaus, T. A. Cool, and P. R. Westmoreland, “‘Imaging’ combustion chemistry via multiplexed synchrotron-photoionization mass spectrometry,” Phys. Chem. Chem. Phys. 10, 20–34 (2008).
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T. T. Luu, Z. Yin, A. Jain, T. Gaumnitz, Y. Pertot, J. Ma, and H. J. Wörner, “Extreme–ultraviolet high–harmonic generation in liquids,” Nat. Commun. 9, 3723 (2018).
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D. L. Osborn, P. Zou, H. Johnsen, C. C. Hayden, C. A. Taatjes, V. D. Knyazev, S. W. North, D. S. Peterka, M. Ahmed, and S. R. Leone, “The multiplexed chemical kinetic photoionization mass spectrometer: a new approach to isomer-resolved chemical kinetics,” Rev. Sci. Instrum. 79, 104103 (2008).
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O. Kfir, P. Grychtol, E. Turgut, R. Knut, D. Zusin, D. Popmintchev, T. Popmintchev, H. Nembach, J. M. Shaw, A. Fleischer, H. Kapteyn, M. Murnane, and O. Cohen, “Generation of bright phase-matched circularly-polarized extreme ultraviolet high harmonics,” Nat. Photonics 9, 99–105 (2015).
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O. Kfir, P. Grychtol, E. Turgut, R. Knut, D. Zusin, D. Popmintchev, T. Popmintchev, H. Nembach, J. M. Shaw, A. Fleischer, H. Kapteyn, M. Murnane, and O. Cohen, “Generation of bright phase-matched circularly-polarized extreme ultraviolet high harmonics,” Nat. Photonics 9, 99–105 (2015).
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Ranitovic, P.

E. Gagnon, P. Ranitovic, X.-M. Tong, C. L. Cocke, M. M. Murnane, H. C. Kapteyn, and A. S. Sandhu, “Soft X-ray-driven femtosecond molecular dynamics,” Science 317, 1374–1378 (2007).
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Read, K.

M. Bauer, C. Lei, K. Read, R. Tobey, J. Gland, M. M. Murnane, and H. C. Kapteyn, “Direct observation of surface chemistry using ultrafast soft-X-ray pulses,” Phys. Rev. Lett. 87, 025501 (2001).
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Figures (4)

Fig. 1.
Fig. 1. Highly cascaded harmonic generation (HCHG). (a) In our experiment, a 1035 nm laser is frequency doubled, and both fundamental and second-harmonic beams are focused into a xenon-filled, 30 µm core diameter, hollow-core negative-curvature fiber to drive the HCHG process. The resulting VUV light is then spectrally selected by a grating-based monochromator. (b) The HCHG process is the result of numerous four-wave-mixing steps, each combining three photons to generate a higher-energy photon. We note that the photon combinations for H4 and higher represent just one possible route to each harmonic.
Fig. 2.
Fig. 2. Spectrum and calibrated photon flux observed for each harmonic. (a) VUV spectra acquired using the high-throughput (purple, log scale) and high-resolution (red, linear scale) monochromator configurations. Harmonics up to H14 are clearly visible. The high-resolution monochromator reveals an intrinsic spectral resolution of 40 meV (${{E}}/\Delta {{{E}}_{{\rm{FWHM}}}} \approx {{250}}$ for H8 and H9). (b) Observed photon flux for each harmonic, measured using the prism monochromator (4–10 eV, blue) and the Wadsworth monochromator (10–18 eV, purple). Above 11 eV, the beamline optics have substantially reduced efficiency.
Fig. 3.
Fig. 3. Simulation of HCHG. (a) The xenon is supplied to the front of the fiber so that the pressure in the fiber decreases to vacuum along the length of the fiber. (b) A finite element simulation of the pressure in the fiber shows that the pressure decreases most rapidly at the end of the fiber, as the flow transitions from viscous flow to molecular flow. (c) Using the pressure profile from (b), numerical simulations using the nonlinear Schrödinger equation (NLSE) confirm the generation of numerous harmonics in the UV and VUV spectral region. (d) Each harmonic is generated throughout the length of the fiber, rather than within a small phase-matched region.
Fig. 4.
Fig. 4. Simulated harmonic flux when one harmonic is severely attenuated. Attenuation of the third harmonic (red) leads to all higher harmonics being severely attenuated. In contrast, attenuation of the fourth harmonic (blue) has only a small effect on the higher harmonic fluxes. This result indicates that multiple pathways can produce each harmonic above the fourth order.

Tables (1)

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Table 1. Observed and Estimated Source Photon Flux for Each Harmonica

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

ω 3 = ω 2 + ω 2 ω 1 ,
Δ k k 1 + k 3 2 k 2 = 2 π N ( δ 3 λ 3 + δ 1 λ 1 2 δ 2 λ 2 ) u 4 π a 2 ( λ 3 + λ 1 2 λ 2 ) ,
ω 4 = ω 3 + ω 2 ω 1 , ω 4 = ω 3 + ω 3 ω 2 , ω 5 = ω 4 + ω 2 ω 1 , ω 5 = ω 3 + ω 3 ω 1 , ω 6 = ω 5 + ω 2 ω 1 , ω 6 = ω 4 + ω 3 ω 1 , ω 7 = ω 6 + ω 2 ω 1 , ω 7 = ω 5 + ω 3 ω 1 , ω 7 = ω 4 + ω 4 ω 1 ,

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