Tunable coherent light sources operating in the vacuum ultraviolet (VUV) region in the 100–200-nm (6–12 eV) wavelength range have important spectroscopic applications in many research fields, including time-resolved angle-resolved photoemission spectroscopy. Recent advances in laser technology have enabled the upconversion of visible femtosecond lasers to the vacuum and extreme ultraviolet regions. However, the complexity of their experimental setups and the scarcity of bulk nonlinear crystals for VUV generation have hampered its widespread use. Here, we propose the use of a free-standing dielectric nanomembrane as a simple and practical method for tunable VUV generation. We demonstrate that third harmonic VUV light is generated with sufficient intensity for spectroscopic applications from commercially available SiO2 nanomembranes of submicron thicknesses under excitation with visible femtosecond laser pulses. The submicron thickness of the nanomembranes is optimal for maximizing VUV generation efficiency and prevents self-phase modulation and spectral broadening of the fundamental beam. The observed VUV photons are up to 107 photons per pulse at 157 nm with a 1-kHz repetition rate, corresponding to a conversion efficiency of 10−6. Moreover, the central VUV wavelength can be tuned in the 146–190-nm wavelength range by changing the fundamental wavelength. We also explore material and thickness dependence with experiments and calculations. The presented results suggest that dielectric nanomembranes can be used as practical nonlinear media for VUV spectroscopic applications.

Vacuum ultraviolet (VUV) coherent light sources have been a powerful spectroscopic probe,1 allowing the observation of the electronic states of excited atoms2 and molecules.3 In the field of life sciences, electronic circular dichroism (ECD) is a powerful tool because of its sensitivity to structural conformation of biomolecules.4 ECD measurements require efficient sources of VUV light5 but have already shown promise for probing important biomolecules.6,7 Another application that has recently emerged is time-resolved angle-resolved photoemission spectroscopy (ARPES).8–11 By combining ARPES with pulsed lasers in a conventional pump–probe setup, it is possible to directly explore the dynamics of non-equilibrium electronic states. In ARPES, high-energy photons must overcome the work function of solids, typically approximately 5 eV. VUV photons have energies well above this value; this facilitates the effective probing of a large area of the momentum space within the Brillouin zone.12 Moreover, the use of high-energy photons increases bulk sensitivity owing to its increased propagation length in the material.13 This is particularly important for investigating the macroscopic quantum phenomena, such as superconductivity.9 Furthermore, as the intensity of the output VUV light increases, VUV light is expected to be useful for controlling chemical reactions14 and, accordingly, for use in lithography15 and laser processing.16 

Despite its numerous potential uses, coherent VUV light is still challenging to generate. Currently, third harmonic generation (THG)17 and higher harmonic generation (HHG)18 from gases are demonstrated. However, these generation schemes are often complicated and require specialized techniques for stable operation. For its usage to increase, realizing a more practical and convenient solid-state-based method for wavelength conversion into the VUV region is essential. A problem here is that the conventional bulk nonlinear crystals, such as β-BaB2O4, LiB3O5, and CsLiB6O10, cannot be used for generating VUV pulses owing to their strong absorption. An exception is the KBe2BO3F2 (KBBF) crystal;19,20 however, KBBF crystals are difficult to grow and are unavailable.21 Moreover, in these previous methods, the phase matching condition was required to be satisfied to increase the maximum average power of the generated harmonic wave.22 This requirement has limited the choice of materials that can be used as the nonlinear medium.

Recent technological advances have drastically improved the performance of femtosecond lasers. In particular, the use of solid-state laser diodes for pumping Yb-doped media significantly increases the stability and reduces the maintenance cost associated with regenerative amplifiers.23,24 Using these femtosecond lasers for generating second and third harmonics paves the way toward the development of new practical tabletop sources of coherent VUV light. In this case, high conversion efficiency can be expected owing to the high electric field strength of the femtosecond laser that removes the restriction that the phase matching condition must be satisfied and dramatically expands the choice of nonlinear media. In fact, recently, new types of solid nonlinear materials for VUV generation, such as surfaces of transparent solids in the visible region25,26 and dielectric metasurfaces,27,28 which are artificial nanostructures with sizes comparable with or smaller than the light wavelength, have been proposed and demonstrated.

In these methods where the nonlinear medium does not satisfy the phase matching condition, the thickness of the nonlinear medium that contributes to VUV generation should be the same order of the coherent length, which is typically several hundred nm. It is because, even if the thickness of the nonlinear medium is larger than the coherent length, it does not contribute to increase the harmonic intensity.22 In this case, Fmax(nω), which is the maximum photon flux of the nth order harmonic wave can be generated by the femtosecond laser light source with the repetition rate of N, is simply described as
(1)
where Pmax(nω) is the maximum average power of the generated nth order harmonic wave, α is the nth order nonlinear coefficient, and Emax(ω) is the maximum electric field amplitude of the fundamental beam. To increase Fmax(nω), the value of N has been increased using an oscillator with a high MHz-order repetition rate,25,26 and the value of α has been effectively enhanced using the metasurfaces owing to the effect of Mie resonances in the dielectric nanostructures.27,28 Despite these efforts, the power of the VUV light generated from these methods is still too weak to be used for practical applications, such as laser ARPES and ECD spectroscopy. Moreover, these methods relinquish the advantage of phase-matching independence for their power gain, thus losing the ability of simple wavelength tunability; it is difficult to change the oscillator wavelength over a wide wavelength range, and the resonance wavelength of a metasurface is uniquely determined by its shape.

Another way to increase the generated VUV power, as apparent from Eq. (1), is by increasing the maximum electric field amplitude of the fundamental beam Emax(ω). This approach is particularly important for applications where the maximum value of the repetition rate of light source N is fixed, such as time-of-flight-type ARPES.29 However, in the case of femtosecond laser pulse excitation, Emax(ω) is limited by two major factors: the first is the laser damage threshold of solid-state materials; the second is self-phase modulation incurred during propagation through a bulk substrate material. Such nonlinear propagation effects significantly reduce the maximum electric field amplitude of the fundamental beam and the efficiency of wavelength conversion when femtosecond pulses with energies from micro- to milli-joules are used. In the method of the previous research,25–27 although only a very thin region near the surface contributes to VUV generation, the fundamental wave propagates through a bulk substrate before reaching the nonlinear medium, and the effects of nonlinear propagation there are inevitable.

To overcome these problems for increasing the fundamental pulse intensity, in this study, we propose and demonstrate the use of dielectric free-standing nanomembranes with a thickness of several hundred nanometers or less as a new solid-state material for VUV THG. The submicron thickness of the nanomembranes is optimal to maximize the VUV generation efficiency and prevents self-phase modulation and spectral broadening of the fundamental beam. In addition, the high damage threshold of the dielectric facilitates an increase in the excitation power of the fundamental laser pulse. We demonstrate that THG in SiO2 nanomembranes excited at the fundamental 470-nm wavelength with commercially available femtosecond optical parametric amplifiers (OPAs) enables coherent VUV light generation at 157-nm wavelength with sufficient photon flux (∼107 photons/pulse with a 1-kHz repetition rate; 1010 photon/s) to be used as a probe beam for VUV spectroscopy, including laser ARPES. Furthermore, the resonance-free nature of our structure combined with the OPA light source allows continuous tuning of the wavelength in the VUV region (146–190 nm) by simply changing the wavelength of the fundamental beam. We also investigate the dependence of THG intensity on the excitation power as well as the laser damage threshold for materials of different thicknesses. We show that SiO2 can achieve the maximum photon number because of its large damage threshold, whereas epitaxial γ-Al2O3 enables high generation efficiency. As the repetition rate is increased to 100 kHz, the VUV THG intensity linearly increased with it. Owing to these excellent properties and because these dielectric nanomembranes are commercially available and easy to handle, they are promising and practical nonlinear media for wavelength conversion to the VUV region for spectroscopic applications.

First, we estimate the VUV THG intensity generated from a dielectric nanomembrane. When the depletion of the fundamental wave is negligible and the nonlinear material is isotropic, the intensity of the third harmonics (TH) beam, I3, can be expressed using the following equation:22,
(2)
where I1 is the intensity of the fundamental beam, χ1111 is the third-order nonlinear susceptibility, λ3 is the wavelength of the TH beam, L is the thickness of the nonlinear media, and n1 and n3 are refractive indices of the fundamental and TH beams, respectively. k1 = 2πn1/λ1 and k3 = 2πn3/λ3 represent wavenumbers for the fundamental and TH beams, respectively. ε0 (∼8.85 × 10−12 C/m V) is the dielectric constant of vacuum, and c (∼3.00 × 108 m/s) is the speed of light. That is, for a 300-nm-thick SiO2 nanomembrane (χ1111 = 2.8 × 10−22 m2/V2,22, λ3 = 1.57 × 10−7 m, n1 = 1.47 and n3 = 1.66,30 and 3k1k3 = 7.48 × 107 m−1) at a fundamental wavelength of 470 nm (THG is 157 nm) and intensity I1 of 1017 W/m2, the THG conversion efficiency is as high as I3/I1 = 4.2 × 10−6. It is worth noting that for a pulse duration of 100 fs, the chosen intensity of the fundamental beam corresponds to a fluence of 1 J/cm2, which is just below the damage threshold.31 The estimated conversion efficiency indicates that the nanomembrane enables VUV pulse energy that is sufficient for VUV spectroscopy, including laser ARPES. Because third-order susceptibility is of the order of 10−22 m2/V2 22 for most dielectrics, similar conversion efficiency can be achieved using other dielectric membranes.

To demonstrate that the above conversion efficiency can be achieved in practice, we performed THG experiment using commercially available, free-standing SiO2 nanomembranes (100- and 300-nm thick), Al2O3 (100-nm thick), Si3N4 (50-, 100-, and 200-nm thick), and self-made epitaxial γ-Al2O3 (50- and 100-nm thick) (see Sec. 1 of the supplementary material). As a typical example, the microscope image of a 300-nm-thick SiO2 nanomembrane is shown in the inset of Fig. 1(a). The epitaxial γ-Al2O3 was grown on a (100) silicon substrate through chemical vapor deposition,32 whereas the silicon substrate was removed using Deep-RIE to produce a free-standing thin film (see Sec. 1 of the supplementary material). In the epitaxial γ-Al2O3, the crystal axis perpendicular to the substrate is aligned, but the in-plane crystal axis is randomly oriented, the typical domain size of which is approximately several tens nm.33 Therefore, the optical response is isotropic at normal incidence. Stress control is usually important for obtaining flat membranes: when compressive stress is introduced in a film, which is often the case for Si and thermally oxidized SiO2, the film becomes wrinkled.34,35 Here, however, no buckling was observed in the epitaxial γ-Al2O3; thus, a flat membrane could be formed without additional stress-control processes.

FIG. 1.

Vacuum ultraviolet third harmonic generation from dielectric nanomembranes with a 1-kHz repetition rate excitation. (a) Dependence of VUV THG spectra from a 300-nm-thick SiO2 nanomembrane on the excitation power. All spectra presented in Fig. 1 were acquired with a 0.5-s integration time. The inset shows a microcopy image of the sample. The length of the scale bar is 100 µm. (b) Dependence of VUV THG spectra on the excitation wavelength, which changes from 470 nm to 572 nm at 6-nm intervals. Each spectrum is normalized by the peak intensity. (c) Dependence of the intensity of VUV THG from dielectric membrane samples [SiO2 (blue), epitaxial γ-Al2O3 (red), Al2O3 (orange), and Si3N4 (green)] with different thicknesses [50 nm (open circles), 100 nm (filled circles), 200 nm (open triangles), and 300 nm (open squares)] on the excitation power. Peak fluence at the focal point is shown on the top axis, and the VUV photon number per pulse is shown on the right axis. The dashed line indicates cubic dependency.

FIG. 1.

Vacuum ultraviolet third harmonic generation from dielectric nanomembranes with a 1-kHz repetition rate excitation. (a) Dependence of VUV THG spectra from a 300-nm-thick SiO2 nanomembrane on the excitation power. All spectra presented in Fig. 1 were acquired with a 0.5-s integration time. The inset shows a microcopy image of the sample. The length of the scale bar is 100 µm. (b) Dependence of VUV THG spectra on the excitation wavelength, which changes from 470 nm to 572 nm at 6-nm intervals. Each spectrum is normalized by the peak intensity. (c) Dependence of the intensity of VUV THG from dielectric membrane samples [SiO2 (blue), epitaxial γ-Al2O3 (red), Al2O3 (orange), and Si3N4 (green)] with different thicknesses [50 nm (open circles), 100 nm (filled circles), 200 nm (open triangles), and 300 nm (open squares)] on the excitation power. Peak fluence at the focal point is shown on the top axis, and the VUV photon number per pulse is shown on the right axis. The dashed line indicates cubic dependency.

Close modal

For the VUV THG experiment, we used an OPA with a pulse duration of approximately 100 fs at a repetition rate of 1 kHz pumped by using a regeneratively amplified femtosecond Ti:sapphire laser (see Sec. 2 of the supplementary material). The VUV THG spectra of a 300-nm-thick SiO2 membrane excited with a wavelength of 470 nm are presented in Fig. 1(a). This figure presents clear VUV THG signals, which increase with the excitation power, at a wavelength of 157 nm (7.9 eV). Figure 1(b) presents the observed VUV THG spectrum of a 300-nm SiO2 membrane with a peak value when the wavelength of the fundamental beam output from the OPA is changed from 470 nm to 572 nm at 6 nm intervals while keeping the excitation power constant at 10 mW. Each spectrum is normalized by the maximum intensity. We can see that the generation of VUV coherent light from the SiO2 nanomembrane is possible at any wavelength greater than 157 nm, without significantly degrading the signal-to-noise ratio. We also confirmed that the generation of coherent VUV light from the SiO2 nanomembrane is possible at as short as approximately 146 nm (see Sec. 3 of the supplementary material). The shortest wavelength of VUV THG is believed to be determined by the wavelength at which VUV light reabsorption by SiO2 occurs at the bandgap of SiO2 at approximately 7.5 eV.36 

Figure 1(c) presents the excitation power dependence of the THG peak intensity for each nanomembrane when a 157-nm (7.9 eV) THG is generated using a 470-nm (2.6 eV) fundamental beam. It can be observed that, for all nanomembranes, the THG intensity is proportional to the cubic of the excitation power and that the THG signal sharply decreases as soon as the excitation power exceeds the irreversible damage threshold.31 For wide-bandgap materials, such as Al2O3 and SiO2, it is known that the density of free electrons (which are generated through multiphoton or tunneling ionization) increases exponentially due to the avalanche processes. Material damage occurs when it reaches a critical density.37 We did not observe a deviation from the cubic dependence of the THG intensity on the fundamental pulse power until the damage occurred.

Figure 1(c) also shows that the peak damage threshold fluences for Si3N4, Al2O3, and SiO2 nanomembranes are approximately 0.2 J/cm2, 1.2 J/cm2, and 1.8 J/cm2, respectively. Because the bandgap energies of Si3N4, Al2O3, and SiO2 are 4.8 eV,38 6.5 eV,36 and 7.5 eV,36 respectively, one may conclude that the larger the bandgap, the higher the damage threshold. This is consistent with previous results obtained for bulk materials38 and membranes.31 Moreover, the inter-band transition in Si3N4 is a two-photon process, whereas the transition from the valence to conduction band in Al2O3 and SiO2 requires three photons. That is, the damage threshold is significantly increased in Al2O3 and SiO2 because their free-electron generation rate is much lower than that in Si3N4. Although the bandgap of epitaxial γ-Al2O3 has not been experimentally determined yet, it was found that its damage threshold is about 0.5 J/cm2. Figure 1(c) also shows that the damage threshold of the membranes is almost independent of their thicknesses. This is because for subwavelength-thick membranes, the electric field strength at the back surface is maximized due to interference,39 i.e., damage is expected to occur there independent of the thickness.

It is worth noting that the dependence of the THG signal with the thickness varies with the material of the nanomembrane. In the Si3N4 nanomembranes, the 50-nm-thick sample yields a lower TH wave intensity than the 100-nm-thick sample but a higher intensity than the 200-nm-thick sample. In contrast, in the SiO2 nanomembranes, the THG intensity increases approximately by 10 times as the thickness increases from 100 nm to 300 nm. This is because the intensity of the TH beam is determined by the absorption length of the sample rather than the film thickness, as we will discuss later.

In our experiments with a 1-kHz repetition rate and approximately 50-µm beam spot size, the maximum VUV photon flux was achieved by the 300-nm SiO2 nanomembrane when it was excited with a 41-mW fundamental beam power, as shown in Fig. 1(c). This is because the laser damage threshold of SiO2 is higher than that of other nanomembranes, and furthermore, the THG intensity in the SiO2 nanomembrane increases as the film thickness increases. It is worth noting that the epitaxial γ-Al2O3 nanomembrane show the highest VUV THG efficiency below the damage threshold.

We used a photomultiplier as a detector to quantitatively estimate the number of VUV photons generated from the 300-nm SiO2 membrane (see Secs. 2 and 4 of the supplementary material). The VUV THG signal intensity observed at an excitation wavelength of 470 nm and power of 10 mW was 2881 nV s (the data are shown in Sec. 4 of the supplementary material), which approximately corresponds to 2.6 × 105 photon/pulse. The observed THG counts can be converted to photon numbers using this result, as shown on the right axis of Fig. 1(b). The maximum VUV photon number from the samples can also be estimated and summarized, as presented in Table I. Based on this result, the maximum number of photons generated from the 300-nm-thick SiO2 nanomembrane with a 41-mW excitation can be estimated to be about 1.4 × 107 photon/pulse and 1.4 × 1010 photon/s, with a 1-kHz repetition rate, as presented in Fig. 1(b). This corresponds to an average power of about 18.1 nW, which gives a conversion efficiency of about 10−6. Although this value is approximately one order of magnitude lower than the estimated results discussed at the beginning of this paper, it is sufficient for several VUV spectroscopic applications, as discussed later in Sec. V. The reasons for the one order difference of one order of magnitude are presumably that Eq. (2) does not consider the absorption of vacuum ultraviolet light and the Fresnel reflection at the membrane interfaces and that the optical constants of the actual membrane samples differ from the values reported in the literature. Note that the observed VUV intensity is more than two orders larger than that reported in previous methods.25,27,28

TABLE I.

Maximum photon number of VUV THG from nanomembranes.

SampleMaximum photon number of
(thickness)VUV THG (photon/pulse)
SiO2 (300 nm) 1.4 × 107 
SiO2 (100 nm) 2.6 × 106 
Epitaxial γ-Al2O3 (100 nm) 1.1 × 106 
Epitaxial γ-Al2O3 (50 nm) 8.0 × 105 
Al2O3 5.9 × 106 
Si3N4 (200 nm) 2.4 × 104 
Si3N4 (100 nm) 2.6 × 104 
Si3N4 (50 nm) 5.7 × 104 
SampleMaximum photon number of
(thickness)VUV THG (photon/pulse)
SiO2 (300 nm) 1.4 × 107 
SiO2 (100 nm) 2.6 × 106 
Epitaxial γ-Al2O3 (100 nm) 1.1 × 106 
Epitaxial γ-Al2O3 (50 nm) 8.0 × 105 
Al2O3 5.9 × 106 
Si3N4 (200 nm) 2.4 × 104 
Si3N4 (100 nm) 2.6 × 104 
Si3N4 (50 nm) 5.7 × 104 

THG efficiency depends strongly on the thickness of the nanomembranes. Figure 2 presents the results of the THG efficiency as a function of nanomembrane thickness for Si3N4, SiO2, and Al2O340 (see Sec. 6 of the supplementary material). Here, unlike Eq. (2), the refractive indices are treated as complex numbers to consider the effect of absorption in the VUV region, and the Fresnel coefficients at both interfaces of the membrane are considered. All the plots were normalized using the corresponding maximum THG intensity. For SiO2 and Al2O3, oscillations with a period of several hundred nanometers were observed due to phase mismatch. In addition, due to the finite absorption of VUV light, its envelope tends to decrease as the membrane thickness increases. Therefore, in materials with small absorption in the VUV region, the THG efficiency is maximized when the film thickness is about the same as the coherence length (see Sec. 6 of the supplementary material). This corresponds to approximately 400 nm for SiO2 and approximately 200 nm for Al2O3. In contrast, no oscillation was observed in the Si3N4 nanomembrane, and its THG intensity was maximum at a thickness of approximately 100 nm, which becomes nearly constant for thicknesses over 200 nm. This is because Si3N4 has a strong absorption (an absorption coefficient of 7.76 × 107 m−1; see Sec. 6 of the supplementary material) as its bandgap, which is less than the photon energy of the generated VUV light, i.e., only VUV photons generated near the back surface are emitted to the outside.

FIG. 2.

Numerical simulation of the dependence of THG intensity on material thickness. Dependence of THG intensity on membrane thickness for different materials (blue: Al2O3, green: Si3N4, and red: SiO2). Each plot is normalized by the maximum intensity.

FIG. 2.

Numerical simulation of the dependence of THG intensity on material thickness. Dependence of THG intensity on membrane thickness for different materials (blue: Al2O3, green: Si3N4, and red: SiO2). Each plot is normalized by the maximum intensity.

Close modal

We also observed that the spectrum of the fundamental beam pulse is broadened in the bulk dielectric material due to self-phase modulation and that the THG signal decreased significantly (see Sec. 7 of the supplementary material). At a pulse width of 100 fs or higher, it is difficult to avoid self-phase modulation even if pre-chirping is applied to the fundamental beam through pulse shaping. These results are consistent with the dependence of the THG intensity on thickness for the nanomembranes observed in Fig. 1(c), indicating the importance of using nanomembranes rather than the bulk form for an efficient generation of VUV THG.

Because higher repetition rates above 1 kHz are often required in practice, we also examined the VUV THG intensity at a repetition rate of 100 kHz (see Sec. 2 of the supplementary material). The dependence of the obtained THG spectrum and intensity on the fundamental beam intensity is presented in Figs. 3(a) and 3(b), respectively. The THG intensity also shows the cubic dependence on the intensity of the fundamental beam for a repetition rate of 100 kHz. No damage occurred even at an excitation power of 120 mW because the peak fluence (0.55 J/cm2) did not reach the damage threshold (1.8 J/cm2) observed in Fig. 1(c). The number of VUV photons generated at an excitation intensity of 100 mW was estimated using the photomultiplier, as described above. The observed signal intensity was 191.5 nV s/pulse, which corresponds to approximately 1.0 × 104 photon/pulse and 1.0 × 109 photon/s at a repetition rate of 100 kHz. Figure 3(c) shows the relationship between THG intensity and repetition rate under the condition of constant pulse energy (0.1 µJ). It can be clearly observed that the THG intensity increases proportionally with the repetition rate.

FIG. 3.

Results of VUV THG measurement for SiO2 materials with a 100-kHz repetition rate excitation. (a) Dependence of VUV THG spectra from a 300-nm-thick SiO2 membrane on the excitation power. Dependence of the intensity of VUV THG from a 300-nm-thick SiO2 membrane on the excitation power (b) and repetition rate (c). The slope of the straight broken line fitted to the experimental data in (c) is 1.06.

FIG. 3.

Results of VUV THG measurement for SiO2 materials with a 100-kHz repetition rate excitation. (a) Dependence of VUV THG spectra from a 300-nm-thick SiO2 membrane on the excitation power. Dependence of the intensity of VUV THG from a 300-nm-thick SiO2 membrane on the excitation power (b) and repetition rate (c). The slope of the straight broken line fitted to the experimental data in (c) is 1.06.

Close modal

In the 100-kHz rate experiment, the excitation intensity of 100 mW corresponds to a fluence of approximately 0.46 J/cm2. Because the damage threshold of the SiO2 membrane is 1.8 J/cm2 [see Fig. 1(c)], it is expected that the excitation intensity can be further increased by 3.9 times, giving 59 times higher THG intensity. Furthermore, if the repetition rate of the fundamental beam is multiplied by 10, i.e., 1 MHz, the nanomembrane turns to a VUV coherent light source capable of generating 5.9 × 105 photons/pulse and 5.9 × 1010 photons/s. Realizing this requires a femtosecond laser with a repetition rate of 1 MHz and average power of 3 W as an excitation laser. Such lasers are commercially available. For time-of-flight-type ARPES suitable for time-resolved ARPES measurement,29 the number of photons per pulse is limited to 103 photons/pulse or less because the number of photons entering the detector must be at most one, and the maximum repetition rate of light sources is around 4 MHz41 due to the limited response speed of the detector. Thus, the current performance of our membranes is practical for use in typical ARPES setups. Moreover, the results must also be applicable to long-pulse excitation applications, where energy resolution is important. If the pulse width is increased from 100 fs to 1 ps to increase the energy resolution to 2 meV, the peak electric field intensity becomes one-tenth, and correspondingly, the THG becomes one-thousandth the original strength. If we assume the same 1-MHz repetition rate and 3-W average power system, even in this case, the number of photons is 5.9 × 102 photons/pulse, which is sufficient for the measurement. For hemispherical-type ARPES, the maximum photon number is also approximately 109 per second, limited by the damage threshold of the detector.41 Therefore, the above specification is also sufficiently applicable to light sources for hemispherical-type ARPES. The 157-nm VUV observed in Fig. 1 has almost the same wavelength as the VUV emitted from the KBBF crystal,20 so it can be replaced without much difficulty.

In conclusion, we demonstrated the wavelength conversion to the VUV region using THG in dielectric nanomembranes. We showed that a 300-nm SiO2 nanomembrane excited by femtosecond pulses radiated from an OPA pumped by a regenerative amplifier can generate 7.9-eV (157 nm) photons at a 1-kHz repetition rate, with 1.4 × 107 photon/pulse, which corresponds to 18.1 nW and the conversion efficiency of as much as 10−6. Furthermore, wavelength conversion can be performed in a wide wavelength range (146–190 nm) by simply changing the wavelength of the fundamental wave. Our numerical simulation shows that coherent VUV light can be generated with the highest efficiency at 400-nm thickness of SiO2 and 200-nm thickness of Al2O3, which is consistent with the experimental results. We also demonstrated VUV generation at 100 kHz and confirmed the generation of 1.0 × 104 photon/pulse, which is sufficient for laser ARPES applications.

The dielectric free-standing nanomembranes used in this experiment are all commercially available and inexpensive, excluding γ-Al2O3 nanomembrane which we created. In addition, it can generate coherent VUV light simply by placing them in the optical path of the excitation beam. Therefore, by combining a commercially available regenerative amplifier and an OPA system, a practical tunable coherent VUV light source can be configured, which can be applicable for VUV spectroscopic applications, for example, to laser ARPES.

As mentioned in Sec. III, we believe that the shortest wavelength that can be generated by the proposed method is determined by the bandgap energy of the nanomembrane material. Therefore, if dielectrics with a larger bandgap (e.g., CaF2, MgF2, and LiF) can be used, VUV light with a shorter wavelength can be generated. For example, LiF is one of the dielectrics with the largest bandgap (approximately 14 eV42); thus, if a LiF nanomembrane can be fabricated and used as the nonlinear material in the proposed method, VUV generation with a wavelength shortened to around 90 nm can be expected.

As future prospects, the fabrication of nanostructures on nanomembranes has the potential to realize advanced optical control techniques based on structural effects, such as photonic crystals and metamaterials.27,28,43 While this loses the advantage of wavelength tunability, the high damage threshold should allow for continued application to high-peak-intensity pulses. This further allows for the effective use of the solid-state nature of our material, which is difficult with gas-based generation schemes. Combined with nanostructure fabrication, nanomembranes may become a powerful and versatile new platform for VUV upconversion from high-pulse-energy lasers.

See the supplementary material for the details of samples, VUV THG measurements, and their results and the evaluation of generated VUV THG intensity and photon numbers.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

We thank Y. Svirko, H. Sakurai, Y. Arashida, D. Hirano, T. Ikemachi, and N. Kanda for their helpful discussion and E. Lebrasseur, M. Fujiwara, and A. Mizushima for their support in fabricating the device. Fabrication of the samples was performed using the apparatus at the VLSI Design and Education Center (VDEC, currently d.lab) of the University of Tokyo. This research was supported by JST PRESTO (Grant No. JPMJPR17G2), JSPS KAKENHI (Grant No. 18H01147), MEXT Q-LEAP (Grant No. JPMXS0118067246), the MEXT Photon Frontier Network Program, MEXT “Nanotechnology Platform” (Grant Nos. JPMXP09F19UT0013 and JPMXP09A16UT0162), and the Center of Innovation Program funded by the Japan Science and Technology Agency.

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Supplementary Material