Tunable third harmonic generation in the vacuum ultraviolet region using dielectric nanomembranes

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 region^25,26 and dielectric metasurfaces,^27,28 which are artificial nanostructures with sizes comparable with or smaller than the light wavelength, have been proposed and demonstrated.

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.

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.

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

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.

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.

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.