Non-perturbative generation of DUV/VUV harmonics from crystal surfaces at 108 MHz repetition rate

We demonstrate non-perturbative 3 (267 nm) and 5 (160 nm) harmonic generation in solids from a Ti:sapphire frequency comb (800 nm) at 108 MHz repetition rate. The experiments show that non-perturbative low harmonics are dominantly generated on the surface and on the interface between solids, and that they are not produced by bulk processes from the near-surface layer of the material. Measurements reveal that due to the lack of phase matching, the generated harmonics in bulk are suppressed by orders of magnitude compared to the signal generated on the surface. Our results pave the way for the development of allsolid-state high repetition rate harmonic sources for vacuum ultraviolet spectroscopy and high precision frequency comb metrology. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement


Introduction
High harmonic generation (HHG) is an attractive method to convert ultrashort laser pulses from the infrared or visible spectral range into the vacuum ultraviolet (VUV) or soft x-ray spectral range [1].It produces a coherent, wide spectrum of several harmonic lines, which makes HHG a widely used method to generate ultrashort probe pulses for time-resolved spectroscopy supporting temporal resolutions in the few-femtosecond and even in the subfemtosecond time scales and to study ultrafast physical and chemical processes.For a long time, harmonics have been generated in different gases, and HHG from solids has attracted attention only in recent years, after the first successful demonstrations of the phenomenon [2,3] using mid-infrared laser pulses and later THz driving fields [4].
In solids, harmonics can be generated at much lower laser intensities than in gases, promising the extension of HHG into very compact laser sources and with very high repetition rates, reaching even GHz frequencies.Such high repetition rates would be very beneficial for time-resolved spectroscopic applications, and VUV or EUV frequency combs [5][6][7] could also be realized in solids for high precision metrology.Consequently, HHG in solids is being extensively explored both experimentally and theoretically.Experiments using low repetition rate laser sources as pump have demonstrated HHG in different bulk crystals [8][9][10][11] and 2D materials [12][13][14] and the first high repetition rate generation at 70-80 MHz has recently been reported in sapphire [15][16][17].Based on dynamical Bloch oscillations [4,18], non-perturbative generation of HHG in solids is usually explained by interband and intraband transitions of the electrons inside the band-structure of solids as they interact with the incident laser field as bulk processes [10,11,19].In some cases, the generation of harmonics is also described as perturbative cascaded three-wave [20] or four-wave mixing [21] processes.
Several recent studies have suggested the need to further investigate the precise generation of harmonics in solids in order to accurately differentiate between bulk and surface generation, and between perturbative and non-perturbative processes.Indeed, in [15] the generation of harmonics in solids was observed only from the near-surface layer in sapphire, in the 60-120 nm spectral range, and this effect was explained by considering the strong absorption of sapphire, which enables only the last about 10-nm-thick layer of the crystal to contribute to the HHG signal.Other experiments have found that the 3 rd harmonic of a fiber laser at 531 n crystal is ho successfully g harmonic at a In this wo driven nonlin interface betw perturbative o laser intensity generation on distinguishing that are trans frequency com generation of harmonics.W both the 3 rd a surface proce orders of mag

Experim
The experime Systems) deli pulse energy o mirror pairs f fine tuning an sample crysta the crystal.T ~1x10 12 W/cm Fig. 1 = 40 beam nm is also gen owever basical generated in s around 700 nm ork, we show near processes ween solids, an or non-perturba y itself, which n the surface a g between bulk sparent at both mb.We show f harmonics on We then investig and 5 th harmon sses.The samples were tilted by about 10°, see Fig. 1(b), to avoid back-reflection into the frequency comb.The generated harmonic beam was focused with a VUV-grade MgF 2 lens to the input slit of a VUV monochromator (McPherson 234/302) equipped with a 300 l/mm grating.According to earlier measurements [15], the harmonic beams co-propagate with the fundamental laser beam, with any small deviations corrected by the lens that collects them onto the spectrometer slit.The HHG sample and the VUV monochromator were in vacuum with a background pressure of 10 -3 mbar.In certain measurements, a VUV bandpass filter was inserted into the HHG beam at the entrance of the monochromator to suppress the 3 rd harmonic.The spectrally resolved beam was detected with a VUV photomultiplier (Hamamatsu R6836), sensitive in the 115-320 nm spectral range, which prevented us from detecting the 7 th or higher harmonic orders which would also be present.

Harmonic generation on fluoride crystals
In the first measurement series, fluoride crystals, namely LiF, MgF 2 , and CaF 2 were used with different thicknesses.They are commercially available with optically polished VUV windows at crystal orientations of (100), ( 110) and ( 111).These crystals are wide bandgap isolators with absorption edges in the 120-140 nm range.Beyond being transparent in the VUV, these fluoride crystals have small non-linear refractive indexes in the range of 1-2×10 16 cm 2 /W [23], which gives a non-linear phase shift in the order of π/100 causing negligible non-linear spectral or beam profile distortion during propagation in the crystals.Otherwise, our conclusions below are drawn mainly from measurements performed when the focus is before the crystal surface, in vacuum, as shown in Fig. 1(b).The samples were mounted in a motorized rotation stage with the rotation axis perpendicular to the surface, which allows finding the direction of the strongest harmonic signal.Furthermore, the crystals were translated along the optical axis of the laser beam through the focal region (z-scan).
Figure 2(a) shows the measured spectra from the crystals optimally positioned and rotated to get the highest signal.As it will be seen later in Fig. 3, harmonics (especially the 5 th one) are stronger from the back surface.The VUV filter was not used here to be able to measure the weak 5 th harmonic from LiF, and consequently, the 3 rd harmonics saturated the detector.In the case of CaF 2 , the signal would reach about 5-times higher.As it can be seen from Fig. 2, from all fluoride crystals almost the same strong 3 rd harmonic can be generated.The difference however is large in the case of the 5 th harmonic.A suitably strong 5 th harmonic is produced in CaF 2 and a weaker signal is obtained in LiF, while from MgF 2 it was not possible to generate 5 th harmonic.
Moving the CaF 2 crystal along the optical axis away from the optimum position, the laser intensity on the surface is scanned in a wide intensity range and the intensity of the generated 3 rd and 5 th harmonics is measured and plotted in Fig. 2(b).Here we measured the generated harmonics on the front surface, because it was possible to change the laser intensity in a wider range without the interference from the other surface.In the experiments, the laser beam was focused but still with a NA<0.1 so that the paraxial approximation is preserved.To determine the laser intensity on the surface, a focused beam with a certain divergence θ is assumed.The laser intensity depends on the beam radius w(z) as where z 0 is the position of the beam waist, z R is the Rayleigh length, and z = 0 or z = L at the back or at the front surface of the crystal, respectively, with L being the crystal thickness.The intensity of the fundamental laser beam is therefore calculated using Eq. ( 1) and gives the horizontal axi harmonic q ca According to q' is not deter perturbative b harmonics, re for the 3 rd and non-perturbat

Z-scan m
To examine th the crystals al of the generat of CaF 2 , was Fig. 3. Every mea at the zero po one at the po crystal thickn harmonics wa observe an os independent o beam before profiles were the calculation which is deriv is of Fig. 2(b).an be accuratel earlier results rmined and can bulk harmonic espectively.It i d 3.2 for the 5 th tive manner. .As it is well v ly described wi obtained in g n be obtained b cs q'=q-1 [25] is clear from th h harmonic, tha of the 3 rd we show otted with rturbative nd fit by with dark ming bulk l (< 1 %) and divert gnal from signal by (4) The measured curves in Fig. 3(a) and 3(c) are plotted after this background correction.As it can be seen in Figs.3(a)-3(d), i.e. after background correction of the measured signal, the calculated curves fit very well, over 3-4 orders of magnitude of the intensity range, and the fit is only limited by the measurement noise at the very low intensities.The corrected background has a very small contribution to the signal with c 0 /c 1 in the range of 3000-6000.Table 1 summarizes all the used fitting parameters.The data in Table 1 shows that the background should originate from the back surface of the crystal, because the focus position (z 1 ) is shifted.Such a small contribution cannot be observed from the front surface, because it is within the fitting error.Because of the weaker signal of the 5 th harmonic, see Fig. 3(e), it was not possible to perform measurements with a similar dynamic range as in the case of the 3 rd harmonic, but it is still possible to fit Eq. ( 3), and no background correction is necessary.We get a good fit with q'≈3.6±0.2, which is indeed different from the bulk case (q'=4).The fit was limited only by the measurement noise in the case of the front surface or by the added contribution of the other surface in the case of the back surface, as it can be seen in Fig. 3(f).We can conclude from this analysis that assuming non-perturbative harmonics generated on the crystal surface accurately describes the measurements over several orders of magnitude of the intensity range.

Z-scan measurement on the GaN layer on sapphire
In a second measurement series, a GaN layer (a wurtzite crystal structure with thickness of 5 µm) on a sapphire substrate (thickness of 430 µm) having (0001) orientation was used.In these measurements we make use of the fact that GaN is a semiconductor with a bandgap of 3.4 eV and consequently strongly absorbs both the 3 rd and the 5 th harmonic of a Ti:sapphire laser, while the sapphire substrate is transparent at both harmonic wavelengths [26].The sample was again moved along the optical axis of the laser beam through the focal region (zscan) and the intensity of the generated 3 rd or 5 th harmonic were measured with the VUV monochromator.The results are plotted in Fig. 4(a).The measurements were performed when the GaN layer was on the back surface (light/dark-blue lines); on the front surface (orange line) of the substrate; and also with a sapphire sample without GaN layer (thickness of 500 µm, black dashed line) for comparison.As it can be seen in Fig. 4(a), the 3 rd harmonic generated from the GaN layer was up to 2000 times stronger than that from the sapphire sample without the GaN layer.It was only possible to generate 5 th harmonic from the GaN layer (not from the sapphire).The measured spectra from the GaN layer and from a substrate without layer are shown in Fig. 4(b).The spectra of the 5 th harmonic are also shown separately in Fig. 4(c) with linear scale.

GaN layer
the layer ubstrate is ration are substrate ystals, see it a very her value, n the case havior is es and the ation, we -sapphire faces are morphologically different and one can expect a difference in the harmonic generation efficiency.The obtained results can therefore be explained as follows: -Black dashed line (Substrate H3): when a sapphire sample was used without any GaN layer, the 3 rd harmonic signal peaked at the two positions where the focus is at the surfaces.The harmonic signals from the two surfaces were about the same, as expected, because the two surfaces were equivalent.The 5 th harmonic was not generated by the sapphire without a GaN layer.
-Light/dark blue lines (Surface H3/H5): when the GaN layer was on the back surface of the sapphire substrate, a strong 3 rd harmonic signal and a weaker 5 th harmonic were clearly generated from the back surface of the GaN layer (GaN-vacuum interface).These harmonic signals decreased as the laser intensity decreased on the surface, as the focus was moved away from the surface.They were generated at the GaN-vacuum interface because the harmonic signals generated at the GaN-sapphire interface and at the sapphire-vacuum interface (sapphire front surface) were absorbed by the GaN layer.
-Orange line (Interface H3): the GaN layer was on the front surface.At zero focus position (sapphire-vacuum interface) a weak 3 rd harmonic signal was generated, the same as from the sapphire crystal alone, as it would be expected.At the focus position of 430 µm, when the GaN layer was in the focus, a strong 3 rd harmonic signal was generated, but about 4times weaker than in the case that the layer was on the back surface (light blue curve).This harmonic signal did not originate from the front surface of the GaN layer (GaN-vacuum interface), because that signal was absorbed by the GaN layer.Furthermore, the harmonic signal could not be generated inside the bulk GaN layer, as if this were the case it would have shown the same signal strength as in the case where the GaN layer was on the back surface (light blue curve).The harmonic signal was hence generated on the GaN-sapphire interface.The 5 th harmonic signal was too weak to be measured in a z-scan and only the spectrum (at the focus position on GaN) was measured [see Fig. 4(c)].

Conclusion
In conclusion, we generated intense 3 rd harmonic from different fluoride crystals, 5 th harmonic from CaF 2 crystals, and 3 rd and 5 th harmonics from a crystalline GaN layer on a sapphire substrate.We showed experimentally that these harmonics were generated from the surfaces or the interfaces between the crystals in a non-perturbative manner.We find no contribution from perturbative bulk harmonics in the measured signals, meaning that for the 3 rd harmonic non-perturbative surface contribution should be 4-5 orders of magnitude larger.
Further studies are needed to examine the high efficiency of the harmonics generated from the surface, and few new studies already started to address this question.In [27] it is theoretically shown that from topological edge states, harmonics can be 14-orders of magnitude more efficiently generated than from bulk, what may be applicable to surfaces.An experimental study [28] reports that from the interface between two materials the second harmonic can be more efficiently generated.High harmonics on a surface in reflection geometry have also been generated [29].
Based on our findings, suitably nano-engineered surfaces may greatly improve the efficiency of non-perturbative harmonic generation [30][31][32][33].Designed multilayer structures based on surface harmonics can also improve harmonic generation efficiency by means of quasi-phase matching.
values.The laser intensity can be written as Fig. 2 on the intens depen