High-harmonic generation in polycrystalline CdTe nano-�lms via macroscopic investigations

Bright high harmonics generation (HHG) in CMOS-compatible nano-�lms can provide new opportunities for integrated coherent ultra-violet sources and attosecond photonic devices. Up to now, most HHG studies have been limited to single crystals. Polycrystalline materials, which consist of many grains separated by grain boundaries and normally have random crystallographic orientations, have rarely been explored for HHG. Understanding and predicting the HHG properties in polycrystalline nano-�lms are important owing to its merits of low cost and diversi�ed properties, but challenging due to their complicated electronic structures. Here, we for the �rst time experimentally discover the correspondence between HHG in polycrystalline matters and macroscopic material parameters, to the best of our knowledge. Bright and long-term stable harmonics extending to 25th orders are demonstrated in polycrystalline cadmium telluride (CdTe) nano-�lms. It is found that the HHG strengths in the transmission and the re�ection behave differently as a function of the material thickness in the range from 6 nm to 4 μ m, which is highly correlated to the measured macroscopic conductivity. This work provides a simple gauge to study and predict HHG in complicated polycrystalline and amorphous nano-systems, and paves the way for novel strong-�eld nanophotonics based on polycrystalline nano-�lms.

the other extreme, atomically thin two-dimensional materials have also served as a good platform to study the strong-eld ultrafast dynamics including many-body interactions and induced distinctive symmetries [5][6][7] . HHG from the intermedia thin lms with thicknesses of a-few to few-hundred nanometers could not only enable the strong-eld on-chip integrated photonics leveraging on semiconductor technologies 8- 10 , but also open up more advanced research possibilities such as attosecond control of intraband electron motion 11 , ultrafast quasiparticle collision 12 , direct measurement of Berry curvature in solids 13 , and resonant enhancement by epsilon-near-zero effect 14 . Moreover, HHG in solids is commonly explained with the origins of interband recombination induced by polarization between the conduction and the valence bands, and intraband relaxation originated from non-parabolic band dispersion contributions 15 . The microscopic mechanisms of HHG in solids have been investigated in pristine crystals and monolayer materials 16,17 . HHG in polycrystalline and amorphous solids has also been demonstrated 11,13,18,19 , however, the two microscopic HHG mechanisms are not applicable, since they are based on the Bloch theorem and electronic band structures of single crystals. It is a formidable challenge to understand or predict the HHG processes in polycrystalline solids when taking into account the complex effects of crystallite size and texture, grain boundaries, defects, surface states and nonlinear propagations, which hinders the development of strong-eld research in polycrystalline nano-systems.
In this work, we report on experimental studies of bright HHG in polycrystalline cadmium telluride (CdTe) thin lms, for the rst time, in a broad thickness range over 6 nm to 4 µm. Pumped by a mid-infrared (MIR) femtosecond laser centered at 7.1 µm wavelength, the HHG in transmission (THHG) up to 25th and 15th orders are observed in CdTe ultra-thin lms with 50 and 6 nm thickness, respectively, which bridges HHG in monolayer materials and thin lms with hundreds-nanometer thickness. It is measured that the THHG exhibits the strongest HHG emission at two optimal thicknesses of 50 nm and 630 nm, while the intensity of HHG in re ection (RHHG) increases monotonically as the lm thickness decreasing in the range of 4 µm to 30 nm. The thickness-dependent conductivity of the polycrystalline CdTe nano-lms is acquired independently via two methods, namely four-point probe measurement and power transmittance measurement. Both THHG and RHHG strengths with the absorption deducted from the measurement are found to exhibit strong correlation with the measured macroscopic conductivity of the nano-lms which are determined by microscopic factors such as the electronic motion of the bulk material, surface electronic structures and nonlinear propagation effect. This work opens up possibilities to investigate the microscopic HHG processes through macroscopic material speci cations in complicated condense matter systems. It also provides a new path towards to the research of on-chip HHG and attosecond photonics based on CMOS-compatible polycrystalline CdTe thin lms commonly used in the photovoltaic and X-ray detector industry, with the merits of low cost, large size, and good chemical durability.
In our experiment, CdTe nano-lms are deposited on fused silica substrates by magnetron sputtering deposition technique which is commonly used in the semiconductor industry. The details of growth and characterization of polycrystalline CdTe thin lms are presented in the Methods and Supplementary Information. CdTe is chosen for its extraordinary strong-eld characters originated from a at shape of band dispersion near the Fermi level and high carrier mobility 21 , which has recently been observed in crystalline CdTe bulk solid 22 . A MIR femtosecond laser centered at 7.1 µm with a pulse width of 180 fs at 50 kHz repetition rate is employed as the pump source, and both the THHG and RHHG are measured, as depicted in Fig. 1(a). The photon energy of the pump laser is well below the direct bandgap of CdTe bulk crystal (around 1.44 eV 23 ) and thus the multi-photon ionization is negligible to explore the properties of HHG in CdTe nano-lms. The XRD spectrum of 630-nm thick polycrystalline CdTe lm is displayed in Fig. 1(b). The main diffraction peak of < 111 > orientation at an angle of 23.75° dominates the XRD spectrum, while the zoom-in plot shows a serials of diffraction orientations, revealing the polycrystalline nature of the CdTe lm. Figure 1(c) presents the THHG spectra of CdTe lms with the thickness of 6 nm, 50 nm, and 630 nm. Up to 25th (4.36 eV) harmonics are detected in the 630-nm-thick CdTe lm at a peak driving intensity of 0.85 TW/cm 2 . Remarkably, even the 6-nm-thick CdTe can support THHG up to the 15th order with bright visible emission at a pump intensity of 0.4 TW/cm 2 . This bridges the HHG from monolayer two-dimensional materials and thin lms with hundreds nanometer thickness. Only odd harmonics are observed in our measurements because of inversion symmetry in polycrystalline CdTe lms, which is veri ed by the evenly distributed HHG strength along all the polarization directions of the driving led as the case in the atomic system (see Fig. 2(c)). The scanning electron microscopy images of polycrystalline thin lms with the thickness of 50 nm, 630 nm, 1.3 µm, and 4 µm are shown in Fig. 1(dg) manifesting randomly distributed grains which grow in size as the lm thickness increasing. The distinct surface morphology and electronics states may in uence the HHG strength, especially for THHG while the fundamental and harmonics pulses are propagating in polycrystalline lms. The photos of the bright visible THHG emission from the CdTe lms with the thickness of 6 nm, 50 nm and 630 nm are captured and shown in Fig. 1(i-k). It is worth noting that comparable HHG emission from CdTe lms with 50 nm and 630 nm thickness is observed from the photos, because the 630-nm-thick polycrystalline CdTe lm has much bigger grain size and rougher surface morphology, so that stronger HHG emission is scattered to the CCD which is located at a small noncolinear angle with the pump laser. The fused silica substrate is also excited under the same experimental conditions as a comparison, and it exhibits neither visible emission nor infrared spectral signal, as shown in Fig. 1(h). We suppose that the extraordinary HHG emission from the polycrystalline CdTe nano-lms is attributed to both the excellent electronic characteristics inherited from the crystalline bulk which are at shape of band dispersion near the Fermi level (The calculations of atomic and electronic structures of bulk CdTe crystal could be found in Supplementary Information Section 1) and high carrier mobility (The carrier mobility of CdTe pristine crystal is 1100 cm 2 /(V·s) 21 which is 2-orders higher than that of MoS 2 6 ), and the unique features including surface electronic structures, microscopic light propagation, and electronic motion in the polycrystalline nano-lms. More studies are therefore conducted to explore the physical mechanisms behind.
The individual harmonics strengths of 9th -17th orders from the polycrystalline CdTe lm with a thickness of 50 nm are plotted on the logarithmic scale versus the driving-laser intensity ranging from 0.3 to 1.2 TW/cm 2 , as shown in Fig. 2(a). The power-law t curves reveal values of exponent n ~ 2.5 except for the 9th order with n ~ 3.5 (the uorescence signal), which clearly demonstrates the non-perturbative behavior of HHG in CdTe lms. As shown in Fig. 2(a), the 50-nm-thick CdTe lm can support harmonics up to the 13th order at a pump intensity of 0.3 TW/cm 2 . At a higher pump intensity, the long-term stable HHG emission is observed from the polycrystalline CdTe nano-lms as presented in Fig. 2

(b). The 50-nm-thick
CdTe lm is excited at a MIR laser intensity of 1 TW/cm 2 , and harmonics signals of 9th to 17th orders are recorded for 10 minutes. Remarkably, stable long-term HHG output almost without decline is measured, which implies that there is no damage for the polycrystalline nano-lm exposed in such a strong eld.
To investigate the polarization of HHG from polycrystalline CdTe lms and the dependence on the driving laser polarization, the harmonics intensity of 9th -17th orders from a 50-nm-thick CdTe lm are measured by xing the pump polarization and rotating the CdTe nano-lm about the normal. The THHG is detected directly behind CdTe lms at a pump intensity of 1 TW/cm 2 . As presented in Fig. 2(e), THHG of 11th -15th orders in CdTe thin lms has the maximum strength at a thickness of 50 nm, and exhibits an oscillation with respect to the lm thickness. The RHHG is also measured 10-mm in front of the CdTe nano-lms with angles of incident and re ection both as ~ 45 o , under a pump intensity of 0.57 TW/cm 2 . As plotted in Fig. 2(f), unlike the THHG, the RHHG shows a broadband uorescence peak at wavelengths ranging from 400 to 800 nm, which is attributed to surface defects states from polycrystalline thin lms. Intriguing, the RHHG of CdTe nano-lms has the maximum at a thickness of 30 nm and decreases monotonically as the thickness increasing. It is important to note that absorption should be accounted for the THHG with harmonics orders above the bandgap. We observe that the band edge of polycrystalline CdTe nano-lms moves to shorter wavelengths as the lm thickness getting thinner (see the measured transmission spectra of polycrystalline CdTe lms with various thicknesses in Supplementary Information Fig. 4), which is attributed to the quantum size effect 24,25 . This agrees with the observed blue shift of the uorescence envelopes as the thickness decreases, shown in Fig. 2(f). Therefore, distinct absorption of individual CdTe lms with different thicknesses should be deducted to reveal the true THHG strength.
The true strengths of THHG and RHHG in polycrystalline CdTe lms without absorption are therefore properly measured and calculated as presented in Fig. 3, to analyze the thickness dependence of HHG from CdTe nano-lms. The harmonics ranging from 11th to 17th orders are measured and compared with broad lm thicknesses over 30 nm to 4 µm. We calculate the absorption coe cients of CdTe nano-lms with different thicknesses based on the measured transmission curves, and then deduce the true THHG strengths without absorption based on the measured THHG intensity, as shown in Fig. 3(a-d) (the details of the calculation are presented in Supplementary Information Section 4 and 7). THHG shows a clear trend of oscillation with various lm thicknesses, with two maximums at 50 nm and 630 nm. To understand the origin of oscillation, it is noted that HHG strength is directly linked to the microscopic electric current density and thus the conductivity in the medium by , where represents the electric current density and F.T.
denotes the Fourier transform. The current density and conductivity are then linked by , where and are the conductivity and electric eld, respectively. We therefore suggest that in CdTe lms with the thickness of few nanometers the HHG strength increases with the lm thickness, and it soon saturates at around 50 nm and starts to decline, due to the reduced conductivity and current density in the CdTe lm as the thickness increasing. This agrees well with the recent theoretic prediction 20 . While the lm thickness is further increasing beyond around 500 nm, we believe enlarged grain boundaries and defects states of the polycrystalline thin lms start to play a more dominating role to enhance the current density so as the harmonics strengths while the fundamental and harmonic pulses propagating in the CdTe lms. Thus a second peak of THHG is exhibited. Notably, HHG enhancement by defects in solids has been reported before 26 − 28 . It is worth mentioning that in pristine crystals, it has been experimentally observed that the THHG strength from a GaAs crystal drops as the thickness increasing from 45 µm to 650 µm, which is associated with the nonlinear propagation in the periodic solids 29 . It is thus suggested that the randomly distributed grains and voids in the polycrystalline CdTe lm modify the dynamics of nonlinear propagation effect which impact on the harmonics generation. On the other hand, unlike THHG, the RHHG signal declines as the thickness increasing from 30 nm to a few micrometers as presented in Fig. 3(e-h). We suggest that this is because RHHG is less in uenced by the nonlinear propagation effect imposed by the polycrystalline grain and voids, thus a monotonic decline of HHG strength is observed, following the trend of the reduced conductivity and current density in the CdTe lms. Notably, RHHG from extremely thin CdTe lms (few-nanometer) is not measured due to the di culty in collecting the weak RHHG signal in the pump incidence direction.
In a macroscopic perspective, the distinct trends of harmonics in polycrystalline CdTe nano-lms may be related to the conductivity and current density of thin lms with different thickness 20 . To explore the link between the trend of HHG and the macroscopic parameters with respect to the polycrystalline lm thickness, we thus measure the conductivity of CdTe lms with various thicknesses using two methods independently. The four-point probe method is employed as the direct measurement of the conductivity, while the power transmittance measurement is conducted as a replication proof according to , where and denote the linear components of the incident and transmitted elds, d represents the thickness of the thin lm, and c is the speed of light. Two wavelengths of 1 µm and 2.4 µm are used in the power transmittance and re ectance measurement for their negligible absorption in the fused silica substrate. As shown in Fig. 4, the two methods demonstrate generally the same trends with harmonics strengths versus the thickness of polycrystalline CdTe lms. In particular, the conductivity scales inversely proportional to the thickness as shown in Fig. 4(b, e, h), which is consistent with the trend of RHHG in Fig. 3(e-h). This also veri es our assumption that the RHHG is mainly generated in the front few nanometers, and not in uenced a lot by the nonlinear propagation effect. On the other hand, the product of conductivity and the lm thickness, especially measured by the power transmittance method as presented in Fig. 4(f, i) displays qualitatively similar oscillation trend with that of the THHG and shows two local maximums at 50 nm and 600 nm. Notable, the polycrystalline CdTe thin lms with the thickness of 50 nm and 600 nm exhibit two peaks of the measured re ected power at both wavelengths of 1 µm and 2.4 µm, as shown in Fig. 4(d, g), which implies the polycrystalline CdTe thin lms at the particular thicknesses have signi cantly higher conductivity, reaching the level of semimetals. These results suggest that the conductivity of the lm which is not only determined by the electronics structures, but highly in uenced by the surface morphology and defects states in a material is a key factor of HHG in polycrystalline lms. It could serve as a simple gauge in a macroscopic view to analyze the HHG performance in complicated material systems.
In conclusion, we experimentally observe high harmonic generation in both transmission and re ection directions from polycrystalline CdTe lms with various thicknesses ranging over 6 nm to 4 µm, pumped by a MIR femtosecond laser at 7.1 µm center wavelength. The non-perturbative HHG from 6-nm and 50nm thick CdTe lms extends to 15th and 25th order-harmonics, respectively. It is found that THHG and RHHG behave distinctly with respect to the thin lm thickness. THHG is peaked at two thicknesses of 50 nm and 630 nm, while RHHG decreases monotonically as the thin lm thickness increases. The conductivity of the nano-lms is measured to reveal the origin of variation in HHG strengths with respect to the nano-lm thickness, which suggests that the HHG from the polycrystalline CdTe nano-lms is closely related to the macroscopic conductivity of the thin lms. This work demonstrates exciting possibilities in HHG and attosecond nanophotonics in the polycrystalline thin lms, such as CdTe as demonstrated in this work, with extraordinary strong-eld characteristics and stable chemical properties, as well as mature fabrication technologies. Moreover, this work provides a possibility of analyzing and predicting the HHG performance of complicated material systems based on macroscopic parameters, which is otherwise di cult to realize by the existing microscopic models.

Methods
Film growth and characterizations. The CdTe lms are fabricated by magnetron sputtering deposition technique 30 at a temperature of 235 ℃ on 0.5-mm-thick fused silica (JGS2) substrates. The thickness of the CdTe lms is controlled by the sputtering time and measured by atomic microscopy (AFM) (More information could be found in Supplementary Information Section 3). The surface morphology of the polycrystalline CdTe lms is characterized by a scanning electron microscope (SEM) (More information could be found in Supplementary Information Section 2). The crystal orientation of CdTe lms is measured by X-ray diffraction spectroscopy (XRD) using Cu-Kα radiation with 2θ of 10 ~ 90°. The transmittance of CdTe lms with different thickness is characterized by UV-Vis-NIR spectrometry with a wavelength range over 250 nm to 2500 nm (See Supplementary Information Fig. 4).
High-harmonic generation pumped by the MIR femtosecond laser. The pump source of HHG in CdTe is a MIR optical parametric ampli er (OPA) driven by a commercial Yb-doped regenerative ampli er (Pharos) with a maximum 20 W power. The MIR OPA consists of two-stage ampli ers based on LiGaS 2 crystals, as shown in the experimental schematic in Supplementary Fig. 5. The MIR power up to 280 mW at 7.1 µm could be produced. The temporal duration of the MIR pulse is measured by a home-built interferometric autocorrelator (IAC) and reconstructed through a genetic algorithm based on so-called "evolutionary phase retrieval from IAC (EPRIAC)" algorithm. 180 fs pulse width is estimated with more details shown in Supplementary Fig. 6 (b, c). An infrared camera (Dataray, WinCamD-IR-BB-7.5 system) is employed to check the MIR beam pro le and measure the beam size as shown in Supplementary Fig. 6 (d).
CdTe thin lms with various thicknesses ranging from 6 nm to 4 µm grown on fused silica substrates are pumped at an intensity ranging from 0.3 TW/cm 2 to 1.2 TW/cm 2 focused by zinc selenide lenses with a focal length of 100 mm. The HHG spectra are measured by two different Ocean Optics spectrometers (USB 2000 + and Maya 2000 Pro). The spectra are recorded by directly coupling the emission into a silica ber with a 400-µm core diameter at the back surface of the CdTe crystal for the MIR and visible-toultraviolet harmonics measurement, respectively. The long-term stability of generated harmonics signals from the CdTe lms with representative thicknesses of 50 nm, 630 nm and 2.32 µm is measured for 10 minutes by recording the harmonics spectra once per 20 seconds. Data availability. The data that support the ndings of this study are available from the corresponding author upon request.  Dependence of HHG on pump intensity, long-term measurement of HHG, polarization characterization of HHG and spectra of HHG in transmission (THHG) and re ection (RHHG) in CdTe nano-lms with a few representative thicknesses. a, Logarithmic plot of the measured harmonics signals with 9th to 17th orders with respect to the excitation intensity in polycrystalline CdTe lms with a thickness of 50 nm. Fitting of the experimental data based on the power-law equation I ∝ I n ex yields the corresponding exponents (n) for each harmonic (solid lines) ranging from 2.1 to 3.5, which deviates strongly from the conventional perturbative nonlinear response optics n = k (dashed lines, k is the harmonicorder). b, The long-term measurement of the THHG intensity from the CdTe thin lm with a thickness of 50 nm. The harmonics of 9th to 17thorders are recorded for 10 minutes with stable strengths. c, The harmonics strengths of 9th-17th orders with respect to the polarization of pump eld varying from 0° to 180°. d, The THHG spectra in polarizations parallel and perpendicular to the pump led. The harmonics with vertical and horizontal polarizations are separated by using a FLP20-VIS polarizer, and the pump intensity is 0.35 TW/cm2.
Spectra on linear scale of e, THHG and f, RHHG, with the thicknesses in the range of 30 nm to 4 μm. The THHG and RHHG spectra contain 11th to 15th and 9thto 17th orders harmonics, respectively. THHG strength is peaked at 50 nm and oscillates with respect to the lm thickness. While the RHHG has the maximum at a thickness of 30 nm and decreases monotonically as the thickness increasing. Clear uorescence envelopes spanning from 400 nm to 800 nm can be seen from RHHG spectra, which is attributed to the surface defect states in the polycrystalline nano-lms. There exhibits blue shift of the uorescence envelope as the thickness decreases. This is because the band edge of CdTe polycrystalline lms move to shorter wavelength when the lm thickness getting thinner (see the measured transmittance of various thicknesses in Supplementary Information Figure 4)  lms increasing, which qualitatively agrees with the measured trends of RHHG and THHG as shown in Figure 3.

Supplementary Files
This is a list of supplementary les associated with this preprint. Click to download.