High-harmonic generation in CdTe with ultra-low pump intensity and high photon flux.pdf
ARTICLE High-harmonic generation in CdTe with ultra-low pump intensity and high photon ﬂux Zhe Long1,5, Hang Yang1,5, Kan Tian1, Linzhen He1, Rui Qin2, Zi-Yu Chen 3✉, Qi Jie Wang 4 & Houkun Liang 1✉ An ultra-low pump intensity and high photon ﬂux have been long pursuits of high harmonic generation (HHG) in solids. However, there is lack of a criterion to identify a pristine solid material exhibiting such characteristics. Here, we report systematic investigation into HHG from a cadmium telluride (CdTe) bulk crystal with a ﬂat band dispersion near the Fermi level which leads to a large density of states. The measured pump intensity for the 31st harmonics (229 nm) is only 75 GW/cm2, one order of magnitude lower than that of other pristine crystals including two-dimensional materials reported so far. A comparative measurement shows CdTe has two-to-three orders of magnitude stronger HHG than silicon does, and high HHG yields in the ultraviolet region compared to GaSe. A high photon ﬂux of ~ 6 × 1012 photons/s (5th−8th) with a robust long-time sustainability is obtained. This work offers a route towards compact vacuum ultraviolet laser sources. https://doi.org/10.1038/s42005-023-01354-2 OPEN 1 School of Electronics and Information Engineering, Sichuan University, Chengdu, Sichuan 610064, China. 2 National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621999, China. 3 Key Laboratory of High Energy Density Physics and Technology (MoE), College of Physics, Sichuan University, Chengdu 610064, China. 4 School of Electrical & Electronic Engineering & The Photonics Institute, Nanyang Technological University, 639798 Singapore, Singapore. 5These authors contributed equally: Zhe Long, Hang Yang. ✉email: ziyuch@scu.edu.cn; hkliang@scu.edu.cn COMMUNICATIONS PHYSICS |   (2023) 6:228 | https://doi.org/10.1038/s42005-023-01354-2 | www.nature.com/commsphys 1 1234567890():,; H igh harmonic generation (HHG), traditionally occurred in rare-gas atoms irradiated by intense laser pulses, has been extensively explored as coherent light sources with short wavelength in the vacuum-extreme ultraviolet spectral region and ultrashort duration in the attosecond regime. In recent years, HHG in solids has been observed from a wide variety of materials and attracted a great deal of attention. Typical examples include dielectrics such as ZnO1, MgO2, silicon3, SiO24, sapphire5, and GaSe6,7 as well as two-dimensional materials like MoS28, graphene9. In Table 1, we present a survey of representative works of HHG in solids with ﬁve categories of materials as bulk, thin ﬁlms, two-dimensional materials, topologically protected materials, and materials with meta-structures, where the experi- mentally reported key parameters of HHG such as the pump wavelength, the maximal pump intensity, and the highest har- monic energy and order, as well as the corresponding pump intensity, are summarized. Compared to its gas-phase counter- part, HHG in the condensed phase allows more compact coherent ultrafast photonic devices with lower driving laser intensities. The typical laser intensity to drive this extreme nonlinear optical process in solids including bulk and two-dimensional materials is as low as 1011−1012 W/cm2, which is two or three orders of magnitude lower than that in gases. To further lower the pump intensity, near-ﬁeld enhancement methods based on plasmonic resonances employing metallic or dielectric nanostructures deposited on solid surfaces have been demonstrated10–14. The driving laser intensity at the level of 1010 W/cm2 can be achieved. However, apart from manufacturing difﬁculties, the nanos- tructures suffer from shortcomings of low damage intensity and small enhancement areas. Moreover, the resonance-based meth- ods can only enhance laser ﬁelds with a particular wavelength, determined by the materials and their structural designs. To increase the enhancement volume, epsilon-near-zero materials such as indium-doped CdO thin ﬁlm have been adopted15. The pump intensity can be further reduced by one order of magni- tude, however, the laser wavelength that can be enhanced is also ﬁxed by the doping level of the material. In addition, the damage threshold of the doped thin ﬁlm is usually small. Therefore, it is desirable to discover a pristine and versatile solid material exhibiting low pump intensity even without ﬁeld enhancement and high damage threshold. As the microscopic mechanisms of HHG in solids, both interband (induced by polarization between conduction and valence bands) and intraband (originated from non-parabolic band dispersion) contributions, are closely associated with the electronic structure of the material, a possible approach towards searching for ideal material candidates is to generally examine the band structure at ﬁrst. Previous theoretical studies have predicted phosphorene (a monolayer black phosphorus) displaying good HHG properties which can be attributed to its unique band structure16. An impressive feature of the band structure of phosphorene is a relatively ﬂat dispersion of the valence band near the Fermi level, which leads to a large density of states (DOS) and thus substantial excitation of electrons. Aside from that, phosphorene has a moderate and direct band gap of ~2.0 eV17 and high free-carrier mobility of ~1000 cm2/V/s18. These theoretical studies shed light on the signatures of materials suitable for HHG, although HHG in phosphorene is difﬁcult to realize experimentally due to the fabrication requirement and unstable characteristics of phosphorene. Fortunately, there do exist materials not only exhibiting similar electronic properties to that of phosphorene (i.e., ﬂat shape of band dispersion near the Fermi level, moderate direct band gap, and high carrier mobility), but also being chemically stable and robust, as well as easy to obtain. Here we report on systematic experimental investigation to demonstrate cadmium telluride (CdTe) being one of such excel- lent candidates. The electronic structures and ultrafast carrier dynamics of CdTe enable ultra-low pump intensity and high- efﬁciency harmonics emission. In experiment, the measured pump intensity for the 12th and 31st harmonic order is only 30 and 75 GW/cm2, respectively, which is similar to or even smaller than that of the dielectrics with plasmonic meta-structures for the HHG enhancement. The HHG output grows with the pump intensity up to 4.5 TW/cm2 without saturation. A comparative measurement shows CdTe has two-to-three orders of magnitude stronger HHG than that of silicon, and high HHG yields in the ultraviolet region compared to common HHG dielectric such as Table 1 Comparison of HHG in CdTe (yellow) with other commonly used materials of HHG in solids. Materials Pump wavelength (μm) The maximal pump intensity (TW/cm2) The highest harmonic energy (eV) and order (the corresponding pump intensity (TW/cm2)) Reference Si 3.5 6, 17th (0.26) 3 Sapphire 0.8 1.31 20.2, 13th (1.1) 5 ZnO 3.25 5 9.5, 25th (5) 1 GaSe 10 13.7 2.7, 22nd (13.7) 7 Graphene 4.77 1.7 2.3, 9th (1.7) 9 MoS2 4.13 2.2 3.9, 13th (1.8) 8 β-WP2 1.9 1.2 6.5, 10th (0.23) 42 ZnO nanostructure 2~2.3 1 5.4, 9th (1) 14 GaP metamaterial 3.7−4 0.6 2.8, 9th (0.062) 11 Si metamaterial 2.2−2.3 0.3 4.8, 9th (0.2) 10 Si plasmonics 2.1 0.2 5.3, 9th (0.02) 13 Sapphire metamaterial 0.8 0.42 20.2, 13th (0.1) 12 Perovskite thin ﬁlm 3.5 0.45 4.6, 13th (0.45) 25 Si-sapphire interface 2.2 5.6 7.3, 13th (3.2) 43 WSe2 nanosheet 0.764 0.767 35.6, 22nd (0.767) 26 CdO 2.08 0.014 5, 9th (0.014) 14 Bi2Se3 5 0.054 2.7, 11th (0.054) 27 1 T’ MoSSe 5 1.06 4.96, 20th (1.06) 28 CdTe 7.1 4.5 5.4, 31st (0.075) This work The HHG materials are categorized into bulk (green), two-dimensional materials (blue), materials with meta-structures (pink), thin ﬁlms (grey), and topologically protected materials (orange). Parameters of the pump wavelength, the maximal pump intensity, and the highest harmonic energy, as well as the corresponding pump intensity, are summarized. ARTICLE COMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-023-01354-2 2 COMMUNICATIONS PHYSICS |   (2023) 6:228 | https://doi.org/10.1038/s42005-023-01354-2 | www.nature.com/commsphys attributed to intraband mechanism. While for the odd-order harmonics (11th and 13th order), as shown in Fig. 5f, the harmonics polarization exhibits noticeable modulation around the driving laser polarization, similar to the characteristics of odd- order harmonics from TMDCs in ref. 29 which originates from interband contribution. The distinctly different behaviors of HHG polarization angel as a function of MIR polarization angle for different harmonic orders suggest that the even and odd-order harmonics in CdTe may be attributed to different HHG mechanisms. Conclusions In conclusion, we experimentally demonstrate an ultra-low pump intensity and high throughput of HHG emission from the CdTe crystal. The harmonics ﬂux of 6 × 1012 to 1.6 × 1013 photons/s (5th−8th) is obtained, which is sustained for >30 min of exposure. Therefore, a pulse energy of hundreds of nano-joule which could be provided by more compact and cheaper laser apparatus such as Cr:ZnS oscillator and ampliﬁer30 or a single- stage MIR optical parametric ampliﬁer (OPA) is able to excite decent harmonics ﬂux. At meanwhile, thanks to the high damage threshold and centimeter-size crystal aperture, high-harmonics energy could be pursued pumped by the advanced MIR optical parametric chirped-pulse ampliﬁers with multi-milli-joule pulse energy31–34. Moreover, HHG from CdTe in VUV region could be explored in the near future. In addition, beyond light source, HHG in solids serves as a unique tool to investigate light-induced nonequilibrium phases in materials35,36. Studying light-induced nonequilibrium phases and ultrafast carrier dynamics in CdTe have important applications, such as the development of infrared and gamma photon detec- tors, and solar cell thin ﬁlm photovoltaic technology as well, Fig. 5 High-harmonics strength from a CdTe crystal as a function of the pump polarization angle θ and the high harmonic generation (HHG) polarization angle φ. a Schematic diagram of the HHG polarization measurement. The pink arrow represents the pump laser polarization, the dashed grey line indicates the symmetry plane of the crystal, θ is the angle between the pump polarization and the symmetry plane of the crystal, and φ is the harmonics polarization angle. The polarization angle φ is measured with a polarizer. b The polar plot of the high harmonic strength with respect to the pump laser polarization. The excitation strength is ﬁxed at around 0.55 TW/cm2. Both even and odd orders are observed to be modulated with a period of 60°, which reveals the sixfold symmetry of CdTe. The intensity is strongest when the pump ﬁeld is along the CdTe bond direction, i.e., parallel to the mirror plane. c Intensities of the representative 10th to 14th order harmonics in different polarization angle φ for crystal direction θ = 0°. φ = 0 and 180° means harmonic components parallel to the pump polarization. Both the even and odd orders reach their intensity peaks when the harmonic components polarized parallel to the pump. d The same as c, except for θ = 30°. The intensity peaks of even orders (10th, 12th, 14th) rotate by 90° (the perpendicular components) with respect to c. This is attributed to the break of inversion symmetry and Berry curvature term in an intraband semiclassical model. e Odd (11th and 13th in red and orange, respectively) and f, even (12th and 14th in blue and green, respectively) order harmonics polarization angle φ resolved as a function of the MIR pump (in cyan) polarization angle θ. COMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-023-01354-2 ARTICLE COMMUNICATIONS PHYSICS |   (2023) 6:228 | https://doi.org/10.1038/s42005-023-01354-2 | www.nature.com/commsphys 7 where CdTe is an important material that has been widely used. Moreover, high-quality CdTe epi-layers could be grown by mature semiconductor deposition technologies, such as magne- tron sputtering. Thus, we look forward to HHG and attosecond devices fabricated based on CdTe thin ﬁlms. CdTe thin ﬁlms with nanostructures could also be employed to further enhance the HHG yield. Thirdly, the ﬁne HHG property of CdTe induced by its ﬂat shape of band dispersion near the Fermi level, the large DOS, and the high carrier mobility provides a possible criterion in searching for suitable HHG materials, which would deﬁnitely trigger more research. In future, materials with similar band dispersion and large band gaps could be investigated to improve the output yields of harmonics above the bandgap, which would beneﬁt applications such as optical coherence tomography in the DUV- VUV region37, UV multispectral imaging38, investigations of sub- cycle quasi-particle collision26, Valence electron high precision imaging39, and ultrafast electron scattering40. Methods Ab-initio TDDFT simulations of HHG in CdTe. The geometric structure relaxation and ground state electronic structure calculation of the CdTe crystal are performed by solving the Kohn–Sham equation using the CASTEP package within the DFT framework with the local density approximation (LDA) for the exchange–correlation function. A plane wave basis set and ultrasoft pseudopotentials are employed. The plane wave cutoff energy is set to be 330 eV. A 7 × 7 × 7 Monkhorst–Pack k-point mesh for Brillouin zone sampling is used for the conventional cell of CdTe, which contains eight atoms. The atomic positions are relaxed until the maximum force on each atom is less than 0.01 eV/A. The optimized lattice constant along each direction is 6.417 Å, which is in agreement with the reported DFT calculation results. Although it is known that LDA functional gives underestimated band gap, it has been demonstrated that it will not considerably affect the HHG spectra16. The atomic coordinates of the computational models could be found in Supplementary dataset 1. The time evolution of electron wave functions and time- dependent electronic current is then investigated by propagating the time-dependent Kohn–Sham equations in real time and real space using the OCTOPUS package within the framework of TDDFT with the adiabatic LDA functional. The grid spacing of the real-space box is 0.4 Bohr, and the time step for time propagation is 6.05 attosecond. A 20 × 20 × 20 Monkhorst–Pack k-point mesh is used for Brillouin zone sampling of the conventional cell. The fully relativistic Hartwigsen, Goedecker, and Hutter pseudopotential is adopted in the calculations. We consider the driving laser ﬁeld in the velocity gauge with a wavelength of 1600 nm (corresponding to a photon energy of 0.77 eV). The peak laser intensity is 2 × 1011 W/cm2. The laser electric ﬁeld is linearly polarized in the (111) cutting plane of CdTe crystal. The laser pulse has a sine-square envelope f(t) = sin2(πt/2τ) with τ = 20 fs. The carrier-envelop phase is set to be zero, which has been shown to have no inﬂuence on the calculation results. Consideration for the parameters of laser wavelength and pulse duration are mainly for the sake of computational efﬁciency. After obtaining the total time- dependent electronic current j(r, t) from the time-evolved wavefunctions, the HHG spectrum can be calculated as: HHG ω ð Þ ¼ F.T: ∂ ∂t Z jðr; tÞd3r     2 ; where F.T. denotes the Fourier transform. High-harmonic generation experiment. The pump source of HHG in CdTe is a MIR OPA driven by a commercial Yb-doped regenerative ampliﬁer (Pharos, Light Conversion) with a max- imum 20 W power, 250 fs pulses at 1030 nm wavelength, and 50 kHz repetition rate. The MIR OPA consists of two-stage ampliﬁers based on LiGaS2 crystals22. The near-infrared seed pulses are obtained through white light continuum generation in a 10-mm-thick YAG crystal. A 2 W fraction of the pump power is used to drive the ﬁrst OPA stage, which employs an 8-mm-thick LiGaS2 crystal cut for Type I phase matching (θ = 51°) and produces 200 mW signal pulses centered at a wavelength of 1205 nm. The signal pulses are subsequently injected into the second OPA stage, which ultimately produces up to 210 mW 7.1 μm mid-infrared output in another 8-mm-thick LiGaS2 crystal with Type I phase matching (θ = 51°) under 10 W pump power. The LiGaS2 crystals are replaced by KTA crystals to produce the OPA output centered at 3 μm. The mid-infrared power is mea- sured by OPHIR powermeter (StarLite). The temporal duration of the MIR pulse is measured by a home-built interferometric autocorrelator (IAC), and reconstructed through a genetic algo- rithm based on so-called “evolutionary phase retrieval from IAC (EPRIAC)” algorithm. 180 fs pulse width is estimated with more details shown in Supplementary Fig. 2b, c. An infrared camera (Dataray, WinCamD-IR-BB-7.5 system) is employed to check the MIR beam proﬁle and measure the beam size as shown in Sup- plementary Fig. 2d (see Supplementary Note 2). The 3 μm fem- tosecond pump is generated based on the same MIR OPA apparatus but using KTA as the nonlinear crystals. mm-thick CdTe crystal of (111) plane with optical polished surfaces is pumped at a pump intensity ranging from 30 GW/cm2 to 4.5 TW/cm2 focused by zinc selenide (ZnSe) lenses with a focal length of 50–200 mm. The HHG spectra spanning in the mid- infrared, near-infrared, visible, and ultraviolet regions are measured by a scanning-grating monochromator with a liquid- nitrogen-cooled MCT detector, optical spectrum analyzer (YOKOGAWA, AQ6370D) and two different Ocean Optics spectrometers (USB 2000+ and Maya 2000 Pro). 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Acknowledgements We thank Professor Yongfeng Lu for the useful discussions. This work was supported by the National Natural Science Foundation of China (62075144, U22A2090, 12175157), Sichuan Outstanding Youth Science and Technology Talents (2022JDJQ0031), Engi- neering Featured Team Fund of Sichuan University (2020SCUNG105), and the Fun- damental Research Funds for the Central Universities (YJ202025). Author contributions H.K.L. conceived and designed the experiment. Z.-Y.C. and R.Q. conducted the theo- retical simulation. Z.L. and H.Y. carried out the experiment of HHG measurement. H.K.L. and Z.-Y.C. conducted the data analysis. K.T. built the MIR OPA. L.H. measured the MIR pump temporal proﬁle. Z.-Y.C., Q.J.W., H.K.L., Z.L., and H.Y. wrote the manuscript. Z.L. and H.Y. contribute equally. All authors discussed the results and contributed to the manuscript. Competing interests The authors declare no competing interests. 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Title: High-harmonic generation in CdTe with ultra-low pump intensity and high photon flux ​
Authors: Zhe Long, Hang Yang, Kan Tian, Linzhen He, Rui Qin, Zi-Yu Chen, Qi Jie Wang, Houkun Liang ​
Publisher: Nature Communications
Date: 2023
Abstract: The document explores high-harmonic generation in CdTe crystal with ultra-low pump intensity and high photon flux, showcasing its potential for compact vacuum ultraviolet laser 
sources. ​ It highlights the CdTe crystal's strong HHG compared to other materials and its sustained harmonics flux reaching 6 × 10^12 photons/s (5th−8th) for over 30 minutes. ​
