High 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 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 as well as two-dimensional materials like MoS27, graphene8. Compared to its gas-phase counterpart, HHG in the condensed-phase allows more compact coherent ultrafast photonic devices with lower driving laser intensities. The typical threshold laser intensity to drive this extreme nonlinear optical process in solids 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 threshold intensity, near field enhancement methods based on plasmonic resonances employing metallic or dielectric nanostructures deposited on solid surfaces have been demonstrated9-13. The driving laser intensity at the level of 1010 W/cm2 can be achieved. However, apart from manufacturing difficulties, the nanostructures suffer from shortcomings of low damage intensity and small enhancement areas. Moreover, the resonance-based methods 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 have been adopted14. The pump threshold intensity can be further reduced by one order of magnitude, 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 threshold even without field enhancement.
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 extraordinary HHG properties which can be attributed to its unique band structure15. 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 about 2.0 eV16 and high free-carrier mobility of around 1000 cm2/V/s17. These theoretical studies shed a 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 does 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 theoretical and experimental studies to demonstrate cadmium telluride (CdTe) being one of such excellent candidates for ultra-low threshold and remarkable throughput HHG in solids. The measured pump intensity threshold for the 12th and 31st harmonic order is only 30 and 75 GW/cm2, respectively, which is similar 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. A high photon flux of ~ photons/s (5th−8th) with a robust long-time sustainability is also demonstrated.
CdTe is a prototypical group II-VI crystalline compound semiconducting material commonly used in the photovoltaic18 and X-ray detector industry19. CdTe crystal has a cubic zinc blende structure, the same as that of the tetrahedral bonding configuration of diamond with each Cd (Te) surrounded by four Te (Cd) atoms (see Figure 1(a)). The atomic structure is thus lack of spatial inversion symmetry. Although well known as a versatile photon detector for X-ray and widely used in the solar cell thin film photovoltaic technology, the strong-field nonlinear optical properties and ultrafast carrier dynamics of CdTe have never being explored.
Before presenting the experiment data, we first examine the favorable electronic structure of CdTe and its implication for excellent HHG properties using first-principles calculations. Figures 1(b) and 1(c) show the band structure and DOS calculated by density functional theory (DFT), respectively. Around the top of valence band maximum, a relatively flat shape of band dispersion can be clearly seen. This band structure results in a large DOS around the Fermi level. Figure 1(c) compares the DOS per atom of CdTe, phosphorene, and silicon, a commonly used HHG material. CdTe has the largest DOS in the valence bands near the Fermi level, albeit large peaks of DOS are located at higher energy levels above the Fermi level in the conduction bands. Phosphorene exhibits moderately large DOS compared to that of silicon in both the valence and conduction bands near the Fermi level. In particular, CdTe and phosphorene are direct band gap materials while silicon is indirect. This implies that CdTe and phosphorene may offer superior number of excited carriers to silicon. Besides, CdTe also possesses a high carrier mobility of about 1100 cm2/(V·s) 20, close to that of phosphorene. These electronic properties are beneficial for HHG. It has been theoretically demonstrated that phosphorene exhibits extraordinary HHG15, with harmonic intensity one-to-two orders of magnitude higher than that in other typical materials. The similar electronic properties between CdTe and phosphorene suggest that CdTe is also potentially efficient in HHG. These first-principles calculation results, in accordance with our aforementioned hint in search of potential material candidates, serve as a rough guide for experimental investigation. With the prediction of promising HHG in CdTe, we show our experimental HHG characterizations in the CdTe bulk crystal.
The CdTe crystal is excited by a mid-infrared (MIR) femtosecond laser centered at 7.1 µm wavelength with a 180 fs pulse width at 50 kHz repetition rate. The excitation photon energy is well below the bandgap of 1.44 eV21 so that the multi-photon ionization is negligible. Figure 2(a) shows the transmitted high-order harmonic spectrum generated from the 1-mm-thick CdTe crystal at a pump intensity of 75 GW/cm2. Both odd and even harmonics are generated. The highest harmonic reaches the 31st order, corresponding to a wavelength of 229 nm, as shown in the zoom-in inset of Figure 2(a). There are 2 plateaus ranging from the 9th to 14th and 18th to 22nd harmonics, respectively, which may be associated with the band structure of CdTe. Notably the harmonics higher than the 9th order is above the bandgap of CdTe, and the harmonics ranging from the 9th to 31st orders are emitted from the last few nanometers of material. The individual harmonics strength of 15th−22nd orders as a function of the pump intensity from 30 to 140 GW/cm2 are plotted on logarithmic scale in Figure 2(b). All harmonic orders match the exponents of a power-law fit of ~3.8, which clearly demonstrates the non-perturbative character of the HHG processes in CdTe even at an intensity level of 1010−1011 W/cm2.
The pump threshold of HHG in the CdTe crystal as an important parameter is characterized. As shown in Figure 2(c), with a pump intensity of 30 GW/cm2, the 12th-order harmonic is generated. The measured HHG threshold of CdTe is one order of magnitude lower than that of other bulk crystals2,3,5,22,23 and two-dimensional materials7,8. The HHG threshold of CdTe is comparable to or even smaller than that of the dielectrics with the aid of plasmonic meta-structures for the HHG enhancement10-13 and the nano-films such as perovskite layer24 and WSe2 nano-sheet25. The high-harmonic spectra with the harmonic order up to 17, 20 and 23 are measured at a pump intensity of 53, 60, and 68 GW/cm2, respectively, with flat spectra over the entire visible spectral range. The HHG cut off scales linearly with the pump intensities as shown in Figure 2(d), and the 31st-order harmonic is observed at a low pump intensity of only 75 GW/cm2. With the flat harmonics spectra and the linear shape of the HHG cut off with respect to the pump intensity, we suppose HHG emission extending to 100 nm is possible excited by optimized pump wavelength and equipped with extreme ultraviolet spectrometer and vacuum measurement apparatus. To directly see the advantages of CdTe in reducing the HHG threshold, we measure the HHG from a silicon crystal, a common material for HHG with low pump threshold, under the same experimental conditions as a comparison. Notably, a pump intensity of 180 GW/cm2 is required to generate the 14th harmonic, which is 6-time larger than that of CdTe.
The output power of the 5th to 8th harmonics is measured with the pump intensity varying in the range of 0.5 to 4.5 TW/cm2, as shown in Figure 3(a). The HHG output grows exponentially with a power-law fit of 1.6-2.6 over the full range of the pump intensity. 4.9 µw harmonics are obtained at a pump power of 210 mW, corresponding to a power efficiency of ~2.3×10-5. The harmonics output is reversible and almost returns to the previous values when the pump intensity is decreased, which indicates that there is nearly no damage caused by the strong pump within short period of exposure time. We therefore understand that CdTe not only has a low HHG pump threshold, it can also withstand multi-TW/cm2 level pump intensity which is around one order of magnitude higher than that of the meta-structures and nano-films. The long-term stability of the photon flux from the 5th to 8th order harmonics which is below the bandgap is measured at pump intensities of 0.5 and 2 TW/cm2. Photon flux of photons/s is generated at the first few minutes of excitation, gradually reduced and stabilized to 6 photons/s after 20 minutes of exposure at a pump intensity of 2 TW/cm2. The decline of the harmonics photon flux is due to the slow damage of the sample. Strikingly, the harmonics emission is clearly visible in the ambient light environment as shown in Figure 3(e), demonstrating the high brightness of the HHG from CdTe as a light source.
To get a more intuitive sense of the large HHG output from CdTe, we compare its HHG strength with that of silicon under the same experimental conditions. To avoid the measurement error generated from the disturbance of the fluorescence, the HHG strength of CdTe and silicon with photon energy above the bandgap are compared, which means the emission from the last few nanometers of materials are considered. At a pump intensity of 1.1 TW/cm2, 9th and 11th harmonics from silicon are barely visible. In sharp contrast, the HHG emission from CdTe saturates the spectrometer. Hence, we have to reduce the pump intensity to 0.2 TW/cm2 to fit the HHG emission from CdTe within the dynamic range of the spectrometer. As shown in Figure 3(c), the high harmonic spectra from CdTe are still about two orders of magnitude stronger than that of silicon even with 5 times weaker pump intensity. The superior HHG emission from CdTe is confirmed by changing the pump wavelength to 3 μm. As shown in Figure 3(d), with a pump intensity of 0.2 TW/cm2 at 3 μm, the high harmonic signal from CdTe is two-to-three orders of magnitude stronger than that of silicon, which is consistent with the measurement pumped at 7.1 μm. The photos of much brighter visible light emission from CdTe compared to that of silicon pumped at both 7.1 μm and 3 μm in the ambient light environment are captured and shown in Figure 3(e-h), verifying the superior HHG output generated in CdTe.
To investigate the dependence of HHG in CdTe on crystallographic orientation, the high-harmonic strengths of 9th -22nd orders with different angle θ between the pump polarization (solid pink arrow) and the crystal mirror plane (dashed grey arrow) are measured as shown in Figure 4(a). It is observed that both odd and even harmonics are modulated uniformly by every 60° with near unity modulation depth, as presented in Figure 4(b), which reveals the 6-fold symmetry of CdTe. The intensity is strongest when the pump field is along the CdTe bond direction, i.e., parallel to the mirror plane. In addition, the polarization angle of the high harmonic emission from 10th to 14th orders is measured when the pump polarization is along the specific crystal directions θ = 0° and θ = 30°, respectively. As shown in Figure 4(c, d), it is observed that the odd harmonics keep along with the pump polarization at both θ = 0° and θ = 30°, whereas the polarization direction of even orders switches from parallel to perpendicular with respect to the pump when the pump polarization changes from θ = 0° to θ = 30°. This response is similar to the results observed by the previous works in MoS27 and GaSe22 and in accordance with symmetry requirements of the crystals with broken inversion symmetry. When the pump field is parallel to the mirror plane (θ = 0°), no harmonic is allowed in the direction perpendicular to the pump field because the mirror symmetry is not broken in this direction. While the pump field is perpendicular to the mirror plane (θ = 30°), however, the even orders parallel to the pump field must vanish because the required even harmonic optical responses perpendicular to the mirror plane cancel each other as they exhibit equal amplitude but opposite sign, separated by half laser period due to the combined mirror symmetry of crystal and laser field. In this case, even harmonics can still appear in the direction perpendicular to the pump field, the origin of which can be explained by a Berry curvature term in an intraband semiclassical model. Berry curvature can act like an out-of-plane magnetic field that gives rise to an anomalous in-plane current perpendicular to the pump field. Figure 4(d) also shows the even harmonics are comparable to the neighboring odd harmonics, indicating the large effect of Berry curvature and non-perturbative nature of the HHG process. This also shows the important contribution of intraband dynamics to HHG in CdTe.
In conclusion, we experimentally demonstrate an ultra-low threshold and high throughput of HHG emission from the CdTe crystal. 1010 W/cm2-level pump threshold is similar or even smaller than that of the dielectrics with plasmonic meta-structures for the HHG enhancement, while it has much higher pump damage intensity of multiple 1012 W/cm2 for its nature of pristine bulk crystal. The harmonics flux of to photons/s (5th-8th) is obtained, which is sustained for more than 30 minutes 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 amplifier26 or a single-stage MIR optical parametric amplifier (OPA) is able to excite decent harmonics flux. At the 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 energy27-30. In addition, high-quality CdTe epi-layers could be grown by the mature semiconductor deposition technologies, such as magnetron sputtering. Thus, we look forward to HHG and attosecond devices fabricated based on CdTe thin films. Thirdly, the extraordinary 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 researches. Finally, it also opens up the possibilities to investigate ultrafast carrier dynamics in CdTe relevant to important applications for infrared and gamma photon detector and solar cell thin film photovoltaic technology.