## Vol. 68, No. 10 (2019)

##### 2019-05-20

###### GENERAL

2019, 68 (10): 100501.
doi: 10.7498/aps.68.20181848

Abstract +

As a key approach to understanding complex systems (e.g. biological, physical, technological and social systems), the complex networks are ubiquitous in the whole world. Synchronization in complex networks is significant for a more in-depth understanding of the dynamic characteristics of the networks, where tremendous efforts have been devoted to their mechanism and applications in the last two decades. However, many real-world networks consist of hundreds of millions of nodes. Studying the synchronization of such large-scale complex networks often requires solving a huge number of coupled differential equations, which brings great difficulties to both computation and simulation. Recently, a spectral coarse graining approach was proposed to reduce the large-scale network into a smaller one while maintaining the synchronizability of the original network. The absolute distance between the eigenvector components corresponding to the minimum non-zero eigenvalues of the Laplacian matrix is used as a criterion for classifying the nodes without considering the influence of the relative distance between eigenvector components in an original spectral coarse graining method. By analyzing the mechanism of the spectral coarse graining procedure in preserving the synchronizability of complex networks, we prove that the ability of spectral coarse graining to preserve the network synchronizability is related to the relative distance of the eigenvector components corresponding to the merged nodes. Therefore, the original spectral coarse graining algorithm is not satisfactory enough in node clustering. In this paper, we propose an improved spectral coarse graining algorithm based on the relative distance between eigenvector components, in which we consider the relative distance between the components of eigenvectors for the eigenvalues of network coupling matrix while clustering the same or similar nodes in the network, thereby improving the clustering accuracy and maintaining the better synchronizability of the original network. Finally, numerical experiments on networks of ER random, BA scale-free, WS small-world and 27 different types of real-world networks are provided to demonstrate that the proposed algorithm can significantly improve the coarse graining effect of the network compared with the original algorithm. Furthermore, it is found that the networks with obvious clustering structure such as internet, biological, social and cooperative networks have better ability to maintain synchronization after reducing scale by spectral coarse-grained algorithm than the networks of fuzzy clustering structure such as power and chemical networks.

## EDITOR'S SUGGESTION

2019, 68 (10): 100502.
doi: 10.7498/aps.68.20182068

Abstract +

2019, 68 (10): 100503.
doi: 10.7498/aps.68.20190156

Abstract +

For the dynamic reconstruction of the chaotic dynamical system, a method of identifying an exponential weighted online sequential extreme learning machine with kernel(EW-KOSELM) is proposed. The kernel recursive least square (KRLS) algorithm is directly extended to an online sequential ELM framework, and weakens the effect of old data by introducing a forgetting factor. Meanwhile, the proposed algorithm can deal with the ever-increasing computational difficulties inherent in online kernel learning algorithms based on the ‘fixed-budget’ memory technique. The employed EW-KOSELM identification method is firstly applied to the numerical example of Duffing-Ueda oscillator for chaotic dynamical system based on simulated data, the qualitative and quantitative analysis for various validation tests of the dynamical properties of the original system as well as the identification model are carried out. A set of qualitative validation criteria is implemented by comparing chaotic attractors i.e. embedding trajectories, computing the corresponding Poincare mapping, plotting the bifurcation diagram, and plotting the steady-state trajectory i.e. the limit cycle between the original system and the identification model. Simultaneously, the quantitative validation criterion which includes computing the largest positive Lyapunov exponent and the correlation dimension of the chaotic attractors is also calculated to measure the closeness i.e. the approximation error between the original system and the identification model. The employed method is further applied to a practical implementation example of Chua's circuit based on the experimental data which are generated by sampling and recording the measured voltage across a capacitor, the inductor current from the double-scroll attractor, the measured voltage across a capacitor from the Chua's spiral attractor and an experimental time series from a chaotic circuit. The digital filtering technique is then used as a preprocessing approach, on the basis of wavelet denoising the measured data with lower signal-noise ratio (SNR) which can produce the double-scroll attractor or the spiral attractor, the reconstruction attractor of the identification model is compared with the reconstruction attractor from the experimental data for original system. The above experimental results confirm that the EW-FB-KOSELM identification method has a better performance of dynamic reconstruction, which can produce an accurate nonlinear model of process exhibiting chaotic dynamics. The identification model is dynamically equivalent or system approximation to the original system.

2019, 68 (10): 100701.
doi: 10.7498/aps.68.20182272

Abstract +

A series of Sr

_{1.98}(Al_{1–x}Mg_{x})(Al_{1–x}Si_{1+x})O_{7}: 2%Eu^{2+}phosphors is prepared by the high-temperature solid-state reaction method, the crystal structures and luminescent properties of the prepared phosphors are investigated by measuring the X-ray diffraction, luminescent spectra and optical microscope. The isomorphic compounds of Sr_{2}Al_{2}SiO_{7}and Sr_{2}MgSi_{2}O_{7}contain tetrahedra including [MgO_{4}], [SiO_{4}] and [AlO_{4}]. Although the valences of the [MgO_{4}]^{6–}, [SiO_{4}]^{4–}and [AlO_{4}]^{5–}groups are different, the charge imbalance occurs when the [MgO_{4}]^{6–}and [SiO_{4}]^{4–}substitutes of [AlO_{4}]^{5–}and [AlO_{4}]^{5–}, respectively. While the groups are co-substituted, the charge imbalance disappears. And the larger volume of [MgO_{4}] and the smaller volume of [SiO_{4}] together replaces the similar volume of [AlO_{4}], resulting in the decrease of [(Si/Al)O_{4}] and increase of [(Mg/Al)O_{4}]. Moreover, the decrease of unit cell parameters c and the increase of a and V due to the increased replacement of Mg^{2+}(0.57 Å for*CN*= 4) by Al^{3+}(0.39 Å for*CN*= 4) and Si^{4+}(0.26 Å for*CN*= 4) by Al^{3+}(0.39 Å for*CN*= 4) cause the ambient temperature to change, the crystal field splitting of the Eu^{2+}cation to be weakened, and the emission spectra to be blue-shifted from 503 nm to 467 nm, which are closely related to the local coordination environment of the Eu^{2+}, in addition, this reveals that the emission color of this series of phosphors can be tuned from green with color coordinate (0.2384, 0.3919) to blue (0.1342, 0.1673) by adjusting the chemical compositions via the [MgO_{4}]^{6–}and [SiO_{4}]^{4–}groups’ co-substitution for [AlO_{4}]^{5–}. The full width at half maximumof emission band is 120 nm when*x*= 0, the photoluminescence emission width decreases monotonically from 89 to 50 nm as*x*is increased from 0.25 to 1. In other words, the full width at half maximum of emission band exhibits a decreasing trend. The internal quantum efficiency is enhanced with increasing x in Sr_{1.98}(Al_{1–x}Mg_{x})(Al_{1–x}Si_{1+x})O_{7}: 2%Eu^{2+}phosphors. These results verify that the groups’ substitutions are enhanced with polyhedron changing in the solid solutions and contribute largely to the luminescence properties of the phosphor.###### NUCLEAR PHYSICS

2019, 68 (10): 102901.
doi: 10.7498/aps.68.20182192

Abstract +

$ {\rm{K}}/{\text{π}}$ separation is around 7 GeV/c for JLab-SoLID TOF system under high particle rate as high as 20 kHz/cm$ {\rm{K}}/{\text{π}}$ separation is around 7 GeV/c for JLab-SoLID TOF system under high particle rate as high as 20 kHz/cm

^{2}, and the time requirement is around 20 ps. The readout electronics of first two generations is based on time over threshold method, and pulse shape sampling technology will be used in the third-generation TOF. In the same time, the machine learning technology LSTM network is also used to analyze the time performance. As a very successful sample, MRPC barrel TOF has been used in RHIC-STAR for more than ten years and many important physics results have been obtained. A prominent result is the observation of antimatter helium-4 nucleus. This discovery proves the existence of antimatter in the early universe. In this paper, we will describe the evolution of MRPC TOF technology and key technology of each generation of TOFs including MRPC detector and related electronics. The industrial and medical usage of MRPC are also introduced in the work finally.">Particle identification is very important in nuclear and particle physics experiments. Time of flight system (TOF) plays an important role in particle identification such as the separation of pion, kaon and proton. Multi-gap resistive plate chamber (MRPC) is a new kind of avalanche gas detector and it has excellent time resolution power. The intrinsic time resolution of narrow gap MRPC is less than 10 ps. So the MRPC technology TOF system is widely used in modern physics experiments for particle identification. With the increase of accelerator energy and luminosity, the TOF system is required to indentify definite particles precisely under high rate environment. The MRPC technology TOF system can be defined as three generations according to the timing and rate requirement. The first-generation TOF is based on the float glass MRPC and its time resolution is around 80 ps, but the rate is relatively low (typically lower than 100 Hz/cm^{2}). The typical systems are TOF of RHIC-STAR, LHC-ALICE and BES III endcap. For the second-generation TOF, its time resolution has the same order as that for the first generation, but the rate capability is much higher. Its rate capability can reach 30 kHz/cm^{2}. The typical experiment with this high rate TOF is FAIR-CBM. The biggest challenge is in the third-generation TOF. For example, the momentum upper limit of^{2}, and the time requirement is around 20 ps. The readout electronics of first two generations is based on time over threshold method, and pulse shape sampling technology will be used in the third-generation TOF. In the same time, the machine learning technology LSTM network is also used to analyze the time performance. As a very successful sample, MRPC barrel TOF has been used in RHIC-STAR for more than ten years and many important physics results have been obtained. A prominent result is the observation of antimatter helium-4 nucleus. This discovery proves the existence of antimatter in the early universe. In this paper, we will describe the evolution of MRPC TOF technology and key technology of each generation of TOFs including MRPC detector and related electronics. The industrial and medical usage of MRPC are also introduced in the work finally.###### ATOMIC AND MOLECULAR PHYSICS

## EDITOR'S SUGGESTION

2019, 68 (10): 103101.
doi: 10.7498/aps.68.20190067

Abstract +

An amorphous mixing layer (3.5–4.0 nm in thickness) containing silicon (Si), oxygen (O), molybdenum (Mo) atoms, named

*α*-SiO_{x}(Mo), is usually formed by evaporating molybdenum trioxide (MoO_{3}) powder on an n-type Si substrate. In order to investigate the process of adsorption, diffusion and nucleation of MoO_{3}in the evaporation process and ascertain the formation mechanism of*α*-SiO_{x}(Mo) on a atomic scale, the first principle calculation is used and all the results are obtained by using the Vienna*ab initio*simulation package. The possible adsorption model of MoO_{3}on the Si (100) and the defect formation energy for substitutional defects and vacancy defects in*α*-SiO_{2}and*α*-MoO_{3}are calculated by the density functional theory. The results show that an amorphous layer is formed between MoO_{3}film and Si (100) substrate according to*ab initio*molecular dynamics at 1500 K, which are in good agreement with experimental observations. The O and Mo atoms diffuse into Si substrate and form the bonds of Si—O or Si—O—Mo, and finally, form an*α*-SiO_{x}(Mo) layer. The adsorption site of MoO_{3}on the reconstructed Si (100) surface, where the two oxygen atoms of MoO_{3}bond with two silicon atoms of Si (100) surface, is the most stable and the adsorption energy is －5.36 eV, accompanied by the electrons transport from Si to O. After the adsorption of MoO_{3}on the Si substrate, the structure of MoO_{3}is changed. Two Mo—O bond lengths of MoO_{3}are 1.95 Å and 1.94 Å, respectively, elongated by 0.22 Å and 0.21 Å compared with the those before the adsorption of MoO_{3}on Si substrate, while the last bond length of MoO_{3}is little changed. The defect formation energy value of neutral oxygen vacancy in*α*-SiO_{2}is 5.11 eV and the defect formation energy values of neutral oxygen vacancy in*α*-MoO_{3}are 0.96 eV, 1.96 eV and 3.19 eV, respectively. So it is easier to form oxygen vacancy in MoO_{3}than in SiO_{2}, which implies that the oxygen atoms will migrate from MoO_{3}to SiO_{2}and forms a 3.5–4.0-nm-thick*α*-SiO_{x}(Mo) layer. As for the substitutional defects in MoO_{3}and SiO_{2}, Mo substitutional defects are most likely to form in SiO_{2}in a large range of Mo chemical potential. So based on our obtained results, the forming process of the amorphous mixing layer may be as follows: the O atoms from MoO_{3}bond with Si atoms first and form the SiO_{x}. Then, part of Mo atoms are likely to replace Si atoms in SiO_{x}. Finally, the ultra-thin buffer layer containing Si, O, Mo atoms is formed at the interface of MoO_{3}/Si. This work simulates the reaction of MoO_{3}/Si interface and makes clear the interfacial geometry. It is good for us to further understand the process of adsorption and diffusion of atoms during evaporating, and it also provides a theoretical explanation for the experimental phenomenon and conduces to obtaining better interface passivation and high conversion efficiency of solar cell.###### ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS

2019, 68 (10): 104101.
doi: 10.7498/aps.68.20182070

Abstract +

Penetration of a plane electromagnetic wave through the apertures on a perfectly conducting flat plate is a classical electromagnetic problem. In some practical applications like electromagnetic shielding, where only the fields far from the apertures are concerned and the aperture sizes are small compared with a wavelength, the role of apertures can be represented by the equivalent electric and magnetic dipoles located in the centers of the apertures. In principle, the penetration field can be expressed as the superposition of the radiation fields of the dipoles. However, the direct superposition leads to a double series with complex form and poor convergence. On the other hand, this problem may also be solved by full wave numerical simulations. Even so, finding analytical solutions is still desirable considering that it is clear in physical significance and easy to implement. In this paper, the analytical formula of the penetration fields are derived for both TE and TM polarization mode with different angles of incidence. The derivation is carried out firstly by averagely distributing each dipole moment within each periodic unit. As a result, the dipole array is replaced with a flat sheet with uniform magnetization and polarization intensity. Then, the equivalent surface current and charge distributions are obtained directly from the polarization intensity. Finally, the penetration fields are treated as the radiation fields of the surface sources. It is shown that the amplitude of the penetration field is proportional to aperture magnetic polarization coefficient and wave frequency, and it is inversely proportional to the area of a periodic unit. In regard to the effect of the incidence angle, the amplitude of the penetration field is proportional to the cosine of the incidence angle for TE polarization. However, for the TM polarization, the relationship is a little complicated due to the coexistence of electric and magnetic dipoles: the field is not rigorously inversely proportional to the cosine of the incidence angle due to the existence of a correction term involving both the polarization coefficient and the sine of the angle. The formula is used to calculate the shielding effectiveness for several different aperture shapes and different incidence angles. The results are in good agreement with those from the full wave simulation software.

2019, 68 (10): 104201.
doi: 10.7498/aps.68.20182171

Abstract +

When the optical component works in a complicated working environment such as a large temperature difference or a multi-modal state, internal stress accumulation is likely to occur, which affects the overall performance of the optical system. The stress-optical constant of optical component in the infrared range is one of the concerns of many optical systems. In this paper, a method of measuring the internal stress-induced birefringence of optical glass based on the frequency splitting effect of 1556.16 nm erbium-doped fiber laser is proposed. The planar dielectric lenticular and fiber Bragg grating (FBG) are selected to form a linear semi-open resonator by using an erbium-doped fiber as a gain medium, and a 976 nm semiconductor laser (LD) with a single-mode pigtail output for pumping. At the pump power of 200 mW, a laser output with a spectral center wavelength of 1556.16 nm, a spectral 3-dB bandwidth of 0.018 nm, and a longitudinal mode spacing of 40.77 MHz is obtained. The birefringence and its fast axis introduced into the cavity by the fiber itself are analyzed. The force sensing structure of the optical glass to be tested is placed in the cavity, and the frequency splitting of the laser after the stress loading on the optical glass in the cavity is compared with the scenario in the empty cavity, and the bifurcation and cavity birefringence caused by the external load are obtained by combining the Jones matrix transfer equation. The load on the optical glass is gradually increased from 0 to 20 N. In the stress loading process, the direction of the stress birefringence in the optical glass is parallel to the direction of the applied force. The frequency splitting of the inner cavity increases from 35.59 MHz to 35.77 MHz, which corresponds to a 679.18 nm—682.62 nm optical path difference of the cavity. The correspondence between stress and frequency splitting is understood according to the birefringence superposition model and frequency splitting, and the result can be traced back to the basic physical quantity-wavelength. Continuous loading of the optical glass results in a system with measurement repeatability better than 0.0459 MHz. The experiment is designed to avoid the uncorrected systematic error of the system induced by the sub-cavity effect. The non-aligned error equation is obtained, and the error is calibrated. The experimental results show that the sensitivity of the instrument for K9 glass is 22060 Pa/nm and the linearity is 99.44%. The method has no damage to the surface of the optical structure, nor occlusion nor influence of its normal in-service work. It is of significance for optical lens, structural measurement and error correction, and can be widely used for accurately measuring the birefringence of optical components in the infrared band.

2019, 68 (10): 104202.
doi: 10.7498/aps.68.20190184

Abstract +

Different from second-order temporal ghost imaging usually realized by means of second-order correlation measurement, in this paper, we investigate theoretically temporal imaging with temporally thermal light via first-order field correlation based on a Mach-Zehnder interferometer. The paraxial wave equation describing the diffraction of light and the differential equation characterizing the dispersion of light pulse are given. Based on the similarity between these equations, the duality between the paraxial diffraction of the light in the spatial domain and the dispersion of the temporal narrow-band pulse in the dispersive medium (i.e. the space-time duality) is obtained, and the impulse response functions in the time domain for several optical systems are also presented. Then in terms of the space-time duality, we design the scheme for temporal imaging via first-order thermal field correlation based on a Mach-Zehnder interferometer and obtain the intensity expression for first-order temporal imaging according to the temporal impulse response functions, and discuss the influences of the source pulse width and coherence time on the image visibility and resolution. The result shows that the temporal signal can be reconstructed through temporal first-order temporal imaging. Furthermore, when the source’s coherence time is fixed, the image visibility decreases as the pulse width increases. However, the image resolution increases. When the source’s pulse width is fixed, the image visibility increases as the coherence time increases. And yet the image resolution decreases. Specially, when the source’s pulse width is 100 ps and the coherence time is 0.5 ps, the image quality (taking both the visibility and resolution into account) of a temporally rectangular object is satisfactory. In the simulation, the distance and width of the temporal rectangular object are 20 ps and 8 ps, respectively. It is shown that there is a dilemma between the visibility and resolution of first-order temporal imaging which is similar to the result of second-order ghost imaging. Our result discussed herein could be valuable in the reconstruction and detection of temporal signal via first-order temporal ghost imaging with temporally thermal light.

2019, 68 (10): 104203.
doi: 10.7498/aps.68.20190032

Abstract +

θ = 0,

*φ*= 0. It has a great application value in the terahertz wave cloaking.">Metasurface is an artificial structure composed of sub-wavelength units which can realize the arbitrary control of electromagnetic wave energy by coding and arranging metasurface. Unlike the previous coding metasurface with a fixed phase difference of the neighbor coding unit cells, the frequency coding metasurface possesses the main feature that it has the linear change phase difference and different phase sensitivities in the whole working frequency band of the digital unit cells. And it can flexibly control the reflected terahertz waves to the numerous directions by changing the working frequency without redesigning the coding metasurface structure. In this paper, the frequency coding metasurfaces are designed by using four herringbone unit cells with the same shape and different sizes. They have the same phase response at the initial frequency and the different phase sensitivities throughout the frequency band. To describe the frequency coding characteristics of the unit cells, the digital numbers "0" and "1" are used to represent the low phase sensitivity and high phase sensitivity, respectively. Using the frequency digital coding, it can control the electromagnetic wave energy radiations by a single digital coding metasurface without changing the spatial coding pattern. By the combination of the spatial coding and frequency coding, It can manipulate the electromagnetic wave energy radiations more flexibly. We demonstrate 1-bit, 2-bit periodic frequency coding metasurfaces and 2-bit non-periodic frequency coding metasurface. They are all designed in the pre-designed coding sequence to control the electromagnetic wave energy radiations. Numerically simulated results confirm that the frequency coding metasurface can flexibly control the reflected terahertz waves to the numerous directions by changing the working frequency without redesigning the coding metasurface structure. Additionally, the number of the backward diffusion-like scattering beam increases with the change of frequency for the 2-bit random terahertz frequency coding metasurface. It has a good dispersion effect on the main lobe energy of terahertz wave radiation. The radar cross section can be reduced effectively, and the maximum value of radar cross section reduction can reach 29 dB in the direction of*θ*= 0,*φ*= 0. It has a great application value in the terahertz wave cloaking.
2019, 68 (10): 104204.
doi: 10.7498/aps.68.20182216

Abstract +

Incoherent digital holography (IDH) is a recently proposed technique to record three-dimensional (3D) information about the object under incoherent illumination, which breaks the limitation that the holographic recording must be illuminated by coherent light sources and thus makes it usable in white-light and fluorescence illuminating circumstance. In particular, the fresnel incoherent correlation holography (FINCH) is an exemplary method which improves the imaging resolution power and efficiency of incoherent digital holography, and it can obtain 3D distribution of objects swiftly without scanning and moving. However, compared with the conventional optical holography, the FINCH system has a very small field-of-view due to the limitation of the pixel number and size of spatial light modulator (SLM). Therefore, expanding the recording field-of-view of FINCH system is very significant for the application of IDH. In the FINCH, the SLM is used as a diffractive beam splitter so that each spherical beam, originating from each object point, is split into two spherical beams with two different curve radii. Then the interference fringes between the two beams are recorded by CCD. In this paper, the field-of-view angle recorded by the SLM is proposed and analyzed based on the physical and numerical principles of the FINCH system. The field-of-view of imaging system is improved by increasing the effective diameter of SLM through moving the center of the dual-lens optical axis mounted on the SLM to the edge in different directions respectively. An optical setup of reflection mode is constructed to verify the theoretical analysis of this study, and the sub-holograms in different field-of-views are obtained by CCD through changing the masks displayed on the SLM sequentially. Then, the complex holograms in different field-of-views are obtained by using the three-step phase-shifting method, and the reconstructed images are acquired respectively through the angular spectrum method (ASM) by using a computer. Finally, the large field-of-view image is obtained by stitching the reconstructed images in each field-of-view by utilizing the matlab program. The experimental results show that the efficient recording field-of-view of SLM can be increased by 2.77 times with our proposed method. Accordingly, the recording field-of-view of the system is improved significantly. The recording field-of-view of the FINCH system will increase further if the center of the dual-lens optical axis continues to move toward the edge. Therefore, this study provides an important support for the further application of high resolution microscopic imaging with large field-of-view.

2019, 68 (10): 104206.
doi: 10.7498/aps.68.20190112

Abstract +

In recent years, exploring new topological quantum model structures and in depth analyzing the novel physical properties in various multimerized topological lattices have become a hot topic in the field of quantum optics. Among the different model structures, the multimerized non-Hermitian lattice controlled by different parameters in the future research of topological quantum materials, we believe, can exhibit more meaningful novel topological properties. As one of the most classic topological models, the one-dimensional Aubry-André-Harper (AAH) model has received more and more attention in the study of multimerized lattices. In this paper, we focus on the novel topological properties of a trimerized non-Hermitian lattice, and extend the trimer model structure from a one-dimensional chain to a quasi-one-dimensional zigzag structure. The results show that firstly, if the nearest-neighbor forward coupling coefficient in the unit cell is not equal to the backward coupling coefficient, the chiral inversion symmetry of the system is destroyed. It can be observed that the bulk states and the edge states in the trimerization model will be localized on the same edge of the lattice, and the skin effect will appear in the system. With the increase of the nearest-neighbor coupling coefficient, the width of the edge state changes in which the lower edge state of the imaginary part of the spectrum is narrowed until it disappears. The degree of degeneracy of the system changes, and the number of edge states is reduced from four to two. Remarkably, the generalized bulk-boundary correspondence is shown in certain non-Hermitian topological systems. Secondly, when the trimerization model considers the influence of the next-nearest-neighbor coupling, the numerical results show that the upper and lower energy gaps in the energy spectrum and the edge states in the energy spectrum are asymmetrical as the next-nearest-neighbor coupling coefficient is modulated in an appropriate range. The upper energy gaps and the edge states are narrowed, and the edge states of the lower energy gaps are widened. At the same time, the novel topology features of the system can also be used to achieve the quantitative control of the energy spectrum edge states, and other interesting directions are worth exploring.

2019, 68 (10): 104207.
doi: 10.7498/aps.68.20182224

Abstract +

A watt-level passive Q-switched mode-locked operation in Tm: LuAG all-solid-state laser is realized for the first time by using graphene oxide (GO) saturable absorber as a mode-locked starting element. The laser is pumped by a wavelength tunable Ti: sapphire laser operating at 794.2 nm. In this experiment, the maximum continuous-wave (CW) output power of 1440 mW, 2030 mW and 2610 mW are obtained by 1.5%, 3% and 5% output coupled (OC) mirrors respectively, in which the corresponding slope efficiencies are 22.3%, 32.6% and 40.6%, respectively. When the GO is inserted into the cavity, the laser bump threshold is further increased due to more intracavity loss. With a 1.5% OC mirror, the absorbed pump threshold is as low as 325 mW, the maximum output power is 787 mW, and the corresponding slope efficiency is 12.5%. With a 3% OC mirror, the absorbed bump threshold is 351 mW, the maximum output power is 1740 mW, and corresponding slope efficiency is 30.3%. With a 5% OC mirror, the QML operation is not realized due to the increase of intracavity loss. Although the laser pump threshold power of 3% OC mirror differs from that of 1.5% OC mirror by 26 mW, the output power is more than twice higher than that of 1.5% OC mirror. For these reasons, we use a 3% OC mirror in our experiment. In this case, a stable QML operation with a threshold of 3420 mW is obtained. When the pump power reaches 8.1 W, the corresponding maximum output power is 1740 mW, the central wavelength is 2023 nm, the repetition frequency is 104.2 MHz, the maximum single pulse energy is 16.7 nJ, and the modulation depth is close to 100%. According to the symmetrical shape of the mode locked pulse and considering the definition of rise time, we can assume that the duration of the pulse is approximately 1.25 times the pulse rise time. So the width of the mode locked pulse is estimated at about 923.8 ps. The results show that the GO is a promising high power saturable absorber in 2 μm wavelength for the QML solid-state laser. In the next stage, we will increase the pump power, optimize the quality of the GO material, and compensate for the dispersion in the cavity. It is expected to achieve a CW mode-locked operation and femtosecond pulse output.

2019, 68 (10): 104208.
doi: 10.7498/aps.68.20190018

Abstract +

The high-precision structural health monitoring of large civil structures and materials are increasingly demanded with widely using the distributed fiber sensors. A Brillouin optical correlation domain analysis for millimeter-levelhigh spatial resolution sensing using broadband chaotic laser is proposed and demonstrated. Through the analysis of the influence of polarization state and feedback strength on the chaotic laser, we experimentally achieve a broadband chaotic laser with a spectrum over 7.5 GHz in –3 dB which means that the theoretical spatial resolution is 3 mm, and we also successfully measure the distribution of fiber Brillouin gain spectrum with a temperature over 300 m measurement range with 7.05 mm spatial resolution, which is the first time that the sensor system based on chaotic laser has achieved the measurement with millimeter-level. However, there is still a difference in spatial resolution between the experimental and theoretical values. We can find that the chaotic laser has a time-delay feature; besides, with the broadening of chaotic laser, the threshold of stimulated Brillouin scattering in optical fibers increases while the Brillouin gain will weaken if the pump power is not enough here, and the cross-correlation peak of chaotic laser will narrow. All these problems cause the Brillouin gain signal to be easily submerged by noise, so the performance of the chaotic Brillouin optical correlation domain analysis system will decrease ultimately. Therefore, we also propose an optimization of Brillouin optical correlation domain analysis system by introducing the time-gated scheme into pump branch. It is obvious that the peak power of the pump wave is heightened by more than 9.5 dB after being amplitude-modulated by a square pulse with a pulse width of greater than acoustic phonon lifetime, and the signal-to-back ground noise ratio of the gain spectrum is improved effectively in theory; the cross correlation between chaotic pump wave and probe waveis locked within a pulse duration time, and the residual stimulated Brillouin scattering interactions existing outside the central correlation peak can be largely inhibited. In this optimized setup, the performance of the distributed temperature sensing is improved to 3.12 mm spatial resolution, which corresponds well to the theoretical value. The improved chaotic Brillouin optical correlation domain analysis technology will have a great potential application in high-precision structural health monitoring of large civil structures.

2019, 68 (10): 104209.
doi: 10.7498/aps.68.20182137

Abstract +

$ {\rm{2}}n{\text{π}} $ difference between the measured phase difference and the principle phase difference, which is the reason why conventional least-square reconstruction algorithms cannot reconstruct wavefront with branch points. The complex exponential reconstructor is developed to restore the discontinuous wavefront with phase difference replaced by complex exponents. However, thousands of iterations are required by the complex exponential reconstructor before converging to an acceptable solution. In order to speed up the iterative calculation, the cascadic multigrid method (CMG) is introduced in the process of wavefront reconstruction. The proposed method can be used to restore discontinuous wavefront with lower residual error similar to those reconstructed by the direct iteration. The number of float point multiplications required by the CMG method is nearly 2 orders of magnitude lower than that required by the direct iteration. The acceleration of the CMG method increases with the number of subapertures increasing. The performance of CMG method to recover continuous wavefront is also investigated and compared with conventional wavefront reconstruction algorithm based on successive over-relaxation. It is shown that the CMG method has good capability for wavefront reconstruction with high precision and low computation cost no matter whether it is applied to discontinuous or continuous wavefront. Furthermore, the CMG method is used in the adaptive optics for correcting the turbulence aberration. The direct slope wavefront reconstruction algorithm based on the assumption that the measured slope and the control voltage satisfy the linear relationship cannot restore the wavefront with branch points. As a result, the adaptive optics system with the CMG method doubles the correction quality evaluated by the Strehl ratio compared with that with the direct slope wavefront reconstruction algorithm.">When laser beam propagates through the turbulent atmosphere, there are branch points in wavefront, which are caused by deep turbulence or long propagation distance. Conventional least-square reconstruction algorithms cannot restore the discontinuous wavefront, which severely limits correction performance of an adaptive optics system. If the incoming wavefront contains a branch cut, there is $ {\rm{2}}n{\text{π}} $ difference between the measured phase difference and the principle phase difference, which is the reason why conventional least-square reconstruction algorithms cannot reconstruct wavefront with branch points. The complex exponential reconstructor is developed to restore the discontinuous wavefront with phase difference replaced by complex exponents. However, thousands of iterations are required by the complex exponential reconstructor before converging to an acceptable solution. In order to speed up the iterative calculation, the cascadic multigrid method (CMG) is introduced in the process of wavefront reconstruction. The proposed method can be used to restore discontinuous wavefront with lower residual error similar to those reconstructed by the direct iteration. The number of float point multiplications required by the CMG method is nearly 2 orders of magnitude lower than that required by the direct iteration. The acceleration of the CMG method increases with the number of subapertures increasing. The performance of CMG method to recover continuous wavefront is also investigated and compared with conventional wavefront reconstruction algorithm based on successive over-relaxation. It is shown that the CMG method has good capability for wavefront reconstruction with high precision and low computation cost no matter whether it is applied to discontinuous or continuous wavefront. Furthermore, the CMG method is used in the adaptive optics for correcting the turbulence aberration. The direct slope wavefront reconstruction algorithm based on the assumption that the measured slope and the control voltage satisfy the linear relationship cannot restore the wavefront with branch points. As a result, the adaptive optics system with the CMG method doubles the correction quality evaluated by the Strehl ratio compared with that with the direct slope wavefront reconstruction algorithm.

2019, 68 (10): 104701.
doi: 10.7498/aps.68.20182002

Abstract +

$ {a_{\rm wf}}$ . The parameter $ {a_{wf}}$ represents the interaction between wall particles and liquid particles. Our simulation results show that the distributions of the velocity, density, temperature and shear stress compare well with the corresponding analytical solutions with $ {a_{\rm wf}} = 9.68$ , and there is no fluctuation of the fluid density near the wall. This indicates that the no-slip is obtained, and hence the wall is hydrophilic. With ${a_{\rm wf}} > 9.68$ , the wall becomes hydrophobic and the fluid can slip at the wall. The wall becomes more hydrophobic with larger ${a_{\rm wf}} $ , and the stronger hydrophobicity leads to greater slip. The slip velocity and slip length can be used to describe the fluid slip. According to the Navier slip boundary model, the slip velocity and slip length are determined by fitting a straight line (linear fitting) to the velocity profile in the central portion of the channel. The results show that the slip velocity or the slip length is a quadratic function of the parameter ${a_{\rm wf}} $ , namely, the slip velocity or the slip length is a quadratic function of the contact angle. A physical mechanism of the fluid slip over hydrophobic surfaces is also proposed. The density profile is uniform for the no-slip condition, but there is a layer of low density fluid near the wall when the fluid can slip at the wall surface. This low density region can disrupt the momentum transfer between the wall and the fluid, which induces the fluid slip at the wall surface.">The understanding of fluid slip over a hydrophobic surface is of great importance for reducing the drag for fluid flows. Dissipative particle dynamics (DPD) is used to investigate the mechanism of fluid slip at the solid-fluid interface in microchannels. A wall model adopting three layers of frozen particles is proposed for DPD simulation. In addition, a modified bounce-forward reflection is proposed to reintroduce fluid particles back into the fluid region when they " penetrate” into the wall region in the calculation due to the soft potential employed. Then the Couette flow is simulated by using the proposed wall model. The simulation results show that the no-slip or slip of the fluid at the wall can be achieved by adjusting parameter $ {a_{\rm wf}}$ . The parameter $ {a_{wf}}$ represents the interaction between wall particles and liquid particles. Our simulation results show that the distributions of the velocity, density, temperature and shear stress compare well with the corresponding analytical solutions with $ {a_{\rm wf}} = 9.68$ , and there is no fluctuation of the fluid density near the wall. This indicates that the no-slip is obtained, and hence the wall is hydrophilic. With ${a_{\rm wf}} > 9.68$ , the wall becomes hydrophobic and the fluid can slip at the wall. The wall becomes more hydrophobic with larger ${a_{\rm wf}} $ , and the stronger hydrophobicity leads to greater slip. The slip velocity and slip length can be used to describe the fluid slip. According to the Navier slip boundary model, the slip velocity and slip length are determined by fitting a straight line (linear fitting) to the velocity profile in the central portion of the channel. The results show that the slip velocity or the slip length is a quadratic function of the parameter ${a_{\rm wf}} $ , namely, the slip velocity or the slip length is a quadratic function of the contact angle. A physical mechanism of the fluid slip over hydrophobic surfaces is also proposed. The density profile is uniform for the no-slip condition, but there is a layer of low density fluid near the wall when the fluid can slip at the wall surface. This low density region can disrupt the momentum transfer between the wall and the fluid, which induces the fluid slip at the wall surface.

###### Original Articles

2019, 68 (10): 104205.
doi: 10.7498/aps.68.20190024

Abstract +

Unlike classical digital computers in which a bit can represent either 1 or 0 at any time, quantum computers use a two-level system, i.e., a qubit, to implement logical operations based on quantum mechanical laws, which can represent both values at once. Owing to the superposition property of qubits, quantum computers have natural parallel processing advantages and thus have potential to exceed the computational efficiency of classical computers for particular tasks. Quantum logic gates are the generalization of classical logic gates in computational networks. It has been proved that two-qubit quantum gates together with one-qubit quantum gates are adequate for constructing networks with any possible quantum computational property. Directional couplers are the most critical elementsfor constructing the quantum gates. In recent years, photonic quantum technologies have emerged as a promising experimental platform for quantum computing. Single photons have robust noise resistance, long coherence time, high transmission speed and great compatibility with other systems. They can be easily manipulated and encoded in any of several degrees of freedom, for example, polarization, path, spatial mode or time bin. Optical waveguide technology enables the realizing of complex optical schemes comprised of many elements with desired scalability, stability and miniaturization. Femtosecond laser direct writing of waveguide has been adopted as a powerful tool for integrated quantum photonics with characteristics of rapidness, cost-effectiveness, mask-less and single-step process. In particular, it has the ability to build arbitrary three-dimensional circuits directly inside bulk materials, which is impossible to achieve with conventional lithography. In this article we review the femtosecond laser writing and quantum characterization of directional coupler and important one-qubit and two-qubit optical quantum logic gates, such as Hadamard gate, Pauli-X gate, controlled-NOT gate, and controlled-Phase gate. The qubits in these gates are usually encoded through optical paths or polarizations of photons. The key to the realization of polarization-encoded one-qubit gates is to achieve flexible wave-plate operations, which is described in detail. Controlled-NOT gate and controlled-phase gate are the most crucial two-qubit gates in the linear optics computation and sometimes they can be converted into each other by adding some one-qubit gates or special superposition states. Many different kinds of waveguide circuits have been used to implement these two-qubit gates. The outlook and challenges for the femtosecond laser writing of three-qubit gates, such as Toffoli gate and Fredkin gate, are briefly introduced.

###### INVITED REVIEW

2019, 68 (10): 104210.
doi: 10.7498/aps.68.20190011

Abstract +

Silicon photonic switch is recognized as a cost-effective optical switching technology because it has many applications in long-haul telecommunication networks, short-reach data center and high-performance computing. In this paper, the research progress of various silicon photonic switch technologies is reviewed systematically. Firstly, the principles of three kinds of switch technologies including Mach-Zehnder interferometer (thermo-optic and carrier-injection types), micro-ring resonator (thermo-optic and carrier-injection types) and micro-electro-mechanical-system actuated waveguide coupler (electrostatic actuated type) are introduced. The switch technologies with the state-of-the-art insertion loss, crosstalk, switch time, footprint and power consumption are summarized and compared. Then the recent demonstrations of large-port silicon photonic matrix based on the above switch technologies are discussed. In this paper, we also investigate the key technologies such as topological architecture, passive components and optoelectronic packaging, which affect the performance of large-port optical switch matrix. Specifically, we study the scalability of various topologies, low-loss/broadband waveguide components, high-density optical/electrical packaging and control interface to improve the overall performance of the silicon photonic switch matrix. Finally, we discuss the critical technical challenges that might hamper the commercialization of silicon photonic switches and envision their future.

###### PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

2019, 68 (10): 105201.
doi: 10.7498/aps.68.20181983

Abstract +

The radial electric field Er in a magnetic confined machine, such as the compact fusion reactor (CFR), the field-reserved configuration (FRC), and the tokamak, plays an essential role in affecting the confinement properties of the high energy particles. The parallel velocities of the high energy particles will be accelerated or decelerated by applying a radial electric field, which could change the loss rate of the high energy particles in the magnetic confined machines. Unlike the fourth-order Runge-Kutta method RK4, the recently-developed Boris method can strictly preserve energy conservation of the high energy particles in the case without radial electric field. The orbit of high energy α particle in compact fusion reactor (CFR) is simulated by solving the equations of motion numerically with the Boris Algorithm. The effect of radial electric field on the orbit of the high energy α particle is investigated and the confinement of plasma in different radial electric fields in the CFR machine is studied in the present paper. By changing the strength of the radical electric field and the particles' radical locations in the middle plane of the CFR configuration, the confinement property of the high energy α particle is studied. The numerical results indicate that both the positive radial electric field and negative electric field can significantly affect the confinement of the high energy α particle. When the radial electric field is increased to a threshold, the high energy α particle could be confined in the central region of the CFR machine for a long enough time. The threshold of the radial electric field depends on the initial parameters of the confined particle. Systematic investigations of the radical electronic field effect will conduce to greatly improving the performance of the designed CFR machines.

2019, 68 (10): 105202.
doi: 10.7498/aps.68.20190071

Abstract +

Inductively coupled plasmais widely used in semiconductor and display process because of its desirable characteristics such as high plasma density, simple structure and independently controllable ion energy. The driving frequency is a significant parameter that generates and maintains the plasma. However, the effects of different driving frequencies on the radial distribution of the plasma parameters are hardly investigated. So a large area cylindrical inductively coupled plasma source driven separately by 2 MHz and 13.56 MHz is investigated. In order to perform a comprehensive investigation about the effect of driving frequency, the radially resolved measurements of electron density, electron temperature and density of metastable state atoms for the argon discharge are systematically analyzed by Langmuir double probe and optical emission spectroscopy at various power values and gas pressures. It is found that input power values at high frequency (13.56 MHz) and low frequency (2 MHz) have different effects on plasma parameters. When discharge is driven at high frequency, the electron density increases obviously with the increase of power. However, when discharge is driven at low frequency, the electron temperature increases evidently with the increase of power. This can be explained by calculating the skin depths in high and low frequency discharge. When the discharge is driven at high frequency, the induced electromagnetic field is higher than that at low frequency, and the single electron obtains more energy. It is easier to ionize, so the energy is mainly used to increase the electron density. When the discharge is driven at low frequency, the skin layer is thicker, the number of heated electrons is larger, and the average energy of electrons is increased, so the energy is mainly used to raise the electron temperature. At a gas pressure of 10 Pa, the electron density shows a ‘convex’ distribution and increases with the increase of input power for both the high-frequency and low-frequency discharge. While the distributions of electron temperature are obviously different. When the discharge is driven at high frequency, the electron temperature is relatively flat in the center of the chamber and slightly increases on the edge. When the discharge is driven at low frequency, the electron temperature gradually decreases along the radial position. This is due to the one-step ionization in the high-frequency discharge and the two-step ionization in the low-frequency discharge. In order to prove that the low-frequency discharge is dominated by two-step ionization, the spectral intensities of the argon plasma under the same discharge conditions are diagnosed by optical emission spectroscopy. The number density of metastable states is calculated by the branch ratio method. The results are consistent with the analyses. At a gas pressure of 100 Pa, the electron density increases and then decreases with the increase of radial distance, and the overall distribution shows a " saddle shape” for high frequency and also for low frequency discharge. Although the uniformity of electron density improves with the gas pressure, the uniformity at low frequency is better than that at high frequency. The reason can be attributed to the fact that the skin layer of low frequency is thicker and the heating area is wider.

2019, 68 (10): 105203.
doi: 10.7498/aps.68.20190218

Abstract +

Coaxial gun can produce high-speed and high-density plasma jet and has some potential applications in many research areas such as space thruster, space debris impact simulation, nuclear fusion, and material processing. The coaxial gun is usually composed of a pair of coaxial cylindrical and hollow electrodes. The pulsed discharge of coaxial gun has two discharge modes, i.e., deflagration mode and pre-fill mode. Compared with the pre-fill mode, deflagration discharge mode can induce a plasma jet with few impurities, high collimation, and fast speed. In this paper, the effect of gas injection mass and discharge voltage on the discharge characteristic of deflagration mode are studied with electrical and optical diagnosis including the emission spectrum, plasma velocity and discharge current measurements. The experimental results show that when the gas injection mass is relatively low, such as 1.4 mg, many plasma clusters eject from the muzzle. As the gas flowing into the coaxial gun bottom increases, the plasma density increases and the jet velocity decreases. Eventually, when the gas injection mass increases to 2.6 mg, one cluster of plasma is found and ejects from the muzzle of the gun. In the discharge process, as a small quantity of gas flows into the bottom of the coaxial gun through the electromagnetic valve continuously, new current paths will be generated at the bottom of the coaxial gun and move forward. This results in the observation of multiple plasma jet at the exit of the coaxial gun. It is noted that the plasma densities are different for different gas mass flowing into coaxial gun bottom, but the currents have little effect in the first discharge half cycle due to the small plasma inductance in discharge circuit. Meanwhile, the plasma characteristics under different voltages with the fixed gas mass of 2.6 mg flowing into the coaxial gun bottom are experimentally measured. The results show that the plasma density and speed increase with voltage increasing, which is attributed to the stronger discharge current and larger self-induced Lorentz force. More neutral particles can be ionized into plasma with discharge voltage increasing, and the transport speed becomes faster under the enhanced force. In addition, the multiple ionization phenomena are observed again when the discharge voltage increases from 5 kV to 8 kV. This study provides an insight into how to better apply the coaxial gun discharge plasma to practical engineering field. The article further verifies the phenomenon of multiple discharges at the bottom of the coaxial gun by changing the charging capacitance and analyzing the magnetic probe signals.

###### CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

2019, 68 (10): 106101.
doi: 10.7498/aps.68.20190118

Abstract +

The inverse spin Hall effect (ISHE), namely spin flows converted into charge currents due to spin orbital interaction, is investigated extensively in heavy metals, such as Pt, W, Au, etc. Recently, the effect was also found in Cu doped with Au. Their difference is that the spin Hall effect is from the intrinsic effect which is related to the topological character of the electronic bands, while the ISHE is mainly from the extrinsic spin dependent scattering by the impurities. The impurity scattering can give opportunities to tune the effect, for example by impurity concentration, which is impossible by the intrinsic mechanism. In this work, we extend the material to the doped oxides. NiFe films are deposited on undoped and doped SrTiO

_{3}substrates by magnetron sputtering, respectively. The spins are injected from the magnetic thin films by spin pumping through using a shorted microstrip transmission line fixture at different frequencies and room temperature. The spin rectification voltage and the inverse spin Hall voltage in the doped sample are separated by the inverting spin injection direction method, which is realized by flipping the samples. The results show that in the undoped SrTiO_{3}substrate, the voltage curves before and after flipping the sample are basically the same, which is due to the voltage generated by the spin rectification effect of the NiFe film. For Nb-doped SrTiO_{3}substrates with Nb concentration*x*= 0.028, 0.05, 0.1, 0.15 and 0.2, the inverse spin Hall voltage decreases with doping concentration increasing and is not detectable in sample with doping concentration of 0.15, nor with doping concentration of 0.2. The decrease of the ISHE effect may be due to the spin coherent length decreasing with the increase of the impurity concentration. The correlation between spin-charge conversion and transportation needs knowing in detail. Nevertheless, the results show that by doping strong spin-orbit coupling impurities into SrTiO_{3}, thus by changing the doping concentration, the inverse spin Hall effect in SrTiO_{3}can be controlled. This tunable spin-charge conversion provides more possibilities for developing the spintronic devices and it will have great potential applications in the future.
2019, 68 (10): 106102.
doi: 10.7498/aps.68.20182255

Abstract +

Exploring new type of optoelectronic materials has fundamental scientific and practical significance in the development of society and economy. Recently, intense research has focused on the use of the wide band-gap bipolarity semiconductor material CuInO

_{2}which will allow to the fabrication of that total transparent optoelectronic materials. However, the conductivity of CuInO_{2}is significantly lower than other n-type conductivity of other TCOs. As a result, one of the key question is how to improve the electric properties of CuInO_{2}by doping method. Motivated by this observation, in this paper, using the first-principles methods, the formation energetics properties of dopant (Be, Mg, Mn) in transparent conducting oxides CuInO_{2}were studied within the local-density approximation. Substituting dopant (Be, Mg, Mn) for In, substituting dopant (Be, Mg, Mn) for Cu and dopant as interstitial in their relevant charge state are considered. By systematically calculating formation energies and transition energy level of defect, the calculated results show that, substituting Mg for In does not induce the large structural relaxation. in CuInO_{2}. One can expect that substituting the Mg and Mn for In introduces acceptor because the relative lower formation energies, furthermore, Be atoms would be substitute for In atoms when the*E*_{f}move to CBM. In addition, the donor-type extrinsic defects(such as substituting dopant for Cu and dopant as interstitial) have difficulty in inducing n-conductivity in CuInO_{2}because of their deep transition energy level or the higher formation energies. Considering the transition energy level position, Be_{In}, Mg_{In}, and Mn_{In}have transition energy levels at 0.06, 0.05, and 0.40 eV above the VBM, respectively. Thus, for all the acceptor-type extrinsic defects, substituting Mg for In is the most prominent doping acceptor with relative shallow transition energy levels in CuInO_{2}under O-rich condition. Based on our calculated results and discussion mentioned above, in order to increase p-type conductivity in CuInO_{2}, we could substitute Mg atoms for In atoms by the sit-selective doping method through atomic layer epitaxy growth or controlling the oxygen partial pressure in the molecular beam epitaxy or metal-organic chemical vapor deposition crystal growth process. The calculation results will not only provide the guide for design of new type In-based optoelectronic materials, but will also further understand the potential properties in CuInO_{2}.
2019, 68 (10): 106201.
doi: 10.7498/aps.68.20190075

Abstract +

The thermodynamic properties of insensitive high explosive 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) based polymer bonded explosives (PBXs) are investigated by using first principle calculation and molecular dynamics simulation. The results include the phonon dispersion relations, interface thermal conductances, and thermal conductivities of TATB based PBXs. Both TATB and PVDF structures are optimized, in which the optimized lattice constants accord with previous results. The phonon dispersion relation of TATB and PVDF are calculated based on lattice dynamics. All interatomic force constants are calculated by the finite displacement method (numerical derivatives from perturbed supercells). The calculated phonon dispersion relation of TATB and heat capacity are in general agreement with experimental and theoretical results. The imaginary frequencies are observed in both TATB and PVDF dispersion relation. The imaginary frequencies are mainly due to the smaller calculated supercell size and temperature effect. The phonon mode of TATB and PVDF are assigned at Γ point. Based on the calculated phonon dispersion, some information including heat capacity, phonon density of states and phonon mode assignment is derived. The TATB possesses 144 phonon modes including 3 acoustic-phonon modes and 141 optical phonon modes. The anylized phonon mode of TATB shows that -NO

_{2}dominates the phonon DOS in low frequency zone, phenyl rings dominate in middle frequency zone and -NH_{2}dominates in high frequency zone. By analyzing the phonon density of states and capacity, both TATB and PVDF imply that low-frequency vibration dominates the thermal conductivity. The thermal conductivity is determined for TATB by using the equlibrium molecular dynamics method and an established TATB force field. The TATB model is built with 2880 atoms. The structure of TATB is optimized by using molecular mechanics, then this system is relaxed by using a Nose-Hoover thermostat and barostat with a damping factor of 50 fs cin time steps of 0.1 fs. The calcultated thermal conductivity at room temperature shows good agreement with experimental result. The interface thermal conductance of TATB-PVDF is calculated by using a diffusive mismatch model. The interface thermal transport still follows Fourier’s law of heat conduction, and ballistic thermal transport mechanism is not involved. By using the above results, the thermal conductivity of mixture TATB-PVDF system is analized with a simple series model. The particle size smaller than 100 nm significantly suppresses the mixture system thermal conductivity.## COVER ARTICLE

2019, 68 (10): 106401.
doi: 10.7498/aps.68.20190304

Abstract +

The nature of crystallization is considered to be one of the most fundamental research problems in condensed matter physics. With single particle resolution offered by video microscopy, colloidal suspensions provide a novel model system for studying crystallization, melting and other phase transitions, where the structures and dynamics of the particles during the transitions can be quantitatively probed. Traditional systems for studying the crystallization typically focus on the infinitely large systems in order to obtain the equilibrium state. However, studies of the crystallization in finite-sized systems such as crystallization in thin films and porous media, are rare despite the fact that they are the common phenomena in natural world. In this paper, we experimentally investigate the crystallization in a finite-sized colloidal system with attractive interactions. The colloidal suspension is composed of polystyrene microspheres dispersed in a mixture of water and 2, 6-lutidine, in which the interaction between the particles can be tuned by adjusting the temperature. We increase the temperature to 34 °C to induce attractions between the particles and thus producing a cluster, and then reduce the temperature to 33 °C to tune off the attractions. Thus we obtain a finite-sized liquid cluster of the colloidal particles. Crystallization is triggered by increasing the temperature to 34 °C. The crystallization process is recorded by video microscopy and the video data are analyzed by a standard particle tracking algorithm. Through the analysis of radial distribution function, Voronoi diagram, and local order parameter, we find that the crystallization of the finite colloidal system starts from the central dense region of the liquid cluster. This leads to a crystalline phase in the center and a liquid phase on the edge of the cluster. As time elapses, the central crystalline region grows while outer liquid region shrinks. The crystallization process exhibits a two-step scenario: a fast crystallization initially and a slow crystallization at the later stage. At the initial stage, the center of the system forms a dense metastable liquid phase, which lowers the free-energy barrier of crystallization and results in a fast crystallization. As the crystalline region grows, the metastable phase disappears, and thus the crystallization rate decreases. Moreover, a bimodal distribution of the orientational order parameter is observed during the crystallization in our finite-sized colloidal system, which is consistent with that in a large system. This indicates that the bimodal distribution is a common feature of the two-dimensional crystallization.

###### CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES

2019, 68 (10): 107201.
doi: 10.7498/aps.68.20190136

Abstract +

Vanadium dioxide (VO

_{2}) is a typical representative of strongly correlated electronic systems, which undergoes a reversible transition from the insulator phase to metal phase, induced by a certain threshold for each of temperature, electric field, illumination and pressure. The crystal structure of VO_{2}will undergo a reversible transition from monoclinic structure to tetragonal rutile structure when the phase transition happens, which is considered as the microscopic mechanism of VO_{2}metal-insulator transition (MIT). The conductivity of VO_{2}can be increased by 2—5 orders of magnitude when the MIT is induced by electric field, which makes VO_{2}possess good application prospects in the fields of restructurable slot antenna, terahertz radiation, intelligent electromagnetic protection materials, etc. Therefore, the reversible metal-insulator phase transition in VO_{2}, induced by electric field, has long been a research hotspot, which however, has been seldom reported. Firstly, in this paper, the changes of the crystal structure and energy band structure of VO_{2}during MIT are introduced briefly. The methods of regulating the phase transition are given, including temperature control, bandwidth and band-filling control. Then, the important discovery and research progress of VO_{2}MIT induced by electric field based on the research method, response time, critical threshold field and phase transition mechanism are summarized and reviewed comprehensively. The method of studying the VO_{2}phase transition relates to its structure, including planar structure, three-terminal gated ?eld effect switch and sandwiched layer structure. The sandwich layer structure is more suitable for investigating the MIT characteristics of VO_{2}in experimental stage because of its structural advantage of preparation and test. The response time of VO_{2}MIT can be completed in nanoseconds, of which the substantial parameter has been revealed by many reports, also including the excellent reversibility of VO_{2}MIT. The MIT critical threshold field of the VO_{2}film can be tuned by element doping, coexistence of multivalent vanadium oxides and multiple physical field synergism effectively. The MIT mechanism of VO_{2}induced by electric field has been proposed so far, which includes joule heating mechanism and pure electric field mechanism, and the latter is considered to be more likely to give a reasonable explanation. Finally, in the paper the current problems of the VO_{2}MIT research and the near-future development direction of the VO_{2}MIT materials are also pointed out.
2019, 68 (10): 107301.
doi: 10.7498/aps.68.20190062

Abstract +

During the past few decades, surface plasmons (SPs) have become a research hotspot. The SPs are the collective oscillations of free electrons at the interface between metal and dielectric surrounding. Localized surface plasmon resonance (LSPR) for metal nanoparticles (NPs) has a wide application in the light emission enhancement by the selective photon absorption and by increasing local electromagnetic field. Nowadays, many achievements of SP-enhanced-emissions are applied to light emitting diodes. With the advantages of the direct wide band gap (3.37 eV) and large exciton binding energy (60 meV), zinc oxide (ZnO), which is considered as a potential material, has a wide range of applications, especially in ultraviolet (UV) optoelectronic devices. However, the low photoluminescence efficiency of ZnO limits the commercial applications of ZnO-devices. The relevant research shows that the selection of different metal NPs, such as platinum (Pt), aluminum (Al), argentum (Ag), aurum (Au), is one of the approaches to improving the UV emission from ZnO. In this study, two-dimensional arrays of Al NPs are used to improve the LSPR photoluminescence efficiency from ZnO grown by the atomic layer deposition (ALD). The two-dimensional arrays of Al NPs are fabricated on the surfaces of p-type Gallium nitride (GaN) substrates by colloid lithography. With the air-liquid interface self-assembly, the monolayer masks for colloid lithography are obtained on the substrates of p-type GaN. Then, after a 50-nm Al layer is deposited by thermal evaporation, the Al NPs’ arrays are gained by being dipped into toluene and extra sonication to remove the masks. Finally, 15 nm Al

_{2}O_{3}and 200 nm ZnO films are deposited in sequence by ALD at a temperature of 125 ℃. The extinction spectra of Al NPs’ arrays are acquired by an ultraviolet-visible spectrophotometer. The results of the extinction spectra suggest that the radiative recombination rate is increased by the resonance coupling between the localized surface plasmons (LSP) of the Al NPs arrays and the excitons of the ZnO. A 1.91-fold enhancement of photoluminescence integral intensity in band-edge emission is measured because of the Al NP arrays coupled with ZnO. The result means that the LSP of the Al NPs’ arrays can increase the UV-emission of the ZnO. Therefore, this cost-effective and facile approach can be used in high-performance optoelectronic devices.
2019, 68 (10): 107302.
doi: 10.7498/aps.68.20181985

Abstract +

A metal-dielectric-metal (MDM) waveguide coupling two square cavities with double baffles is designed in this paper based on the transmission characteristics of surface plasmon polaritons in subwavelength structure. The independent tuning of the dual Fano resonance is implemented by the interference between the wide-spectrum mode generated by the F-P (Fabry Perot) cavity and the two narrow-spectrum modes generated by the two square cavities. Moreover, the independent tuning of the dual Fano resonance can be achieved by changing the sizes of the two square cavities and filling medium. The coupled-mode theory (CMT) is adopted to analyze the transmission characteristics of the dual Fano resonance. The structure is simulated by the finite element method to quantitatively analyze the influence of structural parameters on the independent tuning of the dual Fano resonance and the refractive index sensing characteristics. The proposed sensor yields respectively sensitivity higher than 1020 nm/RIU and 1120 nm/RIU and a figure of merit of 3.29 × 10

^{5}and 1.17 × 10^{6}by optimizing the geometry parameters. This structure provides an effective theoretical reference in the optical integration of ultra-fast optical switches, multi-function high-sensitivity sensors and slow-light devices.
2019, 68 (10): 107501.
doi: 10.7498/aps.68.20190019

Abstract +

The epitaxial thin films of Ge

_{0.96−x}Bi_{x}Fe_{0.04}Te are deposited on BaF_{2}substrates by using pulsed laser deposition technique. The thin films with three different compositions i.e. Ge_{0.8}Bi_{0.2}Te, Ge_{0.76}Bi_{0.2}Fe_{0.04}Te, and Ge_{0.64}Bi_{0.32}Fe_{0.04}Te are prepared in this wok. Their high-quality epitaxy and crystallinity are confirmed by X-ray diffraction and atomic force microscopy. According to the measurements of Hall effect variation, we find that each of all curves exhibits a negative slope for the different films as the temperature varies from low temperature to room temperature, indicating that Ge_{0.96−x}Bi_{x}Fe_{0.04}Te films are n-type material because the substitution of Bi for Ge makes the carriers change from holes into electrons. Temperature dependence of resistivity confirms that the electronic transport behavior for each of Ge_{0.96−x}Bi_{x}Fe_{0.04}Te thin films exhibits a typical semiconductor characteristic. From the measurements of temperature dependence of electronic transport under various external magnetic fields, we find that the Ge_{0.64}Bi_{0.32}Fe_{0.04}Te thin film shows some magnetoresistive effect while other composition films do not possess such a property. Based on the linear fitting of temperature dependence of magnetic susceptibility in high temperature and low temperature region, the magnetic property of Ge_{0.64}Bi_{0.32}Fe_{0.04}Te thin film changes from 253 K. Together with the study of magnetic susceptibility curve in the paramagnetic region, the Curie-Weiss temperature is determined to be 102 K. At a low temperature of 10.0 K, we observe an obvious ferromagnetic hystersis loop in Ge_{0.64}Bi_{0.32}Fe_{0.04}Te instead of in Ge_{0.76}Bi_{0.2}Fe_{0.04}Te thin film. These results imply that the increase of Bi dopant is main reason for the establishment of ferromagnetic ordering state. The carrier concentration increases and thus promotes the carriers transporting the Ruderman-Kittel-Kasuya-Yoshida interaction, thereby leading to the separated Fe ions producing the magnetic interaction and forming an n-type diluted magnetic semiconductor.
2019, 68 (10): 107502.
doi: 10.7498/aps.68.20182271

Abstract +

Magnetic nanorings can be high-density integrated because their stray field is low in vortex states. In this paper, the magnetic dynamic properties of the defective Fe nanorings are studied. For convenience, we assume the defect to be round in shape, whose coordinate is (0,

*Y*). Based on the Monte Carlo method and fast Fourier transformation micromagnetism method, the magnetic properties of the defective Fe nanorings, such as hysteresis loops, spin configurations, remanence, etc., are studied. The simulation results indicate that the magnetization process of the system can be affected by the sizes and locations of the defects. When the defects are small, the system has a bistable state, which is similar to the system without defects. The transition state of the system increases as the defects are enlarged, and the bistable state will be no longer so visible. The system becomes open when the defects are big enough. Meanwhile, its hysteresis loop presents a rectangular shape which is similar to cluster’s or quantum dot’s. The remanence increases with the radius of defect increasing. These results are in accord with the magnetic properties of asymmetric magnetic nanoring. In order to explain the above results, the spin configurations of the system are shown. The spins of defective nanorings are divided into two parts, i.e., upper half part and lower half part, which are represented as blue and black spins respectively. When the system does not have any defects, the number of blue spins is equal to black spins’. Therefore the remanence is zero when the system is in a vortex state. It is found that the number of blue spins decreases as the radius of defect increases. This situation results in the total magnetic moment increasing, which leads the remanence to increase. However, the relationship between remanence and*Y*(the distance between center of nanoring and center of defect) is nonlinear. The remanence first increases and then decreases with*Y*increasing. The simulation results can be explained by changing the spin configuration. By analyzing the spins of the upper and lower part, the magnetic moment of the system is analyzed. It is found that the number of the spins and the local vortexes can affect the remanence significantly. The results show that the magnetic properties of Fe nanorings can be affected by the defect.
2019, 68 (10): 107801.
doi: 10.7498/aps.68.20190291

Abstract +

Multiexciton generation is a process where multiple excitons are generated by absorbing single photons. Efficient multiexciton generation in quantum dots may be a revolutionary discovery, because it provides a new method to improve the solar-to-electric power conversion efficiency in quantum dots-based solar cells and to design novel quantum dots-based multielectron or hole photocatalysts. However, the mechanism of ultrafast multiexciton generation and recombination remain unclear. In this paper, alloy-structured quantum dots, CdSeS, are prepared by the hot injection method. The generation and recombination mechanism of charge carriers in quantum dots samples are discussed in detail. The bivalent band structure of alloy-structured quantum dots is determined by ultraviolet-visible absorption spectra. It is found that the 1S

_{3/2}(h)-1S(e) (or 1S), 2S_{3/2}(h)-1S(e) (or 2S) and 1P_{3/2}(h)-1P(e) (or 1P) exciton absorption bands of these quantum dots are at 510 nm, 468 nm and 430 nm, respectively. Femtosecond transient absorption spectroscopy and nanosecond time-resolved photoluminescence spectroscopy are used to investigate the ultrafast exciton generation and recombination dynamics in the alloy-structured quantum dots. By fitting the transient kinetics of 1S exciton bleach, an average biexciton decay time is obtained to be about 80 ps, which is almost twice the decay time of traditional quantum dots (less than 50 ps). Combined with the recently developed ultrafast interface charge separation technology that can extract multiple excitons before their annihilation, it will have a promising application prospect. Moreover, there is a hole relaxation on a the time scale of 5-6 ps via a phonon coupling pathway to lower-energy hole states in addition to the above-described ultrafast exciton-exciton annihilation process in 2S and 1P excitons. Furthermore, by nanosecond time-resolved photoluminescence spectroscopy, it can be concluded that the charge separated state is long-lived (200 ns). Our findings provide a valuable insight into the understanding of ultrafast multiexciton generation and recombination in quantum dots. These results are helpful to understand the intrinsic photo-physics of multiexciton generation in quantum dots, to implement the photovoltaic and optoelectronic applications, and to ascertain the exciton relaxation dynamics of quantum dots.###### INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

2019, 68 (10): 108201.
doi: 10.7498/aps.68.20182288

Abstract +

As a new energy storage device, supercapacitor (or electrochemical capacitor) has an ultra-long cycle life, extremely high power density and enhanced energy density. It fills the gap in the energy-power spectrum between traditional capacitor and battery. In general, the traditional energy storage and conversion device cannot have a perfect trade-off between high energy density and high power density. With the rapid development of modern society, developing light, portable, safe and environmentally friendly high-performance energy storage devices has become increasingly vital. Therefore, there are numerous researches of flexible solid supercapacitors emerging at this historic moment. The selection of flexible electrode materials and that of electrolytes are crucial factors in designing the flexible solid state supercapacitors, which have been the research hotspots in recent years. Carbon nanotube array has been widely used in electrode material of super capacitors due to its excellent electrical conductivity, large specific surface area and super high chemical stability. But in assembly process, carbon nanotube array easily collapses and breaks its neat orientation because of its poor mechanical strength. In consideration of environmental contamination and practical demands, in this paper the neutral gel electrolyte is adopted to embed carbon nanotube array to form flexible composite film electrode. Besides the fact that we use hydrophilic flexible carbon cloth as current collector and neutral gel electrolyte as separator to prepare flexible devices, we compare the electrochemical properties among different devices by changing the electrolyte salt added in gel electrolyte. Meanwhile, after continuous bending and folding, the properties of flexible devices have not been significantly damaged, indicating good flexibility and mechanical stability. The specific capacity of the whole device with PVA-NaCl used as gel electrolyte increases up to 104.5 mF·cm

^{–3}, which is much higher than the specific capacity of the composite device formed by organic ionic gels with carbon nanotube array and that of the composite device formed by commercial short carbon nanotubes with hydrogels. A maximum energy density of 0.034 mW·h·cm^{–3}is obtained at the same time. In addition, it has good rate performance, cycling stability, suppressing self-discharge property, and good chemical stability at a high voltage of 1.6 V. Neutral gel/carbon nanotube array composite devices not only meet the needs of the era of green safety, flexible and portable folding, but also open up the future application prospects of medical implants.
2019, 68 (10): 108501.
doi: 10.7498/aps.68.20190265

Abstract +

There is a risk of InGaZnO thin film transistor (IGZO TFT) failure, especially electro-static discharge (ESD) damage of gate driver on array (GOA) circuits, due to the combination of Cu interconnect, InGaZnO (IGZO) active layer and SiN

*/SiO*_{x}_{2}insulating layer used to realize large-scale ultra-high resolution display. It is found that the IGZO TFT damage position caused by ESD occurs between the source/drain metal layer and the gate insulator. The Cu metal of gate electrode diffuses into the gate insulator of SiN_{x}/SiO_{2}. The closer to the ESD damage area the IGZO TFT is, the more serious the negative bias of its threshold voltage (*V*_{th}) is until the device is fully turned on. The IGZO TFT with a large channel width-to-length ratio(*W*/*L*) in GOA circuit results in a serious negative bias of threshold voltage. In this paper, the ESD failure problem of GOA circuit in the IGZO TFT backplane is systematically analyzed by combining the ESD device level analysis with the system level analysis, which combines IGZO TFT device technology, difference in metal density between GOA region and active area on backplane, non-uniform thickness distribution of gate metal layer and gate insulator and so on. In the analysis of ESD device level, we propose that the diffusion of Cu metal from gate electrode into SiN_{x}/SiO_{2}leads to the decrease of effective gate insulator layer, and that the built-in space charge effect leads to the decrease of the anti-ESD damage ability of IGZO TFT. In the analysis of ESD system level, we propose that the density of metal layers in GOA region is 4.5 times higher than that in active area of display panel, which makes the flatness of metal layer in GOA region worse. The non-uniformity of thickness of Cu metal film, SiN*film and SiO*_{x}_{2}film around glass substrate lead to the position dependence of the anti-ESD damage ability of IGZO TFT in the GOA region. If there is a transition zone of film thickness change in IGZO TFT with large area, the ESD failure will occur easily. Accordingly, we propose to split large area IGZO TFT into several sub-TFT structures, which can effectively improve the ESD failure.
2019, 68 (10): 108701.
doi: 10.7498/aps.68.20182147

Abstract +

Terahertz vortex beam generators have potential applications in optical micro-manipulation, terahertz communications and many other fields. A broadband vortex beam generator in a terahertz frequency range is proposed based on the metasurface of double-split resonant rings’ array. The designed structure consists of two layers, i.e., the top layer, which is a metasurface of double-split resonant rings, and the bottom layer, which is the dielectric layer of polymide. The numerical simulation of the cell structure array is performed by using the CST microwave studio. In order to obtain the best performance, the structure parameters of metasurface are continuously optimized and a set of optimal geometric parameters is finally determined. The simulation results show that the circularly polarized incident light can be converted into corresponding cross-polarized transmitted light. By rotating the metal resonant ring on the top layer, the cross-polarized transmitted light can be controlled to have the same amplitude and correspondingly different phases. The relationship between the phase change and the angle of rotation conforms to the P-B phase principle. These cell structures are arranged according to a specific order and can form the vortex phase plates for generating the vortex beams with different topological charges. Taking the topological charge numbers 1 and 2 for example, two kinds of vortex phase plates are designed. The characteristics of the circularly cross-polarized vortex beams generated by a circularly polarized wave perpendicularly incident on the vortex phase plates are numerically analyzed. The results show that the ideal vortex beams with different topological charge numbers are generated. The characteristics of vortex beams appear to be consistent with those theoretical results. Moreover, the vortex beams can be generated in a frequency range from 1.39 THz to 1.91 THz. The operating bandwidth is much wider than the previously obtained result of the transmission terahertz vortex phase plates. The transmission is higher than 20%, and the maximum value of transmission can reach 24%, which is close to the theoretical limit value of the single-layered transmission-type metasurface. This work provides a reference for generating the terahertz vortex beams based on metasurface. It is expected to possess a practical application in generating the device of terahertz vortex beam.

###### GEOPHYSICS, ASTRONOMY, AND ASTROPHYSICS

2019, 68 (10): 109401.
doi: 10.7498/aps.68.20182281

Abstract +

There occur frequently the ionospheric scintillation events at low and middle latitudes, which seriously affect the radio transmission process of satellite link, resulting in the decline of satellite communication and navigation signal quality and even interrupt. During the gestation period before the ionospheric scintillation, the growth rate of plasma instability can be reduced and thus suppress the scintillation events by releasing the electron density-enhancing chemicals in the ionosphere plasma bubble, filling with plasma bubble, changing the plasma environmental characteristics, and regulating the ionospheric dynamics process. The theory and method of suppressing the ionospheric scintillation based on chemical release are tnvestigated. According to the change of the plasma environment caused by the chemical release, and the quantitatively calculating of the contribution of control factors to the growth rate of instability, an ionospheric scintillation suppression model is built, which is based on chemical release into ionosphere. The process of plasma bubble filling out is simulated and the results of the simulation show that the plasma cloud is completely filled with plasma bubbles after 1200 seconds, which reduces the plasma density gradient and suppresses the growth of plasma instability. The growth of plasma instability decreases from 0.2 before releasing to about 0.0004 after releasing, and no new instability is excited within 20 minutes after the plasma bubble has been filled up. Guangdong, South China Sea and other regions in China are at the peak of equatorial anomalies, and the occurrence rate and severity of scintillation are more significant than those in the equatorial and Polar Regions, thus these regions become the regions where there occur most frequently the scintillation and the most serious influence globally. The research work of this paper will lay a solid theoretical foundation for the technology of suppressing the satellite signal ionospheric scintillation in middle and low latitude area of China.

## EDITOR'S SUGGESTION

2019, 68 (10): 109501.
doi: 10.7498/aps.68.20190217

Abstract +

The frequency comb which is characterized by equally-spaced frequency lines with high mode coherence has received much attention since its first demonstration in near-infrared and optical frequency range. In the terahertz frequency range, the electrically-pumped terahertz quantum cascade laser (THz QCL) based on semiconductors is an ideal candidate for achieving frequency comb operation in a frequency range between 1 THz and 5 THz. The group velocity dispersion (GVD) is a key factor for the frequency comb. A higher GVD can pull the frequencies from their equidistant values and limit the comb bandwidth. Therefore the laser dispersion needs to be compensated for in order to make the total GVD sufficiently low and flat, such as using a Gires-Tournois interferometer (GTI) or the double chirped mirror (DCM). However, a successful design still depends on the knowledge of the total GVD in the laser. In this paper, we show how to calculate the GVD in metal-metal waveguide THz QCLs by taking into account the dispersions from the GaAs material, the waveguide, and the laser gain, which conduces to the understanding of the frequency comb behavior. The waveguide loss is modelled by the finite element method. The loss due to intersubband absorption is calculated by Fermi's gold rule. All the losses, i.e., waveguide loss, mirror loss, and intersubband absorption loss, are summed up to calculate the clamped gain. The material loss can be calculated by using the reststrahlen band model. Because of these losses and gain, the refractive index needs to be replaced by a complex refractive index. The real part of the complex refractive index is the refractive index, which can be calculated from the Kramers-Kronig relationship that connects the loss or gain with the refractive index. Then the GVD introduced by the material loss, waveguide loss, and clamped gain can be finally calculated. The results show that the total GVD of THz QCL is approximately –8 × 10

^{5}~8 × 10^{5}fs^{2}/mm which is strongly determined by the clamped gain. Finally, the developed numerical model is employed to study the dispersion compensation effect of a GTI mirror which is coupled into a QCL gain cavity. The design of the THz QCL based on GTI structure is more flexible and feasible than that of the DCM. The result shows that by carefully designing the geometry of GTI, the dispersion of a THz QCL can be compensated for, thus achieving the broadband terahertz frequency combs.