## Vol. 66, No. 4 (2017)

##### 2017-02-20

###### GENERAL

2017, 66 (4): 040201.
doi: 10.7498/aps.66.040201

Abstract +

As is well known, the development of analysis mechanics from Lagrangian systems to Birkhoffian systems, achieved the self-adjointness representations of the constrained mechanical systems. Based on the Cauchy-Kovalevsky theorem of the integrability conditions for partial differential equations and the converse of the Poincar lemma, it can be proved that there exists a direct universality of Birkhoff's equations for local Newtonian system by reducing Newton's equations into a first-order form, which means that all local, analytic, regular, finite-dimensional, unconstrained or holonomic, conservative or non-conservative forms always admit, in a star-shaped neighborhood of a regular point of their variables, a representation in terms of first-order Birkhoff's equations in the coordinate and time variables of the experiment. The systems whose equations of motion are represented by the first-order Birkhoff's equations on a symplectic or a contact manifold spanned by the physical variables, are called Birkhoffian systems. The theory and method of Birkhoffian dynamics are used in hadron physics, quantum physics, relativity, rotational relativity, and fractional-order dynamics.
At present, for a given dynamical system, it is important and essential to determine whether a Birkhoffian function is the first integral of the system. Although the numerical approximation is an important method of solving the differential equations, the direct theoretical analysis is more helpful for refining the general integral method, and more consistent with the usual way of solving problems of analysis mechanics. In this paper, we study how to judge whether a given Birkhoffian dynamical function to be a first integral of Birkhoff's equations, based on the point of Birkhoffian dynamical functions carrying all the informationabout motion of the system, and use the thought of deriving the first integrals of Hamiltonian systems. In Section 2, the normal first-order form and the Birkhoff's equations of the equations of motion of holonomic systems are introduced. In Section 3, we prove that the Birkhoffian function of an autonomous Birkhoffian system must be a first integral, and the Birkhoffian function of a semi-autonomous system must not be a first integral. Moreover, the energy integral, cyclic integral and Hojman integral of the non-autonomous Birkhoffian systems are given. In Section 4, two examples are given to illustrate the applications of the results. In Section 5, the full text is summarized and the results are discussed. It is necessary to point out that the judging method is effective to determine whether a given Birkhoffian functions can be identified to be a first integral of Birkhoff's equations, but other new first integral cannot be found with this method. One possible method of covering the shortage is to obtain other equivalent Birkhoffian functions in terms of isotopic transformations of Birkhoff's equations, and then use our results to seek the new first integral. In addition, we also hope to develop a more direct method of obtaining the first integrals of Birkhoff's equations in the next study.

2017, 66 (4): 040202.
doi: 10.7498/aps.66.040202

Abstract +

The spall behavior of copper at ultra-high strain rate is studied by molecular dynamics simulation combined with an experimental analysis of laser ablation of a bulk copper target by femtosecond laser pulses. In the molecular dynamics simulation, two-temperature model is used, shock wave and spallation characteristics of copper shock-loaded by femtosecond laser are analyzed in detail. It is concluded that the evolution of pressure indicates a triangular waveform of the shock wave, and the spall strength of copper is about 19 GPa at strain rates ranging from 109 s-1 to 1010 s-1, while higher pressure would melt the sample and the spall strength decreases to 14.89 GPa. Normally, the spallation is characterized by the sample free-surface undergoing alternately acceleration and deceleration, and the spallation mechanism could be explained by void nucleation, growth, coalescence that leads to the final fracture. An experiment is conducted to achieve high strain rate load on copper. The driving laser has a pulse width of 25 fs and central wavelength of 800 nm, the thickness values of the shocked copper foils are (5025) nm, fabricated by electron beam sputtering deposition onto 180 upm cover slip substrates. The driving laser beam with maximum intensity 5.51013 W/cm2, is focused on the front surface of the copper through the transparent substrate. Movements of the free rear surfaces of the copper foils are detected by chirped pulse spectral interferometry, and the theoretical time resolution is 1.3 ps. As a result, the free surface displacement and velocity evolution profile of the shocked area are obtained in a single measurement, and the results directly show that the maximum free surface velocity is 0.43 km/s and no alternately acceleration and deceleration appears. According to the shock wave relations, the maximum pressure near free-surface is 8.18 GPa. Meanwhile, derived from the velocity evolution profile, the strain rate is 7.3109 s-1. Combining with the above molecular dynamics simulation results, it is concluded that there is no spallation in the copper foil. Furthermore, we recover the sample targets and observe the microstructures by using scanning electron microscope. The copper foils are peeled off, but no spall scab is observed, indicating that the internal stress is between the copper spall strength and the bonding strength of copper foil with the transparent substrate. Ripple structure on copper surface demonstrates the femtosecond pulsed laser has ablated the copper film, and the propagation of the shock in fs regime is sensitive to microscopic defects.

2017, 66 (4): 040501.
doi: 10.7498/aps.66.040501

Abstract +

Various stochastic volatility models have been designed to model the variance of the asset price. Among these various models, the Heston model, as one-factor stochastic volatility mode, is the most popular and easiest to implement. Unfortunately, recent findings indicate that existing Heston modelis not able to characterize all aspects of asset returns, such as persistence, mean reverting, and clustering. Therefore, a modified Heston model is proposed in this paper. Compared with the original Heston model, the mean-reverting Cox Ingersoll and Ross process is modified to include a cosine term with the intention of capturing the periodicity of volatility. The phenomenon that high-volatile period is interchanged with low-volatile periods can thus be better described by adding such a period term to the volatility process. In addition, the geometric Brownian motion is replaced by a random walk in the presence of a cubic nonlinearity proposed by Bonanno et al. By doing so, a financial market with two different dynamical regimes (normal activity and extreme days) can be modeled. Closed-form solution for the modified Heston model is not derived in this paper. Instead, Monte-Carlo simulation is used to generate the probability density function of log-return which is then compared with the historical probability density function of stock return. Parameters are adjusted and estimated so that the square errors can be minimized. Daily returns of all the component stocks of Dow-Jones industrial index for the period from 3 September 2007 to 31 December 2008 are used to test the proposed model, and the experimental results demonstrate that the proposed model works very well. The mean escape time and mean periodic escape rate of the proposed modified Heston model with periodic stochastic volatility are studied in this paper with two different dynamical regimes like financial markets in normal activity and extreme days. Also the theoretical results of mean escape time and mean periodic escape rate can be calculated by numerical simulation. The experimental results demonstrate that 1) larger value of rate of return, smaller long run average of variance and smaller magnitude of periodic volatility will reduce the mean periodic escape rate, and thus stabilize the market; 2) by analyzing the mean escape time, an optimal value can be identified for the magnitude of periodic volatility which will maximize the mean escape time and again stabilize the market. In addition, an optimal rate of relaxation to long-time variance, smaller frequency of the periodic volatility, larger rate of return, and stronger correlation between noises will furtherreduce the mean escape time and enhance the market stability.

2017, 66 (4): 040503.
doi: 10.7498/aps.66.040503

Abstract +

Blind signal reconstruction in sensor arrays is usually a highly nonlinear and non-Gaussian problem, and nonlinear filtering is an effective way to realize state estimation from available observations. Developing the processing problem of blind signal in wireless sensor networks (WSNs) will greatly extend the application scope. Meanwhile, it also meets great challenges such as energy and bandwidth constrained. For solving the constrained problem in WSNs, the observed signals must be quantified before sending to the fusion center, which makes the overall noise unable to be modeled accurately by simple probabilistic model.
To study the reconstruction issue of chaotic signal with unknown statistics in WSNs, a reconstructed method of chaotic signal based on a cost reference particle filter (CRPF) is proposed in this paper. The cost recerence cubature particle filter (CRCPF) algorithm adopts cubature-point transformation to enhance the accuracy of prediction particles, and cost-risk functions are defined to complete particle propagation. The effectiveness of proposed CRCPF algorithm is verified in the sensor network with a fusion center. Moreover, a generalized likelihood ratio functionis obtained by the cost increment of local reconstructed signals in the cluster-based sensor network topology model, which is used to reduce the network energy consumption by selecting working nodes. Simulation results show that compared with CPF and CRPF, the proposed algorithm CRCPF attains good performance in a WSN with unknown noise statistics. Meanwhile, the CRCPF algorithm realizes the compromise between energy consumption and reconstruction accuracy simultaneously, which indicates that the proposed CRCPF algorithm has the potential to extend other application scope.

## EDITOR'S SUGGESTION

2017, 66 (4): 040601.
doi: 10.7498/aps.66.040601

Abstract +

The rapid developments of ultra-intense and ultra-short laser offer the possibility to study laser driven ion acceleration with using solid density target. However, the prepulse and amplified spontaneous emission generated in the amplification can create preplasma at the target front by heating, melting and evaporating a portion of a solid density. The main pulse then interacts with the preplasma, which would be harmful to laser ion acceleration. Therefore, many methods have been developed to enhance the temporal contrast of high power laser system, such as saturable absorber, cross polarized wave generation (XPW) and plasma mirror. With many advantages, such as high conversion efficiency, introducing neither spatial nor spectral distortions, and easy setup compared with other mechanisms, XPW has been used to clean the femtosecond laser system. Besides that, the spectrum of the XPW pulse could be broadened by 3 times under the best condition compared with the initial spectrum. It can solve the spectrum narrowing problem during the laser amplification to obtain ultra-short femtosecond laser pulse. Here, we experimentally investigate the output power, spectrum bandwidth and center wavelength shift of the generated cross-polarized wave according to the input pulse quadratic spectral phase.
The femtosecond laser pulse in compact laser plasma accelerator system at Peking University is used to investigate the role of quadratic spectral phase in characterizing the two crystal cross-polarized generation. The Ti:Sapphire-based laser system has a central wavelength of 798 nm and bandwidth of 35.5 nm which allows the pulse to be compressed down to 40 fs duration (FWHM). Typical the input pulse energy of XPW is 150 upJ and the laser system operates well at 1 kHz repetition rate. The quadratic spectral phase can be increased by changing the position of compressor grating.
The conversion efficiency, spectrum bandwidth and the central wavelength shift by changing the quadratic spectral phase are measured. The conversion efficiency is 17% when quadratic spectral phase 2=0, and decreases as quadratic spectral phase increases. The rapid decrease is caused by negative quadratic spectral phase. The spectrum bandwidth is 62 nm under the optimum condition, and the broadening effect exists when quadratic spectral phase is in a range of -280 fs2 2 1400 fs2. It is slowly blue-shifted when 20 and stays at 772 nm when 21000 fs2. It starts to be red-shifted when 20 and stays at 806 nm finally.
In conclusion, with the increase of quadratic spectral phase, we observe the effects of conversion efficiency and spectrum bandwidth and the shift of central wavelength. Moreover, the influences of positive and negative quadratic spectral phase on characteristics of XPW are different. Our result shows that the negative quadratic spectral phaseis more effective at reducing the conversion efficiency and spectrum bandwidth than the positive one.

2017, 66 (4): 040502.
doi: 10.7498/aps.66.040502

Abstract +

A memristor is a nonlinear nanoscale-sized element with memory function, and it has an italic type 8 voltage-current relation curve that looks like a pinched hysteresis loop characteristic. The memristor is utilized to construct chaotic circuit, which has attracted the attention of the researchers. At present, most of studies focus on applying one or two memristors to the chaotic circuit. In order to study the multi memristor chaotic circuit, in this work we propose a six-order chaotic circuit with two flux-controlled memristors and a charge-controlled memristor. A corresponding six-order nonlinear dynamic differential equation of the circuit state variables is established. The dynamic properties of the circuit are demonstrated in detail. The analyses of equilibria and equilibrium stability show that the circuit has an equilibrium located in the three-dimensional space which is constituted by memristor internal state variables, and it is found that the equilibrium stability is determined by the circuit parameters and the initial states of three memristors. The Lyapunov exponent spectra and bifurcation diagrams of the circuit imply that it can produce two bifurcation behaviors by adjusting its parameters, which are Hopf bifurcation and anti-period doubling bifurcation. The hyperchaos, transient chaos and intermittency cycle phenomena are found in the same system. The dynamical behavior of this circuit is dependent on the initial state of memristor, showing different orbits such as chaotic oscillation, periodic oscillation and stable sink under different initial states. Finally, the simulation results indicate that some strange attractors like lotus type and superposition type are observed when voltage and electricity signal in observing chaotic attractors are generalized to power and energy signal, respectively. And the attractor production between the energy signals of the memristors are studied. Specially, when different initial conditions of three memristors are used to simulate the circuit, we can find the coexistence phenomenon of chaotic attractors with different topological structures or quasi-periodic limit cycle and chaotic attractor.
The six-order chaotic oscillating circuit is mainly composed of three parts:the parallel connection between a flux-controlled memristor and capacitor, the serial connection between a charge-controlled memristor and inductor, and another flux-controlled memristor that is alone and floating, which enriches the application of memristor in high-order chaotic circuit. Compared with most of other chaotic systems, it has many circuit parameters and very complex topological structure, which enhances the complexity of chaotic system and the randomness of the generated signal. It is more difficult to decipher the encrypted information in chaotic secure communication, and thus it has better security performance and safety performance.

###### ATOMIC AND MOLECULAR PHYSICS

2017, 66 (4): 043201.
doi: 10.7498/aps.66.043201

Abstract +

Photoionization processes widely exist in the astrophysical plasma and the high temperature laboratory plasma. Compared with the traditional photoelectron energy spectrum, the photoelectron angular distribution is not only related to the amplitude of the photoionization channels, but also sensitive to the phases of these channels. So the photoelectron angular distribution contains much more quantum information about the photoionization processes and is used to provide stringent tests of our understanding of basic physical processes underlying gas- and condensed-phase interaction with radiation, as well as a tool to probe physical and chemical structure in solids and surfaces. For a long time, the dipole approximation has been the basis in the study of the photoelectron angular distribution, but with the progress of light source, such as the fourth generation synchrotron facilities, more and more attention is paid to the non-dipole effect of the photoelectron angular distribution. In thispresent work, the photoionization processes of sodium-like ions (20Z92) are studied for the different incident photon energies based on the multiconfiguration Dirac-Fock method and the density matrix theory. The influences of the non-dipole terms on the photoelectron angular distributions, which arise from the multipole expansion of the electron-photon interaction, are discussed in detail. The relationship between the dipole and non-dipole parameters of the photoelectron angular distribution along with the atomic number is given. It is found that the influence of non-dipole terms on the photoelectron angular distribution is related to the incident photon energy and the atomic number of the target ion and the subshell of the ionized electron. In general, the influences of the non-dipole terms on the photoelectron angular distribution of p subshell are larger than those of the s subshell. In the electric dipole approximation, the s subshell photoelectron angular distribution is nearly independent of the photon energy and nuclear charge number, but this situation is not for the p subshell. With the increase of photon energy, an abnormal angular distribution is found for the p subshell photoelectron. However, if the non-dipole effects are included, the abnormal photoelectron angular distribution of p subshell disappears and the photoelectron distribution has maximum values respectively near 45o and 135o with respect to the polarization vector of incident light, that is, the photoelectron distribution has an obvious forward scattering characteristic.

###### ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS

2017, 66 (4): 044101.
doi: 10.7498/aps.66.044101

Abstract +

For far-field imaging applications, the imaging resolution of conventional lenses is limited by the diffraction limit because of the exponential decay of high spatial frequency waves. The key to realizing the subwavelength imaging lies in the collection of evanescent informations in far-field region. However, the collection of evanescent waves is not the only thing we need to do. The relation between target position and far-field information is also very important.
In this paper, a far-field time reversal subwavelength imaging system is constructed with the help of an evanescent-to-propagating conversion plate, i. e., a grating plate. The designed grating plate is able to convert evanescent waves into propagating waves through the modulation in space-spectrum domain. In order to clearly understand the conversion, a focusing experiment is conducted with two sources and five time reversal mirror antennas. By recording the amplitudes of the time reversal signals in the two source positions, we can see that the amplitude of the refocusing signal at the original source position is much larger than that of the other signal. Through numerical simulation and experiment, the conversion of evanescent wave into propagative wave is proved finally.
Then, according to the self-conjugation property of time reversal, the result of self-conjugation for channel response in complex environment is nearly the same as an impulse function. The image of source target can be reconstructed without exact prior knowledge of the expression of the spatial channel response. In order to exemplify the super resolution property of our designed system, experiments with simulation data and experimental data are executed with and without our designed grating plate, respectively. For imaging applications, we first record the forward signals received by the time reversal mirror antennas, and then record the refocusing field distribution on the imaging plane to obtain the image of the target. In the reconstruction process, another thing we need to notice is that the original sources should be removed. This is because in a real imaging application, we cannot know the exact position of target inadvance. The imaging results show that the resolution of our imaging system has overcome the diffraction limit.
Compared with the imaging resolution of the imaging system without the grating plate, the imaging resolution of the system with our designed grating plate is improved obviously. Since this kind of method overcomes the intrinsical diffraction limit by transmitting evanescent information to far-field region in a way of converting them into propagative waves. This kind of method offers us a promising alternative to microwave far-field subwavelength imaging applications.

2017, 66 (4): 044102.
doi: 10.7498/aps.66.044102

Abstract +

Multi-beam klystron (MBK) is a promising high power microwave device with the traits of high power, high efficiency, high frequency, etc. For the high power relativistic MBK, the multi-beam rotation around an axis may reduce the transmission efficiency obviously due to the effect of space electromagnetic field. In previous researches, the influence of mirror-image electromagnetic field is ignored, which can play a leading role in some cases. In this study, we present a method by taking into account the mirror-image effect to analyze the angular drift of multi-beam in the hollow cylindrical waveguide. The hollow cylindrical waveguide is a part of relativistic MBK such as input cavity and transition section, which is just behind the diode. In this method, the equation of the multi-beam angular drift is deduced and analyzed quantitatively. Based on the equation, the expression of the angular velocity about the multi-beam in the waveguide is derived, meanwhile the minimum equilibrium magnetic field, called Brillouin magnetic field, is obtained. To verify the effectiveness of the method, numerical simulations are carried out by the three-dimensional (3D) code and the results show good agreement with the theoretical results. The theoretical analysis and simulation results show that the mirror-image electromagnetic field can dominate the multi-beam angular motion in some conditions, especially when the number of the multi-beams and the distance between the conducting wall and the multi-beam are both small. In this case, the mirror-image electromagnetic field can be much higher than the self-induced electromagnetic field. Nevertheless, as the the number of the multi-beams or the distance between the conducting wall and the multi-beam increases, the mirror-image electromagnetic field decreases and approaches to zero rapidly and the self-induced electromagnetic field controls the angular movement. Interestingly, in general cases, it is found that the change rate of the angular speed is not related to the number of multi-beams, nor the radius of waveguide, nor the distance between the multi-beam, nor waveguide, etc, except for the accelerating voltage. In addition, we experimentally investigate the angular drift of the multi-beam at a voltage of about 670 kV, current of about 7 kA and length of waveguide about 100 mm. The experimental results show that the multi-beam distorts obviously, which changes the beam spot shape from circle to ellipse. To solve this problem, we simultaneously investigate the multi-beam emission and transmission in simulation experiment. The analogue results not only reveal that the distortion is mainly caused by the emission of the multi-cathode rods, but also provide a new phenomenon that the angular drift distance in the accelerating gap of the diode is twice as large as that in the cylindrical hollow waveguide due to the low beam speed along the axis and high electrostatic field in the accelerating region. It is also found that the distortion is more evident as the rod radius decreases. Furthermore, we propose an optimization design to improve the relativistic multi-beam system by inclining the multi-cathode rods, which is proved to be effective by simulation. This study could provide theoretical basis for studying the relativistic MBK.

2017, 66 (4): 044201.
doi: 10.7498/aps.66.044201

Abstract +

With the advantages of simple structure, low-cost, large field of view, and high image quality, the transmission optical system is widely used in detection system, microscope, telescope, etc. However, the research on the illumination distribution law in the focal plane of transmission optical system is rarely reported. In this paper, this issue is studied. During the study on the first-order scattered light distribution law in the focal plane of the transmission optical system, the limitations of the two-parameter Harvey bi-directional scatter distribution function (BSDF) scattering theory are found, namely in the condition of small scattering angle, the two-parameter Harvey BSDF theory cannot accurately describe the scattering properties of the optical surface material. So the scattering model of the transmission optical system under small scattering angle is established by introducing parameter l, and the accuracy of the new theoretical model is verified experimentally. This model complements the two-parameter Harvey BSDF scattering model and broadens the application scope of the Harvey BSDF scattering model so that it can better explain the imaging law of scattered light spot in the focal plane of transmission optical system. At a small scattering angle, the conclusions can be drawn from the new theoretical model as follows. 1) The irradiance of the final image plane increases linearly with the increase of the incident optical power. 2) In the transmission optical system, the contribution of each optical surface with the same scattering properties to scattered spot irradiance in the final image plane can be expressed by a Gaussian function. 3) The irradiance of scattered spot in the final image plane can be expressed as the superposition of n Gaussian functions, where n is the number of optical surfaces with different scattering properties in the transmission optical system.

2017, 66 (4): 044202.
doi: 10.7498/aps.66.044202

Abstract +

In this paper, a new approach to identity authentication is proposed, which takes advantage of the two-beam interference setup and the nonlinear correlation technique. According to the traditional two-beam interference encryption/decryption structure, we design a modified iterative phase retrieval algorithm (MIPRA), which takes the random binary amplitudes as the constraints at the input plane to encode different images (standard reference images) into a set of sparse phase distributions. In the MIPRA, a given random phase distribution serves as a system lock, and it is placed at one of the arms of the two-beam interference setup and keeps unchanged in the whole iterative phase retrieval algorithm but equivalently provides a fixed shifting vector toward the output complex amplitude field. While the peak-to-correlation value (between the output intensity and the original image) reaches a presetting threshold value, or the iterative numer of time reaches a presetting maximum value, the MIPRA stops. Here, the phase lock is assumed to be the same for all the users and thus it is placed and fixed in the system, while the calculated phase distributions vary from the MIPRA to different binary constraints, which are related to different users. Meanwhile, we also study an extension version of the proposed method. By using a superposition multiplexing technique and a nonlinear correlation technique, we can realize a function of hierarchical authentication for various kinds of users through a similar but more smart decision strategy. For example, we adopt the MIPRA four times with different constraints (random binary amplitude distribution) to obtain four phase distributions, the sum of them will be regarded as a final phase key and is designed to the user with the highest privilege. He is then able to pass all the authentication process for each standard reference image with his multiplexed phase key, that is to say, there are obvious peaks in all the nonlinear correlation maps between all the output images and the corresponding standard reference images. In a similar way, the user with the lowest privilege can only pass one authentication process. Compared with the previous identity authentication methods in the optical security area, the phase key for each user, no matter what level he belongs to, is easy to be stored and transmitted because its distinguishing feature of sparsity. It is worthwhile to note that the cross-talk between different output images are very low and will has no effect on the authentication decision since we deliberately assemble all the binary distributions, which act as constraints at the input plane in the MIPRA. Moreover, the output results are all noise-like distributions, which makes it nearly impossible for any potential intruders to find any clues of the original standard reference images. However, on the other hand, with the nonlinear correlation technique, we can easily extract enough information from these noise-like output results to authorize any users, usually we can obtain an obvious peak at the center of the correlation results but there is no peak if we adopt the traditional correlation algorithms. This feature helps reduce the risk of information leakage, thereby providing an additional protection layer. Also, weinvestigate the robustness properties by taking the sparsity ratio, Gaussian noise, and shear/occluded attack into consideration. Some previous tests alsoindicated that our scheme can resist the attack employing incorrect random phase keys. Theoretical analysis and a series simulation results are provided to verify the feasibility and effectiveness of the proposed scheme.

2017, 66 (4): 044204.
doi: 10.7498/aps.66.044204

Abstract +

A new triple correlation technique for measuring intensity profile of single-shot ultrashort laser pulse is described. The technique uses two consecutive second-order nonlinear interactions of replicas of the pulse for generating a two-coordinate output intensity distribution that corresponds to a third-order correlation function and offers advantages over the previously techniques such as frequency-resolved optical gating, self-referencing spectral phase interferometry for direct field reconstruction because it requires no additional spectral information to profile the pulses. This intensity distribution is recorded, and the pulse profile can be obtained by analytical calculation. Combining the reconstructed intensity profile with its corresponding optical spectrum, the exact phase variation in time can be recovered with Gerchberg-Saxton algorithm through an iterative calculation.

2017, 66 (4): 044206.
doi: 10.7498/aps.66.044206

Abstract +

Chirped biphotons generated via spontaneous parametric down-conversion in chirped quasi-phase-matched nonlinear crystals have ultrabroadband frequency spectra. However, the presence of quadratic frequency phase factor restricts their applications in quantum metrology and quantum lithography due to simultaneously lengthening the correlation times of biphotons. The key point to improve the temporal correlation of chirped biphotons is how to compensate for or remove the quadratic frequency phase factor. Phase compensation methods have been demonstrated to solve this problem in earlier reports. But the compressed efficiencies of these methods are strongly dependent on the length of the utilized dispersive medium and decreased by the higher-order dispersion of the dispersive medium. In this paper, based on the phase transform of a lens for a light field in spatial domain, we theoretically propose a method of the equivalent removal of the quadratic phase by realizing a Fresnel-zone lens-like modulation on the biphotons spectrum in frequency domain, thereby compressing the correlation time of chirped biphotons to the Fourier-transform limited width. By analogy to the idea of Fresnel wave zone plate, this lens-like modulation can be realized by dividing the biphoton spectrum into Fresnel frequency zones and applying only binary spectral phase (0, ) sequentially to these zones. The theoretical results show that the correlation time width of chirped biphotons can be reduced, and the correlation signal intensity can be increased compared with the original one, by a factor about 100 and 30, respectively. The physical reason is that these Fresnel frequency zones under binary spectral phase modulation will lead to constructive interference at zero delay and destructive interference elsewhere. This method can significantly enhance biphoton time correlation without biphoton signal loss and avoids the limitations of phase compensation methods. Therefore, we can obtain biphotons with both ultra-broad bandwidth and ultra-short correlation times by using our proposed method. The attainable compression efficiency is constrained by the division resolution of the Fresnel frequency zones and the precision of applied binary phase modulations. It should be noted that a constraint condition about crystal length, chirp parameter and the number of frequency zones is summarized in designing the experimental parameters for the desired compression goal. Since binary spectral phase and 0 are easy to obtain and calibrate in practice, we thus believe that our proposed method is feasible to implement experimentally. Moreover, the proposed method can also be generalized to other fields relating to the quadratic phase factor, such as two-photon absorption, second-harmonic generation and chirped pulse compression.

2017, 66 (4): 044207.
doi: 10.7498/aps.66.044207

Abstract +

Scattering process of aerosol particles plays an important role in atmospheric radiative transfer since it can modify the transmission, reflection and absorption ability of atmospheric system. Owning to the uncertainty of aerosol particles' scattering properties, which results from their complicated geometries and inhomogeneous compositions, there still exists a considerable uncertainty in the radiative transfer numerical simulation, and simulating the scattering properties of aerosol with irregular shapes has become a hotspot in meteorological study. To this end, a new aerosol scattering model is developed based on multi-resolution time-domain (MRTD), by which the scattering processes of nonspherical and inhomogeneous particles can be simulated. In this model, the near electromagnetic field is calculated by MRTD technique. Considering the particularity of aerosol medium, a transformation technique from near field to far field is derived based on volume integration method, and then the scattering amplitude matrix and Meller matrix can be calculated by the obtained far electric field as well. The models for particle extinction and absorption cross section are derived from Maxwell's curl equations in the frequency domain, by which the integration scattering properties can be simulated accurately. The MRTD scattering model is validated by comparing with Mie theory and T matrix method for spherical particle, ellipsoidal particle and cylindrical particle, and the influence of grid size on the simulation accuracy is analyzed subsequently. In the last part, the efficiency of the MRTD scattering model is quantitatively discussed. The simulation results show that the relative errors of scattering phase function simulated by our model are less than 8%, and the errors in forward scattering direction are much smaller, which are less than 4%. The precisions for extinction and absorption efficiency are much higher than the results from the scattering phase function, and the relative errors can reduce to 0.1% for particles with their radii comparable to the wavelength of incident light. The gird size has a significant influence on model precision; to achieve the same accuracy, the grid size first increases with increasing particle radius, and then decreases as a function of particle size for particles with size parameter less than 20. In the next step, we will try to establish the scattering property database of nonspherical particles based on the MRTD scattering model developed here.

2017, 66 (4): 044701.
doi: 10.7498/aps.66.044701

Abstract +

Axisymmetric thermal flows in cylindrical systems are widely encountered in engineering practices. Typically, axisymmetric thermal flows belong in three-dimensional (3D) problems. However, taking advantage of the axisymmetric condition, the 3D axisymmetric flows can be reduced to quasi two-dimensional (2D) problems in the meridian plane, which significantly reduces the computational requirements and avoids treating the curved boundary. In recent years, various 2D lattice Boltzmann (LB) models, including single relaxation time LB (SRT-LB, or LBGK) and multiple relaxation time LB (MRT-LB) models, for axisymmetric thermal flows have been proposed. In the LB community, it is well accepted that the MRT-LB is superior to the LBGK in terms of numerical stability. The existing MRT-LB model for axisymmetric thermal flows are developed based on orthogonal basis vectors obtained from the combination of the lattice velocity components, i.e., the transform matrix in the existing MRT-LB is an orthogonal one. Unlike the existing MRT-LB model, in this paper, a non-orthogonal multiple-relaxation-time lattice Boltzmann (MRT-LB) method of simulating axisymmetric thermal flows is proposed. In the proposed MRT-LB method, the velocity field is solved by a D2Q9 discrete velocity set while the temperature by a D2Q5 discrete velocity set. The main advantage of the present MRT-LB model is that the transform matrix of the model is a non-orthogonal one, which is comprised of some proper non-orthogonal basis vectors obtained from the combination of the lattice velocity components. The non-orthogonal transform matrix of the present MRT-LB model contains more zero elements than the classical orthogonal transform matrix, and thus the present MRT-LB model is expected to be more efficient than the existing orthogonal-based MRT-LB model. The equilibrium velocity and temperature moments of the present MRT-LB model are expressed by mapping the equilibrium distribution functions onto their moment spaces through using the non-orthogonal transformation matrix. Also the vectors in the forcing term are modified according to the matrix mapping. Through the Chapman-Enskog analysis, it is demonstrated that the macroscopic governing equations in the cylindrical coordinate can be recovered from the present MRT-LB model. Then several numerical tests, including thermal Womersley flow, Rayleigh-Bnard convection in a vertical cylinder and natural convection in a vertical annulus, are conducted to validate the present model. It is found that the present numerical results are in good agreement with the analytical solutions and/or other numerical results reported in the literature. Numerical stability is also tested, and the results suggest that the present MRT model shows better numerical stability than its LBGK counterpart. Moreover, the numerical results also indicate that the present MRT-LB model is more computationally efficient than the existing MRT-LB model for axisymmetric thermal flow. These findings indicate that the present MRT-LB model can serve as a powerful method of computing the axisymmetric thermal flows.

2017, 66 (4): 044703.
doi: 10.7498/aps.66.044703

Abstract +

Study of the liquid flowing behavior through the micro-structure array has aroused the significant interest due to its key roles in the fields of microfluidics, micro-mixers, micro-heat exchangers, tribology, etc. Micro-structure array can significantly affect the liquid flowing characteristics of the near-surface layer and the solid-liquid interfacial properties, like adhesion, surface wetting, shear viscous resistance, interfacial slip, etc. The researches indicate that the stripe- and square-patterned electrodes can improve the storage properties of the lithium-ion battery due to its ability to promote the diffusion of the liquid electrolyte. Micro-structure array patterned micro-channel can reduce the friction drag of liquid flowing through it. And the surface fabricated with lotus-leaf-like dual-scale structure array can achieve the super-hydrophobicity.
For a micro-structure array, its influences on the liquid flowing behaviors greatly depend on the shape and size of the micro-structure, and the porosity, arrangement and size of the array. Here, we mainly focus on the influences of the micro-structure shape and surface topography on the liquid flowing behaviors, by adopting the same array porosity, arrangement and size, and the same feature size of the micro-structure. In the present paper, we prepare three different surfaces, which are the micro-pillar array surfaces, micro-hole array surface, and dual-scale micro-pillar array surface (i.e., micro-pillar with rough top surface), respectively. Their influences on the liquid flowing characteristics of the near-surface layer are investigated by quartz crystal microbalance (QCM). The QCM is a powerful and promising technique in studying the solid/liquid interfacial behaviors. Its main output parameters are frequency shift and half-bandwidth variation, which are closely related to the rheological properties and flow characteristics of the near-surface liquid layer. When the QCM chip is patterned with micro-structure array, it will inevitably influence the liquid motion and makes it more complicated, like the generation of non-laminar motion, the trapping of liquid in the gap, and the conversion of the in-plane surface motion into the surface-normal liquid motion. The experimental results show that for the same tested liquid, the frequency shift caused by the micro-hole array is higher than that by the micro-pillar array with the same feature size. And the dual-scale micro-pillar array surface results in a higher half-bandwidth variation than the micro-pillar array surface with the same feature size. It demonstrates that micro-hole tends to confine the liquid motion and make the trapped liquid oscillate with the substrate like a rigid film, thus resulting in a higher frequency shift. The dual-scale micro-structure will render the flow behavior of the near-surface layer more chaotic, thus showing a larger half-bandwidth variation. This study provides an experimental basis for selecting the type of micro-structure used in the microfluidic chip to better control the liquid flowing and mixing.

2017, 66 (4): 044704.
doi: 10.7498/aps.66.044704

Abstract +

A radial basis function ghost cell immersed boundary method of simulating flows around arbitrary complex or multiple immersed boundaries is proposed in this paper. In this method, incompressible Navier-Stokes equations are discretized on fixed Cartesian staggered gridby the finite difference method. A fractional step method is used for time integration, together with third order Runge-Kutta scheme. A high-order TVD MUSCL (total variation diminishing monotonic upstream-centered scheme for conservation law) scheme is used to discretize convective terms. Two salient features are emphasized in the present study. First, boundary conditions at the immersed interface are enforced by a continuous ghost cell method to consider the influence of immersed boundary on the flow field. The immersed bodies are treated as virtual boundaries immersed in the flow. And Navier-Stokes equations are solved in the entire computation domain, including solid domain. Therefore, programming complexity is greatly reduced and the treatment of immersed boundaries is simplified. Second, a polynomial and radial basis function is introduced to implicitly represent and reconstruct arbitrary complex immersed boundaries. Iso-surface distance functions about interface geometries are fitted with some sampling points of body surfaces. It is flexible and robust. Moreover, the information about interface positions on the background grid can be easily identified by the signed distance functions. Based on our in-house developed immersed boundary method solver, typical test cases are simulated to validate the proposed method. The flows around a cylinder at Reynolds numbers of 40, 100 and 200 are first simulated and a grid resolution study is carried out. Good agreement is achieved by comparing with previous numerical results, which shows that this method is accurate and reliable. In the second case of flow around airfoil, the good agreement with previous study shows that the present method has the ability to simulate complex immersed boundary flow. In the last case of flow around array of thirteen cylinders, the ability of present method for multiple immersed boundaries is well proved. And hydrodynamic interaction among multiple bodies is briefly analyzed.

2017, 66 (4): 044203.
doi: 10.7498/aps.66.044203

Abstract +

Bessel beam is one of diffraction-free beams and has some peculiar properties. Varieties of its applications have been found, such as microparticle manipulating, material processing and biological studies. In this work, we propose a method of creating a Bessel beam by manipulating Pancharatnam-Berry phase. Using femtosecond laser, nano waveplatelets are written on a fused silicon glass to form a metasurface. The optical axis of waveplatelets rotating in the radial direction can produce the space-varying Pancharatnam-Berry phase. The designed metasurface acts as a planar axicon to generate Bessel beams by replacing the traditional one. A Jones calculation is employed to analyze the transformation of the metasurface. The theoretical results indicate that a left-handed circularly polarized light passing through the planar axicon is convergent, while a right-handed circularly polarized one is divergent. The intrinsic physical reason is that Pancharatnam-Berry phase is spin-dependent. Therefore, Bessel beams are generated by the planar axicon only when a left-handed circularly polarized light inputs the system. It is notable that the maximum nondiffracting distance is determined by the rate of rotation of the metasurface microstructure. By reducing the rate of rotation, we can easily obtain a longer nondiffracting distance, thus avoiding the problem that the base angle of the traditional axicon is too small to fabricate. According to the Fresnel diffraction integral, we simulate the propagation of the field emerging from the planar axicon and obtain the intensity distributions behind the planar axicon with different distances. The results show that the intensity pattern remains unchanged in the propagating process and possesses the propagation properties of Bessel beam. It implies that approximate nondiffraction Bessel beams can be achieved by employing the planar axicon with metasurface. Finally, we set up an experimental system with the Pancharatnam-Berry phase metasurface with period d=1000 upm to verify the theoretical analysis. Theoretically, the maximum nondiffraction distance is 7.9 m. In the shaded region, we measure the intensity distributions at different distances. The experimental results are in good agreement with the simulation results, so the planar axicon based on Pancharatnam-Berry phase can be an effective Bessel beam generator. We believe that these results are helpful for developing more spin-dependent photonic devices.

2017, 66 (4): 044208.
doi: 10.7498/aps.66.044208

Abstract +

Owing to increasingly severe environmental pollution, food safety and other problems, higher and higher requirements for the detecting technique of poisonous and harmful biochemical molecules have been put forward. The conventional biochemical detector has the disadvantages of large size, high cost and inability to realize far-end and in-situ detection functions. Based on the requirements of the biochemical molecular detection technology for high sensitivity, miniaturization, far-end detection, insitu detection, real-time analysis and the like, a detection method using a fiber surface-enhanced Raman scattering (SERS) probe to carry out Raman signal detection has been put forward in recent years. The detection method not only realizes far-end and insitu detection functions, but also has a relatively high sensitivity. In this paper, a taper and cylinder combination type fiber probe is made by adopting a simple tube corrosion method, Under the situation of fixed temperature, cone-cylinder combined fiber probes with different diameters are obtained by controlling the corrosion time, and silver nanoparticles are bound to the surface of a silanized silicon dioxide fiber probe through electrostatic forces. Then, the sizes and morphologies of silver nanoparticles on the surface of the fiber probe are observed under a scanning electron microscope. Besides, the detection limit of a rhodamine 6G (R6G) solution is used to manifest both the activity and the sensitivity of the fiber probe, and the self-assembly time of the silver nanoparticles are further optimized to be 30 min and the diameter of the fiber probe to be 62 upm. When the concentration of a silver sol solution is constant, a high-sensitivity fiber SERS probe can be prepared. Through far-end detection, the detection limit of the R6G can reach 10-14 mol/L, and the enhancement factor is 1.36104. This work can serve as an experimental basis for a novel fiber surface-enhanced Raman scattering sensor in such aspects as high sensitivity and low cost. The studies of this paper are expected to provide an appropriate detection technique for rapid quantitative detection of biochemical molecules, and further provide a reference for various application fields of environmental monitoring and food safety analysis in future in terms of realizing rapid and accurate in-situ detection. Therefore, the fiber SERS probe has large application foreground in molecular detection.

2017, 66 (4): 044301.
doi: 10.7498/aps.66.044301

Abstract +

It is well known that acoustic wave carries momentum and energy. An object in a sound field, which absorbs or reflects sound energy, can be subjected to the acoustic radiation force (ARF), and thus can be manipulated in the contactless and noninvasive manners. This effect has potential applications in the fields of environment monitoring, microbiology, food quality control, etc. Obtaining a tunable trapping or pushing ARF should enable the design of an incident beam profile. However, the conventional acoustic manipulation system with plane wave, standing waves or Gaussian beams, which is usually generated directly by acoustic transducer, cannot be redesigned easily, nor can the corresponding ARF be modulated efficiently. Phononic crystals, which are artificial periodic structure materials, exhibit great advantages in modulating the propagation and distribution of acoustic wave compared with conventional materials, and thus have potential applications in tunable particle manipulation. Here, we present a theoretical study of the ARFs exerted on a cylindrical polystyrene foam particle near the surface of a one-dimensional (1D) grating in air. By using the finite element method (FEM) to investigate the transmission spectra and field distribution of the 1D grating and the FEM combined with momentum-flux tensor to obtain the ARF on the particle, we find that there are two resonance modes in the 1D grating, which origin from the coupling between the diffractive waves excited from the export of periodic apertures and the Fabry-Perot resonance mode inside the apertures. In addition, it can be seen from field distribution that in the first resonant mode, the resonance wavelength is approximate to the period of grating, and the enhanced spatial confinement of acoustic wave is located at the surface of the plate besides in the aperture. In the second resonant mode, the corresponding wavelength is more than twice the period of grating, and the enhanced spatial confinement of acoustic wave is mainly located in the aperture. Moreover, due to the gradient field distribution at the surface of slits and plate in these resonance modes, particles at the surface can be under the action of tunable negative ARFs. In the first resonance mode, the particle can be trapped on the surface of grating. While in the second resonance mode, the particle can be trapped in the aperture, and the amplitude of ARF of this mode is far smaller than that of the first mode. Thus, this system in the first resonance mode may have potential applications in air acoustic manipulation, aligning, and sorting micro-particles.

2017, 66 (4): 044702.
doi: 10.7498/aps.66.044702

Abstract +

Explosion in shallow water or small depth water will generate upward water jet, mainly because bubbles generated by explosion will interact with the surface of water. Different underwater depths can result in upward water jets with different kinds of shapes, such as water column, water plume, jet, spall dome, splash, spike, etc. To reveal the formation mechanisms of different types of water jets, a spark bubble experiment platform is set up, and the motions of bubble and free surface are studied experimentally by high-speed photography. The dynamic images for the formation process of the water jets under different initial depths of bubble are obtained. Through theoretical analysis and direct observation of the experimental data, the interaction process between the oscillating bubble and free surface are clarified, and the evolution rule of water jets is obtained. It is found that the key factor affecting the formation of different shapes of the water jets is the superposition of the disturbance of the second bubble pulse and the simple-shape jet induced by the first bubble pulse. Five types of the superpositions are summarized:1) All-fit type, with a large depth of initial bubble, the first and the second bubble impulse fit well to form a smooth and slightly arched water dome; 2) partial-fit type, with a less large depth of initial bubble, higher arched water dome is formed due to the raising effects of second bubble pulse partially fit the initial water dome shape; 3) catch-up type, with a mediate depth of initial bubble, the free-surface jet caused by first bubble pulse will be caught up from the bottom by the second pulse, and form a thin and high velocity jet; 4) run-after type, with a smaller depth of initial bubble, the free-surface jet caused by first bubble pulse will be raised from the bottom by the second pulse, and form a jet with thin head and thick pedestal, sometimes form a crown-type splash; 5) non-superposition type, the depth of initial bubble is so small that the bubble will break up, and no superposition will happen. In summary, the ratio of the initial depth to the maximum radius of bubble is found to be a decisive factor of the superposition type. The initial bubble is described by a dimensionless distance. These conclusions well explain the phenomena observed in experiment, and can provide a new vision and reference to the understanding of the formation mechanism of water jets induced by the interaction between bubble and free surface.

2017, 66 (4): 044205.
doi: 10.7498/aps.66.044205

Abstract +

The generation of pulse radiation with different frequency based on nonlinear optical frequency conversion technology is an effective method to produce lasers with the wavelength in the visible light or ultraviolet (UV) light range. In recent years, the developments of photonic crystal fiber (PCF) technology and ultra-short pulse technology have brought new solutions to the problems that the system needs great maintenance work, has low frequency conversion rate and much difficulty in popularizing, which the traditional frequency conversion system based on nonlinear crystal is confronting. Research on UV pulse radiation has been consistently attracting much attention of many academics. Particularly, narrowband and broadband UV pulse radiation sources are complementary, each having its own characteristics and scope of applications. The generation of narrowband UV pulse radiation of high sensitivity and high resolution through third harmonic generation (THG) in PCF has already been reported. However, the frequency conversion rate of narrowband UV pulse radiation is relatively low and the tunable ability of the spectrum is limited. These imperfections can be exactly completed by broadband UV pulse radiation. Broadband UV pulse radiation based on THG in PCF can be realized efficiently in PCF. This means that the conversion of UV light increases substantially, and simultaneously, the narrowband UV radiation of any wavelength in a certain range can be acquired more easily and the tunable ability of narrowband UV pulse radiation can be enhanced further. In this paper, the femtosecond pulse with a central wavelength of 1035 nm at a pulse repetition rate of 50 MHz is coupled into a highly nonlinear photonic crystal fiber with an appropriate length. The Raman self-frequency shift soliton produced from the ultra-short input pulse acts as a pump resource of third harmonic, transmitting through fundamental mode in PCF. Phase-matching between the fundamental mode and the high order modes is achieved and the third harmonic transmitted by specific high order modes (such as HE13) at deep UV wavelength is acquired effectively. Besides, the very high order UV mode (HOUVM) transmitting third harmonic with shorter wavelength is stimulated when intentionally inputting the ultra-short pulse into the PCF in the direction of a certain angle deviating from the axis of fiber core. Broadband deep UV (320-360 nm) pulse radiation with a UV light conversion rate of 3.6% can be acquired effectively in nonlinear PCF by stimulating a number of adjacent HOUVMs and achieving phase matching between the modes. Good agreement between theoretical results and experimental results is achieved.

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

2017, 66 (4): 045101.
doi: 10.7498/aps.66.045101

Abstract +

High power microwave injection into the troposphere is a feasible approach to the decomposition of chlorofluorocarbon (CFC). However, in existing researches, there are only basic principles which lack quantitative tests. Hence, in this article we introduce the finite-difference time-domain method to quantitatively analyze the decomposition of CFC under high power pulses. We first investigate the principal chemical reactions of CFC decomposition induced by high power microwave injection and find that dissociation attachment is a dominant process of the microwave discharge decomposition of CFC. We use an empirical formula to calculate the decomposition efficiency of CFC. The result shows that 20% of the initial content of CFC molecules will be dissociated over 100 microseconds where we assume the electron number density to be 1013 cm-3. Then according to Maxwell's equations and the current density equation, we adopt the finite difference time domain method to simulate the generation process of a large number of free electrons induced by injecting the high power microwaves into the troposphere. The ionized electron generated by the high power microwave in troposphere is in favor of CFC decomposition since the electron affinity of CFC is larger than dissociation energy of CFC molecules. The simulation results indicate that the number density of electrons grows up to 1017 cm-3 exponentially with the injection time and will grow faster at higher height (10 km) or by the larger field intensity. During the pulse, the higher electron energy corresponds to a smaller dissociative attachment coefficient. Thus, most of the CFC molecules are decomposed during the electron-decay phase. During the relaxation period, the electron energy will return to the natural state within 0.01 ns. The number density of electrons decreases slower than the electron energy and it will take 1 ms to reach the natural state. From the results we can also see that the decay rates of the electron energy and number density decrease with the increase of the height. In this paper, two methods of calculating the CFC decomposition rate are utilized. One method is from the chemical reaction and the other method is based on an empirical formula which is mentioned before. It is shown that the results of these two methods present obvious consistency. The simulation results demonstrate that the CFC decomposition rate will increase with larger microwave intensity or higher frequency and can approach up to 6%. In conclusion, this study gives the quantitative analyses of the CFC decomposition induced by high power microwave injection in the troposphere for the first time.

2017, 66 (4): 045201.
doi: 10.7498/aps.66.045201

Abstract +

Helicon wave discharge has higher coupling efficiency than capactively coupled and inductively coupled discharge in low static magnetic field. In the wave sustained mode, a large volume and large area plasma can be produced at lower pressure by using comparable discharge power, and thus it expands the helicon wave plasma applications in material surface modification, thin film deposition, dry etching and thruster usage. However, the application of helicon wave source still faces challenges, such as the controversial power coupling mechanism, operation stability and the plasma distribution uniformity in the experiment. The wave mode existing in bounded helicon wave plasma column generally consists of helicon and Trivelpiece-Gould (TG) components, and their mode transitions and different transverse wave field distribution regions, and the propagating characteristic of the helicon wave are directly related to the power coupling and plasma density distribution in the source region, then affect the uniformity of material processing and film deposition in the diffusion chamber. In this paper, the plasma azimuthal non-uniformity, with using Doubble Saddle antenna, 100 G static magnetic field in helicon wave plasma source, is studied by electrical characteristic (power-current) curve, intensified charge coupled device (ICCD) image and magnetic probe measurements. The electrical characteristic curve indicates two discharge stages with different effective resistances. Meanwhile, in the second stage, the higher effective resistance would result in higher coupling efficiency and higher plasma density. But the ICCD image demonstrates the azimuthal non-uniformity of plasma, indicating that the main heating points at the diagonal edge are linked to the stationary transverse electrical field line pattern of azimuthal mode number m=+1 helicon wave, and the magnetic probe is used to measure the helicon wave magnetic field Bz component along the quartz source tube axially. The magnetic probe results show that the standing wave appearing below the antenna even though in the upper region of the antenna is characteristic of the traveling wave. Furthermore, at the plasma boundary, the standing wave can be coupled to the TG wave, and not like travelling wave it has no angular rotation of the electric field and may cause the non-uniform coupling between the helicon and TG components. The TG wave then has azimuthal non-uniform electron heating. Therefore, the standing helicon wave below the antenna is the key factor to the plasma non-uniformity problem. Changing the propagating characteristics of the helicon wave further in the plasma column will be of positive significance for optimizing the discharge efficiency of the plasma source and controlling the plasma distribution uniformity, stability and other operations as well.

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

2017, 66 (4): 046101.
doi: 10.7498/aps.66.046101

Abstract +

Understanding how the groups at interface influence the friction of carbon nanotubes can provide reference for their applications. In this paper, we investigate the influences of hydroxyls on motion and friction of carbon nanotube on graphite substrate by molecular dynamics simulation. The simulation cases include the ideal vertical carbon nanotube on the ideal graphite substrate, the ideal vertical carbon nanotube on the graphite with hydroxyls on the top layer, the carbon nanotube and the graphite both with hydroxyls on the surface. The results show that the lateral force of carbon nanotube changes when hydroxyls are introduced into the interfaces. If hydroxyls are only on the graphite, the fluctuation of lateral force increases obviously. The reason can be attributed to the increase of atomic surface roughness. Moreover, due to the small contact area between vertical aligned carbon nanotube and substrate, the mean friction becomes raised with hydroxyl content increasing, which is different from the conclusion obtained from silicon tip sliding on graphene with hydrogen on the surface. In that case, owing to the large contact area, the mean friction of tip reaches a maximum value at hydrogen content in a range between 5 and 10% because of the competition between the increase in the number of hydrogen atoms and the weakening of the interlock due to the increase in separation of tip from substrate. Hydrogen bond and Coulomb force appear between interfaces when hydroxyls are both on carbon nanotube and on graphite, which significantly increases friction force on carbon nanotube. And slip interfaces translate rapidly from between carbon nanotube and graphite into between graphite layers. Like the case with hydroxyls only on the graphite, the sliding of carbon nanotube perpendicular to the initial velocity also occurs when carbon nanotube and graphite are both with hydroxyls. This phenomena can be explained as the fact that the introduction of hydroxyls breaks the equilibrium of the force on the carbon nanotube in the Y direction. Moreover, the random distribution of hydroxyls causes the random motion of the carbon nanotube.

2017, 66 (4): 046801.
doi: 10.7498/aps.66.046801

Abstract +

All planned inertial confinement fusion (ICF) capsule targets except machined beryllium require plastic mandrels with tight requirements on which the ablator is built. In this paper, the fabrication of poly(-methylstyrene) (PAMS) mandrel is studied. PAMS mandrels are produced by using microencapsulation technique. This technique involves producing a water droplet (W1) encapsulated by a flourobenzen (FB) solution of PAMS (O) with a droplet generator, and this droplet is then flushed off by external phase (W2), forming a water-in-oil-in-water (W1/O/W2) compound-emulsion droplet, which is suspended in a stirred flask filled with external phase to cure. The encapsulation process is based on a microfluid technique, which can achieve the controlled production of millimeter-scale PAMS mandrels. In this work, capillaries-based co-flowing microfluidic triple orifice generator is designed and built to fabricate W1/O/W2 droplets. Two configurations of the droplet generator:one-step device and two-step device, are employed in this experiment. In one-step device, the end of oil phase capillary is located at the same position as the end of inner water phase capillary. So the core droplet and the shell droplet break off from their capillaries ends at the same time, forming a W1/O/W2 droplet. While in the two-step device, the W1 phase capillary tip is located upstream to the W2 phase capillary tip. As a result, the core droplet and the shell droplet depart from the ends of their capillaries respectively, forming a W1/O/W2 droplet as well. Differently, the shell droplet contains only one core droplet in one-step generator, while several core droplets are contained in the shell droplet in two-step generator. In this paper, the mechanism of the droplet formation and the effect of the flow rate on the size of the droplet are studied with these two configurations. Results show that tiny difference between the two generators will lead to great differences in droplet formation mechanism and size control. In the two-step generator, the inner phase flow rate has little influence in the outer diameter of the compound-emulsion droplet. The diameters of the compound-emulsion droplets have a similar change to the diameters of the single droplets (O/W2). In one-step device, the inner phase flow rate has a significant influence on the outer diameter of the double-emulsion droplet because of the existence of W1-O interface. Finally, the compound-emulsion droplets fabricated in this experiment are cured in external phase, after which PAMS mandrels are fabricated. The diameters of the final PAMS mandrels are measured with optical microscope. The distribution of the diameters well concentrates in an area of (200010) upm, which is favorable for producing the PAMS mandrels with a diameter of 2000 upm.

2017, 66 (4): 046802.
doi: 10.7498/aps.66.046802

Abstract +

Considerable interest has been aroused in the study of the spin dynamics in semiconductors due to its potential applications in spintronics and quantum computation. In this paper, time-resolved circularly polarized pump-probe spectroscopy is used to study the carrier density dependences on the electron spin relaxation in approximately symmetrical and completely asymmetrical doping (110) GaAs/AlGaAs quantum wells. With the increase of the carrier density, the spin relaxation time first increases and then decrease obviously in both of the quantum wells, and the measured spin relaxation time of the approximately symmetrical doping quantum wells is always longer than that of the asymmetrical doping one. By analysis, we find that the spin relaxation is not dominated only by the Bir-Aronov-Pikus (BAP) mechanism in (110) GaAs quantum wells, that though the Dresselhaus spin-orbit coupling does not lead to any spin relaxation, the asymmetry of the doping position contributes to the asymmetry of potential energy structure, thus the built-in electric field which can induce the Rashba spin-orbit coupling to appear, and that the effective magnetic field induced by the Rashba spin-orbit coupling normal to the growth direction can lead to spin relaxation along the growth direction. Therefore, the Dyakonov-Perel (DP) mechanism plays an important role in asymmetrical doping (110) GaAs/AlGaAs quantum wells. In the approximately symmetrical and completely asymmetrical doping (110) GaAs/AlGaAs quantum wells, the DP mechanism dominates the spin relaxation at low carrier density, thus the spin relaxation time increases with carrier density increasing due to the strengthening of the electron-electron scattering and the decreasing of the momentum relaxation time. However, at high carrier density, BAP mechanism plays an important role, thus the spin relaxation time decreases obviously with carrier density increrasing, but the decay rates in both of the quantum wells are slower than that in the casethat only BAP mechanism dominates, because both the DP and BAP mechanism play an important role. The strength of the Rashba spin-orbit coupling depends on the symmetry of the quantum well. The DP mechanism in a completely asymmetrical doping quantum well is stronger than that in an approximately symmetrical doping quantum wells, thus the decay rate in a completely asymmetrical doping quantum wells is always slower than that in an approximately symmetrical doping quantum wells, and the spin relaxation time in a completely asymmetrical doping quantum wells is shorter than that in an approximately symmetrical doping quantum wells.

###### INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

2017, 66 (4): 048102.
doi: 10.7498/aps.66.048102

Abstract +

Magnetic flux leakage (MFL) has been widely applied to the nondestructive testing (NDT) of ferromagnetic materials due to its simple operation, low cost, and steady signal. Its defects are evaluated based on the relationship between MFL signal and the geometrical characteristic of defect. In this paper, a three-dimensional (3D) mathematical model is developed for the magnetic leakage field of surface-breaking defects that are arbitrarily oriented inside ferromagnetic material. Firstly, a finite-length rectangular slot is used as a simplified and convenient representation of a surface-breaking defect. Then, the magnetic charge densities of slot walls in different surface-breaking orientations are analyzed theoretically. The distribution of the magnetic leakage field can ultimately be derived by vector synthesis. Both simulations and experiments are conducted to analyze the magnetic leakage field distributions in different magnetization orientations. The results show that with increasing the angle between the defect orientation and the magnetic field, the horizontal component of the leakage magnetic field increases as demonstrated by increasing the prominence of its single peak. At the same time, however, the vertical component shows a bimodal distribution. The proposed model can effectively describe the influence of defect orientation on MFL signals, which can offer practical guidelines for optimizing MFL detectors and improving defect assessment.

2017, 66 (4): 048401.
doi: 10.7498/aps.66.048401

Abstract +

In order to further improve the capabilities of clutter suppression and target detection in airborne multiple-input multiple-output (MIMO) radar space-time adaptive processing (STAP), the polarization-space-time adaptive processing (PSTAP) method based on polarization array MIMO radar is proposed. Firstly, by applying the novel polarization array to airborne MMO radar, the signal model of airborne polarization array MIMO radar PSTAP is established. Then based on the idea of resolution grid, the influence of clutter can be equivalent to the formation of independent point sources of clutter related to the clutter degree of freedom, and an equivalent expression for the covariance matrix in polarization array MIMO radar PSTAP is obtained. Next, combined with the equivalent covariance matrix, the signal-to-clutter-plus-noise ratio (SCNR) performance of the polarization array MIMO radar PSTAP is derived and analyzed. The effects of the polarization, spatial and temporal matching coefficients are discussed. When the target is located in the side-looking direction of the airborne radar, the normalized spatial frequency of the target is zero. Then the spatial transmit and spatial receive matching coefficients between the target and the clutter point source in the center of the space-time plane both approach to one. Meanwhile, the normalized Doppler frequency of the side-looking target is in direct proportion to the target speed. When the target speed decreases to zero, the temporal Doppler matching coefficient between the target and the central clutter source is near to one. Thus taking the spatial and temporal matching coefficients into consideration, the SCNR loss of the traditional MIMO-STAP is approximate to zero. It indicates that for traditional MIMO-STAP, its performance of detecting low-speed target is severely degraded by the clutter source, and target detection can hardly be realized just in space-time domains. However, through utilizing the additional polarization information to take advantage of the polarization matching coefficient, the polarization array MIMO radar PSTAP increases the SCNR loss and remarkably lessens the influence of the central clutter source. According to the above theoretical analysis, we can come to the conclusion that the polarization array MIMO radar PSTAP can effectively promote the capability of clutter suppression compared with the traditional MIMO-STAP, which is beneficial to the detection of the moving target with low-speed. Moreover, the improvement of output SCNR performance becomes more significant with increasing the differences between the polarization parameters of target and those of clutter. Therefore, the polarization array MIMO radar PSTAP has great application value for practical engineering. The simulation results verify the validity and superiority of the proposed polarization array MIMO radar PSTAP method.

## EDITOR'S SUGGESTION

2017, 66 (4): 048701.
doi: 10.7498/aps.66.048701

Abstract +

In the ray-optics (RO) model of optical tweezers, tracing refractive and reflected rays with vectors play important roles in calculating the trapping forces. Traditional ray-tracing method with solid geometry, to some extent, is complicated in determining the orientations of those refractive and reflected rays according to spatial incident rays. It is difficult to calculate the trapping forces for irregular particles. In this paper, quaternion is proposed to rotate ray vectors for simplifying the traces of all kinds of spatial rays. Then, it is appropriate to calculate the trapping force of an ellipsoid bead. Based on the algorithm of quaternion and the convention between the interface normal and angular directions, the direction of normal always points from optically denser medium to thinner medium. The rotation axis is the cross product of the incident ray and the interface normal. And the positive angular direction can be determined by right-hand rule based on the orientation of the rotation axis. According to Snell' law, the rotation angle between the incident ray and refractive/reflected ray can be determined. The quaternion for rotation consists of rotation axis and angle. So the refractive and reflected rays are both determined by quaternions of incident ray and rotation based on rotation rules. Furthermore, the force on interface can also be calculated according to momentum changes of the photon before and after the interface refraction and reflection. The quaternion method is used to analyze the effects of coverslip position and deformation ratio on the trapping efficiency of ellipsoid particles. Our simulative results show that the lateral and axial trapping efficiencies are obviously affected by the deformation of the ellipsoid itself. No matter whether the bead deforms transversely or axially, the transverse and axial trapping efficiencies both become larger at a specific deformation. Meantime, the increase of the spherical aberration reduces the maximum axial trapping efficiency, and the equilibrium position of the bead becomes farther away from the center. Using quaternion method, the calculation of refractive lightvector can be simplified in comparison with by using the method of Euclidean geometry or transformation matrix. Theoretically, this quaternion can be used to trace rays on any irregular geometric surfaces. In conclusion, the method of quaternion can make ray tracing easier and extend the applications of RO model.

2017, 66 (4): 048101.
doi: 10.7498/aps.66.048101

Abstract +

Nanostructured carbon materials possessing good mechanical properties, adsorption characteristics and electrochemical performances, are the most promising candidate for electrode materials of supercapacitors. Among all synthesis methods, hydrothermal synthesis of porous carbon nanosphere (PCNS) is mostly used. Structure-directing agent F108 (PEO132-PPO50-PEO132) has a similar function to popular agent F127(PEO106-PPO70-PEO106) and P123 (PEO20-PPO70-PEO20) used in hydrothermal synthesis, but has greater relative molecular mass and higher hydrophilic/hydrophobic volume ratio, so using block copolymer F108 as soft template will obtain PCNS with special physicochemical properties.
In this paper, PCNS is prepared by post-processing, including carbonization and subsequent KOH activation, of phenolic resin nanoparticles obtained by hydrothermal synthesis through using phenolic resin as a carbon source and block copolymer F108 as a soft template. The as-prepared PCNS sample is characterized by scanning electron microscope (SEM), transmission electron microscope (TEM), X-ray diffraction, nitrogen adsorption and FTIR, etc. The images of SEM, TEM and results of nitrogen adsorption show that the obtained PCNS has the advantages, such as uniform particle size about 120 nm, high spherical degree and large specific surface area of 1403 m2/g and also wide pore size distribution. The results show that post-processing has an important influence on the physicochemical property of PCNS sample such as specific surface area, pore size distribution, crystallinity and surface chemistry. The activation temperature plays an important role in forming pore structure as the specific area of PCNS sample increases from 519 m2g-1 to 1008 m2g-1 after activation at 700℃ (PCNS700), while the activation temperature changes to 900℃ (PCNS900), the specific area rises up to 1403 m2g-1. The pore size distributions show that the peaks are at the same position, which suggests that KOH activation at high temperature makes the primary pore of PCNS deeper. PCNS900 contains more mesopores than PCNS700, so it can be concluded that at the higher activation temperature, the deeper pores inside PCNS are formed, and it is worth noting that pores near 2 nm are largely produced when the temperature arrives at 900℃. KOH processing and high temperature processing contribute greatly to structural ordering, which means that PCNS samples are greatly graphitized. Last but not least, both KOH processing and high temperature processing reduce the number of functional groups on the surface of PCNS samples. Using PCNS samples as activated material to make electrodes, we study how the different physicochemical properties of PCNS samples affect the performance of PCNS electrode. As a result, PCNS700 and PCNS900 show notably larger specific capacitance than PCNS due to their great larger surface specific areas and more structural orderings in graphitic layer stacking. However, PCNS700 shows a lager specific capacitance of 146.75 F/g than PCNS900 (132 F/g) due to its higher number of surface functional groups than PCNS900, though its lower specific surface area. The pore size distribution has a huge influence on the supercapacitor rate capability as the PCNS900 which has more mesopores and the most structural orderings in graphitic layer stacking shows excellent rate capability as well as superior long-term cycling stability (97.5% capacitance retention over 10000 cycles). In summary, PCNS obtained by hydrothermal synthesis through using block copolymer F108 as soft template shows the special physicochemical properties which make it an ideal candidate for the electrode materials of supercapacitor. Moreover, the larger the specific area, more structural orderings in graphitic layer stacking, more appropriate content of mesopores and surface functional groups, the superior performance the electrode materials of surpercapacitor exhibit.

2017, 66 (4): 048501.
doi: 10.7498/aps.66.048501

Abstract +

Light-emitting diode (LED) failure mechanism plays an important role in studying and manufacturing LEDs. In this paper, X-ray perspective instrument is used to carry out the non-invasive and real-time X-ray imaging detection of the representative LED packaging products purchased from 5 Chinese companies. A large number of the welded voids are founded in the thermal pad and the void ratio of thermal pad, which represents the ratio of void area to pad area, is more than 30% for all samples. 1 W warm white light LED of GaN-based vertical via structure is selected to study the mechanism of short-circuit invalidation. The method is carried out by the following steps. Firstly, the surface morphologies of failure samples are compared with those of normal samples by visual observation. Secondly, antistatic electric capacity testing instrument is used to detect the existences of the electrical parameter abnormalities of the failure of non-short-circuit samples. Thirdly, decapsulations are operated on samples by using Silica gel dissolving agent. And the microtopographies of the samples are characterized by optical microscope, energy dispersive spectrometer and scanning electron microscopy. Then the cross-sectional morphologies of failure samples are observed. The failure mechanism can be drawn from the characterizations mentioned above. The study shows that the failure mechanism of the vertical structure of GaN-based vias is that the existences of voids in the Ni-Sn alloy back gold layer and solid-crystal layer reduce the interface bonding strength and thermal conductivity of the LED chip. The heat building-up leads to thermal expansion of the air inside the voids, which increases the electrical stress and thermal stress distribution at the LED chip vias. Long-term heat accumulation and higher electrical stress in the through-hole region, where the chip current density is greatest, lead to the crack and break of GaN epitaxial layer, which is so brittle and fragile, around the through-hole region. It can eventually lead to short-circuit of PN junction and then failure of LED. Back gold layer is the heat-conductive and electric-conductive channel of LED. The concentrations of thermal stress and electrical stress caused by voids in the back gold layer further lead to the uneven current distribution on the chip. This is the main reason why GaN epitaxial layer cracks and breaks. Voids in the back gold layer and solid-crystal layer are the direct and indirect causes of LED short-circuit failure, respectively. Therefore, the packaging process should be standardized to avoid the void occurrence, based on the reasons why voids exist. It can finally improve reliability of LED.

2017, 66 (4): 048801.
doi: 10.7498/aps.66.048801

Abstract +

The traditional lattice matched GaInP/(In) GaAs/Ge triple-junction (3J) solar cell has no much room to enhance its practical achievable conversion efficiency because of its inappropriate ensemble of bandgap energies. According to the P-N junction formation mechanism and the close equilibrium condition, we explore a series of computational codes in the framework of MATLAB to simulate and optimize the inverted structure of series-connected 3J solar cells with a fixed top bandgap of 1.90 eV on GaAs substrate. In this paper, structural optimization is conducted in the real device design, because the realistic (QE) is closely related to a set of material parameters in the subcell, i.e., the absorbtion coefficient of material, subcell thickness, minority carrier diffusion length, surface recombination velocity, etc.
The results indicate improved inverted 3J solar cells with nearly optimized bandgaps of 1.90, 1.38, and 0.94 eV, by utilizing two independently lattice-mismatches (0.17% and 2.36% misfit respectively) to the GaAs substrate. A theoretical efficiency of 51.25% at 500 suns is demonstrated with this inverted design with the optimal thickness (4 m GaInP top and 3.1 m InGaAs middle). By contrast, the efficiency with the infinite thickness of subcells is reduced by 1%, which is mainly attributed to the effect of minority carrier recombination on Jsc. Exactly speaking, if photo-generated carriers make a contribution to Jsc, they must be collected effectively by the P-N junction before recombining. A new model is proposed based on the effect of dislocation on the metamorphic structure properties by regarding dislocation as minority-carrier recombination center. Our calculation indicates that threading dislocations density in the middle junction is approximate to 1.70105 cm-2 when dislocations in the gradient buffer layer are neglected. The theoretical efficiency is increased by 0.3% compared with the inverted design containing a single metamorphic junction.
As a result, based on the two metamorphic combinations, a solar cell with an area of 30.25 mm2 is prepared. The efficiency of the designed cell with two lattice-mismatched junctions reaches 40.01% at 500 suns (AM1.5D, 38.4 W/cm2, 25℃), which is 0.4% higher than that of the single metamorphic junction 3J solar cell.

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

2017, 66 (4): 049401.
doi: 10.7498/aps.66.049401

Abstract +

Incoherent scatter radar is one of the most important detection instruments of the space plasma. But because of the low dust density in natural space plasma, the contribution of charged dust to incoherent scatter spectrum can be completely ignored, therefore the incoherent scattering theory has not appeared in dusty plasma. In the solid rocket plume, the propellant combustion can form a large number of nanometer- and micronmeter-sized dusty particles, and produce a high electron density from high temperature ionization, which makes considerable contributionto charged dusty particles with the high density. Therefore, we develop the incoherent scattering theory of dusty plasma in order to calculate the scattering characteristics of high density dusty plasma produced by rocket plume, for example. The theoretical model including electrons, ions and dusty particles is established by combining effects of charged dusty particles. The incoherent scatter spectral lines of ion resonance region and dust resonance regionare calculated. The effects of dusty particle radius, temperature and density on spectral line structure are discussed. With the increases of dusty particle radius and density, the amplitude of power spectrum increases. With the increase of dust temperature, the amplitude of power spectrum decreases. In the dust resonance region, the control mechanism of dust in spectrum is similar to that of the ions. With the increase of particle size (mass) and decrease of the temperature, the spectrum width narrows, and amplitude and area increase with the increase of density. But in the ion resonance region, the dust control mechanism is completely different, and the influence of the dust on ion line is in the way of attracting ions. So with the increase of dust density, ion line characteristics do not show that the area increases, and dust controls ions by adjusting the Debye radius or electrostatic shielding ball size. By comparing the ion lines with and without dust under the same parameters conditions, the amplitude of the ion line with dust is much larger than that without dust, and the resonance frequency of the ion line is greatly changed. With the dust particles of a relatively high density, one can enhance the ion line, hence the incoherent scattering phenomenon can be more easily observed in rocket plume. On the other hand, due to significant changes of frequency and amplitude in the ion line spectrum, the incoherent scattering inversion method based on the traditional theory will cause a large error in the inversion parameter, even a failure of parameter retrieval. The incoherent scattering theory and relevant physical laws of dusty plasma are presented, which are of great significance for establishing the incoherent scattering theory system and studying the rocket plume parameters.

2017, 66 (4): 049201.
doi: 10.7498/aps.66.049201

Abstract +

The events near their extreme values are termed nearly extreme events. The generalized density of states is proposed that is defined by a probability density function. The rate of nearly-extreme events to the total sample size at a given point is the crowding of nearly extreme events, which is an important index used in many fields. Based on the estimation of the generalized state density of nearly extreme events, the parameters of the generalized state density of nearly-extreme anomalous temperature events are constructed with the temperature daily maximum data in summer and daily minimum data recorded in China in winter in 1961-2013. The daily maximum and minimum temperatures recorded at 174 observed stations in 1961-2013 are selected based on the requirement of data continuity from the climate dataset over China, released by the China Meteorological Administration. According to the analysis of the single station Nanjing, the maximum probability density of occurrence about nearly extremely anomalous temperature is marked as max and the corresponding r of max is marked as rp, which indicates that when the difference between nearly extremely anomalous events and extremely anomalous events is rp, the probability of occurrence is maximum. Then rp is defined as the most probable intensity of nearly extremely anomalous temperature events. max and rp can show the crowding degree characteristics about nearly extremely anomalous temperature events and can carry significant physical meanings in the practical application. So the spatial distribution characteristics of max and rp about nearly extremely anomalous temperature events in China in summer and winter are analyzed respectively. In summer, in the west part of Northwest China, South China and south part of Southwest China easily happen the extremely warming events when the most probable intensity of nearly extremely warming temperature event rp values are 1.0℃ and 2.8℃ and the maximum probability density of occurrence about nearly extremely warming temperature max is up to 44%. In South China, south part of Southwest China and Xizang easily occur the extremely cooling events when the most probable intensity of nearly extremely cooling temperature event rp values are 0.5℃ and 2.5℃ and the maximum probability density of occurrence about nearly extremely cooling temperature max is up to 34%. In winter, the warning information about extremely warming events should give to Southwest China when the most probable intensity of nearly extremely warming temperature events rp values are 1℃ and 2℃ and the maximum probability density of occurrence about nearly extremely warming temperature max is up to 32%. The warning information about extremely cooling events should give to Southwest China, South China and south part of the Yangtze River when the most probable intensity of nearly extremely cooling temperature events rp are 1.0℃ and 4.0℃. Therefore, the maximum probability density of occurrence max and the most probable intensity rp of nearly extremely anomalous temperature events can give some early warning information about the coming extremely anomalous temperature events.

2017, 66 (4): 049501.
doi: 10.7498/aps.66.049501

Abstract +

Spectral radiation detection in deep space background is an important fundamental research in the field of infrared target detection and identification. Based on the spectral radiation and scattering theory, the spatial distribution model of aerial target reflecting background radiation under complex environment is first built. Then the horizontal and pitch spectral radiation models of target are built based on target skin temperature distribution caused by aerodynamic heating. Combining the target motion equation and relative rotation matrix between target matrix and detector matrix, the process-oriented characteristic of spectral response signal with spatiotemporal variation is emphatically analyzed. The simulation results indicate that different target maneuver modes cause different characteristics of spectral response signal, which shows that a remarkable mapping relationship exists between the target maneuver mode and spectral response signal characteristic. Thus using the spectral response signal to identify target maneuver mode provides a feasible method, and the target posture and relative position are the main factors to affect the spectral response signal characteristic.

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

2017, 66 (4): 047201.
doi: 10.7498/aps.66.047201

Abstract +

Explosive-driven ferroelectric generator (EDFEG) has important applications due to its excellent properties of high energy density and small volume. The output of EDFEG is based on the depolarization of ferroelectric during shock wave compression. In a normal mode configuration, a planar shock wave propagates in a direction perpendicular to the polarization axis. If the resulting depolarizing current passes through a large resistive load or a small capacitive load, high electric fields can be produced within the ferroelectric sample. In this case, a portion of the depolarizing charges are lost in the sample due to finite resistivity of shocked ferroelectrics during shock wave transit. But it is very difficult to accurately measure the resistivity of shocked ferroelectric during shock wave compression, due to high pressure and short duration time. In previous studies, the value of the resistivity of shocked Pb(Zr0.95Ti0.05)O3 (PZT95/5) ferroelectric was obtained from the experimental output charge difference for different large resistive loads or by fitting the experimental current histories. However, the current leakage was not observed directly in experiment in the past. Furthermore, the value of the resistivity obtained in each of all these studies was a time-averaged value. In the present work, a new experiment method is developed to investigate dynamic resistivity of PZT95/5 under shock wave compression, in which a pulse capacitor is used as an output load. The current leakage in shocked PZT95/5 is observed in the experiment at a shock stress of 3.5 GPa after the depolarization of all ferroelectrics. This current leakage is just related to the resistance of shocked PZT95/5 and the voltage applied. The experimental results show that the resistivity of shocked PZT95/5 continuously changes in a range of 2.2104 cm-3.5104 cm for time more than the shock transit time of the sample. Based on the experimental results, a dynamic resistance model is established to analyze the resistivity of depolarized PZT95/5 ferroelectric ceramic during shock wave transit in ferroelectric. The simulation results reveal dynamic characteristic of the resistivity of depolarized PZT95/5 ferroelectric ceramic under shock wave compression. The further analysis of experimental results shows that the resistivity continuously changes between 2.0104 cm and 8.0104 cm during shock transit in ferroelectrics. It is believed that dynamic characteristic of the resistivity of shocked PZT95/5 ferroelectric ceramic is related to pressure, electrical field applied and the defects in the material. The dynamic resistivity of shocked PZT95/5 obtained in this paper and its dynamic resistance model will be helpful for designing EDFEGs and their applications in the future.

Sparse inversion method of T2 spectrum based on the L1 norm for low-field nuclear magnetic resonance

2017, 66 (4): 047601.
doi: 10.7498/aps.66.047601

Abstract +

The technology of low-field nuclear magnetic resonance (LF-NMR) is commonly used in food, agriculture, energy and chemical sectors due to its non-destructive, non-invasive, in situ, green and other advantages. Recently, this technology played an increasingly large role in the field of food-safety supervision especially. In oil product quality testing, conventional T2 spectrum inversion methods such as the non-negative singular value decomposition (SVD) algorithm can only reflect T2 spectrum in a smooth model. However, for a sparse model, the inversion result of non-negative SVD algorithm is expected to be very glossy, leading to low resolution of T2 spectrum and inaccurate analysis of sample property. To solve this problem, we propose a sparse T2 spectrum inversion algorithm based on the L1 norm minimization constraint. In this paper, we establish the sparse model expression of NMR echo curve, and obtain the T2 sparse spectrum inversion results based on the inner truncated Newton-point method. Furthermore, the effectiveness of L1 sparse inversion algorithm is examined by the synthetic data of the smooth model and the spare model which have different peak numbers and signaltonoise ratios (SNRs). Synthetic results show that compared with the non-negative SVD algorithm, the L1 sparse algorithm is appropriate for both the smooth model and the sparse model with higher inversion accuracy. When the number of T2 peaks in a sparse model changes from a single peak to a quad peak, the L1 sparse algorithm can still obtain accurate inversion results, while the SVD algorithm results in a gradual deterioration, and cannot even determine the peak number. Under the sparse model, when the SNR of the measured NMR curve is gradually changed from 5 dB to 50 dB, the L1 sparse algorithm at 20 dB or more can obtain accurate inversion results which have less than 10% peak error and less than 5% peak position error and amplitude average error. However, the non-negative SVD algorithm cannot obtain accurate results at each SNR. Finally, multiple sets of frying oil samples are utilized to prove the accuracy and robustness of L1 sparse inversion algorithm. Inversion results of seven sets of frying oil samples show that the L1 sparse algorithm prefers the non-negative SVD algorithm. The obtained T2 spectrum by the L1 sparse algorithm shows three peaks obviously, and the T21 peak area ratio S21 and the single component relaxation time T2w are higher linear with respect to frying time than the results by non-negative SVD algorithm, which is useful for detecting the frying oil quality change. The inversion results of the T2 spectrum at different SNRs are consistent with the synthetic results, i.e., when the SNR is reduced, the T2 spectrum inversion results from the L1 sparse algorithm are better than those from the non-negative SVD algorithm when SNR is greater than 20 dB.

## EDITOR'S SUGGESTION

2017, 66 (4): 047801.
doi: 10.7498/aps.66.047801

Abstract +

Unlike the finger-like n-contact that is prepared after the wafer bonding and the N-polar GaN surface roughening for GaN-based vertical structure light-emitting diodes (LEDs) grown on Si substrates, the embedded via-like n-contact is formed prior to the wafer bonding. The high temperature process of the wafer bonding often causes the electrical characteristics of the via-like embedded n-contact to degrade. In this paper, we study in detail the effect of plasma treatment of the n-GaN surface on the forward voltage of GaN-based LED grown on Si substrate. It is shown that with no plasma treatment on the n-GaN surface, the forward voltage (at 350 mA) of the 1.1 mm1.1 mm chip with a highly reflective electrode of Cr (1.1 nm)/Al is 3.43 V, which is 0.28 V higher than that of the chip with a pure Cr-based electrode. The LED forward voltages for both kinds of n-contacts can be reduced by an O2 plasma treatment on the n-GaN surface. But the LED forward voltage with a Cr/Al-based electrode is still 0.14 V higher than that of the chips with a pure Cr-based electrode. However, after an Ar plasma treatment on the n-GaN surface, the LED forward voltage with a Cr/Al-based electrode is reduced to 2.92 V, which is equal to that of the chip with a pure Cr-based electrode. The process window of the n-GaN surface after the Ar plasma treatment is broader. X-ray photoelectron spectroscopy is used to help elucidate the mechanism. It is found that Ar plasma treatment can increase the concentration of N-vacancies (VN) at the n-GaN surface. VN acts as donors, and higher VN helps improve the thermal stability of n-contact because it alleviates the degradation of the n-contact characteristics caused by the high temperature wafer bonding process. It is also found that the O content increases slightly after the Ar plasma treatment and HCl cleaning. The O atoms are mainly present in the dielectric GaOx film before the Ar plasma treatment and the HCl cleaning, and they exist almost equivalently in the conductive GaOxN1-x film and the dielectric GaOx film after Ar treatment and HCl cleaning. The conductive GaOxN1-x film and the VN donors formed during the plasma treatment can reduce the contact resistance and the LED forward voltage.