## Vol. 64, No. 24 (2015)

##### 2015-12-20

###### REVIEW

2015, 64 (24): 247804.
doi: 10.7498/aps.64.247804

Abstract +

In recent decades, the positron annihilation spectroscopy technique has been used to characterize the microdefects of materials due to its advantages of non-destruction and high sensitivity on an atomic level. Positron annihilation spectroscopy technique is widely used in the microstructure study of thin film material surface and interface due to the rapid development of the slow positron beam technology. The slow positron beam technique can provide depth distribution information about material surface microstructure. Therefore, it is widely used to study the distributed defect concentrations in crystalline materials and the properties of thin films, surfaces and interfaces of layered materials. This article summarizes the slow positron beam technique applications and progress in the study of metal alloy materials. Firstly, this article introduces the slow positron beam technology development and application research achievement in detail. Secondly, it provides how to acquire the slow positron beam, introduces some kinds of and the principles of experimental measurements, and the major methods include Doppler bradening spectroscopy, coincidence Doppler broadening and PL. Thirdly, according to the defects induced by different ways, the latest experimental results about the material internal microdefect formation mechanism, evolution mechanism, defect feature research, such as microstructure, chemical environment, electron density and momentum distribution are introduced. The methods of inducing defects mainly include irradiation, physical deformation and chemical corrosion. Particles irradiation can be classified as four parts according to the different types of particles. In addition, monolayer and multilayer thin films have also been summarized. Finally, the new technique of thermal desorption spectroscopy and experimental measurements of age-momentum correlation are proposed. We can know that positron annihilation spectroscopy technology is a very special and effective nuclear spectroscopy analysis method in material microstructure study, and the slow positron beam technique makes it possible to study the depth distribution information about the thin film material surface microstructure. There is no doubt that this technique will play a huge role in the progress of material science and the creation of industrial material.

###### GENERAL

2015, 64 (24): 240201.
doi: 10.7498/aps.64.240201

Abstract +

Radiative imaging of combustion flame in furnace of power plant plays an increasingly important role in combustion diagnosis. The flame radiation image taken by a charge-coupled device (CCD) camera can reconstruct three-dimensional flame temperature distribution in the furnace. CCD cameras are used for capturing the flame images to obtain the line-of-sight radiation intensities. The temperature reconstruction matrix equation is a seriously pathological equation. Thus the temperature field reconstruction problem is an ill-posed problem. The two algorithms (Tikhonov regularization and truncated singular value decomposition (TSVD)) for solving the temperature field reconstruction are introduced. The size of the numerical simulation system is 10 m × 10 m × 10 m, which is divided into 10 × 10 × 10 volume elements in the three dimensions. Each volume element is a unit cube. Generalized cross-validation (GCV) is used to select the correct regularization parameter. The measured data are simulated by adding different random errors to the exact solution of the direct problem. The reconstructed temperature deviation is calculated by the two algorithms separately. When the measuring errors are 0.05 and 0.10, the reconstruction errors based on Tikhonov are respectively 19.3% and 7.0%, less than those based on TSVD. When the measuring errors are 0, 0.01, 0.03 and 0.07, the differences between the two kinds of errors are all less than 3%. Both the algorithms can reconstruct the correct temperature field. The times required to reconstruct the temperature field by the two algorithms are compared and their effects of the maximum temperature are also compared. When the measuring errors are 0, 0.01, 0.03, 0.05, 0.07 and 0.1, the reconstruction times based on Tikhonov are respectively-0.0917,-0.049, 0.161, 0.002, 0.135 and 0.091 s, shorter than the reconstruction times based on TSVD. There is singular value decomposition (SVD) in TSVD. And this process takes more than 2 s. If the problem is more complicated, SVD takes much more time. The errors of the maximum reconstruction temperature under Tikhonov are smaller. And the position of the maximum reconstruction temperature under Tikhonov is near the position of the exact maximum temperature in space. The maximum reconstruction temperature under TSVD is not so good as that under Tikhonov. Preliminary results indicate that the Tikhonov-based reconstruction is slightly better than the TSVD-based reconstruction, especially in reconstruction error, reconstruction time, and effects of the maximum temperature.

2015, 64 (24): 240301.
doi: 10.7498/aps.64.240301

Abstract +

As a new quantum computing model, quantum walk has been widely studied in recent years. It consists of discrete time quantum walk and continuous time quantum walk. Discrete time quantum walk includes coin quantum walk and scattering quantum walk. Meanwhile as a quantum search algorithm, Grover algorithm can search an unsorted database in time complexity of O(√N) . Recent years quantum walk has been used to solve search problems and some of them have been proved to be as efficient as Grover algorithm. Making full use of the novel properties of quantum walk, the quantum walk search algorithms on the 2D grid and hypercube have been proposed. Inspired by phase matching condition of Grover algorithm, we propose a new quantum walk search algorithm which is based on coin quantum walk. Firstly we give the graph to the quantum walk, and then describe the algorithm in detail. Algorithm uses different coin operators and shift operators for two different cases and draws the corresponding iteration operators. Then we prove that iteration operators used in the algorithm are unitary operators. Then we analyze the time complexity and probability of success of the algorithm. Analysis indicates that the time complexity of the algorithm is the same as that of Grover algorithm, however when the targets to be searched are more than 1/3 of the total targets, the algorithm probability of success is greater than that of Grover algorithm. Finally we give the circuit implementation of the algorithm.

2015, 64 (24): 240302.
doi: 10.7498/aps.64.240302

Abstract +

On the basis of quantum-classical correspondence for two-dimensional anisotropic oscillator, we study quantum-classical correspondence for two-dimensional rotation and translation harmonic oscillator system from both quantum-classical orbits and geometric phases. Here, the two one-dimensional oscillators refer to a common harmonic oscillator and a rotation and translation harmonic oscillator. In terms of the generalized gauge transformation, we obtain the stationary Lissajous orbits and Hannay's angle. On the other hand, the eigenfunctions and Berry phases are derived analytically with the help of time-dependent gauge transformation. We may draw the conclusion that the nonadiabatic Berry phase in the original gauge is-n times the classical Hannay's angle, here n is the eigenfunction index. As a matter of fact, the quantum geometric phase and the classical Hannay's angle have the same nature according to Berry. Finally, by using the SU(2) coherent superposition of degenerate two-dimensional eigenfunctions for a fixed energy value, we construct the stationary wave functions and show that the spatial distribution of wave-function probability clouds is in excellent accordance with the classical orbits, indicating the exact quantum-classical correspondence. We also demonstrate the quantum-classical correspondences for the geometric phase-angle and the quantum-classical orbits in a unified form.

2015, 64 (24): 240303.
doi: 10.7498/aps.64.240303

Abstract +

According to the map of a qubit, a scheme for protecting entanglement of two-qubit by the weak measurements at finite temperature is proposed. Since the choices of the channel parameters and initial states are very different for different weak measurement strengths, two local unitary equivalent initial entangled states |ψ> and |φ> are chosen. Weak measurements are performed when two initial entangled states go through the generalized amplitude damping channel, and the analytical expressions of getting maximum concurrence entanglement Cr and weak measurement parameters m and n can be obtained by performing an overall optimization for four weak measurement parameters. What is more, the relationship between the weak measurement parameters and the channel parameters is further explored. Theoretical results show the entanglement protection project based on weak measurements can effectively enhance the entanglement and even prevent the sudden death of entanglement in some cases. When the channel parameter r is fixed, for different values of parameter p, the concurrence is centered at p = 0.5, and the weak measurement parameters of the maximum concurrence entanglement are the same as those for initial state |ψ>, while they are different for initial state |φ>. Under the condition of different values of r, for the fixed p and initial state |ψ> or |φ>, the weak measurement parameters remain constant as the entanglement reaches the maximum and the concurrence decreases with the increase of parameter r. Through the analysis of channel parameters, higher entanglement can be obtained by choosing appropriate channel parameters and initial state.

2015, 64 (24): 240304.
doi: 10.7498/aps.64.240304

Abstract +

The optimal relay path calculation and selection are important factors to affect the performance of quantum communication network. Current researches seldom consider the quantum path selection in real noisy environments. One of the difficult problems is how to analyze the influence of the noise on the quantum communication in multi-hop channels. This paper aims to solve the path selection problem of the quantum teleportation network in noisy environments. The process of entanglement swapping in the phase damping channel is first studied with an example of two-hop quantum channel, whose damping factors are p1 and p2. The entanglement states |φ> 12+ and |φ> 34+ are distributed separately in each hop. After the entanglement swapping, the density matrix of the entanglement state of photon 1 and photon 4 is obtained by performing a partial trace over the environment. Then, the Bures fidelity of this entanglement is calculated. After that, we define the path equivalent damping factor to describe the characteristic of the two-hop noisy quantum relay path. With an equivalent calculation method, the results above can be generalized to multi-hop channel. The path equivalent damping factor of the multi-hop amplitude damping channel is also obtained. According to these results, we propose an optimal relay protocol for the quantum teleportation network with the criterion of path equivalent damping factor, which means that a relay path with the minimum path equivalent damping factor can obtain the highest teleportation fidelity. The types and parameters of the messages used in the protocol are given. The processes of the relay protocol are described specifically, including neighbor finding, quantum link noise measurement, and quantum link status transmission. An improved Dijkstra algorithm is used in the optimal path calculation. Furthermore, because the entanglement resources maintained in the quantum nodes are limited and may be exhausted in superior quantum links, we propose a resource reservation method to avoid the failure of the relay path setup. Theoretical analysis and simulation show that our method can obtain a lower average equivalent damping factor and higher teleportation fidelity. It can also be seen that increasing the number of the entanglement resources will raise the performance of the quantum network, however, it brings higher cost and complexity. Therefore, the entanglement resources maintained in the quantum nodes must be configured reasonably according to the network scale, the cost, the time delay and the need of the users.

2015, 64 (24): 240501.
doi: 10.7498/aps.64.240501

Abstract +

As one of the most important aspects of spreading dynamics on networks, propagation of rumor, which includes the process of rumor diffusing and elimination, plays an important role in the understanding of information dissemination within social networks. However, the current understanding of rumor propagation within networks is far from clear, especially the full analysis of the process of rumor diffusing and elimination is lacking. Here, with the rumor elimination process supplemented to the susceptible-infective-refractory (SIR) rumor spreading model, a modified rumor spreading model is established and defined as spreader-ignorant-eliminater-Rstifler-Estifler (SIERsEs) model. The developed mean-field equations of SIERsEs model, with the diffussing and elimination thresholds calculated, could describe the theory of steady-state dynamics of the rumor propagation. Simulation analysis is performed to assess the interaction between the diffussing and elimination process, and estimate the influences of diffusing rate, estimation rate, and averaged degree of the network, on the rumor spreading. The results show whether low or high value of average network degree would accompany a low level of the influence of rumor propagation. In addition, the shortcomings of the traditional immunization strategies, such as targeted immunization and acquaintances immunization, are pointed out. Based on this understanding, we propose two optimized immunization strategies, defined as active immunization and passive immunization, and we further evaluate how different parameters (forgetting rate of spreader, forgetting rate of eliminater and the starting time of immunization) affect the suppression effectiveness of the newly developed active and passive immunization strategies. Importantly, some so-called rumor-inhibition strategies actually could not inhibit but enhance the rumor propagation instead. These obtained findings in the present study could not only elaborate our understandings in spreading dynamics within network, but also provide an insight into the developing effective strategies of inhibiting rumor propagation.

2015, 64 (24): 240502.
doi: 10.7498/aps.64.240502

Abstract +

Periodic potential system is widely used in a lot of areas such as biological ratchet model of motor, Josephson junction in the field of physics, engineering mechanics of the damping pendulum model, etc. Meanwhile, in the study of stochastic resonance, noise is crucial for dynamical system evolution. There are mostly colored Gaussian noises with nonzero correlation times in practical problems. Dichotomous noises belong to the color noises, and they have some simple statistical properties. In this paper, we study the motion of a Brownian particle in a periodic potential, driven by both a periodic signal and a dichotomous noise. The periodic potential system is different from the bistable system, so we use multiple indexes to explain the stochastic resonance. We calculate the average input energy of the system and the average output signal amplitude and phase difference by using stochastic energetics. Then we discuss the influences of the dichotomous noise intensity, noise correlation time and asymmetric coefficient of potential energy on the stochastic resonance. The results show that with the increase of the noise correlation time, a minimum value and a maximum value occur on the curve of the average input energy, meanwhile, the phenomenon of resonance appears in the system. With the increase of the noise intensity, the value of noise correlation time becomes greater when the phenomenon of stochastic resonance appears. Therefore, the region of stochastic resonance becomes bigger as the noise intensity or the asymmetry coefficient increases. Moreover, with the increase of the noise intensity, a mono peak is found for the signal-to-noise ratio (SNR) of the system and the stochastic resonance appears in this system. With the increase of the noise intensity, we compare the change of the SNR, the average input energy, and the average output signal amplitude. We find that the values of the amplitudes of the average output signal and SNR are basically the same, while the values of the amplitude of the average input energy of the system are a little different. This is because during the process of periodic signal doing work to the system, noise does work and passive dissipation energy of the system occures. In addition, when the curves of the amplitude of the average output signal and SNR reach their corresponding minimum values, the phase difference between the output signal and input signal is minimal.

2015, 64 (24): 240503.
doi: 10.7498/aps.64.240503

Abstract +

Random number generator (RNG) plays an important role in many areas including image encryption, secure communication, radar waveform generation, etc. However, existing analog methods for random number (RN) cannot satisfy the demand of bit rate. In the even worse case, system parameters from analog devices are easily distorted by surroundings, leading to a weak system robustness. As a result, researchers start to turn to digital implementation which is stabler and more efficient than analog counterpart to produce RN. However, digital methods suffer dynamical degradation due to the limited word length effect. Though some remedies, such as increasing computing precision, cascading multiple chaotic systems, pseudo-randomly perturbing the chaotic system, switching multiple chaotic systems, and error compensation method, are proposed, the limitations are even inevitable. Recently, some continuous-time chaotic oscillators combined with digital devices were used to realize RNG, and a novel approach was proposed to solve the dynamical degradation of digital chaotic system by coupling the given digital chaotic map with an analog chaotic system, where the analog chaotic system is used to anti-control the given digital chaotic map. But this method requires a whole continuous-time system realized with analog devices which restrict the performance of the integral system.#br#In this paper, a novel digital-analog hybrid chaotic system with only one analog device is constructed for the production of RN. The chosen analog device is a generalized memristor consisting of a diode bridge and a parallel RC filter.#br#Memristor is the fourth fundamental electronic component which has provoked extensive researches since the successful realization by Stan Williams's group at HP Labs in 2008.#br#The paper is arranged as follows. Firstly, a generalized memristor realized by a memristive circuit is introduced and its basic properties are given. Then the block diagram of the digital-analog hybrid system based on a single memristor feedback is depicted, and the mathematical model of the system is derived from the block diagram. Thirdly, the simple Logistic map is applied to the hybrid model and its dynamic behaviors are simulated and compared with those from the ideal Logistic before a more complex two-way coupled saw tooth map is applied to the same simulation, verifying the effectiveness of the proposed hybrid system. Finally, the complex coupled map is applied to the practical circuit producing RN which passes the NIST test suite smoothly.#br#The hybrid system has the following advantages: firstly, the introduction of the analog memristor is able to overcome the dynamical degradation in a digital system, avoiding the limited word length effect essentially. Secondly, the least analog device alleviates the sensibility to parameters and the restriction on bit rate in analog systems, ensuring that the hybrid system is robust. Thirdly, the system structure can be easily integrated into a relevant system. By designing the circuits of the system, the field programmable logic gate array of digital part can be used to realize chaotic map while the single memristor acts as a feedback to the digital part.#br#The experimental results show that the novel hybrid system is insensitive to the variations of circuit parameters and the produced RN is of great randomness, satisfying the practical applications.

2015, 64 (24): 240504.
doi: 10.7498/aps.64.240504

Abstract +

Pores, which have remarkable influence on many properties of coatings such as wear resistance, anti-corrosion, thermostability, etc. are the natural structure formed in plasma sprayed coatings, and have been regarded as one of the most important indexes in spraying parameter refining. Hence, it is of great significance to comprehensively characterize the structural parameters of pores in the coatings, especially for the accurate evaluation of the coating quality. In this paper, probability statistics method, fractal method and digital image analysis technique are used to investigate the number, shape, size and distribution of the pores. Besides, the formation mechanism of the coatings is discussed. First, Fe-based coatings with different porous structures are fabricated at different spraying powers. Second, the digital image analysis technique is used to process the scanning electron microscope micrographs of coatings with different pores. Finally, the Weibull statistical model is utilized to analyze the distribution law of perimeter and area of the pores. The power law of area-perimeter which originats from fractal theory is employed to quantitatively characterize the irregular morphology of the pores. In order to investigate the formation mechanism of the pores, the Spraywatch is used to monitor the flying condition of the spraying particles in the whole experimental process. The result shows that fractal dimension (FD) can characterize the irregular morphology of pores. The area becomes bigger and the border becomes more complex when the FD is larger, and there is a good relationship between FD and the formation mechanism of the pores. Besides, the areas and perimeters of the pores obey the binomial Weibull distribution obviously, namely, the shape parameter (β) turns larger as pore size becomes smaller. The spraying power has a different effect on the distribution law of pore size. With the increase of the spraying power, the molten state is improved. As a result, the size of the pore decreases obviously. When the area or the perimeter is less than their corresponding characteristic values, the probability density of the pores with the same area or perimeter becomes closer to each other, which indicates that the effect of spraying power on the pores of small size is much lower.

2015, 64 (24): 240505.
doi: 10.7498/aps.64.240505

Abstract +

We present a novel laser system with an external cavity delay feedback semiconductor laser under the control of Faraday effect. To study the chaos-control and chaos-anti-control of the laser system, we construct two types of optical path structures as two control systems of the negative feedback and the ring cavity by using the combination of the Faraday effect controller, the polarizer and the mirror. We give a physical model of laser dynamics with the delayed negative feedback or the delayed positive feedback under the control of Faraday effect. Using the Faraday effect principle of magnetic rotation and the characteristics of the system, we can achieve the double parameter control of the laser. We can shift the optical rotation angle by operating Faraday effect controller and modulate the optical delay time by performing the mirror to vary the double parameter. The laser can be controlled to a double-cycle, a tri-cycle, a multi-cycle, and beat phenomenon by using the control system of the negative feedback, etc. The periodic laser can be anti-controlled to chaos by using the control system of the ring cavity. Some control and anti-control areas formed with the distribution of magnetic rotation angular are found in the laser. For the negative feedback system under the some control cases, the chaotic laser can be controlled to some tri-cycle states between π/14 and π/9. By shifting the control parameters, the chaotic laser can be controlled to some cycle-7 states between 10π/133 and 10π/108 and another tri-cycle region is found from 10π/96 to π/8. Under other control parameters, the chaotic laser can be controlled to some cycle-8 or cycle-9 states. For the ring cavity system under the some control cases, the dual-cycle region is between π/10 and π/30, the cycle-6 region is between π/4 and π/5, the cycle-13 region is found to be from π/6 to 10π/76. In another control case, the large chaos-anti-control region is found to exist between 0 and π/12. Dynamic controls of the chaotic laser and the periodic laser are also studied while the transformation and evolution of laser states are discussed. It is found that it takes about 10 ns for one state to change into another state when the control operation is applied to the laser. The control method is very useful for studying chaos-control, new laser system and its application.

2015, 64 (24): 240506.
doi: 10.7498/aps.64.240506

Abstract +

Unknown time-varying parameters, including time-delay and system parameters, commonly exist in chaotic systems. These unknown parameters increase the difficulties in controlling the chaotic systems, and make most of the existing control methods fail to be applied. However, if these parameters can be estimated, they will facilitate the controller design. Therefore, in this paper, a parameter identification problem for a general time-delay chaotic system with unknown and time-varying parameters is considered, where these unknown time-delay and parameters are slow time-varying. It is very difficult to solve this problem analytically. Thus, a unified identification method is proposed to solve the identification problem numerically. To solve this identification problem, firstly, the time horizon is divided into several subintervals evenly. Then the time-varying parameters are approximated by piecewise constant functions. The height vectors of the piecewise constant functions are unknown and to be determined. Furthermore, the heights of the piecewise constant functions keep constant between each pair of the successive partition time points but switch values at the partition time points. After the approximation, the original identification problem for finding the nonlinear functions of the unknown parameters is transformed into a problem of selecting approximate parameter vectors, where the heights of the piecewise constan functions are unknown parameter vectors to be determined. Secondly, to solve the problem of selecting approximate parameter vectors quickly, the partial gradients of the objective function with respect to the parameter vectors are derived; and they are then integrated with a gradient-based procedure to obtain the unknown heights. As the number of partitions for the piecewise function increases, the optimal results of the approximate problem will approach to the optimal results of the original parameter identification problem. Hence, the optimal piecewise functions will approach to the real nonlinear functions for the unknown parameters. Finally, parameter identification experiments on time-delayed Mackey-Class and time-delayed logistic chaotic systems are carried out. The effects of the partition number on the estimated results are discussed. Numerical results demonstrate that when some switching times of the unknown parameters do not coincide with any partition time points, small error between the estimated results and the real values are present. However, these errors can be filtered and the estimated results are consistent well with the real values. Hence, the proposed method is reasonable and effective.

## EDITOR'S SUGGESTION

2015, 64 (24): 240601.
doi: 10.7498/aps.64.240601

Abstract +

Absolute calibration can be realized by means of correlation photon which is generated by the parametric down conversion. The main difficulty lies in obtaining correlation information about photon flux when this method is applied to analog detector calibration process. A novel method of processing the photocurrent on the basis of detecting multimode spatial correlation is proposed. By converting the charge quantity contained in the photocurrent detected in a certain time interval into the photon counting, and by using double channels balance detection and measuring mean photon counts of each model to correct the dual channels fluctuations, the high accuracy calibration of quantum efficiency can be achieved. The photon fluxes of two channels are balanced by inserting an adjustable attenuator in one optical path. The cross section of pumping beam is comparable to the detection area to ensure three-wave colinearity, and the coherent area of the correlation photons is obtained by measuring pump beam waist and lens focus length. With the known detection area, coherence time and coherence area, the average photon number of each mode is computed. This process should be performed under the average photon number of each mode as a reference which could be used for the proportional scaling of equivalent photons of two channels. Based on this new approach, the absolute power responsivity of an InSb detector is calibrated at 3390 nm with correlated photon pairs at 631 and 3390 nm. The calibration procedure and experiments are described and the uncertainty of this method is analyzed. The results show a relative combination uncertainty of about 7.785% for this calibration method, which agrees well with the result independently obtained in the national photoelectronic metrology laboratory within a relative difference of about 3.6%. This result verifies that the quantum efficiency of an analog detector can be calibrated by the correlated photon method, which has potential applications in highly accurate radiometric calibration without external standards.

2015, 64 (24): 240701.
doi: 10.7498/aps.64.240701

Abstract +

Reconstruction of a sample photoacoutic (PA) image is the research focus in PA imaging system that is based on acoustic lens. Among all existing reconstruction methods, the reconstructing PA image is usually obtained by the projection of the absorption distribution which is regarded as PA signal of a sample. However, this equivalent relationship is just approximate and not accurate in theory. In this paper, the accurate relationship between the absorption coefficients of the sample placed on the object plane and its PA pressure signals focused on the image plane is successfully demonstrated. Both the integral and the extraction envelope methods are firstly proposed to reconstruct the axial PA image of an absorbent sample. The resolution of the reconstructed PA image obtained by Hilbert transform is theoretically higher than that by integral method, and the reason is explained. Different samples are chosen to experiment on the acoustic lens PA imaging system. A three-dimensional fast PA imaging of the absorbent sample is realized by combining its axial imaging capability with its lateral imaging capability of acoustic lens. The reconstruction result shows that both the lateral and the axial resolutions of the reconstruction image are both about 1 mm. The quality of a sample PA image obtained by Hilbert transform is better than that by integral method.

2015, 64 (24): 240305.
doi: 10.7498/aps.64.240305

Abstract +

There are two approaches to investigating the quantum mechanics for a particle constrained on a curved hypersurface, namely the Schrödinger formalism and the Dirac theory.#br#The Schrödinger formalism utilizes the confining potential technique to lead to a unique form of geometric kinetic energy T that contains the geometric potential VS and the geometric momentum p,#br#T=-ħ2/(2m)▽2+VS=-ħ2/(2m)[▽2+(M2-K)],p=-iħ(▽2+Mn),#br#where ▽2 is the gradient operator on the two-dimensional surface. Both the kinetic energy and momentum are geometric invariants. The geometric potential has been experimentally confirmed in two systems.#br#The Dirac's canonical quantization procedure assumes that the fundamental quantum conditions involve only the canonical position x and momentum p, which are in general given by#br#[xi,xj]=iħÂij,[pi,pj]=iħΩij,[xi,pj]=iħΘij#br#where Âij, Ωij, and Θijare all antisymmetric tensors. It does not always produce a unique form of momentum or Hamiltonian after quantization. An evident step is to further introduce more commutation relations than the fundamental ones, and what we are going to do is to add those between Hamiltonian and positions x, and between Hamiltonian and momenta p, i.e.,#br#[x,Ĥ]=iħÔ({x,HC}c) and [p,Ĥ]=iħÔ({p,HC}c)#br#where {f,g}c denotes the Poisson or Dirac bracket in classical mechanics, and Ô({f,g}c) means a construction of operator based on the resulting {f,g}c, and in general we have [f,ĝ]≠Ô({f,g}c). The association between these two sets of relations means that the operators {x,p,H must be simultaneously quantized. This is the basic framework of the so-called enlarged canonical quantization scheme.#br#For particles constrained on the minimum surface, momentum and kinetic energy are assumed to be dependent on purely intrinsic geometric quantity. Whether the intrinsic geometry offers a proper framework for the canonical quantization scheme is then an interesting issue. In the present paper, we take the catenoid to find whether the quantum theory can be established satisfactorily. Results show that the theory is not self-consistent. In contrast, in the threedimensional Euclidean space, the geometric momentum and geometric potential are then in agreement with those given by the Schrödinger theory.

###### NUCLEAR PHYSICS

2015, 64 (24): 242801.
doi: 10.7498/aps.64.242801

Abstract +

Neutron holography is a new imaging technique based on the recording of the interference pattern of two coherent waves emitted by the same source, which allows observing the spatial order of microscopic objects like molecules or atoms in crystal sample. Two approaches can be used in neutron holography measurements. One is called inside-source holography, in which both the reference wave and object wave come from embedded atoms in the sample and propagate toward the detector outside the sample. The second approach called inside-detector holography is the inverse method of inside-source holography, in this case the reference wave is the initial neutron beam coming from a distant source outside the sample, while the atoms embedded in the sample act as detectors. In an ideal inside-source holography experiment, the sample should be fixed and the detector moves on a sphere, which is not practical because the detector system is usually heavy and far from the sample. In order to minimize the operation space, the detector always moves on a circle around sample or is located at a fixed position, while the sample rotates in an appropriate way to imitate the motion of the detector in a sphere. However, the orientation of the sample relative to the incident neutron beam is changed during sample rotation, and part of the inverse hologram is recorded together with the inside-detector hologram, which can cause distortion in the holographic reconstruction. In this paper, we simulate neutron holograms and reconstructions based on three different sample/detector rotations. In the first case, the detector moves on a circle, while the sample rotates about an axis perpendicular to the detector moving surface. In the second case, the detector is fixed, while the sample rotates around two perpendicular axes, the θ axis rotating the sample through πradians is perpendicular to the incident beam-detector plane, while the θ axis rotating the sample through 2πradians moves on a circle parallel to the incident beam-detector plane, this rotation can be carried out on a 3-axis spectrometry. In the third case, the detector is also fixed and the sample rotates around two perpendicular axes, but the θ axis is parallel to the sample-detector direction, while the θ axis moves on a circle perpendicular to the incident beam-detector plane, this rotation can be carried out on a 4-cycle spectrometry. The distortions and corresponding correcting methods of three kinds of rotations are discussed. The result shows that most distortions can be corrected by using special measurement or reconstruction techniques. Furthermore, pure sample rotation based on 3-axis spectrometer can achieve the best reconstruction result, so this rotation approach is preferred if conditions permit.

###### ATOMIC AND MOLECULAR PHYSICS

2015, 64 (24): 243101.
doi: 10.7498/aps.64.243101

Abstract +

The ground state X3Σ- and low-lying excited electronic state A1Π of AsS+ ion are investigated employing the full valence complete active space self-consistent field method combined with the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach. The basis set used in the calculations is Dunning correlation-consistent basis set, aug-cc-pV5Z. To improve the quality of the potential energy curves (PECs), three kinds of corrections are considered in the present work. First, the Davidson modification is adopted to deal with the size-extensity errors from the MRCI calculations. Then, relativistic correction is calculated by the second-order Douglas-Kroll Hamiltonian approximation at the level of cc-pVQZ basis set. Finally, to eliminate the truncation errors of the basis set, the PECs of the two electronic states for each species are extrapolated to the complete basis set limit by the two-point energy extrapolation scheme. Two large basis sets, i.e., aug-cc-pVQZ and aug-cc-pV5Z, are used to perform the extrapolation calculations. With the aid of VIBROT program, all the PECs of X3Σ- and A1Π obtained here are fitted to the analytical forms, which are used to derive the spectroscopic parameters (De, D0, ωeχe, αe and Be) of 75As32S+ and 75As34S+. The effects of the Davidson modification, relativistic correction and basis set extrapolation are discussed respectively. The results indicate that the quality of almost all the spectroscopic parameters is improved by considering these corrections, which exhibit excellent agreement with the experimental data. Besides, the first 10 vibrational states for the two electronic states of 75As32S+ and 75As34S+ are determined when the rotational quantum number J equals zero. For the first 10 vibrational states, the vibrational level G(ϒ), inertial rotation constant Bv, and centrifugal distortion constant Dv are evaluated when J=0.

2015, 64 (24): 243102.
doi: 10.7498/aps.64.243102

Abstract +

Micro-defects in an energetic material is an important factor for the formation of “hot spots” and successive explosive detonation. However, an understanding of the micro-mechanism of forming “hot spots” is limited and the development and application of energetic materials are hindered due to the less knowledge of micro-defects inside the materials. In order to understand the characteristics of micro-defects and explore the basic mechanism of forming “hot spots” caused by defects, the effects of molecular vacancy defect on the geometrical structure, electronic structure and vibration characteristics of Hexogeon (RDX) energetic materials are studied using the first-principle method, and the basic formation mechanism of initial “hot spot” is discussed. The effects of molecular vacancy defect on the RDX geometrical structure, electronic band structure, electronic density of states and frontier molecular orbitals are analyzed using the periodic model, while the influences of molecular vacancy defect on the vibration characteristics of RDX systems are calculated using the cluster model. Infrared vibration spectra and vibration characteristics of the internal molecules at the same vibration frequency for the perfect and defective RDX systems are obtained. It is found that vacancy defect makes the N–N bond near the defect long, and the molecular structure loose; some degenerate energy levels in the conduction band present separation and the electronic density of states decreases; the bottom of the conduction band and the top of the valence band contributed by N-2p and O-2p orbitals shift to the Fermi surface, which reduces the energy band gap and increases the activity of system. At the same time, the calculations of the frontier molecular orbitals and the infrared vibration spectra show that the molecular defect makes the charge distributions of highest occupied moleculer orbital concentrated mainly in the molecule near the defect, and the C–H and N–N bond energies decrease. For the defective system, some molecules around vacancy have large vibration amplitude towards the vacancy direction. This will be likely to cause hole to collapse and realize the conversion of energy. These characteristics indicate that the presence of molecular vacancy defect causes the energy band gap to decrease, the structures of the molecules near the defect become loose, the charge distribution increases and the reaction activity augments. When the defective system is loaded by external energy, the molecules near the defect are expected to be unstable. The C–H or N–N bonds in those molecules are more prone to rupture to cause chemical reaction and release of energy, which is expected to be responsible for the forming of “hot spot”. These results provide some basic micro-information about revealing the formation mechanism of “hot spots” caused by molecular vacancy defects

2015, 64 (24): 243103.
doi: 10.7498/aps.64.243103

Abstract +

Atomic packing structures of a melted TiAl alloy nanoparticle on TiAl(001) substrate at different temperatures are investigated by molecular dynamic simulation within the framework of embedded atom method. In order to obtain a melted TiAl alloy nanoparticle, a larger TiAl alloy bulk in nano-size is initially constructed, subsequently it is heated up to 1500 K and finally melted. A smaller sphere is extracted from the center of the melted bulk to serve as the melted nanoparticle. Periodic boundary conditions are employed in the x and y directions when constructing the sheet-like TiAl alloy substrate. In this simulation, the melted nanoparticle at 1500 K is laid on a TiAl(001) substrate, separately, at 1100, 1000, 900, …, 200 and 100 K as integral systems, and then they experience rapid solidification process. With the analysis of atomic arrangements of the nanoparticle and substrate surface layer by layer, it is found that temperature greatly affects the atomic packing structure of the nanoparticle. When the temperature of the substrate is 1100 K, most atoms in the nanoparticle disorderly pack, indicating that the nanoparticle is still melted at this temperature. At 1000 K, nearly all the atoms in the nanoparticle occupy TiAl lattice points, indicating that the nanoparticle is already solidified at this temperature. With the substrate temperature decreasing, most atoms in the nanoparticle are still of orderly pack. Meanwhile, a pyramid-like inner region, which takes TiAl(001) crystallographic plane as undersurface and TiAl [101], [101], [011], and [01 1] crystallographic axis as edges, abruptly emerges in the nanoparticle. Different atomic packing structures are observed inside and outside this region. Atomic layers composed of atoms inside this region are parallel to the (001) crystallographic plane of TiAl alloy substrate while atomic layers composed of atoms outside this region arranges along other different directions, which therefore leads to four interfaces separating the inner region from other parts of the nanoparticle. At low temperatures, this inner region still exists but its volume decreases with temperature decreasing. Besides, more and more atoms in the upper part of the nanoparticle gradually pack disorderly, which makes it more difficult to distinguish the inner region. In addition, the melted nanoparticle has very limited influences on the central and bottom parts of the substrate. However, thermal motion of atoms of substrate surface which touches the nanoparticle is intensified, thus leading to more obvious lattice distortion.

2015, 64 (24): 243201.
doi: 10.7498/aps.64.243201

Abstract +

Based on the laser-induced-phase model, periodic quantum phase modulation of the dipole response in atomic He is studied theoretically. The two-level system of the transition 1s2→1s2p with a delay width of 1.8 × 109 s-1 and an energy difference of 21.2 eV between the excited state and the ground state is used in the calculation. The system is excited by attosecond laser pulse from high harmonic generator, and the spectral response of the system is of single isolated symmetric Lorentzian absorption line. After the excitation, near infrared (NIR) femtosecond laser pulse train with a repetition rate of 5 GHz, central frequency 780 nm, and pulse duration of 100 fs, is utilized to periodically modify the spontaneous decay of the excited 1s2p level. The incremental phase step Δφ depends on the intensity of the NIR laser pulse, while the initial offset phase φ can be controlled independently by partially overlapping the first NIR pulse with the excitation. Simulated results show that the Lorentzian absorption line is transformed into comb-like spectral structure with equal gap depending on the repetition rate of the NIR pulse train. The line shape of each comb tooth is symmetric Lorentzian line by setting φ = Δφ/2 = π/2, while it is Fano line by setting φ = Δφ = π. The location of the comb structure is mainly dependent on the energy difference between the excited state and the ground state, while it can be slightly tuned by controlling the incremental phase step Δφ. We develop an analytic description of the comb-like spectral structure by Fourier analysis, depending on both the atomic and the phase-control properties. The analytical expressions can be readily used to estimate the exact experimental parameters. The universality of this mechanism allows the spectral modulation in arbitrary atomic system at arbitrary frequency, including the hard X-ray regime, by using reference transitions in highly charged ions. The generalization of this approach should thus not only enable relative frequency measurement and relevant applications at extremely high frequencies, but also open the way for pulse shaping at arbitrary frequencies.

## EDITOR'S SUGGESTION

2015, 64 (24): 243202.
doi: 10.7498/aps.64.243202

Abstract +

We present a simple, versatile and reliable phase-locked laser system. The system consists of an external cavity diode laser, Ti: Sapphire laser, fast detector, phase frequency detector (PFD) and loop filters. The beat signal of the laser is detected with a detector. From the PFD, we can obtain an error signal. The loop filter converts the output of the PFD into a control voltage and thus drives piezoelectric ceramic transducer (PZT) and current of diode laser. After locking, the bandwidth of the beat signal is reduced form MHz to Hz. So the line-width of the diode laser is almost close to that of Ti: Sapphire laser. The locking range is from sub-MHz to 10 GHz. So it is used for the ground hyperfine state transition of 87Rb. Through the use of the phase-locked loop system, we can drive the transition of 87Rb atoms between two ground hyperfine states F=2 and 1. The system is used to demonstrate Raman transition between two states through changing the detuning of the beat signal. From this, we can obtain Rabi frequency = 10 kHz. So, this system can be used to induce an effective vector gauge potential for 87Rb Bose-Einstein condensed and realize the spin-orbit coupling.

2015, 64 (24): 243301.
doi: 10.7498/aps.64.243301

Abstract +

In order to obtain the Er3+/Yb3+ co-doped BaGd2ZnO5 up-conversion phosphor which has the maximum green and red emission intensity, firstly, the method of homogeneous design rooted in the experimental optimal design is employed to search optimum Er3+/Yb3+doping concentration preliminarily. Next, the quadratic general rotary unitized design is adopted to further optimize the experiment, and the regression equation in green and red emission intensity is established as a function of the doping concentration of Er3+/Yb3+. Finally, the optimal solution, that is, the doping concentration of Er3+/Yb3+ corresponding to the maximum emission intensity, is calculated by genetic algorithm. The optimal Er3+/Yb3+co-doped BaGd2ZnO5 phosphor is synthesized by the conventional high temperature solid state method. The crystal structure of as-prepared products is characterized by X-ray diffraction (XRD), and the results show that all the Er3+/Yb3+co-doped BaGd2ZnO5 phosphors we synthesized are of pure phase. The steady-state up-conversion (UC) emission spectra of products are measured under the excitation of a continuous 980 nm laser diode at different working currents. From the UC luminescent spectra of Er3+/Yb3+co-doped BaGd2ZnO5 phosphor, we can see a red emission centered at 662 nm, two green emissions centered at 551 nm and 527 nm, which are assigned to 4F9/2→4I15/2, 4S3/2→4I15/2 and 2H11/2→$4I15/2 transitions of Er3+ ion, respectively. The dependences of green and red UC emission intensities of optimal samples on working current are investigated, indicating that the red emission and green emission of optimal samples both originate from two-photon process. From the normalized green UC emission spectra, it can be concluded that the experimental laser working current induced temperature variation of samples can be omitted. According to Boltzmann distribution law and the thermal equilibrium existing between the levels of 2H11/2 and 4S3/2, the relationship between green emission and temperature in the optimal green UC emission sample is discussed in depth, and the energy level gap between 2H11/2 level and 4S3/2 level is calculated to be 926.11 cm-1. Through the study of the temperature effect on the optimal green UC emission sample, we find that the emission intensity decreases with the increasing of the temperature, owing to the thermal quenching effect. Furthermore, we calculate the activation energies of the samples, the activation energies of the green emission, red emission, and the overall emission are deduced to be 0.45, 0.46, and 0.45 eV, respectively.

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

2015, 64 (24): 244201.
doi: 10.7498/aps.64.244201

Abstract +

Ptychographic iterative engine (PIE) is an ideal phase microscopic method for imaging with short wavelength including X-ray and electron beam. The traditional PIE algorithm requires a purely coherent illumination. Since the coherencies of X-ray and electron beam are always much lower than coherency of the laser, it is greatly important to develop new algorithm for enhancing the capability of PIE in handling the incoherence of the illumination. A method, named polyCDI (coherent diffraction imaging), which can generate clear reconstruction with the illumination of partial coherency, was proposed recently, however due to the use of tiny pinhole in the data acquisition the view field of the reconstructed image is limited. The polyPIE algorithm, which combines the principles of polyCDI with PIE, can realize the imaging of large object with partially coherent illumination. In this paper, an improved polyPIE algorithm is developed to realize the high-resolution phase imaging under incoherent illumination by bringing the shape of the illuminating pinhole and the spectral distribution of the light source into the iterative computation. The image of the object and the illuminating probe are reconstructed for each spectral component, and the shape of the pinhole forming the illumination is used as the same spatial constraint for all the reconstructed probes on the pinhole plane. With this method a very high convergence speed and reconstruction accuracy as well as a wide view field can be achieved. This method can find many applications in the imaging with X-ray and electron beam, which are of low coherence in most of cases. The influence of the spectral width on reconstruction accuracy is also analyzed by imaging the object with illuminations of different spectral widths. It is found that the improved polyPIE algorithm can accurately reconstruct the phase and modulus images of the object when the width of the incoherent illuminating source is smaller than 10% of the central wavelength, otherwise, the convergence speed and reconstruction accuracy will become remarkably lower. By bringing the shape of the pinhole into the iterative computation, the relevance of the reconstructed illuminating probes of different spectral components is used and accordingly the reconstruction speed can be obviously accelerated. The feasibility of this suggested method is verified by a series of numerical simulations.

2015, 64 (24): 244202.
doi: 10.7498/aps.64.244202

Abstract +

Spin-orbit interaction of light in metasurface is investigated in this paper. We theoretically analyze the transfromation of circularly and linearly polarized light by metasurface with Jones matrix. The results indicate that the interaction of light with spatially inhomogeneous and anisotropic metasurface leads to a coupling of spin-orbital angular momentum. The nanostructrues of metasurfaces are arranged at a definite rate of rotation, which induces an additional space-variant geometrical phase (i.e., Pancharatnam-Berry phase). The Pancharatnam-Berry phase is dependent on the polarization handedness of the incident wave. This characteristic can result in spin-dependent split. A left/right-circular polarized beam is transfromed into a right/left-circular polarized vortex beam by the metasurfaces. In the convertion process, the sign of spin angular momentum of photons is inversed. At the same time, each photon can acquire orbital angular momentum from the inhomogeneous and anisotropic media. The case that a linearly polarized beam inputs the metasurfaces also is considered. A linearly polarized wave can be regarded as the linear superposition of left-circular and right-circular polarized wave. The two circularly plarized components are respectively converted into circularly polarized vortex beam with reverse polarization handedness. The coherent superposition of the two output components forms a cylindrical vector beam. Finally, we adopt the combination of a metasurface and spiral phase plate to verify the theoretical results. The vortex phase can be eliminated by the spiral phase plate when a left-circular polarized light is input, while topological charge of vortex phase will increase when a right-circular polarized light is input. For the case of inputting linearly polarized beam, one of the two outputing circularly polarized components can be eliminated by the helical phase through using the spiral phase plate, while the topological charge of another component increases. It results in the fact that the intensity pattern splits into two parts. The central part does not have helical phase, while the ambient ring-shaped intensity has helical phase. In order to judge the polarization handedness of output wave, the Stokes parameter S3 is measured by inserting a Glan laser polarizer and a quarter wave plate behind the spiral phase plate. The experimental results are in good agreement with theoretical analyses. These results are helpful for understanding the manipulation of light with metasurface.

2015, 64 (24): 244203.
doi: 10.7498/aps.64.244203

Abstract +

Nondiffracting optical beams play an important role in contemporary optics due to their special propagation characteristics, i.e., nondiffracting in a diffraction-free zone, shape recovering behind obstacles or self-healing property. Liquid crystal spatial light modulators (LC-SLM) are widely used for generating nondiffracting optical beams in virtue of programmable and dynamic features. In this paper, we propose a complex amplitude modulation technique that can encode any scalar complex fields for generating the complex nondiffracting beams. Before experiment, the phase modulation curve of the phase-only LC-SLM is optimized into being linear in a range of 0-2πby gamma correction in the way of variable binary phase gratings. Then, we experimentally generate the nonaccelerating beams, e.g., two zero-order Bessel beams with variable intensity distributions, and the nondiffracting petal-like beams generated by interfering with two coaxial Bessel beams. By scanning a reflection mirror near the focal region along the optical axis, a stack of two-dimensional images is acquired, and then a three-dimensional intensity profile of the beam is reconstructed with a software. We also experimentally demonstrate a new kind of multi-main-lobe accelerating beam with parabolic accelerating trajectory by modifying the spatial spectrum of classical Airy beam. Compared with the so-called vectorial accelerating beam with multiple main lobes in spheroidal coordinates, our generated two-main-lobe accelerating beam has a very high energy efficiency. The self-healing property of the two-main-lobe accelerating beam is also demonstrated. The presented technique can generate a variety of complex nondiffracting optical beams rapidly and obtain their three-dimensional intensity distributions accurately, which has potential applications in the fields of optical microscope, optical date storage, optical trapping, optical micromachining, etc.

2015, 64 (24): 244204.
doi: 10.7498/aps.64.244204

Abstract +

By using the truncated equations of the coupled wave, the expressions of the normalized electric field and the normalized intensity of the frequency doubling beam are derived in the cases with and without walk-off effect, caused by the off-axial vortex beam propagating through the negative uniaxial crystal. The influences of the off-axial magnitude, the weak walk-off angle and the crystal length on the output frequency doubling beam are mainly investigated. It is shown that while the walk-off angle is neglected, the two dark cores of the frequency doubling beam coincide with the point (0, 0); but while the weak walk-off angle is taken into account, the dark cores move along the direction where the walk-off effect is generated, and the two coincident dark cores separate in the direction perpendicular to the direction where the walk-off effect is generated on the cross-section. Especially, the distance the dark cores move is related to the off-axial magnitude, the weak walk-off angle and the crystal length. But the separation distance of the two dark cores is only related to the weak walk-off angle and the crystal length. The exact details show that when the off-axial magnitude increases, the distance the dark cores move along the direction where the off-axial magnitude is generated increases at the same time, but the separation distance has no connection with he off-axial magnitude. When the weak walk-off angle and the crystal length increase, the distance the dark cores move and the separation distance of the two dark cores increase. In addition, it can be found by comparison that when the crystal length reduces, the distance the dark cores move will decrease. And also the separation distance of the two dark cores will reduce, which is induced by the walk-off effect and the off-axial magnitude. Therefore, by reducing the crystal length, the output frequency doubling beam can be modified to a certain degree.

2015, 64 (24): 244205.
doi: 10.7498/aps.64.244205

Abstract +

The slow light technology of the rectangle signal propagating in erbium-doped fiber (EDF) has potential applications in the fields of all optical communication and optical fiber sensing. The method of using harmonics fractional delay to evaluate the slow/fast light of rectangle signal propagating in the EDF is proposed, and the characteristics of phase delay for fundamental and high order harmonics components are analyzed for the first time based on the rate equations and the theory of the coherent population oscillations (CPO). We experimentally demonstrate the dependences of fundamental fractional delay on input power and optical gain. The maximum fractional delay 20% is obtained when the input power is about 8 mW without pump. The negative fractional delay-20% is also achieved and it will increase with the rising of the optical gain. The Nth-order fractional delays (N=1, 3, 5, 7) of rectangle signal propagating in EDF without pump are investigated. Their maximum fractional delays are all about 0.07 and the corresponding fundamental modulation frequencies are 22, 7, 5 and 3 Hz, respectively. What is more, the Nth-order fractional delays (N=1, 3, 5, 7) with pump are also investigated. Their maximum fractional delays are all about-0.135 and the corresponding fundamental modulation frequencies are 175, 58, 35 and 25 Hz, respectively. The experiments indicate that the maximum Nth-order fractional delays are equal and they will be achieved at the frequency f/N (the fundamental harmonic fractional delay is maximum at the modulation frequency f). The results show good agreement with CPO and the frequency is also located in the spectral burning hole.

2015, 64 (24): 244206.
doi: 10.7498/aps.64.244206

Abstract +

A differential absorption lidar (CO2-VDIAL), which is designed for vertical CO2 profile retrieving by using aerosol-scattered signals, is demonstrated in this paper. To our knowledge, it is the first time that a dye laser has been utilized to realize the wavelength modulation for a CO2-DIAL/IPDA system. Such a design scheme greatly reduces both the threshold and the cost to develop a CO2-DIAL. However, two key problems emerge in this system, i.e., wavelength stability and broad bandwidth. By adopting the CO2-VDIAL, a dual-path gas cell, and the Voigt fitting procedure, the accurate wavelength calibration of infrared pulse laser is achieved. Experimental results show that the error of wavelength calibration can be suppressed under 0.1 pm. And a wavelength stability of ～2 pm is then achieved. For tackling the error introduced by using the laser of a broad bandwidth, simulated experiments are carried out to estimate its influence. On that basis, we propose a method to calculate the correction coefficient and demonstrate the process via experiments by using a gas cell. It is demonstrated that the bandwidth of the output infrared laser is around 600-700 MHz. Hence, the broad bandwidth correction is an indispensable step for this CO2-VDIAL. Finally, horizontal, vertical and continuous detections are carried out to verify the precision and the accuracy of our CO2-VDIAL. The slope method is used to retrieve the XCO2 in the above experiments. In the horizontal detections, an R2 of 0.999 is achieved, suggesting that the precision of the system is excellent. By comparison with the in-situ measurements, a difference is found to be lower than 4 ppm. Consequently, it is concluded that the CO2-VDIAL is capable of providing retrievals with the high precision and accuracy. Moreover, the XCO2 decreases with increasing altitude according to the vertical detection experiment in the midnight on June 19m th 2015 at an urban site, demonstrating that the CO2-VDIAL is capable of providing retrievals of ranged-resolved. Finally, temporal characteristic of XCO2 can be also revealed by the CO2-VDIAL in light of continuous detections. The CO2-VDIAL has already been assembled in a container which is due to be transported to Huainai for further verifications in late 2015. Once we finish the performance optimization, the CO2-VDIAL will be installed in Tibet for long period observation.

2015, 64 (24): 244301.
doi: 10.7498/aps.64.244301

Abstract +

The precipitation is an important physical phenomenon. The real-time, accurate measurement of rainfall intensity has important significance in meteorological support, agriculture, weather forecasting, transportation industry and military mission. However, current methods, such as the rain gauge, the weather radar and meteorological satellite, are unable to meet the needs in all the areas above at present. The network of rain gauge is costly. Meanwhile, rain gauge has low spatial and temporal resolution. And the weather radar has a big deviation because of the ground clutter. Besides, the meteorological satellite is unable to measure the surface rainfall. Thus, a method of using the measurement of microwave rain-induced attenuation for rainfall estimation has been presented in meteorological field recently by meteorological experts and it has made some progress. The method based on microwave link has low cost because of using preexisting microwave device. There are also many preexisting microwave transmission networks, which can be used by rainfall field inversion in the future research. The method measures rainfall intensity more accurately because the propagation path of microwave is close to the surface. Many models for inversing rainfall intensity by rain-induced microwave attenuation have been put forward on account of the method advantages. The commonly used model for inversion of rain rate is given by International Telecommunication Union (ITU). However, the model presented by ITU ignores a number of meteorological factors such as temperature, humidity and air pressure, which to some degree reduces the accuracy of the rainfall inversion based on microwave link. Thus, based on the theory of support vector machine (SVM), an inversion method of the path rainfall intensity by using a microwave link is proposed. Starting from the theory of Mie scattering and the atmospheric gas absorption attenuation model, a model of rainfall intensity inversion of line-of-sight microwave links is proposed, which is based on support vector machine, the microwave rain attenuation characteristics and the Gamma drop-size distribution. One line-of-sight microwave link is designed and used to measure the microwave rain-induced attenuation and inverse rainfall. Compared with actual rainfall intensity measured by a disdrometer, inversion rainfall intensity shows a satisfactory result. The correlation coefficient of rain rate is inversed by microwave link based on SVM and that of disdrometer is higher than 0.6 mostly, and the maximum value is 0.9674; the minimum value of the root-mean-square error of the rain rate is 0.5780 mm/h; the minimum value of the error of accumulated rain amount is 0.0080 mm; the relative error of accumulated rain amount is less than 10% and its minimum value is 0.7425%. All these parameters above are superior to ITU's. Therefore, the inversion result demonstrates the validity, feasibility and accuracy of rainfall inversion model using a microwave link based on SVM. The model we present is of great significance for further improving the accuracy of inversion of rain rate based on microwave link and rainfall monitoring.

2015, 64 (24): 244401.
doi: 10.7498/aps.64.244401

Abstract +

Entransy dissipation and entropy generation both can be used as measures of the irreversibilities of heat transfer problems. Nowadays those who oppose the entransy theory insist that the entransy is needless. In order to illustrate the necessity of the entransy theory, demonstration is made from the viewpoint of effectiveness which is based on the fact that when describing the variation of the irreversibility in the process of heat transfer, the exact analytical solution of the entransy dissipation exists, but that of the entropy generation is difficult to obtain. In this paper, one-dimensional (1D) and multi-dimensional heat conduction models within isolated systems are constructed, among which, the former is to illustrate the deriving process concisely, and the latter is to verify the universal existence of the analytical solution of entransy dissipations. In the 1D model, two bodies with the same geometrical and thermophysical properties but different initial temperatures transfer heat through the contacting surfaces; while in the three-dimensional (3D) model, the initial condition is arbitrary. According to the literature, the primary expression of the total entransy dissipation is derived when substituting the series-typed expression of temperature gradient into the universal calculating equation, which is in the form of a multi integral of a multi series. To reduce such an expression to the simplest form without performing any integral calculation, the orders of the integral and the series are exchanged, and considering the independence between the concerning variables and functions, the multi integral calculation is simplified into the product of several 1D integrals, one relates to time and is easily solved, and the others are dependent on space, of which the dimension is reduced by using the inherent orthogonality of the characteristic functions. The ultimate solutions of the entransy dissipation for all the models are expressed as the summation of a stationary item and a transient item, and the former is consistent with the result obtained from the viewpoint of thermodynamics given by the literature, and the latter has the limitation of zero when time tends to infinity. In order to verify the correctness of the universal solution of the entransy dissipation, a concrete 2D heat transfer problem is constructed, in which four bodies transfer heat through connecting faces, of which the initial temperature is centrosymmetric in the isolated system, and uniform within each body. The analytical solution of the entransy dissipation to the 2D problem has the same tendency and limitation as those of the 1D model, but varies faster on condition that the thermopysical properties of the bodies in both models are identical. In order to make comparison, the calculating equation of the entropy generation for the 1D model is also derived, which has the form of the integral of the logarithm of the series-typed temperature, and such an integral is hard to solve mathematically, which suggests the limitation of entropy when describing the variation of irreversibility from the viewpoint of heat transfer instead of thermodynamics. Through the derivation and comparison shown in this paper, the following conclusions are reached: owing to the differences in complicity between obtaining analytical solutions of the entransy dissipation and those of the entropy generation, the former is more effective when describing variation of the irreversibility in heat transfer process; for heat transfer problems of different dimensions in isolated systems, analytical solutions of the entransy dissipation are expected to be obtained when the precondition that the analytical solutions of the temperature exist, is satisfied.

2015, 64 (24): 244701.
doi: 10.7498/aps.64.244701

Abstract +

In this paper, the evolution of the fluid surface wave on an inclined waving wall is investigated. The waving wall is assumed to have a sinusoidal fluctuating surface, and the linear stability of the liquid film flow is analyzed. In addition, the evolutions of the disturbance wave under different tilt angles, and the variations in this wave when passing through different wall shapes are studied. It can be observed that the time evolution of the disturbance wave appears to be a near periodic variation of a larger wavelength. Further, by comparing its flow structure with that for the flat plate wall, it is found that the wave conditions are more complex. When the fluid flows through the waving wall, the disturbance wave no longer displays a regular change in space, and its amplitude increases with the tilt angle of the wall increasing. For the same tilt angle, the amplitude of the disturbance wave in the waving wall is greater than that for the flat plate wall, and the distortions in waveform are more obvious. As Re increases, the amplitude of the disturbance wave increases gradually, and the distortion of the corresponding wave increases as well. Further, with the increase of wall surface amplitude, the amplitudes of the static and disturbance waves increase, whereas the corresponding traveling-wave period remains unchanged. Finally, the influence of the wall tilt angle on flow stability is analyzed.

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

2015, 64 (24): 245201.
doi: 10.7498/aps.64.245201

Abstract +

Ag nanowires have attracted much attention due to their potential applications in spontaneous emission amplifiers, logic gates, single photon sources, and biomolecule detection. Single crystal Ag nanowires are prepared by chemical method. The Ag nanowires exhibit pentagonal cross sections with an average radius of 80 nm. Two enhanced emission peaks (345 and 383 nm) are observed in ZnO quantum dots when mixing with Ag nanowires. To explore the origination of the enhancement, the localized surface plasmon resonance modes of Ag nanowires are investigated theoretically by the finite difference time domain method. The extinction spectrum, electric field distribution and electric field enhancement factor versus excitation wavelength of Ag nanowires are simulated. The results show that the Ag nanowires have two extinction peaks in the ultraviolet region: the 340 nm peak originating from the transverse dipole resonance (DR) and the 375 nm peak belonging to the transverse quadrupole resonance (QR). The same extinction peaks are also observed in the experimental measurement, which are consistent with the emission enhancement peaks of ZnO quantum dots. Compared with that of the DR peak, the red shift of the QR peak becomes more obvious with the increase of Ag nanowire radius. The resonance mode of the extinction peak depends on the cross sectional shape of the Ag nanowire. In the case of the traditional Ag nanowire with circular cross section, DR is excited by long wavelength light while QR is excited by short wavelength light. According to the curves of electric field enhancement factor vs excitation wavelength, the maximum enhanced electric field is observed at the apex of the pentagonal section of Ag nanowire, and the enhancement factor reaches 180 times for excitation wavelength of 377 nm. However, the electric field at the pentagon edge is enhanced only by several times. The simulation results give a reasonable explanation to the emission enhancement in Ag nanowire/ZnO quantum dot system, and indicate that Ag nanowires can be applied to improving the luminescent efficiency of semiconductor materials, biological detection, etc.

2015, 64 (24): 245202.
doi: 10.7498/aps.64.245202

Abstract +

Concentric-ring pattern is observed in an Ar/air mixture dielectric barrier discharge. The discharge images within one half voltage circle are taken by an intensified-charge coupled device camera, indicating that the discharge filaments are the basic units of the concentric-ring pattern. By comparing the six instantaneous images corresponding to three successive positive and negative half voltages, it is proved that the concentric-ring pattern seen with naked eyes is formed by the numerous discharge filaments located at different positions during successive acquisition intervals. With applied voltage increasing, concentric-ring pattern can transform into spiral, and then into concentric-ring pattern again. By analyzing the features of formation and transformation of these two patterns, it is inferred that the two patterns have similar dynamic mechanisms. Discharge powers of concentric-ring pattern and spiral are calculated respectively, and the results show that the power increases linearly approximately with applied voltage increasing. The correlation coefficients of concentric-ring pattern are compared with those of spiral, and the results show that the correlation coefficient of concentric-ring pattern is relatively low and irregular, while the correlation coefficient of spiral is relatively high and has an oscillatory characteristic.

2015, 64 (24): 245203.
doi: 10.7498/aps.64.245203

Abstract +

In recent years, a great many of effect data obtained from the high current pulsed electron beam play an important role in the studying of X-ray thermal-mechanical effects. Energy deposition profile is the criterion to measure the equivalence of thermal-mechanical effects between high-current electron beam and X-rays. To adjust the energy deposition profiles to improve the equivalence of the simulations of X-ray and thermal-mechanical effect, the intense electron beam energy deposition profile measurement should be studied. Two-dimensional distribution measurement which is an important part of the energy deposition profile is to obtain a two-dimension (r, θ) incidence angle distribution. A new method of measuring the incidence angle based on small Faraday cup array covered with aluminum films, called modified multi-layer stacking, is presented in this paper. With the help of the filtered Faraday cups, the transmission fraction of the electron beam confined at a specific position and time is stored. Two-dimension incidence angle distribution on the anode target that changes over the working time is obtained with these transmission fractions by computer calculation. The result indicates that the two-dimension incidence angle distribution has a close relationship with the pinch of the beam. The electrons tend to move vertically to the equipotential line when the diode is under Child-Langmuir flow, then they hit the target in a small angle range (E×B drift, the trajectory of the electrons becomes a slanted helix with pitch changing. The incidence angle then increases to about 60° from small angle.

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

2015, 64 (24): 247101.
doi: 10.7498/aps.64.247101

Abstract +

Using the dynamical mean field theory with Lanczos method as its impurity solver, we study the orbital-selective Mott transition (OSMT) in the two-orbital J model and Jz model. In the multi-orbital systems, the Mott metal-insulator transition occurs successively when the widths of the bands are different. As the narrow orbital becomes Mott insulator while the wide orbital is still in metallic phase, we find an orbital-selective Mott phase (OSMP). There are two different Hubbard models that are frequently used to describe the OSMT, which are named J model and Jz model, respectively. The J Model is composed of the whole Hund's rule coupling terms, including the spin-flip term, the pair-hopping term and the Ising type Hund's rule coupling term. However, there is only Ising type Hund's rule coupling term in the Jz model.#br#We study the ratio of bandwidth W2/W1 on the OSMT by analyzing the results of the density of states and quasi-particle weight. Comparing the phase diagrams obtained from the J and Jz models with the Hund's rule coupling J(Jz)=U/4, we find that the OSMP region of the J model is much larger than that of the Jz model when W2/W1=0.5 or W2/W1=0.2. When the ratio of bandwidth increases to W2/W1=0.8, the OSMP disappears completely in the Jz model. However in the J model, we can still find the OSMT but the area of the OSMP shrinks significantly. Therefore, the OSMT happens more easily in the J model than in the Jz model.#br#In order to discuss the cooperative effect of the bandwidth and Hund's rule coupling on the OSMT, we compare the phase diagrams for different Hund's rule couplings J(Jz)=U/4 and J(Jz)=U/2. We find that when the bandwidth W2/W1≥q 0.7, the OSMT disappears in Jz model in the case of either Jz=U/4 or Jz=U/2. However, the OSMP always exists in the J model if the bandwidths of the two orbitals are different, suggesting that the rotation invariances of the Hund's rule couplings can protect the OSMP. Therefore, one should be more careful when using the Jz model instead of the J model to study the OSMP.

2015, 64 (24): 247201.
doi: 10.7498/aps.64.247201

Abstract +

The experimental studies of the effect of W-doping on conductivity of anatase TiO2 have opposite conclusions when the W-doping concentration is in a range from 0.02083 to 0.04167. To solve the conflict, two supercell models for Ti0.97917W0.02083O2 and Ti0.95833W0.04167O2 are set up for optimizing their geometries and calculating their band structures and the densities of states based on the first-principles plane-wave norm-conserving pseudopotential of the density functional theory. The electron concentration, electron effective mass, electronic mobility, and electronic conductivity are calculated as well. The calculated results show that both electronic conductivity and conductive property of the doped system increase while the electron effective mass decreases, with the increase of W-doping concentration in the presence or absence of electron spin. The conductive property of Ti0.95833W0.04167O2 system is better than that of Ti0.97917W0.02083O2 system, which is further proved by the analyses of ionization energy and Bohr radius. To analyze the stability and formation energy of W-doped anatase TiO2, two more supercell models for Ti0.96875W0.03125O2 and Ti0.9375W0.0625O2 are set up combined with the geometry optimization. The calculated results show that the total energy and the formation energy increase while the stability of the doped system decreases, with the increase of W-doping concentration in a range from 0.02083 to 0.04167 in the presence or absence of electron spin. Meanwhile the W-doping becomes more difficult. A comparison of the doped system with the pure anatase TiO2 shows that the lattice constant along the a-axis of the W-doped anatase TiO2 increases, and its lattice constant along the c-axis and volume increase as well. The calculated results agree with the experimental results. The doped system becomes a half-metal diluted magnetic semiconductor with a room temperature ferromagnetism in the presence of electron spin.

2015, 64 (24): 247202.
doi: 10.7498/aps.64.247202

Abstract +

In NiFe/Pt bilayer, when spin current originating from the magnetization procession of NiFe is inject into the adjacent Pt layer under ferromagnetic resonance (FMR), the direct current (DC) voltage VISHE generated by inverse spin Hall effect (ISHE) will be added to the voltage VSRE generated by spin rectification effect (SRE), therefore the measured voltage in experiment is the sum of VISHE and VSRE. It is crucial to separate these contributions, which has been often overlooked before, in order to make a reasonable comparison of the ISHE among different materials. The voltages having symmetric (Lorentz type) and anti-symmetric (dispersive type) components both vary with the static magnetic field strength. However, they have different static magnetic field angle dependences according to our theoretical analysis. In order to distinguish the contribution of ISHE from that of SRE, in this paper, we employ a method, in which the voltage across the sample is measured when the static magnetic field is applied to different directions, to analyze the voltage by varying magnetic field angle in a range from 0° to 360° in steps of 10°, thereby separating the VISHE. The separation is carried out by fitting the angle dependent symmetric and anti-symmetric curves to different theoretical formulas of ISHE and SRE. The voltages of the two different contributions together with the phase angle of the microwave are obtained. At the same time, the FMR line width and the resonant field can be read out. The results show that the ferromagnetic resonance line width in NiFe(20 nm)/Pt(10 nm) sample is larger than that in NiFe(20 nm) sample due to the injection of spin current from NiFe to Pt in the bi-layer sample. We notice that in the curves of voltage vs. static magnetic field, the Lorentz symmetry components of the voltage from the bi-layer sample weight more than those from the single-layer sample. This is explained as a result of the existence of the ISHE in the bi-layer sample, where the spins are pumped from the magnetic layer to the adjacent nonmagnetic layer. The spin pumping effect does not show up in the single-layer sample. There are a large portion of symmetric components in the double layer sample, which is attributed to the ISHE. Although the voltage caused by the SRE is smaller than that by the ISHE, the SRE voltage cannot be ignored. Our work is crucial to understanding the spin-related effects in ferromagnetic/nonmagnetic metal material and provides an improved analysis method to study the spin pumping and the ISHE.

2015, 64 (24): 247301.
doi: 10.7498/aps.64.247301

Abstract +

Micro-nano structure optical device based on surface plasmon polariton such as super lens, micro-nano resonators and waveguides, etc. owns great applications in different research fields, especially in integrated optics and nanophotonics, for it has extremely small size and can be integrated into a micro-nano optical system. Comparatively, the directional wave exciter attracts much attention since it breaks the symmetries of wave propagation and excitation and can be applied to a micro-nano optical logic modulation system in the future. In order to realize the high-efficiency directional excitation in ultra-small structure based on surface plasmon polariton, a newly designed metal insulator metal waveguide based surface plasmon directional exciter with multiple channels and nano antenna is presented in this paper. The basic structure of the surface plasmon directional exciter is a two-slit metal plate, and the directional propagation surface plasmon wave is generated according to wave interference. To obtain a single surface plasmon wave in the specific orientation, a phase difference of π/2 between the surface waves generated by slits is necessary. To achieve the different phase differences, both heights and widths of the channels are calculated according to the waveguide mode function. It is worth noting that the directional wave exciter with dual channels is able to generate unsymmetrical wave propagation, however, the excitation efficiency is rather low, which restricts its potential applications in micro-nano optical system. In the paper, in order to further raise the coupling efficiency of the excited surface plasmon wave, and increase its propagation, other additional channels are designed in the directional wave exciter structure. Compared with the traditional dual channel system, the additional channels with similar parameters, and the same interference features are introduced in the surface plasmon directional exciter to increase the light transmission and surface wave energy. In addition, a nano antenna structure based on resonance is presented on the structure surface to enhance the surface plasmon excitation as well. The design tactics of the directional surface plasmon wave exciter are analytically explained in the paper. With numerical calculation based on the finite difference time domain method, the simulation result proves that the proposed surface plasmon wave directional exciter is able to generate single orientation surface wave with extremely high coupling ratio. Moreover, with additional multiple channels and nano antenna, the energy of the directional coupled surface plasmon wave is improved obviously, which indicates that the propagation distance of the surface plasmon wave is increased. In the simulation, both the additional channels and nano antenna are able to increase the energy and propagation distance of the surface plasmon wave obviously: the energies of directional propagated surface plasmon waves of four and six channel directional wave exciters with nano antenna are 6.74 times and 9.30 times that of the traditional dual slit directional wave exciter without nano antenna, respectively. Moreover, it is worth noting that the newly designed nano antenna based multi-channel enhanced surface plasmon wave directional exciter owns compact structure and can be easily fabricated at low cost. It is believed that this work can be an important reference for designing micro and nano photonic and plasmonic elements in integrated optics.

2015, 64 (24): 247302.
doi: 10.7498/aps.64.247302

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According to Debye relaxation, the polarization of electric dipole can be accomplished in 10-10 s under the action of an alternating electromagnetic filed with a frequency of 2.45 GHz, so it is feasible to obtain nano powder by carrying out solid reaction in microwave at low temperature in a short time. In this work, the syntheses of Mg2Si0.4Sn0.6-yBiy (0 ≤ y ≤ 0.03) solid solution thermoelectric materials are successfully achieved by microwave-assisted solid state reaction at low temperature with MgH2 serving as one reactant instead of Mg, and their transportation mechanisms are studied based on the SPB (single parabolic band) model as well. The results indicate that the volatilization and oxidation of Mg can be suppressed effectively in this process. Fine stoichiometric product can be achieved with nano-lamellar structure with an interlayer spacing of about 100 nm by carrying out the reaction between MgH2 and Si, Sn in microwave at 400℃ in 15 min. The introduction of Bi dopant can increase carrier concentration and lattice distortion. With the cooperation between the nano lamellar structure and lattice distortion, the phone is scattered so effectively that the sample owns a lowest thermal conductivity, κmin of 1.36 W·m-1·K-1 at 550 K based on the fact that the phonon scattering is dominant in the heat transfer process. The calculated results show that the theoretical κmin is 0.93 W·m-1·K-1, which is lower than 1.36 W·m-1·K-1. Therefore, by further adjusting the process parameters and increasing the effective doping rate of Bi and the density of the lattice defects, it is expected to obtain lower thermal conductivity. The band convergence is also verified by increasing the density-of-state effective mass. The apparent increase in m* is due to a gradual increase in carrier concentration with increasing temperature. Despite the agreement between the data and the model, the irregular behavior between m* and temperature is a very strong indication and the electric transmission performance of the sample is likely to be influenced by the structure of the multi band structure. Owing possibly to the low reaction temperature, there are Bi precipitates at the grain boundary. In addition to the phonon scattering and the alloy scattering, the Bi segregation and the scattering of carrier by nano-lamellar structure make the carrier mobility of the sample slightly lower. The lower effective doping rate and complex band structure make the carrier concentration and density-of-state effective mass low coupled with the low carrier mobility, which leads to low material factor β with a ZT of 0.66 at 600 K consequently.

2015, 64 (24): 247401.
doi: 10.7498/aps.64.247401

Abstract +

The flux pinning performance of the superconductor is important for the applications of the GdBa2Cu3O7-δ superconductor bulk. To introduce the suitable secondary phase into the GdBa2Cu3O7-δ matrix is an important way to enhance the performance of flux pinning. By using top-seeded melt texture growth process, single domain GdBa2Cu3O7-δ superconductor bulks (20 mm in diameter) doping with different quantities of BaFe12O19 nano-particles (12O19(x=0, 0.2 mol%, 0.4 mol%, 0.8 mol%)+ 10 wt% Ag2O+ 0.5 wt% Pt. The effects of different quantities of BaFe12O19 nano-particles on superconducting properties and microstructure are also investigated. The result shows that the critical current density, JC, with 0.2 mol% BaFe12O19 additions reaches a maximum value in the zero field, which is about 5.5 × 104 A/cm2. And the critical current density JC, almost increases in the whole field compared with those of the undoped bulks. The microstructure and chemical composition of GdBa2Cu3O7-δ bulk with BaFe12O19 nano-particles are implemented by the SEM-EDS technique. It is found that BaFe12O19 nano-particles keeps a similar form to that of the precursor in the final superconductor bulk. The average size of Gd2BaCuO5 particles is reduced from 1.4 μm in the undoped bulk to 0.79 μm in the bulk with 0.2 mol% BaFe12O19 nano-particles. We suggest that BaFe12O19 nano-particles may form effective magnetic flux centers in the bulks, which affects the homogeneous distribution and refinement of Gd2BaCuO5 particles. Therefore, the improvements in the critical current density and the trapped field are observed in the GdBa2Cu3O7-δ bulk with low-level doped content. The superconducting transition temperature TC, can be maintained at around 92.5 K. However, with the addition of 0.4 mol% BaFe12O19 nano-particles, the critical current density and superconducting transition temperature decrease obviously. It indicates that the excessive addition of BaFe12O19 nano-particles may affect the superconductivity properties to reduce the critical current density, JC. The result indicates that the low-level content BaFe12O19 nano-particles can be an effective second phase for the improvement of the GdBa2Cu3O7-δ superconductor bulks, which is very important for the further enhancing the superconducting properties of GdBa2Cu3O7-δ bulks by introducing the flux pinning of nano-particles.

2015, 64 (24): 247501.
doi: 10.7498/aps.64.247501

Abstract +

Recently, the physical properties and applications of the magnetic nanotube have attracted a great deal of theoretical and experimental attention. The magnetization and phase transition of spin-1 Blume-Capel model on a cylindrical Ising nanotube with bimodal random crystal fields are investigated by using the effective field theory. Employing numerical calculations, we obtain the phase diagrams and the magnetization, which depend on the temperature and the parameters of random crystal fields. Our obtained results are as follows. (i) Changing the probability (p) and the ratio of the crystal fields (), the bimodal random crystal fields may describe different doped atoms acting on spins. Especially, for p = 0.5, choosing = 0,-1.0,-0.5 and 0.5, the bimodal random crystal fields can respectively degrade four typical distributions of random crystal fields, i. e., the distribution of diluted crystal fields, the distribution of symmetry staggered crystal fields, the distribution of non-symmetry staggered crystal fields, and the distribution of same-direction crystal field. (ii) The system exhibits different magnetic properties and phase transition behaviors in the diluted, staggered and same-direction crystal field. The diluted and staggered crystal fields may reduce the magnetization of the system, resulting in the ground state saturation value of magnetization, which is less than 1, while the same-direction crystal fields cannot result in a similar behavior. (iii) The system shows several phase transition temperatures, i.e., first-order and second-order phase transitions and reentrant phenomenon as the parameters of bimodal random crystal fields change. The tricritical point and reentrant phenomenon do exist for certain values of the probability, the negative crystal field and the ratio of the crystal fields in the system. The relevant experiment is needed to verify the above-mentioned theoretical results.

2015, 64 (24): 247502.
doi: 10.7498/aps.64.247502

Abstract +

Multiferroic Bi1-xCaxFeO3 (x=0, 0.05, 0.1, 0.15, 0.2) ceramics are prepared by sol-gel method. The effects of Ca doping on the structure, delectrical, ferromagnetism properties and high temperature magnetic behavior of BiFeO3 ceramics are studied. The structures of BiFeO3 ceramics are characterized by X-ray diffraction (XRD). The results show that all the peaks for Bi1-xFexO3 samples can be indexed according to the crystal structure of pure BiFeO3. The characteristic diffraction peaks of Bi1-xCaxFeO3 samples become gradually wider and the (104) and (110) peaks of BiFeO3 merge partially into a broadened peak (110) with Ca2+ doping increasing. XRD analysis reveals a phase transition in Ca-doped BiFeO3 from rhombohedral to orthorhombic when x is larger than 0.15. The scan electron microscope images indicate that Ca2+ doping significantly increases the grain sizes of BiFeO3 ceramic. The average grain sizes of Bi1-xCaxFeO3 samples range from 0.5 to 2 μm.#br#The dielectric behaviors of Bi1-xCaxFeO3 ceramics change with content x and frequency. The dielectric constant measured at 1 kHz reaches a maximum value of εr=4603.9 when x=0.1, seven times as big as that of pure BiFeO3. With further increasing the Ca content (x=0.15, 0.2), the value of the dielectric constant is back to the level of pure BiFeO3. The dielectric constant of Bi0.8Ca0.2FeO3 (εr=57) is less than one-tenth that of BiFeO3 (εr=629.9). The dielectric losses of Bi1-xCaxFeO3 samples become smaller than that of BiFeO3 ceramic. This dramatic change in the dielectric properties of Bi1-xCaxFeO3 samples can be understood in terms of orientational relaxation of dipoles and the space charge limited conduction associated with crystal defects at low frequency.#br#The magnetic measurements show that all samples possess strong ferromagnetism at room temperature expect BiFeO3 which is weakly ferromagnetic. The X-ray photoelectron spectroscopy spectrum indicates the coexistence of Fe2+ and Fe3+ in Bi1-xCaxFeO3 samples. The ratios of Fe2+/Fe3+ are 21/79, 23/77, 27/73, 32/68, and 32/68, respectively. The ratio of Fe2+/Fe3+ increases with doping Ca content increasing, and the magnetic preparation of BiFeO3 is enhanced.#br#It is evidenced that the ferromagnetic phase transitions of Bi1-xCaxFeO3samples occur at 878 K from M-T curve and the phase transition of BiFeO3 happens at 878 K by DSC measurement. The change in TN of Bi1-xCaxFeO3 depends mainly on the Fe-O-Fe super-exchange strength and magnetic structure of relative stability.

2015, 64 (24): 247503.
doi: 10.7498/aps.64.247503

Abstract +

Transition metal (TM=Cu, Ni, Mn, Fe and Co)-doped ZnO:F thin films are deposited on glass substrates by a sol-gel method through using ethanol as solvent. All the samples are checked by using X-ray diffraction (XRD), atomic force microscope (AFM), X-ray photoelectron spectroscope (XPS), photoluminescence, UV spectrophotometer, and vibrating sample magnetometer. The XRD reveals that Cu, Ni, Mn, Fe and Co occupy the Zn sites successfully without changing the wurtzite structure of ZnO at moderate doping concentration, and no evidence of any secondary phases is found. The AFM measurements show that the average values of crystallite surface roughness of the samples are in a range from about 2 to 12.7 nm. The surface of ZnO:F thin film becomes less compact and uniform when ZnO:F thin film is doped with TM ions. The TM ions are indeed substituted at the Zn2+ site into the ZnO lattice as shown in the results obtained by XPS and XRD. Further studies show that most of the ZnO films exhibit preferred (002) orientations, while the best c-axis orientation occurs in Zn0.93Co0.05F0.02O film. However, the crystalline quality and preferential orientation of ZnO film become poor in Zn0.93Mn0.05F0.02O. The optical bandgaps of all the ZnO:F films decrease after doping TM. All the samples show high transmittance values in the visible region. Strong ultraviolet emission and weak blue emission are observed in the photoluminescence spectra measured at room temperature for all the samples. The Zn0.93Mn0.05F0.02O film shows the weakest ultraviolet emission peak and strongest blue emission peak, corresponding to the strongest ferromagnetism; while for the Zn0.96Cu0.02F0.02O film, the strongest ultraviolet emission peak and weakest blue emission peak are observed, accompanied by the weakest ferromagnetism. To determine the optical bandgap (Eg) of TM-doped ZnO:F thin film, we plot the curve of (α hv)2 versus photon energy (hv). It is found that the Eg decreases from 3.16 eV to 3.01 eV with the TM ions doping. We show the variations of saturation magnetization with the Vm O concentration for TM-doped ZnO:F thin films with the different transition metal ions. In the case of Cu-doped ZnO:F thin films, the ZnO sample shows that a weaker magnetism. ZnMnFO film exhibits well-defined hysteresis with a coercive field of 7.28×10-5 emu/g. Further studies reveal that these interesting magnetic properties are correlated with the defect-related model for ferromagnetism. Our results will expand the applications of ZnO:F thin films in visible light emitting diode, photovoltaic devices, photoelectrochromic devices, etc. Meanwhile, extreme cares should be taken to control the codoping of ZnO:F thin films for tuning the magnetization.

2015, 64 (24): 247504.
doi: 10.7498/aps.64.247504

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In this paper, the influence of Mo capping layer on magnetic anisotropy of MgO/CoFeB/Mo with varying thickness is studied. It is found that Mo capping layer shows more saturated magnetic moments than Ta capping layer. The direction of the external magnetic field has a great influence on the magnetic anisotropy. The MgO/CoFeB/Mo sample prepared in an applied magnetic field parallel to the plane shows in-plane magnetic anisotropy (IMA). IMA becomes weak as the CoFeB thickness decreases, and it still exists when the thickness decreases to 1.1 nm. At the same time, the saturation field vertical to the plane decreases. When the thickness of CoFeB layer decreases to 0.9 nm or less, the IMA disappears. In our study, the saturated magnetization and magnetic dead layer are 1600 emu/cm3 and 0.26 nm at the annealing temperature 200 ℃, and the interface anisotropy is 0.91 erg/cm2, which is smaller than previous research results. Increasing the annealing temperature helps the sample keep the saturated state under a small magnetic field vertical to the plane, and makes IMA weak and transform into PMA. The variation of the Mo capping layer thickness affects the saturation magnetic moment of the sample. The magnetic moment shows a sharp downtrend when the Mo layer is between 1.2 and 1.6 nm, then it turns stabler with Mo capping layer thickening. Meanwhile, when the Mo capping layer is 1.6 nm, the external vertical saturation field becomes smallest. However under the parallel magnetic field, changing the thickness or annealing temperature, or changing both leads to no PMA occurring. When the magnetic field direction changes from parallel to vertical direction, some of the samples show PMA after the annealing process. The magnetic anisotropy of MgO/CoFeB/Mo varies with the thickness of Mo capping layer. IMA is present when the Mo capping layer is 1 nm or less while PMA is present when the Mo capping layer is between 1.2 and 5 nm. The sample coercive force in the vertical direction varies with thickness, and its magnetic hysteresis loss is much larger when the thickness of Mo capping layer is 1.4 nm.

2015, 64 (24): 247505.
doi: 10.7498/aps.64.247505

Abstract +

For a nanodisk, magnetic vortex characterized by a curling magnetization is an energetically stable state. The magnetization in the center of the magnetic vortex is directed upward or downward, namely, the vortex core polarity p=+1 or p=-1 refers to up or down, respectively. The curling direction of magnetization, namely, the vortex chirality, is either counter-clockwise or clockwise. Thus, different combinations of chirality and polarity in a vortex structure demonstrate four stable magnetic states, which can be used to design a multibit memory cell. Such a multibit memory application requires the independent controlling of both the vortex chirality and vortex polarity, which has received considerable attention recently. Switching the vortex polarity has been achieved by using either a magnetic field or a current. The vortex chirality can be controlled by introducing asymmetric geometry of nanodisks. In this article, by using micromagnetic simulations, we present an effective method to simultaneously control the vortex chirality and polarity in a spin valve structure, in which the fixed spin polarizer layer is magnetized in the film plane when the free layer has a magnetic vortex configuration. The free layer is designed into a ladder shape with the right part being thicker than the left part. Our simulations indicate that a combination of desirable vortex chirality and polarity can be easily controlled by a Gaussian current pulse with proper strength and pulse duration through the spin-transfer torque effect. The insight into physical mechanism of the controllable vortex is demonstrated by a series of snapshots. If the magnetic moment of the free layer is saturated in the direction of 0θ θ is the angle between the magnetization and+x axis, the vortex with the counter-clockwise chirality will be generated after the pulse. In contrast, if the free layer magnetization is saturated along the direction πθ <2π, after the pulse, the vortex will have the clockwise chirality. The core polarity of the remanent vortex state is determined by the sign of the magnetic charges which are formed in the step-side of nanodisk during the current pulse.

2015, 64 (24): 247701.
doi: 10.7498/aps.64.247701

Abstract +

(1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 materials near the morphotropic phase boundary are selected for tentative electron emission experiments due to their excellent piezoelectric and ferroelectric properties and relatively high dielectric constants. The influences of ferroelectric and dielectric properties of ferroelectric cathode material on its threshold voltage are studied. The relationship between emission current and triggering voltage is investigated, and the relationship between emission current and extracting voltage is studied as well. The electron emission mechanism is also analyzed. The results show that emission threshold voltage of the relaxation ferroelectric 0.9Pb(Mg1/3Nb2/3) O3-0.1PbTiO3 is smaller due to its high dielectric constant at room temperature and large polarization variation. Low threshold voltage means low power consumption. This is an important factor to be considered in actual application for ferroelectric cathode and it has an important reference value. Electron emission is associated with fast polarization reversal and the formation of the plasma. The self-emission current starts on the falling edge of the triggering voltage pulse, which means that it is caused by polarization reversal. The amplitude of the self-emission current grows exponentially with the increase of triggering voltage. The amplitude of emission current shows a linear growth with the increase of extracting voltage when it is larger. It indicates that large current is determined mainly by extracting voltage. Larger current needs larger extracting voltage. The emission current starts on the rising edge of the triggering voltage pulse. It is associated with the field enhancement effect near “three interface points” and the formation of the plasma. An emission current of 210 A is obtained from the ferroelectric cathode under an extracting voltage of 2500 V, and the corresponding current density is 447 A/cm2.

2015, 64 (24): 247801.
doi: 10.7498/aps.64.247801

Abstract +

In this paper, SrZn2(PO4)2:Sn2+ (SZ2P:Sn2+), SrZn2(PO4)2:Mn2+ (SZ2P:Mn2+), SrZn2(PO4)2:Sn2+, and Mn2+ (SZ2P:Sn2+, Mn2+) phosphors are prepared by high temperature solid state reaction. The X-ray diffraction patterns and photoluminescence spectra of the phosphors are investigated in detail. The emission spectrum of SZ2P:Sn2+ is a wide band peaking at 461 nm due to 3P1 →1S0 transition of Sn2+, and overlaps effectively with the excitation spectrum of SZ2P:Mn2+, which shows that the absorption of SrZn2(PO4)2 host, and a series of peaks at 352, 373, 419, 431, and 466 nm, corresponding to 6A1(6S)→4E(4D), 6A1(6S)→4T2(4D), 6A1(6S)→[4A1(4G), 4E(4G)], 6A1(6S)→4T2(4G) and 6A1(6S) →4T1(4G) transition, respectively, are assigned to a wide band ranging from 200 nm to 300 nm. Therefore, luminescence intensity of Mn2+ is enhanced significantly by co-doping Sn2+ in SrZn2(PO4)2 host. According to the Dexter's energy transfer formula of multipolar interaction and Reisfeld's approximation, it is demonstrated that the energy transfer between Sn2+ and Mn2+ is due to the quadripole-quadripole interaction of the resonance transfer. The critical distance (Rc) of energy transfer is calculated to be about 1.78 nm. The tunable color is achieved by changing the doping concentrations of Sn2+ and Mn2+. The SZ2P:Sn2+, Mn2+ phosphor could emit strong blue-white light under the excitation of 254 nm ultraviolet (UV) light. The result shows that the SZ2P:Sn2+, Mn2+ is a promising phosphor for compact fluorescent lamp, and with the development of short wave UV semiconductor chip, this phosphor has potential applications in white light emitting diodes in the near future.

2015, 64 (24): 247802.
doi: 10.7498/aps.64.247802

Abstract +

The defect luminescences of types IIa, Ib and Ia diamond are investigated by the low-temperature micro-photoluminescence microspectroscopy. The results show that with the increase of nitrogen content, the interstitials and vacancies are trapped by the nitrogen atoms, then the luminescences of intrinsic defects such as GR1, 533.5 nm and 580 nm centers are weakened, while the emissions of nitrogen-related such as NV and 523.7 nm centers are strengthened. After high temperature annealing, the interstitials and vacancies in diamond become movable. The NV0 center is found in the IIa diamond, and the type Ib diamond presents the only strong NV luminescence. The H3 and N3 centers are observed due to the aggregation of nitrogen in Ia diamond. In addition, the nitrogen benefits the formations of the negative defects (3H center, NV- center) as the donor atom.

2015, 64 (24): 247803.
doi: 10.7498/aps.64.247803

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Single quantum dots (QDs) always exhibit strong blinking in fluorescence intensity when they are on some inert substrates. The blinking activity is attributed to the photoinduced charging of QDs by electron transfer (ET) to trap states in QDs and the surrounding matrix, which has been considered as an undesirable property in many applications. Here, we use N-doped indium tin oxide (ITO) semiconductor nanoparticles to suppress fluorescence blinking activity of single CdSe/ZnS core/shell QDs. The fluorescence characteristics of single QDs in ITO and on SiO2 cover glass are measured by a laser scanning confocal fluorescence microscopy, respectively. It is found that the on-and off-state probability densities of QDs on different substrates both can be fit by a truncated power law. Blinking rates for single QDs on glass and in ITO are also calculated. By contrast, single QDs doped in ITO show that their blinking rate and fluorescence lifetime both decrease. The on-state probability density of single QDs in ITO is approximately two orders of magnitude higher than that of QDs on SiO2 cover glass. It means that single QDs doped in ITO have a longer time to be on-state. Because the Fermi level in QDs is lower than in ITO, when they are in contact, electrons in ITO will transfer to QDs. As a result, the equilibration of their Fermi levels leads to the formation of negatively charged QDs. These electrons fill in the holes of QDs shell and enhance the on-state probability of QDs. Fluorescence decays of single QDs on glass and in ITO are measured by TAC/MCA, and they can be fit by biexponential function. The two lifetime values correspond to the single exciton lifetime and biexciton lifetime of QDs, respectively. It is worth noting that the distribution of the amplitude weighted average lifetime for single QDs in ITO is approximately 41% of that for single QDs on SiO2 cover glass and its full width at half maximum (FWHM) is changed to 50%. For the conduction band potential of QDs is higher than that of ITO, which contributes to photoinduced interfacial electron transfer from QDs to ITO and leads to the increase of nonradiative transition. These indicate that ITO can reduce single exciton and biexciton lifetime of QDs. The study demonstrates that ITO can effectively suppress the blinking activity of QDs.

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

2015, 64 (24): 248101.
doi: 10.7498/aps.64.248101

Abstract +

Tin oxide (SnO2) is a wide-band-gap semiconductor with a bandwidth of 3.6 eV at room temperature, which is widely used in many fields, such as gas sensors, transparent electrodes and optoelectronic devices due to its high optical transparency, low resistivity, and higher chemical and physical stability. However for the real applications of SnO2 based optoelectronic devices, it is necessary to obtain both n-type and p-type SnO2 materials. Unfortunately, SnO2 is intrinsically an n-type semiconductor material, therefore most efforts have been made to obtain p-type SnO2 materials. In this paper, SnO2 thin films with different Sb12 concentrations are grown on Al2O3 substrates by chemical vapor deposition method through using Sb2O3 and SnO as reaction source. The surface morphology, elemental concentration, and structural properties of SnO2 thin films with different Sb concentrations are investigated by field-emission scanning electron microscopy, energy-dispersive spectroscopy and X-ray diffraction, respectively. As the Sb content increases, the SnO2 thin films become more smooth and the grain size increases, indicating that the crystal quality of the thin film is improved. It is also found small amount of Sb doping of SnO2 thin film can be act as a surfactant. Moreover, the Hall measurement results indicate that the Sb doped SnO2 thin film has a p-type conductivity for an optimum Sb2O3/SnO mass ratio of 1:5. The optical absorption spectrum measurement indicates that the energy gap of sample is evidently blue-shifted with increasing Sb doping concentration. Furthermore, the Sb doped p-SnO2/n-SnO2 thin film homojunction is successfully fabricated to verify the p-type conductivity of Sb doped SnO2. The Sb doped p-SnO2/n-SnO2 homojunction device shows good rectifier characteristics, and its forward-turn-on voltage is 3.4 V.

2015, 64 (24): 248201.
doi: 10.7498/aps.64.248201

Abstract +

The electronic structure and properties of silicate polyanion Li2FeSiO4 in the orthorhombic crystal structure with Pmn21 symmetry and the relevant delithiated system LiFeSiO4 are investigated by the first principles method in the framework of the density functional theory with the generalized gradient approximation. The WIEN2k software is used for the self-consistent calculation of the crystal structure to obtain the energy band, density of states, and charge density. Boltzmann transport theory is further used to obtain the values of ratio σ /τ of Li2FeSiO4 and LiFeSiO4 based on the results of the first-principles calculations. The structural stability of Li2FeSiO4 system is demonstrated by calculating and analyzing the lattice parameter and the bond length. The results indicate that Li2FeSiO4 crystal has only 2.7% volume variation in the lithiation/delithiation process and the change of the Si–O bond length is very small, which suggests that the bonding nature between silicon and oxygen atoms remains unchanged. The results of charge density analysis show that the structural stability of Li2FeSiO4 crystal during lithium deintercalation is actually a consequence of a strong covalent interaction between silicon and oxygen atoms. An analysis of density of states shows that the density in the high-energy range near the Fermi level mainly comes from Fe-3d electron states. The Fermi level moves towards the lower energy end during the deintercalation of lithium ions and the electronic conductivity decreases with the decreasing of lithium ions, indicating that the conductive properties of Li2FeSiO4 are better than those of LiFeSiO4. It suggests that Li2FeSiO4 could be modified by doping atoms to affect the electrons in orbital Fe-3d and enhance conductive properties in future research. The calculations of transport properties show that the electronic conductivity of Li2FeSiO4 is not sensitive to temperature in a range from 300 to 800 K, and Li2FeSiO4 material is a potential candidate for heat-resisting cathode material. It also indicates that Li2FeSiO4 owns a better electronic conductivity than LiFeSiO4, which is consistent with the analyses of band structure and density of states. This research reveals the microscopic mechanism such as electronic structure and electronic transport properties of Li2FeSiO4 crystal in theoretical calculations, and provides a theoretical basis for the further improvement of electrochemical properties of lithium-ion battery.

## EDITOR'S SUGGESTION

2015, 64 (24): 248701.
doi: 10.7498/aps.64.248701

Abstract +

The plant mutation effects induced by ionizing radiation involve a rather complex process which is composed of physical, chemical, biochemical and biological stages. Nowadays, although ionizing radiation has been widely used in plant mutation breeding, the theoretical explanations for the mechanism of the ionizing radiation caused plant mutation effects are insufficient. Especially, a saddle shape relationship between the plant survival rate and radiation dose is found in the mutagenis effect of ionizing radiation on plants. The underlying mechanism of the saddle shape relationship remains unclear and challenges to all extant models.To explain this relationship, a damage-repair model for the plant mutation effects induced by ionizing radiation is proposed in the present work. Our model is based on the rate theory of ionizing radiation in which the cell damage and repair are taken into account simultaneously together with the micro-and macro-biological mutation effects of plant caused by ionizing radiation. The states of the radiated plant individuals are grouped into three categories: normal, damaged and lethal categories in our model. The evolution dynamics of the relative concentrations of the three categories are determined by a set of coupled equations which are mathematically the same as the Crow-Kimura equations in species evolution theories. With the numerical solution of our model in its steady state, the relative steady state concentration distributions of different categories of the radiated plants with increasing radiation dose are obtained. It is shown that without the plant repair effect, the relationship between the plant survival rate and radiation dose appears to be a conventional shoulder type one. With the plant repair effect, our model gives a saddle shape survival-dose relationship which has been observed commonly in the experiments on the radiated plants by ionizing radiation. To further test the model, the experimental data on the inbred lines of maizes radiated by heavy ion 7Li are used to determine the parameters of the model. It is shown that the theoretical results are basically consistent with the experimental ones. In addition, the mutation characteristic of the survival plants also appears to be a saddle effect-dose relationship, for which the theoretical model could also give a reasonable explanation. Our damage-repair model explains the saddle shape relationship between the plant survival rate and radiation dose, which indeed illuminates its power. And it provides a theoretical basis and reference for studying the biological effect mechanism of plants induced by ionizing radiation and conducting ionizing radiation plant breeding.

2015, 64 (24): 248702.
doi: 10.7498/aps.64.248702

Abstract +

Synchronization analyses of electroencephalogram (EEG) and electromyogram (EMG) could reveal the functional corticomuscular coupling (FCMC) between sensorimotor cortex and motor units firing in a target muscle. In order to quantitatively analyze the nonlinear functional coupling characteristics of EEG and EMG on a multiple time scale, a multiscale transfer entropy (MSTE) method based on the transfer entropy theory is proposed. Considering the multi-scale characteristics of EEG and EMG signals, the EEG and EMG signals are firstly decomposed into multiscale ones, respectively, to show the information on different time scales. Then the signals on different time scales are decomposed into different frequency bands to show the frequency domain characteristics. Finally, the EEG and EMG in different frequency bands on different scales are calculated by the MSTE method to obtain the FCMC characteristics on different time scales and in coupling frequency bands. In this study the MSTE is used to quantitatively analyze the nonlinear functional connection between EEG over the brain scalp and the surface EMG from the flexor digitorum surerficialis (FDS), which are recorded simultaneously during grip task with steady-state force output.#br#In the process of data processing, the coarse graining method is introduced firstly to decompose the EEG and EMG recorded in the task. Secondly, MSTEs between EEG and EMG on various scales are calculated to describe the nonlinear FCMC characteristics in different pathways (EEG→EMG and EMG→EEG). Furthermore, a significant indicator of MSTE is defined to quantitatively analyze the discrepancy between FCMC interaction strengths in the specific frequency band. The results show that the functional corticomuscular coupling is significant in both descending (EEG→EMG) and ascending (EMG→EEG) directions in the beta-band (15-35 Hz) in the static force output stage, especially that the interaction strength in descending direction is stronger in beta2-band (15-35 Hz) than that in the ascending direction. Meanwhile, the maximum FCMC strength value and the maximum or minimum discrepancy value between coupling directions on different scales almost occur on the high scales (15-30). Our study confirms that beta oscillations of EEG travel bidirectionally between the sensorimotor cortex and contralateral muscles in the sensorimotor loop system, and beta2 band is likely to reflect the motor control commands from the cortex to the muscle. Additionally, the discrepancy varies on different time scales and in different coupling frequency bands. The results show that the MSTE can quantitatively estimate the nonlinear interconnection and functional corticomuscular coupling between the sensorimotor cortex and the muscle.

2015, 64 (24): 248801.
doi: 10.7498/aps.64.248801

Abstract +

Metal nanoparticles with low cost and high performance have good potential applications in light-trapping of solar cells. In this paper, a three-dimensional model is proposed to simulate the light absorption of microcrystalline silicon (μc-Si:H) thin film solar cells. The effects of spherical and hemispherical Al nanoparticle arrays located on the front surfaces of solar cells are investigated, and the particle radius and array period are optimized by the finite element method. The results show that the optimal Al nanoparticle arrays can enhance broadband absorption in thin film solar cells. For spherical particle arrays, the key parameter that influences light absorption in solar cells is period/radius ratio (P/R) or particle surface coverage. When P/R=4-5, the optimum integrated absorption enhancement (Eabs) is over 20% under AM1.5 illumination compared with the solar cell without nanoparticles. The value of Eabs is small and decreases with the increase of P/R when P/R>5, and Eabs is less than zero when P/RP=500 nm and R=120 nm, the spectral absorption rate as a function of wavelength shows broadband absorption including four distinct peaks, which are attributed to quadrupole plasmon resonance mode, dipole resonance mode and waveguide mode respectively according to the electric field distribution in the solar cell. For hemispherical particle arrays, the maximum value of Eabs is 24.5%, which is higher than that of the solar cell with optimized spherical particle arrays. This is due to the high coupling efficiencies of the particles, so that most of the scattered light is directly coupled into the substrate. However, the value of Eabs is very sensitive to the hemispherical particle radius. As the radius decreases, the scattering cross-section and scattering efficiency of the particle decrease dramatically. As the radius increases, the dipole plasmon resonance wavelength rapidly shifts towards longer wavelength (red shift). Both of these are detrimental to absorption enhancement of solar cells. Thus we conclude that spherical Al particle arrays are more preferable in actually fabricating the light-trapping of solar cells.

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

2015, 64 (24): 249601.
doi: 10.7498/aps.64.249601

Abstract +

The solar magnetic activity is produced by a complex dynamo mechanism and exhibits nonlinear dissipation behavior in nature. The chaotic and fractal properties of solar activity phenomena are of great importance for understanding the nonlinear dynamo actions, especially nonlinear dynamo models. To study the chaotic and fractal properties of solar activity phenomena at the high-and low-latitudes, the polar faculae and sunspot numbers in the time interval from 1952 February to 1998 June are used to investigate their nonlinear dynamical behavior by the recurrence analysis method and Grassberger-Procaccia (G-P) algorithm. Firstly, the monthly average value of both polar faculae and sunspot numbers are smoothed to filter the noisy signal by the 13-point smoothing method. This procedure can keep the original dynamical information. Secondly, the correlation coefficient of these two solar activity indicators is analyzed, and the analysis results indicate that there is a negative correlation between polar faculae and sunspot numbers. To obtain more accurate results, the recurrence quantification analysis (RQA) is used to obtain the average value of the rate of DET by selecting four groups of different parameters. And then, we use the G-P algorithm to draw the correlation integral curve graphs and to obtain the correlation dimension of polar faculae and the sunspot numbers. Finally, the analysis results given by RQA and G-P algorithm are analyzed and compared by advanced statistical method. The main conclusions of this paper are as follows. 1) From a statistical point of view, the chaotic and fractal properties of high-and low-latitudes solar activity are different between in the northern hemisphere and in the southern hemisphere, owing to the fact that the temporal variation of solar activity is closely related to the magnetic field evolution. This result is in agreement with the previous results given by the polar faculae. It should be pointed out that this result is not the main goal of this article, we only reinforce this conclusion by the recurrence analysis and G-P algorithm. 2) The chaotic behaviors of solar magnetic activity at high latitude are stronger than at low latitude. Furthermore, the high-latitude solar activity in the northern hemisphere has the most complex fractal structure. Based on the solar nonlinear dynamo theory, the polar magnetic fields are the seed fields of the solar activity. That is to say, the physical meaning of polar faculae is more important than sunspot numbers. We think that our results are useful for understanding the physical nature of the systematic regularity of solar activity phenomena.