## Vol. 65, No. 21 (2016)

##### 2016-11-05

###### GENERAL

2016, 65 (21): 210201.
doi: 10.7498/aps.65.210201

Abstract +

Recently,tensor models (or multi-way arrays) play a vital role in many applications,such as wireless communication systems,blind source separation,machine learning,signal (audio,image,speech) processing,chemometrics,data mining, arithmetic complexity,environmental sciences,etc.Parallel factor (PARAFAC) analysis,also known as canonical polyadic decomposition,is a common name for low rank decomposition of tensors.A traditional way to fit the PARAFAC model is the alternating least squares (ALS) algorithm,which can transform a nonlinear optimization problem into some independent linear least squares problems.However,the ALS scheme for computing the decomposition of the tensor is known to converge slowly if one or some modes include nearly collinear columns.Particularly,if the collinearity is presented in all modes,the ALS will end in a convergence bottleneck.Hence,it is necessary to develop a robust and fast algorithm to compute the decomposition of the tensor.In this paper,a novel channel estimation algorithm using the Levenberg Marquardt (LM) method based on a third-order tensor model is presented in a multi-user uplink amplify-and-forward (AF) relay system.As the relay nodes all operate with half-duplex mode to aid the transmission,the overall transmission period is partitioned into two transmission subprocesses.In the first transmission sub-process,the users transmit channel training sequence to the relay nodes.This stage requires time block once.During the second transmission sub-process,a set of diagonal amplifying factor matrices are utilized by the relay nodes to amplify the received data.Then,the relay nodes transmit each of the amplified data to the base station.This stage requires time blocks K times.With the help of the channel training sequence and the relay amplifying factor matrices,the received data at the base station can be stacked up into a third-order PARAFAC model. And then based on this tensor model an LM channel estimation algorithm is proposed to provide the individual channel state information of both user-to-relay and relay-to-base station channel links.As the channel sequence is transmitted by the users only once,the proposed scheme has a higher spectral efficiency than the case that the channel sequence is transmitted K times by the users.Numerical experiments are shown to demonstrate the efficacy of the proposed LM channel estimation algorithm.The results are as follows.Firstly,the LM approach has the same channel estimation performance as the bilinear alternating least-squares method.Secondly,the proposed estimator yields much faster convergence speed when the relay amplifying factor matrix is a random matrix or a highly collinear one.Finally,the proposed scheme performs well in both independent identically distributed channels and correlated channels scenarios,which means that the proposed channel estimator can provide the robust and reliable feature for multi-user uplinks AF relay systems.

2016, 65 (21): 210202.
doi: 10.7498/aps.65.210202

Abstract +

Bimetallic Pd-Pt clusters have attracted wide interest because of their special catalytic, optical, electronic, and magnetic properties. However, the geometrical optimization of Pd-Pt cluster has been a difficult task due to the homotopic problem, i.e., in some binary clusters, these clusters are identical in configuration, but different in relative arrangement of two types of atoms. For a fixed geometrical configuration the iterated local search（ILS) method is adopted to search the optimal homotop. By the combination of the merit of heuristic optimization algorithm and the idea of dynamic lattice searching（DLS), an adaptive immune optimization algorithm（AIOA) is modified, and the modified AIOA is called AIOA-BDLS-ILS method. To evaluate the efficiency of the improved method, the optimization of binary Lennard-Jones clusters up to 100 atoms is performed. The Results show that the CPU time for one hit of the global minima is less than 5000 s for all clusters and it is less than 1000 s for most clusters. Compared with previously reported BDLS-ILS method, the proposed method is very efficient. The method is thus proved to be efficient. It can be deduced that the method should be a universal algorithm for the fast optimization of binary or bimetallic clusters. Furthermore, the Gupta potential is used to describe the interatomic interactions in Pd-Pt clusters, which is based on the second moment approximation to tight binding theory, and the corresponding potential parameters are fitted to the experimental values of cohesive energy, lattice constant, and elastic constants for the face centered cubic crystal structure at 0 K. The structural optimizations of Pd-Pt clusters with 34, 50 and 79 atoms are performed by the AIOA-BDLS-ILS method. Results show that for optimizing the 34-atom Pd-Pt clusters, 12 new structures with lower energies are found. In 34-atom bimetallic Pd-Pt clusters, the motifs can be categorized into five classes, i.e., 12 decahedral structures, 3 decahedral structures with close packing anti-layers, 7 incomplete Mackay icosahedral structures, 6 poly-icosahedral structures, and 5 structures composed of two 19-atom double icosahedra. In 50- and 79-atom Pd-Pt clusters, the structural characteristics and the atomic distributions are analyzed. The results indicate that the decahedral and decahedral structures with close-packed configurations are dominant, and twin face centered cubic and partial icosahedral structures are also found. Moreover, the order parameter is adopted to analyze the distributions of different types of atoms in Pd-Pt clusters, which are calculated by the average distance of Pd or Pt atoms from the center of a cluster. The results show that there exists the segregation phenomenon of Pd and Pt atoms in Pd-Pt clusters, i.e., Pd atoms tend to occupy the surface sites, and Pt atoms prefer to occupy the inner core sites. This is explained by the lower surface energy of Pd（125-131 meV-2) than that of Pt（155-159 meV-2).

2016, 65 (21): 210501.
doi: 10.7498/aps.65.210501

Abstract +

Vibroimpact dynamics has been widely studied by experts and scholars in the fields of physics, engineering and mathematics. Most of the researches focus on vibroimpact systems under deterministic excitations by using numerical methods. However, random excitation often exists in vibroimpact system, whose roles cannot be neglected, sometimes may be quite important. Stochastic bifurcation is one of the most critical parts of stochastic dynamics, but the relevant researches about vibroimpact system are rarely seen so far due to the fact that the analytical method has its inherent difficulty. This paper aims to investigate the P-bifurcations of a Duffing-Rayleigh vibroimpact system under stochastic parametric excitation based on an equivalent nonlinear system method and the catastrophe theory. Firstly, the original Duffing-Rayleigh vibroimpact system is transformed into a new system without velocity jump by using the nonsmooth transformation method and Dirac function. Then, the equivalent nonlinear system method is introduced to obtain the stationary probability density of the response. Finally, the explicit parameter conditions for stochastic P-bifurcations are derived based on the catastrophe theory. Besides, the effect of stochastic parametric excitation on the system response is also discussed.

2016, 65 (21): 210502.
doi: 10.7498/aps.65.210502

Abstract +

Neural firing rhythm plays an important role in achieving the function of a nervous system. Neurons with autapse, which starts and ends in the same cell, are widespread in the nervous system. Previous results of both experimental and theoretical studies have shown that autaptic connection plays a role in influencing dynamics of neural firing patterns and has a significant physiological function. In the present study, the dynamics of a neuronal model, i.e., Rulkov model with inhibitory autapse and time delay, is investigated, and compared with the dynamics of neurons without autapse. The bifurcations with respect to time-delay and the coupling strength are extensively studied, and the time series of membrane potentials is also calculated to confirm the bifurcation analysis. It can be found that with the increase of time-delay and/or the coupling strength, the period-adding bifurcation of neural firing patterns can be induced in the Rulkov neuron model. With the increase of the period number of the firing rhythm, the average firing frequency increases. When time-delay and/or coupling strength are/is greater than their/its corresponding certain thresholds/threshold, the average firing frequency is higher than that of the neuron without autapse. Furthermore, new bursting patterns, which appear at suitable time delays and coupling strengths, can be well interpreted with the dynamic responses of an isolated single neuron to a negative square current whose action time, duration, and strength are similar to those of the inhibitory coupling current modulated by the coupling strength and time delay. The bursts of neurons with autapse show the same pattern as the square negative current-induced burst of the isolated single neuron when the time delay corresponds to the phase. The bifurcation structure of the neural firing rhythm of the neuron without autapse can be obtained with the fast-slow dissection method. The dynamic responses of the isolated bursting neuron to the negative square current are acquired by using the fast-slow variable dissection method, which can help to recognize the new rhythms induced by the external negative pulse current applied at different phases. The new rhythm patterns are consistent with those lying in the period-adding bifurcations. The results not only reveal that the inhibitory autapse can induce typical nonlinear phenomena such as the period-adding bifurcations, but also provide the new phenomenon that the inhibitory autapse can enhance the firing frequency, which is different from previous viewpoint that inhibitory effect often reduces the firing frequency. These findings further enrich the understanding of the nonlinear phenomena induced by inhibitory autapse.

2016, 65 (21): 210301.
doi: 10.7498/aps.65.210301

Abstract +

The birefringence is one of the most important properties of all kinds of optical materials. and is widely used in many basic researches and industrial fields. By utilizing high birefringent materials or waveguides, a variety of unique and interesting optical features or functions can be achieved, such as in manipulating the polarization of an optical beam in a miniaturized way and providing the organic electro-luminescence display. Crystals, liquid crystals, semiconductor, silicon, ferroelectric material and polymer can exhibit their birefringences. While polymer materials are commonly used to fabricate optical films and waveguides, most polymer materials show relatively weak birefringences, and thus they are restricted in realizing novel functional photonics devices. In the past, such a weak birefringence has been roughly characterized in experiment. There is a lack of systematic method to theoretically calculate the birefringences of polymer materials, especially at a molecular level. This restricts the research on enhancing the birefringences of polymer materials. To study the birefringences in fluorinated polymers and find the way to enhance them, the origin of the birefringence in fluorinated polymer should be investigated in depth and the birefringence should be exactly calculated. In this paper, a theoretical method is established to calculate the birefringence of polymer systematically from the monomer unit to the molecular chain. Based on this method, the limiting factor that leads to a weak birefringence in polymer material is investigated. Taking the polymethyl methacrylate（PMMA) for example, the density functional theory（DFT) is first used to study the intrinsic birefringence of PMMA, where the intrinsic birefringence value is indeed the birefringence of the monomer unit and is also a maximum birefringence of the polymer material when the molecular chains are fully oriented. In the DFT, a stable structure of the PMMA monomer unit is constructed, and the intrinsic birefringence of this PMMA monomer unit structure is calculated. The calculation result shows that the intrinsic birefringence of PMMA monomer unit can reach up to 0.0738, the dispersion curve of the average birefringence of the monomer unit is also given. Furthermore, the molecular dynamics is used to study the material birefringence of the PMMA material consisting of 20 molecular chains. The calculation results show that although the intrinsic birefringence is much larger, the material birefringence of the PMMA is only 0.00052, due to the low degree of orientation of molecular chain in the PMMA. It is found that the molecular structure and the molecular orientation of the polymer are the two main factors influencing the birefringence. The theoretical method established in this work and the calculation results provide a research basis for enhancing the birefringences of polymer materials.

2016, 65 (21): 210601.
doi: 10.7498/aps.65.210601

Abstract +

Laser proximity fuze is a kind of active detecting system which has been extensively equipped in both conventional and guided missile ammunitions. It uses a pulsed laser for detecting and ranging a target, accurately providing information about target angle and distance. The system emits a short pulse of laser beams which come into contact with the target and receives the light scattered back. After transducing light into electric signal, target range could be obtained with proper signal processing technique. The width and amplitude of the echo could vary if targets are of different characteristics, which leads to distributed target ranging results. Therefore, a better understanding of the relationship between target characteristic and ranging distribution can increase the precision of the pulsed laser proximity detecting system.In this paper, the emitted laser is modeled as a Gaussian pulse. The corresponding impulse response equation and echo equation of the pulsed laser for the planer target are derived. Considering the echo broadening effect, relative broadening ratio is determined from the echo equation. Then the relationships between the echo broadening coefficient and the parameters of tilt angle of planar target, laser divergence angle, and laser pulse width are analyzed. The results show that relative broadening ratio increases with the increase of the tilt angle of planar target or laser divergence angle, and decreases as the laser pulse width decreases. Based on the echo equation of pulsed laser and constant threshold leading edge detection, the probability density function of the planar target ranging is derived analytically. The influences of changing parameters of tilt angle of planar target, power of emitted laser, laser divergence angle, and threshold-to-noise ratio（TNR) on statistical ranging distribution are simulated.Monte Carlo simulation is performed for the whole waveform ranging experiment. The pulsed laser ranging platform is built and 20 m ranging experiment is conducted. The result shows that the ranging probability density distribution from Monte Carlo simulation is close to that from the experiment. As the tilting angle of target increases, ranging mean and variance both increase. When the tilting angles are 0, 20, 40 or 60, the signal-to-noise ratio（SNR) is larger than the TNR, and the ranging distribution is Gaussian. When the tilting angle is 70, the SNR is smaller than the TNR, and the ranging distribution is distorted with a longer rising edge and a shorter falling edge from the original Gaussian profile. This study could provide theoretical basis for the research of the ranging distribution of pulsed laser detector with the consideration of target characteristic.

2016, 65 (21): 210701.
doi: 10.7498/aps.65.210701

Abstract +

The time delay estimation is widely used in wireless location field, and is the research emphasis in complex environment of this field. The current delay estimation algorithms can be classified as five methods of correlation, high-order statistics, self-adaption, maximum likelihood and subspace. However, the existing algorithms can hardly achieve an ideal performance in small sample（single snapshot) and low signal-to-noise ratio environment during wireless location. In order to solve the problem about the insufficiency of the current algorithms in the above conditions, many new methods have been introduced into the delay estimation problem. The compressed sensing sparse reconstruction method has been applied to the signal processing field as a newly-proposed algorithm in recent years. The delay estimation is realized by using the method of sparse reconstruction, in which the sparse representation of the signal is the premise. The rational construction of the measurement matrix and the design of the signal reconstruction algorithm are the core of correct estimation.The purpose of this article is to deal with the lack of measurement data in small sample（single snapshot) and low signal-to-noise ratio environment during wireless location. In the model of wireless location, the signal can be represented as a sparse matrix form by selecting suitable sparse representation matrix. The wireless multi-channel is measured in the time domain, the propagation delay varies with channel and the delay representation in the time domain is sparse, so that it can be directly constructed into the form of sparse signal. Since the necessary and the sufficient condition of the coefficient sparse matrix successfully reconstructed by the measurement matrix are the measurement matrix meeting the restricted isometry property（RIP). The orthogonal measurement matrix based on the steering vector by the method of Gram-Schmidt is proven to achieve the RIP. A novel sparse reconstruction algorithm based on backtracking filter is constructed to estimate the time delay. In order to guarantee that the first selection includes the optimal atom, several atoms are selected. And then the backtracking mechanism is introduced, and the selected atoms are approached by the method of the minimum square to sequence the obtained signals and select the optimal atom. Therefore, this method can be used to guarantee that the optimal atom is selected. The presented algorithm can achieve the delay estimation by using the corresponding relation between the time delay and the measurement matrix in a high precision. Furthermore, the Cramer-Rao bound（CRB) of this model is derived. Finally, simulations show that the proposed approach is suitable for small sample（single snapshot) and low signal-to-noise ratio environment. The proposed method can achieve a higher precision than Root-Music and improve performance at low complexity cost compared with OMP algorithm. The simulation result proves that the algorithm is stable and reliable.

2016, 65 (21): 210702.
doi: 10.7498/aps.65.210702

Abstract +

In order to measure a weak alternating magnetic field, an optically-pumped Rb magnetometer based on pump-probe structure is investigated and demonstrated. The pumping light and probing light propagate along the z axis and x axis, respectively. A constant polarization magnetic field along the pumping light is applied, which not only stabilizes the polarization of Rb atoms but also tunes resonance frequency of Rb atoms. When a weak alternating magnetic field is applied perpendicularly to the constant magnetic field, the magnetic moment will tip off the z axis and rotate around the z axis. And then the polarization plane of probing light is modulated correspondingly. The x component of the magnetic moment can be obtained with a balanced detector. As a result, a signal proportional to weak alternating magnetic field can be obtained.In order to obtain the magnetic response of the magnetometer, we analyze the signal amplitude as a function of polarization magnetic field strength B0 and transverse relaxation time 2 with numerical simulation. The amplitude-frequency response of the magnetometer is determined mainly by two parameters, namely cutoff frequency c=1/2 and resonance frequency 0= B0, where is the gyromagnetic ratio of Rb atom. At low frequency, that is a0 and a 0c2, the magnetometer has a flat response, here a is the frequency of the weak alternating magnetic field. If 0c, the signal amplitude will be large for large 0 or small c. For a given c, the peak response appears at 0=c. In the vicinity of resonance frequency, if c0, a peak will appear and if c 0, no peak occurs. At high frequency, the amplitude will decrease with the increase of a.We verify the above analyses in experiment. A vapor cell with a short transverse relaxation time is used to obtain large frequency response bandwidth. Through optimizing the powers and frequencies of pumping laser and probing laser, high polarization and detection sensitivity of atomic spin can be obtained. Moreover, through choosing an appropriate polarization magnetic field, the magnetometer can be maximally sensitive to the magnetic field to be measured. The experimental results show that the magnetometer has a sensitivity of about m 0.2; pT/HzHz and bandwidth of about 3.5 kHz. It can be used to detect low field magnetic resonance and high frequency abnormal physical phenomena.

###### NUCLEAR PHYSICS

2016, 65 (21): 212801.
doi: 10.7498/aps.65.212801

Abstract +

Beryllium is an important nuclear material, and the reliability of the data for neutron-induced nuclear reactions of beryllium is of significant importance for nuclear engineering. The evaluated nuclear data for beryllium have been improving from ENDF/B-VI to ENDF/B-VⅡ.0 and then to ENDF/B-VⅡ.1. The comparisons between the calculated and experimental results of the criticality benchmark experiments are the essential means to test the reliability of nuclear data and indicate the direction of the improvement of nuclear data. There are several series of criticality benchmark experiments with beryllium reflector available for testing beryllium nuclear data. However, the calculated results are not consistent across these benchmarks. Two series of these benchmarks that are similar to each other, namely HMF058 and HMF066, are selected for discussion. HMF058 and HMF066 are both highly enriched metal fast benchmarks, with five cases of experiments in HMF058 benchmark and nine in HMF066. With ENDF/B-VⅡ.1 cross sections, a clearly increasing C/E keff bias is observed with increasing beryllium reflector thickness for the five cases in HMF058 benchmark, while using ENDF/B-VⅡ.0 cross sections, all the C/E values for keff remain within the experimental uncertainty. However, HMF066 are calculated very well with ENDF/B-VⅡ.1 cross sections, but a bias of about 500 pcm is observed with ENDF/B-VⅡ.0 data. These results are particularly puzzling since there is little difference between the configurations of HMF058 and HMF066, so the quality of beryllium nuclear data cannot be evaluated and the direction for improvement cannot be figured out either. The similarity method, based on the use of sensitivity coefficients calculated by sensitivity and uncertainty code SURE, is used to analyze the similarity between two series of benchmark experiments. First, the neutronics similarity index between each pair of the total of fourteen cases of experiments from the two benchmarks is calculated. Then, the most similar experiments from HMF066 to each case of the five experiments from HMF058 are selected by similarity index, and the experiments are grouped into five similarity suites, each with one from HMF058 and the others from HMF066. The experiments in the same similarity suite are highly similar to each other on neutronics. In a similarity suite, the deviations of calculated results and experimental values are disagreed for experiments from different series, but the deviations agree with each other for experiments from the same series. This shows that the agreement between the calculated results and experimental values cannot be improved by revising the nuclear data. It is necessary to carry out the detailed reevaluation of the benchmark experiments, or to develop reliable new integral experiments to exclude unreliable experiments, in order to avoid the misleading of the nuclear data testing.

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

2016, 65 (21): 214101.
doi: 10.7498/aps.65.214101

Abstract +

Electromagnetic scattering characteristics change significantly from breaking waves, which is considered to be one reason for sea spike phenomenon（HH polarization scattering intensity close to or even greater than VV polarization scattering intensity). Spiky sea clutter is often treated falsely as targets, which affects radar performance in target detection in the sea surface background. Thus the investigation on the physical mechanism of the sea spike phenomenon can help mitigate false alarms. In this paper, the authors investigate the microwave backscattering from the wedge-shaped breaking waves, which is simulated with the dihedral impedance wedge of finite length. The physical optical field of the breaking waves is calculated with the Kirchhoff approximation. Based on the Maliuzhinets method with using the precise impedance boundary condition, the impedance wedge scattering solution in spectral integral representation is presented. The spectral function is derived by the perturbation method with respect to the oblique incident angle based on the incidence normal to or grazing to the edge. After obtaining the spectral function, the asymptotic theory is used to determine the diffraction field of impedance wedge at an arbitrary skew incidence. The equivalent edge currents are derived from the uniform diffraction of impedance wedge by combining the physical optical coefficients and diffracted coefficients. Backscattering radar cross-sections（RCSs) of the diffracted field from 120 impedance wedge are calculated in both HH and VV polarizations, and the effects of frequency and permittivity on the wedge diffraction are discussed as well. The physical optical field backscattering from 135 impedance wedge is compared with the total field with considering the diffraction effects. Further calculations and analyses for backscattering from the three-dimensional extension breaking waves are presented by using the contribution of edge diffraction field to correct the physical optics field. Numerical results show that the backscattering RCS of impedance diffracted field in HH polarization is greater than that in VV polarization in the Keller cone. Therefore, the diffraction effects will make the backscattering RCS of the total field in HH polarization greater than that in VV polarization when the breaking wave grows to near-collapse stage at a small grazing angle with upwind observation. This indicates that the wedge diffraction is one of the causes of sea spike phenomenon.

2016, 65 (21): 214201.
doi: 10.7498/aps.65.214201

Abstract +

A highly nonlinear microstructured fiber with single-zero-dispersion wavelength is designed and drawn by reducing the core area in order to observe two groups of four-wave mixing processes by a single pump. The foundational material of the fiber is silica and its cladding is comprised of seven-layer air holes. The air holes are arranged in a hexagonal lattice and the lattice pitch is =2.5 m. The radius of each of the air holes is r=1.03 m. There is just one zero-dispersion wavelength in our considerable wavelength range for the microstructured fiber and the corresponding wavelength D is nearly 0.85 m（D=0.85 m). The basic properties of the fiber including effective refractive index, dispersion coefficient, and nonlinear coefficient are calculated by the finite element method. The effective mode area is 4.4 m2 and the nonlinear coefficient is 0.057 m-1W-1 for the foundation mode near the wavelength of 0.8 m, and the nonlinear coefficient reaches 0.053 m-1W-1 near the zero dispersion wavelength of 0.85 m. In short, the optical fiber has a stable and high nonlinear coefficient in the whole experimental band（0.80-0.83 m), which provides an important guarantee for the occurrence of four-wave mixing double parameter gain process. In addition, the phase mismatch curve is simulated by using the four-wave mixing phase mismatch formulation. Numerical simulation shows that two sets of four-wave mixing processes can occur in the designed fiber. At the normal dispersion wavelengths of 0.800, 0.810 and 0.820 m with different powers, the experimental result shows a significant feature of four gain wavebands located at both sides of the pump wavelength. By comparing experimental data with the phase mismatch curve, we find that the band generation meets four-wave mixing phase matching condition, thus, the simultaneous occurrence of two groups of four-wave mixing processes observed in the experiment is explained in theory. The experimental results are consistent well with the theoretical predictions. This also proves the theoretical predictions that two sets of parametric gain processes and two pairs of signal and idle frequency waves can be generated in PCF. The four-wave mixing effect occurring in the normal dispersion region can be attributed to the contribution of negative fourth-order dispersion to the phase matching process. The present work can provide valuable reference to designing the microstructure fibers and developing the multi-wavelength conversion technology based on four-wave mixing effect. At the same time, this work can also supply guidance for developing the uncommon waveband lasers and broadband light sources.

2016, 65 (21): 214202.
doi: 10.7498/aps.65.214202

Abstract +

The conventional partially coherent beam has a Gaussian correlated Schell-model function. In 2007, Gori and Santarsiero[Gori F, Santarsiero M 2007 Opt. Lett. 32 3531] discussed the sufficient condition for devising a genuine correlation function of a partially coherent beam. Since then, a variety of partially coherent beams with nonconventional correlation functions, such as nonuniform correlated beam, Hermite-Gaussian correlated beam, Laguerre-Gaussian correlated beam and beam with optical coherence lattices, have been introduced, and such beams display many extraordinary propagation properties, such as self-focusing, self-shifting, self-splitting, self-shaping and periodicity reciprocity, and they have useful applications in many areas, such as free-space optical communication, particle trapping, image transmission and optical encryption.In most of previous studies, the correlation function of the partially coherent beam was assumed to be isotropic. In this paper, we introduce a new kind of partially coherent beam with anisotropic correlation function, which is named nonuniform Laguerre-Gaussian correlated（NLGC) beam. The NLGC beam has a nonuniform correlated function in the x-direction and Laguerre-Gaussian correlated Schell-model function in the y-direction. Furthermore, we explore the propagation properties of the NLGC beam in free space and in turbulent atmosphere comparatively with the help of the extended Huygens-Fresnel integral. In free space, it is found that the intensity distribution of the NLGC beam displays self-focusing and self-shifting behaviors in the x-direction and self-splitting properties in the y-direction during its propagation, which may be useful for particle trapping, and the distribution of the degree of coherence also varies during its propagation. In turbulent atmosphere, the NLGC beam displays similar propagation properties at short propagation distance because the influence of turbulence can be neglected, while with the further increase of the propagation distance, the influence of turbulence accumulates and both the intensity distribution and the degree of coherence distribution evolve into Gaussian profiles. We also find that the evolution properties of the intensity distribution and the degree of coherence are closely related to the mode order m of the correlation function, e.g. the intensity distribution and the degree of coherence distribution evolve into Gaussian profiles more slowly as the mode order m increases, which means that the NLGC beam with larger m is less affected by turbulence, which may be useful in free-space optical communication.Our results clearly show that modulating the correlation function of a partially coherent beam provides a novel way of manipulating its propagation properties, and will be useful in many applications, where light beam is required to possess a prescribed beam profile and controlled propagation properties. In this paper, only the NLGC beam is treated theoretically, and such a beam deserves further experimental investigation.

2016, 65 (21): 214203.
doi: 10.7498/aps.65.214203

Abstract +

With the rapid development of computer network technology, information security has attracted increasing attention. Due to the characteristics of multi-dimensional operation and parallel processing capability, optical image encryption techniques have been receiving more and more attention. Since the well-known double random phase encoding technique was proposed, many other methods based on optical information processing means such as the use of optical transform, interference, and polarized light encoding, have been proposed for optical image encryption. However, recent researches have demonstrated that traditional optical encryption techniques are symmetric cryptosystems, in which decryption keys are identical to encryption keys and they have been found to be vulnerable to different types of attacks, such as known plaintext and chosen plaintext attacks. To overcome this shortcoming, asymmetric cryptosystems based on nonlinear phase-truncation techniques and phase retrieval algorithm have been proposed. Asymmetric cryptosystem is a cryptographic system in which encryption keys are different from decryption keys. The encryption keys are used as public keys which are disseminated widely, and the decryption keys are used as private keys which are known only to the authorized users. So, asymmetric cryptosystem can offer a higher-level security than symmetric cryptosystem. However, asymmetric cryptosystems based on phase retrieval algorithms require a lot of computational time, and asymmetric cryptosystems based on phase-truncated Fourier transforms have been found to be vulnerable to special attack. Therefore, in this paper, a novel asymmetric image encryption method is proposed by using the gyrator transform and vector operation. The original image is encrypted into two phase masks with vector operation. One is a random phase mask and the other is a phase mask related to the original image. In the encryption process, the random phase mask is used as a phase key and the other phase mask is transformed by gyrator transform. The transform result is performed by Fourier transform after being modulated by a phase distribution. The ciphertext is the amplitude of the above result. Compared with previous encryption schemes, the suggested method has two advantages. Firstly, we have proposed a new asymmetric encryption method based on the gyrator transform and vector operation. The decryption process is different from the encryption process. The gyrator transform and Fourier transform are used in the encryption process, while only the inverse operation of Fourier transform is employed in the decryption process. In addition, the decryption keys produced in the encryption process are different from the encryption keys. Therefore, the proposed scheme has high resistance against the conventional attacks. Secondly, the encrypted result is real-valued, which is convenient for display, transmission and storage.Numerical simulations illustrate the feasibility and effectiveness of the proposed encryption scheme.

2016, 65 (21): 214204.
doi: 10.7498/aps.65.214204

Abstract +

Cavity-optomechanics has emerged as a new interdisciplinary research field,which studies the interaction between light field and mechanical systems of micro-and nanoscale.It is a promising avenue to solid-state quantum optics and has potential applications in high sensitivity measurement of weak force,tiny displacement and mass,and quantum information science.As a solid-state system of quantum optics,it has many interesting coherent phenomena,such as optomechanically induced transparency (OMIT),which is the optomechanical analog of the well-known phenomenon of electromagnetically induced transparency (EIT).However,due to diversity in structure,OMIT systems must have many new phenomena which do not exist in ordinary EIT systems.On the other hand,whispering-gallery-mode (WGM) microresonators have been investigated extensively.WGM microresonators have a wide range of applications due to their high quality factors and microscale mode volumes.WGM microresonators can also be used for OMIT systems,which have been investigated extensively.In this paper,we study the coherent control of an double-cavity optomechanical system which is composed of two WGM microresonators.We assume that the two WGM microcavties are driven by two strong control fields and two weak probe fields,and,one of the two cavities can create a macroscopic mechanical breathing mode under the action of a radiation pressure force.We also assume that the two WGM microcavties are directly coupled by an evanescent field.We theoretically study the quantum coherent control of electromagnetically induced transparency in this system,and find that in contrast with ordinary EIT systems,there are many new properties in this OMIT system, for example if two control fields with appropriate amplitudes and detunings are used to drive the system,the probe field, which is input to one of the two cavities,will be completely output from the other cavity,i.e.,the perfect transparency of the quantum coherence phenomenon can occur in this system.We also find that the electromagnetically induced transparency can be realized and controlled in this optomechanical system by adjusting the relative intensity and the relative phase between the two input probe fields,and the width and depth of the EIT window are sensitive to the relative intensity of the two control fields,which may be used for switching between fast and slow light.These results indicate important progress toward signal amplification,light storage,fast light,and slow light in quantum information processes.Considering the fact that WGM microresonators are the frontier research subjects ranging from biosensing, nonlinear optics,and laser physics,to fundamental physics such as cavity quantum electrodynamics,we believe that the results in this paper have a wide range of applications.

2016, 65 (21): 214205.
doi: 10.7498/aps.65.214205

Abstract +

The reliable functioning and continual optimizing of ArF excimer laser system is of importance when it comes to productization into the market from a laboratory test machine. The analysis of dynamic characteristics of the system is vital to understanding its operating mechanism and optimizing the design theoretically. In this article, one-dimensional fluid model is used to analyze the excimer laser discharge mechanism, and the content ratio of fluorine gas, argon gas, and neon gas, which constitute a gas mixture, is studied in a simulated ArF excimer laser system. Particles are treated as a fluid, which significantly reduces the computing cost in fluid model, and therefore is suitable for high-pressure situation. Four equations are included in one-dimensional fluid model, i.e., Boltzmann equation that describes electron energy distribution, ion continue equation that illustrates ion number density, Poisson's equation that shows the distribution of electric field, and photon rate equation that demonstrates laser outputting process. By combining these four equations, high pressure plasma discharge process and particles stimulated radiation process are studied, and calculation continues from one time step to another until the end of discharging process. The result of the calculation presents energy transfer process from three aspects:energy deposition efficiency, ArF* formation, and laser outputting. In the energy deposition process, the energy deposition efficiency is sensitive to the change of fluorine gas ratio while the variation of the content ratio of other two gases has a less influence on this process. In addition, there exists an optimal fluorine gas ratio that causes the highest energy deposition efficiency. In the ArF* formation process, the reaction between excited argon ions and fluorine gas is the main channel that generates ArF*. The proper increasing of fluorine gas ratio helps form ArF*. In the laser outputting process, photon loss is mainly because of the reaction between fluorine negative ions and photons. Therefore superfluous fluorine gas in the mixture leads to less photons, which eventually results in low energy efficiency of laser. By summarizing the three aspects of energy transfer process, the fluorine gas ratio in the gas mixture plays a significant role in determining the energy efficiency of ArF excimer laser system. This theory is verified by experiments, showing that the deviation of the optimized fluorine gas ratio severely reduces energy efficiency. This conclusion can guide us in optimizing the design and steady reliable function of ArF excimer laser system.

2016, 65 (21): 214206.
doi: 10.7498/aps.65.214206

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Based on the spin flip model, four schemes for the polarization switching of the 1550 nm vertical cavity surface emitting laser are studied by using numerical simulation, which are free running laser orthogonal injection free running laser, free running laser orthogonal injection polarization maintaining optical feedback laser, polarization maintaining optical feedback laser orthogonal injection free running laser, and polarization maintaining optical feedback laser orthogonal injection polarization maintaining optical laser. We can draw three conclusions from the numerical results. Firstly, changing the feedback strength can make the polarization switching point of the injection intensity in the different regular movements when the normalized injection current is small. The injection intensity of the polarization switching point increases with the increase of the feedback strength for the free running laser orthogonal injection polarization maintaining optical feedback laser; the injection intensity of the polarization switching point decreases with the increase of the feedback strength for the polarization maintaining optical feedback laser orthogonal injection free running laser; the injection intensity of the polarization switching point is nonlinear and fluctuates with the increase of the feedback strength for the polarization maintaining optical feedback laser orthogonal injection polarization maintaining optical laser. The reason is that the non dominant X polarization component cannot go up when the normalized injection current is small, then, as the feedback intensity increases, the difference between the two polarization components will be increased. Secondly, when the normalized injection current is large, changing the feedback intensity can make the polarization switching point of the injection intensity in the irregular movement. The reason is that the non dominant X polarization component can go up when the normalized injection current increases up to a certain value, which can form the significant nonlinear wave together with the dominant Y polarization component. Thirdly, changing the frequency detuning can make the polarization switching point of the injection intensity in the same regular movement. The injection strength required for the occurrence of polarization switching point first decreases and then increases for the four schemes, when the frequency detuning is from approximately -60 GHz to the minimum, presenting the symmetrical distribution of V type with -60 GHz as the axis. The same regular movement of the polarization switching point of the injection intensity is not changed with the change of the normalized injection current.

2016, 65 (21): 214208.
doi: 10.7498/aps.65.214208

Abstract +

We present a theoretical expression in the form of the Pearcey function by deducing the Fresnel diffraction distribution of an elliptic line. Then, we numerically simulate and experimentally generate this kind of new Pearcey beams by using the Fresnel diffraction of optical ellipse line. This kind of beams can be referred to as Bi-Pearcey beams because their appearance of the topological structure is very similar to the combination of two face-to-face classical Pearcey beams. It is no doubt that so-called Bi-Pearcey beams are the new member of a family of form-invariant Pearcey beams. Subsequently, we also provide the theoretical mechanism of generating Bi-Pearcey beams based on the Zeeman catastrophe machine of catastrophic theory. By solving the critical equation of potential function of Bi-Pearcey beams generated by an ellipse line, we find that the optical morphogenesis of Bi-Pearcey beams is determined by the number of roots of the critical equation. The critical equation of potential function of Bi-Pearcey beams is a classical Cartan equation, which has at most three real roots. For the Fresnel diffraction of ellipse line, three real roots of the critical equation are corresponding to three stable points and represent three diffraction lines, hence they can be used to examine the optical topological structure of Bi-Pearcey beams. By choosing the appropriate control variable of Bi-Pearcey beams, two diffraction lines of an ellipse line overlap, and the strong caustic line of Bi-Pearcey beams is correspondingly generated when the two of the three real roots of the critical equation are equal. If the three real roots of the critical equation are all equal, the strongest cusps of Bi-Pearcey beams are generated, accordingly. Moreover, the equation of the caustic line and their positions of four cusps of Bi-Pearcey beams are given by solving the control variable equation of Bi-Pearcey beams. In conclusion, we elucidate the mathematical mechanism of topical morphogenesis of Bi-Pearcey beams based on catastrophic theory.

2016, 65 (21): 214209.
doi: 10.7498/aps.65.214209

Abstract +

Under suitable external perturbation such as optical feedback, optical injection or optoelectronic feedback, semiconductor lasers can be driven to realize diverse dynamic outputs including period-one, period-two, multi-period, pulse packages（PPs), chaos, etc., which have potential applications in optical secure communications, microwave photonics, lidar, high speed random signal generation, etc.. For the PPs dynamics, most of previous relevant investigations are usually based on a system composed of discrete elements. In this work, we experimentally investigate the PP dynamical characteristics in a three-section monolithically integrated amplified feedback laser（AFL) composed of a distributed feedback（DFB) laser section, a phase（P) section, and an amplified feedback（A) section. For the AFL, the sections P and A act as a compounded feedback cavity in which the feedback phase and strength can be varied by adjusting the current in section P（IP) and the current in section A（IA), respectively. Via the power spectrum and self-correlation function curve of the time series output from the AFL, the influences of IP and IA on repeated frequency（PP) and regularity of PPs are analyzed in detail. The results indicate that, for the section DFB, whose current（IDFB) is biased at a relatively large level, the AFL can realize two-mode oscillation. After further choosing appropriate IP and IA, the AFL can behave as the dynamical state of PPs. Under IDFB=86.15 mA and IP=96.00 mA, through varying IA in a range of 6.50-10.50 mA, there exist two separated regions for IA to make the AFL operate at PPs. For the region with relatively small value of IA, both PP and the secondary maximum（) of self-correlation curve characterizing the regularity of PPs monotonically decrease with the increase of IA. However, for the region with relatively large value of IA, with the increase of IA, PP first decreases and then fluctuates in a tiny range, but first increases, and further reaches an extreme value, and then decreases. Under IDFB=86.15 mA and IA=9.00 mA, the output characteristics of PPs are significantly affected by IP. With IP increasing from 90.5 mA to 96.5 mA, PP first decreases, and then increases after reaching a minimal value, meanwhile shows an approximately opposite variation trend. Finally, for IDFB=86.15 mA, the mapping of PPs in the parameter space of IP and IA is given and the evolution regularities of PPs are also presented.

2016, 65 (21): 214302.
doi: 10.7498/aps.65.214302

Abstract +

The wideband source localization is analysed widely in shallow water. It is pointed out that its performance is poor when the number of array elements is few or the ocean environment is uncertain. A method of estimating the range and depth is studied by using a single hydrophone based on the relationship of the horizontal wavenumber difference between two modes with the waveguide invariant for low frequency underwater acoustic pulse signals in a range-independent shallow water waveguide. This localization method estimates the source range by using the rangedispersion two-dimensional（2D) plane focus phenomenon and also the source depth by matching the modal energy. So it can separately estimate the source range and source depth by single hydrophone. First, the signal received on a single hydrophone can be decomposed into a series of modes within the framework of normal mode theory. In order to obtain a better localization performance, the first few order modal dispersion parameters and waveguide invariant are regarded as the unknown parameters. And then the first few order modal dispersion parameters and waveguide invariant can be estimated by comparing the differences between the modal phase velocity calculated by Eq.(8) and that calculated by the Kraken model. Second, using the estimated dispersion parameters and waveguide invariant for dedispersion transform, the amplitudes of each normal mode can achieve maximum values but only when the range of the received signal after dedispersion transform is equal to the range of source. On range-dispersion 2D plane, there appears the sound pressure focus phenomenon, and this phenomenon can be used to estimate the source range. Simulation results from a shallow water Pekeris waveguide show that the time-frequency distribution represents well the dispersion characteristics of the underwater acoustic pulse signal and the dedisperision transform can eliminate this dispersion at the range of source, so that the source range can be estimated. Besides, the first few order modal signals received are clearly separated in time domain after dedispersion transform, and the first few order modal energy can be calculated accurately. So the source depth can be estimated by matching the modal energy. The errors in range estimation and depth estimation are little in simulation. Finally, the data collected from airgun sources during an experiment in the shallow water are used to verify the presented method, and the experimental results obtained using airgun sources on a straight line are shown. The presented method is very significant for estimating the range and depth in shallow water.

2016, 65 (21): 214401.
doi: 10.7498/aps.65.214401

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The natural phenomena which we are familiar with, such as the convections in reservoir, ocean, atmosphere, etc., all occur in nonequilibrium open systems away from heat equilibria. The Poiseuille-Rayleigh-Bnard flow in a horizontal fluid layer heated from below has always been a typical experimental system for studying the nonlinear problem and the pattern formation. The experimental system can be accurately described by the full hydrodynamic equations. Therefore, the researches of the convection spatiotemporal structure, stability and the nonlinear dynamics by using the Poiseuille-Rayleigh-Bnard flow model possess certain representative and theoretical significance and practical value. So far, the investigation on the Poiseuille-Rayleigh-Bnard flow in a horizontal layer heated from below has concentrated mainly on the stability and made remarkable progress. However, a partition of convection pattern and growths of different patterns in the Poiseuille-Rayleigh-Bnard flow have been seldom studied in theory. By using a two-dimensional numerical simulation of the fully hydrodynamic equations in this paper, the research is conducted on the partition of convection pattern, growth and the effects of horizontal flow on the characteristic parameters of different patterns in the Poiseuille-Rayleigh-Bnard flow in a rectangular at an aspect ratio of 10. The SIMPLE algorithm is used to numerically simulate the two-dimensional fully hydrodynamic equations. The basic equations are solved in primitive variables in two-dimensional staggered grids with a uniform spatial resolution based on the control volume method. The power law scheme is used to treat the convective-diffusive terms in the discrete formulation. Results show that a flow zone is divided into three zones by the upper and lower critical Reynolds numbers Reu and Rel, i.e., traveling wave zone, localized traveling wave zone, and horizontal flow zone, where each of the Rel and Reu is a function of reduced Rayleigh number r and increases with increasing r. In the growth stage of the convection pattern, the growth processes of three kinds of patterns with time are different, but the convection rolls all start to grow from the downstream. The variations of characteristic parameters with time are also different, with maximum vertical velocity wmax and Nusselt number Nu of traveling wave and localized traveling wave entering into the stable stage of the cycle variation after the exponential growth stage, and the wmax and Nu of horizontal flow pattern decrease down to a stable constant after slow increase. The values of wmax and Nu of three types of patterns decrease with increasing Reynold number Re, with different laws being in the different pattern areas. In this paper, formulas for computing the Rel and Reu varying with r and formulas for computing the wmax and Nu varying with Re in different convection patterns are suggested.

2016, 65 (21): 214501.
doi: 10.7498/aps.65.214501

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Dense granular jet impingement widely exists in numerous natural flow phenomena and industrial processes. It is significant to investigate the influencing factors of the flow patterns of dense granular jet impingement and reveal the evolution rules of flow patterns. The dynamic behaviors of dense granular jets impinging on a flat target are experimentally studied by a high-speed camera and image processing software of NIH. The effects of the particle diameter（Dpar), the granular jet velocity（U0) and the solid content of the granular jet（X) on the flow patterns and surface waves of granular sheet are investigated. Two patterns, i.e., the liquid-like granular film and the scattering pattern are identified from the dense granular jet impingement. The results show that with the increase of the particle diameter, the solid content of the granular jet reduces, and the interparticle collision frequency decreases, which results in the granular sheet evolving into the scattering pattern. The opening angle of the granular sheet（) is bigger than that of the liquid sheet, and the granular jet velocity plays an insignificant role in the opening angle. The interesting behaviors of liquid-like surface waves are identified in the granular sheet. The frequency of surface wave of the granular sheet（f) is an order of magnitude smaller than that of the liquid sheet. The surface wave length（) increases and frequency decreases with the increase of radial position, as the surface waves merge during the granular sheet spreading radially. The surface wave spreading velocity normalized by the granular jet velocity is a constant of about 0.4. With the increase of the granular jet velocity, the pulsation of granular jet occurs due to the pressure fluctuation in the discharge process under the effect of gas-solid interaction. The frequencies of surface waves of both the granular sheet and the granular jet pulsation become the same generally. It is indicated that the surface wave is primarily caused by the granular jet pulsation. The results in this paper present the knowledge of the dense granular jet impingement and provide some principles for the steady operation of dense granular jet impingement in industrial process.

2016, 65 (21): 214207.
doi: 10.7498/aps.65.214207

Abstract +

Without discrete optical components influencing the fiber format, all-fiber mode-locked laser has tremendous potential practical applications due to its advantages of better stability, alignment free, and better compaction. All-fiber laser mode-locked by nonlinear polarization evolution（NPE) can obtain good performances in terms of pulse duration and spectrum. But the effective saturable absorption mirror can be overdriven at high peak power, which leads to multiple pulses, limiting the output pulse energy. And there is a trade-off between avoiding overdriving the NPE and ease of self-starting. In addition, the polarization of the pulse propagating in a long fiber is so sensitive to the environment vibration that it is difficult to implement a stable lone-time operation.All-fiber ring laser mode-locked by NPE alone is analyzed and realized. The simulation results show that even a polarization vibration of up/38 can break the mode-locking completely. Experimentally, after carefully adjusting, single-pulse mode-locking is achieved with the spectrum centered at 1053.4 nm and a maximum pulse energy of 82 pJ. But the output parameters change continually during operating. After 60 min, the mode-locking is broken. The conclusion is obtained that instability and unreliability of self-starting are inevitable for such a laser.Here, we show significant improvements of the pulse energy, operating stability, and self-starting reliability from an all-fiber Yb-doped mode-locked fiber laser. The laser is mode-locked by NPE combined with chirped pulse spectral filtering（CPSF). In order to easily self-start and stabilize mode locking, a spectral filter is employed in the all-normal group velocity dispersion NPE cavity to provide additional amplitude modulation. Combined effects of NPE and CPSF result in desirable pulse output, desirable operating stability, and reliable self-starting simultaneously. Stable mode-locking centered at 1053 nm is achieved with a 3 dB spectral bandwidth of 9.1 nm and pulse duration of 17.8 ps. The average output power is 66.9 mW at a repetition rate of 15.2 MHz, corresponding to a pulse energy of 4.25 nJ. Especially, high operating stability and easily one-button self-starting are achieved simultaneously. The fluctuations of output parameters including pulse energy, pulse duration, and spectrum are within 0.3% during 150-min operation. Self-starting reliability is tested. The testing time lasts two weeks. During the two weeks, the laser is turned off and turned on 48 times by using a power supplying button, without any adjustment. And the re-turned on intervals change randomly. Each time, the mode-locking can start itself. The repeatabilities of output parameters including pulse energy, pulse duration, and spectrum are within 0.55%.

2016, 65 (21): 214301.
doi: 10.7498/aps.65.214301

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In the diffuse ultrasonic backscatter describing the scattering of elastic waves from polycrystalline metal material, the spatial variance of the signal is used as a primary measure of microstructure.Previously,theoretical singly-scattered response models have been developed for the diffuse backscatters of elastic waves within polycrystalline materials,which take into consideration both transducer beams and microstructural scattering information.However,the surface roughness of the liquid-solid interface induces a noticeable change of spatial variance amplitude,and its effect on the diffuse ultrasonic backscatter that can severely degrade the accuracy and practicability of the microstructure parameter evaluation was neglected in previous models.Therefore,a new singly-scattered response model for the rough surface polycrystalline samples is developed by following the forms similar to previous models for longitudinal-to-longitudinal scattering at normal incidence.In particular, we assume that the surface is slightly rough,specifically,the surface roughness value should not be larger than the magnitude of the wavelength.Hence,the modified expressions of ultrasonic reflection and transmission coefficients for the randomly rough interface can be applied to the singly-scattered response model.Then,with the modified transmission coefficient,a Gaussian beam is adopted to model the transducer beam pattern at normal incidence for longitudinal wave propagation through a rough liquid-solid interface to the polycrystal.Next,the Wigner transform of the displacement field is derived with a parameter of the surface roughness root mean square value.After that,a new expression of the calibration parameter including the modified reflection coefficient is given to provide a conversion between the displacement field and the experimental transducer voltage.Finally,the rough surface singly-scattered response model is built and the surface roughness correction coefficient is presented here to quantify the effect of the surface roughness on diffuse ultrasonic backscatter.The numerical results show that the Wigner distribution amplitude decreases and the acoustic energy coverage shrinks with the increase of the surface roughness.The theoretical spatial variance amplitude decreases by about 79.2% when the root mean square roughness value is set to be 40 m.The surface roughness correction coefficient is usually smaller than 1 when the reference calibration sample is smooth,but it can be bigger than 1 when the reference sample is rough.The results from the developed theory are then compared with the experimental measurements associated with a pulse echo transducer configuration for 304 stainless steel by using the smooth and rough surface samples.From these measurements,the mean grain size of the stainless steel can be determined.The experimental results show that although the corrected and uncorrected models both fit the experimental spatial variance curve from the smooth surface sample well,the uncorrected model fails to extract the grain size of the rough surface sample.The relative error of the grain size between optical microscopy and the uncorrected model can reach -21.35%.In contrast,good agreement with optical microscopy is observed by using the surface roughness corrected model,and the relative error is only 1.35%.In conclusion,the ultrasonic waves transmit though the rough interface twice,and the diffuse scattering which happens in these processes reduces the number of backscatter waves that can return to the transducer,so the spatial variance amplitudes drop dramatically.The correction coefficient presented here can describe the effect of surface roughness on diffuse ultrasonic backscatter.Moreover,it can improve the accuracy of grain size evaluation effectively.Thus,the surface roughness corrected ultrasonic backscatter model may be applicable for quality control of roughwrought castings or forgings during the manufacturing.

2016, 65 (21): 214701.
doi: 10.7498/aps.65.214701

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Flow around a circular cylinder is a classic scenario which invariably draws the attention of the fluid mechanics circle, because its relevant studies are of both theoretical and practical significances. However, most experiments are conducted below transcritical Reynolds number（Re) regime（Re3.5106) due to the limitations of the wind tunnel modeling technique, which makes the obtained results inapplicable to some full-scale conditions. To this end, the field measurements for wind-induced pressures on a 167-meter high large cooling tower are conducted at Re=6.59107 to enrich the experimental results of flow past a circular cylinder in transcritical Re regime. Besides, the wind effects at low Re（Re=2.1105-4.19105) are also obtained by tests on a 1:200 rigid cooling tower model in a wind tunnel with considering 4 types of wind speeds, 8 types of surface roughness, and 2 flow fields. Employing the data obtained from both field measurements and wind tunnel model tests, the variations of static/dynamic flow characteristics with Re increasing are studied. It is found that 1) with the increase of Re, the drag coefficient for the smooth-walled tower in the uniform flow field decreases dramatically in the critical Re regime and increases slowly in the supercritical regime, which accord with Roshko's and Achenbach's results; 2) for smooth-walled tower, both the base pressure coefficient and pressure coefficient increase significantly with the increase of Re in critical and supercritical regimes, which qualitatively accord with Shih's results; and 3) the finding of the Strouhal number is supportive to Shih's result（i.e., shedding from the rough cylinder persists throughout the Re range tested). More importantly, special attention is paid to the Re-independence phenomenon of fluid flow, which is a typical phenomenon occurring in transcritical Re regime. Results indicate that the Re-independence exists in an Re range from 2105 to 1108 for a circular cylinder with a relative roughness greater than 0.01, and the increased free-stream turbulence can also induce Re-independence which probably exists in a narrow low Re range. Considering the flow mechanism, a reasonable explanation can be found for the Re-independence phenomenon, i.e., the critical and supercritical regimes narrow and move to lower Re range with the increase of surface roughness or the increase of free-stream turbulence, so Re independence can occur at a very low Re.

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

2016, 65 (21): 216301.
doi: 10.7498/aps.65.216301

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The first-principle technique is employed to determine the structure of the BP3S monomer, the structures of the molecular chains and monolayers on virtual Au（111), and the atomic structure of BP3S/Au（111) adsorption system. The results show that the BP3S monomer presents a symmetric structure, and the angle between two benzene rings is 3510. At first, many BP3S monomers are assembled into one stable molecular chain in the virtual Au（111), the distance between the neighbor monmers is 0.516 nm, and the bind energy between the monmer and the molecular chain is 0.071 eV. It is a self-assembly system. Then many molecular chains are assembled into two stable monolayers in the virtual Au（111)-(37) and Au（111)-(313), and their coverages are 0.20 ML and 0.14 ML, respectively. In the virtual Au（111)-(37) and Au（111)-(313), the angles between the molecular chains and the virtual surface are 60 and 30, respectively, and the binding energies between the monmer and two monolayers are 0.101 eV and 0.125 eV, respectively. They are both the self-assembly systems. Finally, two monolayers are adsorbed on the Au（111)-(37) and Au（111)-(313) at four adsorption sites. The S atom is easy to obtain two electrons and turn into S2- ion, and the Au atom is easy to lose one electron and become Au+ ion, so the bridge site（two Au+ ions) is more stable than the top site（one Au+ ion), while the hcp and fcc hollow sites（three Au+ ions) are both unstable. In the Au（111)-(37), the chemisorption energy of the bridge site（-1.879 eV) is lower than that of the top site（-1.511 eV). And in the Au（111)-(313), the chemisorption energy of the bridge site（-1.691 eV) is lower than that of the top site（-1.492 eV). The results are confirmed in the other S-Au adsorption systems, such as the C6H13S/Au（111). A comparison between the structures of the BP3S monolayer before and after being adsorbed on Au（111) clearly shows that the structural parameters of the adsorption system depend mainly on the interaction in the monolayer, and that the contribution of Au（111) to the structure of the monolayer is weak. These results are confirmed in the other self-assembly adsorption systems.

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

2016, 65 (21): 217501.
doi: 10.7498/aps.65.217501

Abstract +

Magnetic anisotropy is one of the most important fundamental properties of magnetic film.For the high-frequency applications,the magnetic anisotropy determines the ferromagnetic resonance frequency of magnetic film.Due to the directionality of conventional static magnetic anisotropy in magnetic film,the high-frequency device usually exhibits a remarkable angular dependent behavior.Only when the microwave magnetic field is perpendicular to the magnetic anisotropy,can the device work at the best performance.The magnetic film with a thickness beyond a critical value displays a stripe domain structure as well as an in-plane rotatable magnetic anisotropy,which can be an important strategy to solve the problem of magnetic field orientation dependent performance in high-frequency device.Thus, the fabrication,the magnetic anisotropy,the magnetic domain and the high-frequency behavior for magnetic film with stripe domain structure have received extensive attention.Previously,a lot of studies have qualitatively indicated that the different fabrication processes could change the critical thickness values of displaying stripe domains,the magnetic domains,and the magnetic anisotropies in many magnetic films.However,the quantitative investigation,especially regarding the magnetic anisotropy which determines the high-frequency behaviors of magnetic films,is less.NiFe alloys display excellent soft magnetic properties,which have been extensively applied to various spintronic devices.In addition, the stripe magnetic domain is discovered for the first time in NiFe film.In this work,we fabricate NiFe magnetic thin films by using radio frequency magnetron sputtering technique at room temperature and quantitatively study the effects of film thickness,sputtering power density and Ar pressure on the magnetic domain structure,in-plane static magnetic anisotropy,in-plane rotatable magnetic anisotropy and out-of-plane magnetic anisotropy.For NiFe films fabricated at a power density of 15.6 W/cm2 and an Ar pressure of 2 mTorr (1 Torr=1.33322102 Pa),the critical thickness values for the appearance of stripe domain structures in NiFe films are between 250 and 300 nm.The out-of-plane magnetic anisotropy field of 300 nm NiFe film is nearly twice as that of 250 nm NiFe film,which gives rise to the occurrence of stripe domain structure as well as the in-plane rotatable magnetic anisotropy.The high sputtering power density could reduce the critical thickness for the occurrence of stripe domains.For 300 nm NiFe film fabricated at a power density of 15.6 W/cm2,with Ar pressure increasing from 2 to 9 mTorr,the out-of-plane magnetic anisotropy field increases from 1247.8 to 3248.0 Oe (1 Oe=79.5775 A/m) and the in-plane rotatable magnetic anisotropy field increases from 72.5 to 141.9 Oe.Meanwhile,the stripe magnetic domain structure changes from well aligned to disordered state,and the corresponding wavelength of stripe domain is reduced from 0.53 to 0.24 m.The cross-sectional characterizations of NiFe film indicate that the formation of columnar structure produces an out-of-plane magnetic anisotropy,giving rise to the appearance of stripe magnetic domain structures.The low Ar pressure is in favor of the formation of columnar structure in magnetic film under the high sputtering power density,which gives rise to the appearance of well aligned stripe magnetic domains.However,the high Ar pressure leads to a fibrous columnar structure,which enhances the out-of-plane magnetic anisotropy and reduces the critical thickness for the occurrence of stripe domains.Our investigation provides an important reference to fabricating magnetic films and controlling their static and rotatable magnetic anisotropies for the application in high-frequency devices.

2016, 65 (21): 217801.
doi: 10.7498/aps.65.217801

Abstract +

The localized surface plasmon resonance can be generated on the surface of the nano-metamaterial by the interaction between the nano-metamaterial and the light field, and also many plasmon oscillation modes can occur in the process of the hybridization between many infinitesimal composite structures, which is widely used for adjusting the resonant frequency in the optical frequency domain. Recently, analogue of the electromagnetically induced transparency（EIT) has been realized in the low-loss nano-metamaterial, and is well known as the plasmon induced transparency（PIT). In atomic physics, EIT is an effect which originates from the destructive quantum interference of two different excitation pathways. A sharp dip of nearly ideal transmission can arise within the broad absorption profile, which indicates that the EIT can be used in the fields of slow slight, delay lines and low-loss metamaterial. In this paper, a trimer consisting of a vertical nanorod（serving as a dipole antenna) and two parallel nanorods（used as a quadrupole antenna) is employed to investigate the process mechanism of the PIT in detail. It is found that the vertical nanorod with a large broad linewidth can be strongly coupled with the light. However, the parallel nanorods are weakly coupled with the light and their narrow linewidths are almost from the intrinsic metal loss（Drude damping) that is much smaller than the radiative damping of the dipole antenna. These two antennas can be strongly coupled due to their close similarities. Moreover, the absorption spectra of the trimer obtained by using three-dimensional finite element method vary with its coupling distance and geometry size, and the dipole bright mode corresponding to the dipole antenna splits under the action of the dark mode for the quadrupole antenna. Thus, a fresh physical interpretation is given:the PIT is mainly due to the coherent superposition after the splitting of the dipole oscillation mode in the vertical nanorod, rather than the parallel nanorods. Taking into consideration the phase correlation associated with coupling process of two oscillators, we introduce a modified Lorentzian oscillator model to investigate the effects of the coupling phase factor on the modulation of the absorption spectra and the coherent superposition between the splitting bright modes on the PIT. These findings will provide theoretical references for the applications of artificial atom, optical switching and slow light devices designed in the nanosize range.

2016, 65 (21): 217101.
doi: 10.7498/aps.65.217101

Abstract +

Using the first principle calculation based on the density functional theory, we systematically investigate the stabilities and the structural and electronic structures of fully hydrogenated and fully fluorinated SbAs and BiSb. The results show that the SbAs and BiSb transform the buckled structure into quasi-planar structure after being fully hydrogenated or low-buckled structure after being fully fluorinated. Stability studies show that both the SbAs and BiSb structures（intrinsic, full hydrogenated, and fully fluorinated) are highly stable, and thus likely to be obtained in experiment. The electronic structure study shows that both SbAs and BiSb turn from wide band gap semiconductors into narrow direct-gap semiconductors after being fully hydrogenated and fully fluorinated, meanwhile the band structures still have good linear dispersion. Based on further analyses of the electronic structures of quasi-planar or low-buckled SbAs and BiSb, the reasons for the changes of band structures are revealed. Calculations show that the fX-SbAs（X=H, F) films on h-BN substrate can maintain the direct band gap characteristics because of the weak coupling between them, indicating that they may have great applications in the field of optoelectronic devices in the future.

2016, 65 (21): 217503.
doi: 10.7498/aps.65.217503

Abstract +

The polarity of magnetic vortex core can be switched by current or magnetic field through a vortex-antivortex pair creation and annihilation process, in which the significant change of the exchange energy during the switching takes an important role. To further unveil the energetic origin of magnetic vortex switching, we investigate the evolution of the maximum exchange energy density of the sample by using micromagnetic finite-element simulations based on the Landau-Lifshitz-Gilbert equation including the adiabatic and the nonadiabatic spin torque terms. Our micromagnetic calculations indicate that maximum exchange energy density for the considered sample must exceed a critical value of ~3.0106 J/m3 in order to achieve the magnetic vortex switching. The threshold value corresponds to the maximum exchange energy density at the time of creation of new vortex-antivortex pair. Following the nucleation of antivortex, the maximum exchange energy density increases rapidly with the antivortex approaching the original vortex. The maximum exchange energy density can become large at the time of annihilation of two vortexes. To explain well the critical value of the local maximum exchange energy density, we use the rigid vortex model（in which the spin distribution is unchangeable while vortex is displaced) to develop an analytical model. For a magnetic vortex confined in a thin ferromagnetic nanodisk, the magnetization distribution is unchanged along the thickness and can be seen as a two-dimensional model when the thickness is less than or on the order of the exchange length. The components of vortex magnetization vector in a ferromagnetic dot can be expressed by using a complex function w(,). Corresponding to the trivortex state appearing in vortex core reversal process, the local exchange energy density Wex around the vortexes cores is obtained. Simultaneously, we obtain the maximum exchange energy density:Wex2.3106 J/m3. In a realistic system, the shape of vortexes will deform during the vortex core reversal, which leads to the analytical result lower than the simulation value. Based on this reason, the analytical result matches well with our simulation value.

2016, 65 (21): 217802.
doi: 10.7498/aps.65.217802

Abstract +

Metamaterials or metasurfaces have been widely studied to manipulate the propagation of light by controlling the wavefront. In previous work, more and more structures were designed to study the reflected or the transmitted light. However, as far as we know, it is rarely reported how to efficiency tailor the wavefront, especially for transmitted light. Helical metamaterial, which has a relatively strong coupling effect among the helical nanowires, may provide an alternative to the wavefront control. In this study, a kind of complementary helical metamaterial with a left-handedness and a right-handedness helixes coupled to each other is proposed. The complementary helical metamaterial has a strong circular conversion dichroism, and it is expected to be a good candidate for generating phase shift and controlling wavefront with high efficiency. Using the finite-difference time-domain method, we find that this kind of helix has a high circular polarization conversion in a broadband, which often implies a high efficiency of the transmitted light. Moreover, it is also found that the structure will introduce a controllable phase shift（) between the incident and the transmitted light whose polarizations are orthogonal to each other. By calculating the surface current density of the helix, the performance of high circular polarization conversion is explained. Meanwhile, we also find that the phase shift has a linear relationship with the initial angle of the helix（), which is =2. This relationship can be explained exactly by Jones calculus. According to the generalized Snell's law, the refracted beam can have an arbitrary direction by designing a suitable constant gradient of phase discontinuity. And then, by arranging 12 helixes in an array with a constant phase gradient along the X-axis, the phenomenon of anomalous refraction with a high efficiency（64%) is observed in the near infrared range（1.0-1.4 m). The angle of the anomalous refraction is in good agreement with the theoretical value. Compared with the metasurface, the helical metamaterial has a relatively complex structure. But with the development of the nanotechnology, there are several methods that can complete the propagations of nano helical structures, such as the direct laser writing, the glancing angle deposition, and the molecular self-assembly techniques. And by carefully designing the structure parameters of the helix, this kind of complementary helical metamaterial is expected to be an ideal candidate not only for traditional optics but also for biological detection and medical science.

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

## EDITOR'S SUGGESTION

2016, 65 (21): 218201.
doi: 10.7498/aps.65.218201

Abstract +

The optical signals of single molecules provide information about structures and dynamic behaviors of their nanoscale environments, and eliminations of space and time averaging effect. These are particularly useful whenever complex structures or dynamic behaviors are present, especially in polymers. The single molecules absorbed onto polymer chains rotate with rotational relaxation of polymer chains. Thus, we can measure the dynamic properties of polymer thin films by measuring the rotational properties of single molecules. Here, we use single Nile Red（NR) dye molecules as nano-probes to measure polymer dynamic behaviors of poly（methyl acrylate)（PMA) polymer film. The polymer films are prepared on cleaned glass coverslips by spin-coating 1.0 wt.%solution of PMA containing ~10-9 mol/L NR molecules in toluene. Defocused wide-field fluorescence microscopy is used to measure the three-dimensional molecular rotational diffusion of single NR molecules in PMA polymer thin film. The local environmental change driven by heterogeneous dynamics of the polymer can be probed by parallel imaging of several molecules. It is found that at Tg+19 K, rotations of NR single molecules in different nano-areas are in two different ways, i.e., rotational way（rotational molecules account for ~83%) and non-rotaional way（non-rotational molecules occupy~17%). The rotational molecules include the single molecules of intermittent rotation with a short time and a long time. The different rotational patterns indicate that there is still a spatial and temporal heterogeneity of dynamics in PMA polymer film at a temperature of Tg+19 K. The autocorrelation function C(t) of angular change of dipole orientation of NR single molecules is calculated to reveal the property of polymer dynamics. The decay of C(t) can be fitted by Kohlrausch-Williams-Watt stretched exponential function. The averaged timescale of rotational diffusion c for 183 rotational NR single molecules indicates that the timescale of polymer dynamics at 300 K is~3 s. In order to investigate the temporal heterogeneity of PMA polymer dynamics, we define a threshold to separate the single molecular rotation into two parts:rotational state and non-rotational state. According to the statistics of duration time of rotational state and non-rotational state, we can obtain the probability densities of duration time of rotational states and non-rotational states of the single molecules. The probability densities obey a truncated power law, which indicates that there are still the behaviors of trapping and self-trapping in PMA polymer chains at Tg+19 K. The researches of spatial and temporal heterogeneity of dynamics of PMA polymers in nano-environment have great significance for preparing the high performance materials.

Optimization of magnetic resonance imaging high-order axial shim coils using boundary element method

2016, 65 (21): 218301.
doi: 10.7498/aps.65.218301

Abstract +

In this paper, we present a novel nonlinear optimization algorithm for designing a shim coil system, especially a high-order axial shim coil, for a magnetic resonance imaging（MRI) system. In an MRI equipment, in order to eliminate higher-order harmonic components of the magnetic field within the volume of interest（VOI), passive shimming（PS) is adopted in traditional methods. However, such a method is suitable for the global shimming with low accuracy and poor target. Active shimming（AS) makes up for the shortcomings from PS with a set of shim coils which are designed to generate a specific magnetic fields to improve magnetic field homogeneity within the VOI. Because the complexity of wire pattern increases with the order of AS coil increasing, conventional optimization model cannot meet the design requirements for producing the complicated magnetic field. In this paper, we propose a nonlinear optimization method of designing the axial shim coils for an open-style bi-planar MRI system, based on boundary element method. The optimization model is built in light of influence extents of the various parameters on the coil characteristics for different shim coils. In such a new method, the field error between the magnetic field produced by designed shim coil and the desired target value is selected to be an optimal value subjected to some constraints including line spacing and coil radius, which makes it possible to realize the manufacture process. Meanwhile, the more design parameters, which involve not only the stream function values at each node, but also the compensation parameters and/or the number of grid nodes, are regarded as optimized variables to control the magnetic deviation and characteristics of designed coil. By using some designed shim coils for a 0.5 T open style bi-planar superconducting MRI, including Z1, Z2, Z3 and Z4, the efficiency of such a numerical design method is displayed. Especially for high-order shim coils, more optimized parameters are involved to control the magnetic deviation of the coils, thereby providing a more flexible and straightforward method of designing the axial shim coils.

## EDITOR'S SUGGESTION

2016, 65 (21): 218702.
doi: 10.7498/aps.65.218702

Abstract +

Homologous recombination（HR) is essential for maintaining the genome fidelity and generating genetic diversity. As a prototypical member of the recombinases, RecA from Escherichia coli has been extensively studied by using single-molecule FRET（smFRET), magnetic tweezers, optical tweezers, etc. However, these methods cannot meet the needs of wide-ranged observations nor high spatial resolution at the same time. For sequence comparison, the average base-to-base distance of the homologous dsDNA will be stretched from 0.34 nm to 0.51 nm. The increment for per base pair is 0.17 nm, which is far beyond the spatial resolution of magnetic tweezers so that it cannot be directly measured. As a high-resolution technique, the smFRET enables us to observe more details of reactions. However, its valid measuring distance is 3-8 nm, which limits the observation range. Here, we propose an approach by combining magnetic tweezers with DNA hairpin, which may solve the problem effectively in the study of HR. In this paper, one end of the DNA molecule with a 270 bp hairpin is immobilized onto the surface of the flow cell, while a magnetic bead is attached to the other end. An external magnetic force is applied to the magnetic bead by placing a permanent magnet above the flow cell. The first 90 bp（from the junction of the hairpin) of the hairpin is homologous to the ssDNA within the ssDNA-RecA filament. Thus, the filament searches for homology along the hairpin, and incorporates into the homologous segment for strand exchange. After that, the displaced strand can be opened by pulling at a force of ~7 pN, and each opened base pair results in a 0.82 nm increase in DNA extension. By using this approach, we show that 1) RecA-mediated strand exchange proceeds in a stepwise manner and the average speed is ~7.6 nt/s, which is in accordance with previous result; 2) the dynamic interaction between the second DNA-binding site（SBS) and the displaced strand can be observed in real-time, and the binding force is calculated accurately through the x-dimensional fluctuations; 3) the processes of strand-exchange in different directions can be observed, and the directions are distinguishable through the reaction patterns. The results suggest that the combination of magnetic tweezers with DNA hairpin is a potential approach to the study of RecA or other recombinases. Therefore, our design can be an important single-molecule approach to the research of HR mechanism.

2016, 65 (21): 218701.
doi: 10.7498/aps.65.218701

Abstract +

Major depressive disorder (MDD) is a kind of mental disease which has characteristics of the low mood,sense of worthless,less interest in the surrounding things,sadness or hopeless,slow thinking,intelligence,language,action,etc. The aim of this research is to find the differences between entropy values and ages,genders of MDD patients,MDD patients and healthy controls.Twenty-two MDD patients (male 11;age 18-65) and their matched healthy controls in gender,age,and education are examined by analyzing (blood oxygenation level dependent-functional magnetic resonance imaging,BOLD-fMRI) signals from nonlinear complexity perspective.As the BOLD-fMRI signals have limited time resolution,so they are very difficult to quantify the complexities of fMRI signals.We extract the corresponding signals from the fMRI signals.The complexities of the age,gender,MDD patients and healthy controls can be predicted by the proposed approach.However,information redundancy and other issues may exist in non-linear dynamic signals. These issues will cause an increase in computational complexity or a decrease in computational accuracy.To solve the above problems,we propose a method of fuzzy approximate entropy (fApEn),and compare it with sample entropy (SampEn).The addition and subtraction under different emotional stimuli as a multi-task are used to coordinate brain sense with motion control.The 12-channel fMRI signals are obtained involving the BOLD signals on resting signals (about 24 s).The methods of the fApEn and SampEn are proposed to deal with the BOLD-fMRI signals in the different ages and genders,and those between MDD patients and healthy controls from the differences between fApEn and SampEn of different genders,main effect and interaction effect analysis of fApEn and SampEn measures, regression curve between entropy and age of the whole sample,correlations of fApEn and SampEn with age,fApEn-age correlation and magnitude in gray matter and white matter,multiple regression analysis of fApEn with age for the whole sample,also the receiver operating characteristic analyses of fApEn and SampEn,the relationship between fAPEn and N aspects.The results show that 1) the complexities of the resting state fMRI signals measured are consistent with those from the Goldberger/Lipsitz model:the more the health,the greater the complexity is;2) the mean whole brain fApEn demonstrates significant negative correlation (r=-0.512,P0.001) with age,SampEn produces a non-significant negative correlation (r=-0.102,p=0.412),and fApEn also demonstrates a significant (P0.05) negative correlation with age-region (frontal,parietal,limbic,temporal and cerebellum parietal lobes),there is non-significant region between the SampEn maps and age;3) the fuzzy approximate entropy values of major depressive disorder patients are lower than those of healthy controls during resting.These results support the Goldberger/Lipsitz model,and the results also show that the fApEn is a new effective method to analyze the complexity of BOLD-fMRI signals.

###### REVIEW

## EDITOR'S SUGGESTION

2016, 65 (21): 217502.
doi: 10.7498/aps.65.217502

Abstract +

Magnetocaloric effect（MCE) is the intrinsic property of a magnetic material near transition temperature and the magnetic refrigeration based on MCE has been demonstrated as a promising alternative to the conventional gas compression or expansion refrigeration due to its high energy efficiency and environmental friendliness. The development of magnetic refrigeration technology depends on the research progress of magnetic refrigerant materials with large MCEs. Lots of researches of material exploration and material optimization have promoted the progress of magnetic refrigeration technology in recent decades. In this paper, we introduce the basic theory of MCE and the development of refrigeration technology, review the research progress of large MCE materials both in low temperature range and in room temperature range, and specifically focus on the latest progress of some MCE materials. Low temperature MCE materials mainly include those rare earth based materials with low transition temperatures, such as binary alloys（RGa, RNi, RZn, RSi, R3Co and R12Co7), ternary alloys（RTSi, RTAl, RT2Si2, RCo2B2 and RCo3B2), and quaternary alloys（RT2B2C), where R denotes the rare earth and T represents the transition metal. Those materials mainly possess the second-order phase transitions and show good thermal hysteresis, magnetic hysteresis, and thermal conductivities. Room temperature MCE materials are mainly Gd-Si-Ge intermetallic compounds, La-Fe-Si intermetallic compounds, MnAs-based compounds, Mn-based Heusler alloys, Mn-based antiperovskite compounds, Mn-Co-Ge intermetallic compounds, Fe-Rh compounds, and perovskite-type oxides. The above materials usually have the first-order phase transitions and most of these materials possess the large MCEs in room temperature range, therefore they have received much attention home and abroad. Among those room temperature MCE materials, the La-Fe-Si series is considered to be the most promising magnetic refrigerant materials universally and our country has independent intellectual property rights of them. The further development prospects of MCE materials are also discussed at the end of this paper.

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

2016, 65 (21): 219501.
doi: 10.7498/aps.65.219501

Abstract +

High spatial coherent and bright X-ray beam is necessary condition for acquiring high quality radiography image. However, traditional X-ray tube can only provide high flux X-ray light or high spatial coherent light. In general, X-ray photons are generated by using energetic electrons with several tens or even hundreds keV to hit a target. Unfortunately, over 99% electron energy are converted into heat rather than the energy of X-ray photons. Thus, the heat dissipation of the target restricts the emission power and radiation flux. Increasing the emission area of X-ray can relieve the heat dissipation, but it would bring another serious problemlow spatial coherence that is in inverse proportion to emission area or focal spot. In order to solve the conflict between brightness and spatial coherence, an X-ray source with one-dimensional coherence is proposed in this work. The new X-ray source has a special focal spot where one side is small enough to ensure the spatial coherence and the perpendicular side is big enough to provide sufficient X-ray flux. In the direction of long side, the long size of focal spot will result in losing the image details. Consequently, an algorithm of superposition and rotation, in which many images with different rotation angles are added together, is proposed to retrieve the lost information. On the other hand, the spatial transfer function of superposition is analyzed in the frequency domain, and the result shows that the method of superposition can transfer more components of frequency than single image. Based on a traditional X-ray tube, a line focal spot source is designed and fabricated. Two series of experiments are performed for different destinations. After 17 images of a chip with different rotation angles and the line focal spot are collected, those images are rotated in the reverse direction and added together. The image of superposition clearly presents some details which are invisible in one of 17 images. At the same tube voltage and for the same object, some comparative experiments with micro-focus source, line focal spot source and normal focal spot source are presented. Compared with traditional X-ray tube, line focal spot source can provide high-resolution image. In the aspect of image visibility, the new source has definite advantages compared with micro-focus source, despite no improvement in imaging resolution. Finally, the reason for the difference in imaging resolution is discussed from the aspects of spatial coherence and light flux.