## Vol. 66, No. 12 (2017)

##### 2017-06-20

###### GENERAL

2017, 66 (12): 120202.
doi: 10.7498/aps.66.120202

Abstract +

The extraction of terahertz dispersion parameters is confined in a limited region due to the limitation of the existing THz techniques. A method of studying the dispersion model of metals from the measurements of reflection spectrum and analysis of Kramers-Kronig (KK) relation is proposed. The reflection spectrum is measured by Vertex 80V Fourier transform spectrometer. In order to eliminate the signal noise of measured reflection spectrum, the measured spectrum is smoothed by Drude estimation. Using the smoothed reflection spectra of copper (Cu) alloy and aluminum (Al) alloy in a range of 440 THz, the complex refractivities are inversed based on the KK relation of amplitude and phase of reflective coefficient. The constant extrapolations at lower frequencies and the exponential extrapolation at higher frequencies are adopted in the KK integration. The exponential extrapolation index is adjusted according to the calibrating complex refractivity measured from far-infrared ellipsometer. According to the inversed complex refractivity, the plasma frequency and damping frequency in Drude model are optimized using the genetic algorithm. The objective function is defined as the error between the fitted complex refractivity and KK inversion. Since the optimal plasma frequency and damping frequency are different for different fitting frequencies, the obtained Drude parameters are averaged in order to reduce the influences of errors from KK inversion, measured reflection spectrum and calibrations. The complex refractivity indexes in a range from 15 THz to 40 THz, calculated by the established Drude model, are in good agreement with the measured calibrations from ellipsometer, which demonstrates the accuracy of the established Drude dispersion model. The reflection spectra below 4 THz are greatly distorted due to the signal noise, and the calibrating refractivity is located in the far infrared region, thus the complex refractivity is inversed in a region of 440 THz by KK algorithm. The complex refractivity indexes in a range of 0.120 THz, obtained by the proposed scheme, are for the vacancy, which will provide great support for the dispersion analysis in the whole terahertz gap. The procedures are helpful for extrapolating the dispersion information to terahertz band from the far infrared region. The scheme takes the advantage of the spectrometer and ellipsometer, and it requires high experimental precisions of reflection spectrum and calibrating refractivity. In addition, the scheme is adaptive to both metals and nonmetals by applying proper dispersion model which depends on the property of the reflection spectrum. The established model determines the microscopic dispersion parameters of material, which provides great support for the investigation of terahertz dispersion analysis, scattering mechanisms and imaging processes.

2017, 66 (12): 120301.
doi: 10.7498/aps.66.120301

Abstract +

The characterization of the quantum phase transition in a lowdimensional system has attracted a considerable amount of attention in quantum manybody systems. As one of the fundamental models in quantum magnetism, spin-1 models have richer phase diagrams and show more complex physical phenomena. In the spin-1 antiferromagnetic XXZ model, the Haldane phase and the Nel phase are the gapped topologic phases which cannot be characterized by the local order parameters. To characterize the nature in such phases, one has to calculate the non-local long range order parameters.
Normally, the non-local order parameter in the topological phase is obtained from the extrapolation of finite-sized system in numerical study. However, it is difficult to extract the critical exponents with such an extrapolated non-local order parameter due to the numerical accuracy. In a recently developed tensor network representation, i.e., the infinite matrix product state (iMPS) algorithm, it was shown that the non-local order can be directly calculated from a very large lattice distance in an infinite-sized system rather than an extrapolated order parameter in a finite-sized system. Therefore, it is worthwhile using this convenient technique to study the non-local orders in the topological phases and characterize the quantum criticalities in the topological quantum phase transitions.
In this paper, by utilizing the infinite matrix product state algorithm based on the tensor network representation and infinite time evolving block decimation method, the quantum entanglement, fidelity, and critical exponents of the topological phase transition are investigated in the one-dimensional infinite spin-1 bond-alternating XXZ Heisenberg model. It is found that there is always a local dimerization order existing in the whole parameter range when the bond-alternative strength parameter changes from 0 to 1. Also, due to the effect of the bond-alternating, there appears a quantum phase transition from the long-rang ordering topological Nel phase to the local ordering dimerization phase. The von Neumann entropy, fidelity per lattice site, and order parameters all give the same phase transition point at c = 0.638.
To identify the type of quantum phase transition, the central charge c 0.5 is extracted from the ground state von Neumann entropy and the finite correlation length, which indicates that the phase transition belongs to the two-dimensional Ising universality class. Furthermore, it is found that the Nel order and the susceptibility of Nel order have power-law relations to |-c|. From the numerical fitting of the Nel order and its susceptibility, we obtain the characteristic critical exponents ' = 0.236 and ' = 0.838. It indicates that such critical exponents from our method characterize the nature of the quantum phase transition. Our critical exponents from the iMPS method can provide guidance for studying the properties of the phase transition in quantum spin systems.

2017, 66 (12): 120501.
doi: 10.7498/aps.66.120501

Abstract +

Brownian motion in a washboard potential has practical significance in investigating a lot of physical problems such as the electrical conductivity of super-ionic conductor, the fluctuation of super-current in Josephson junction, and the ad-atom motion on crystal surface. In this paper, we study the overdamped motion of a Brownian particle in a washboard potential driven jointly by a periodic signal and an additive Gaussian white noise. Since the direct simulation about stochastic system is always time-consuming, the purpose of this paper is to introduce a simple and useful technique to study the linear and nonlinear responses of overdamped washboard potential systems. In the limit of a weak periodic signal, combining the linear response theory and the perturbation expansion method, we propose the method of moments to calculate the linear response of the system. On this basis, by the Floquet theory and the non-perturbation expansion method, the method of moments is extended to calculating the nonlinear response of the system. The long time ensemble average and the spectral amplification factor of the first harmonic calculated from direct numerical simulation and from the method of moments demonstrate that they are in good agreement, which shows the validity of the method we proposed. Furthermore, the dependence of the spectral amplification factor at the first three harmonics on the noise intensity is investigated. It is observed that for appropriate parameters, the curve of the spectral amplification factor versus the noise intensity exhibits a peaking behavior which is a signature of stochastic resonance. Then we discuss the influences of the bias parameter and the amplitude of the periodic signal on the stochastic resonance. The results show that with the increase of the bias parameter in a certain range, the peak value of the resonance curve increases and the noise intensity corresponding to the resonance peak decreases. With the increase of the driven amplitude, comparing the changes of the resonance curves, we can conclude that the effect of stochastic resonance becomes more prominent. At the same time, by using the mean square error as the quantitative indicator to compare the difference between the results obtained from the method of moments and from the stochastic simulation under different signal amplitudes, we find that the method of moments is applicable when the amplitude of the periodic signal is lesser than 0.25.

2017, 66 (12): 120502.
doi: 10.7498/aps.66.120502

Abstract +

The researches on higher-order coherence and quantum statistics of light field are the important researching issues in quantum optics. In 1956, Hanbury-Brown and Twiss (HBT) (Hanbury-Brown R, Twiss R Q 1956 Nature 177 27) revolutionized optical coherence and demonstrated a new form of photon correlation. The landmark experiment has far-reaching influenced and even inspired the quantum theory of optical coherence that Glauber developed to account for the conclusive observation by HBT. Ever since then, the HBT effect has motivated extensive studies of higher-order coherence and quantum statistics in quantum optics, as well as in quantum information science and cryptography. Based on the HBT scheme, the degree of coherence and photon number distribution of light field can be derived from correlation measurement and photon counting technique. With the rapid development of the photoelectric detection technology, single-photon detection, which is the most sensitive and very widespread method of optical measurement, is used to characterize the natures of light sources and indicate their differences. More recently, HBT scheme combined with single-photon detection was used to study spatial interference, ghost imaging, azimuthal interference effect, deterministic manipulation and detection of single-photon source, etc.
Due to broadband RF spectrum, noiselike feature, hypersensitivity to the initial conditions and long-term unpredictability, chaotic laser meets the essential requirements for information security and cryptography, and has been developed in many applications such as chaos-based secure communications and physical random number generation, as well as public-channel secure key distribution. But the research mainly focused on macroscopic dynamics of the chaotic laser. Moreover, the precision of measurement has reached a quantum level at present. Quantum statistcs of light field can also uncover profoundly the physical nature of the light. Thus, it is important to exploit the higher-order degree of coherence and photon statistics of chaotic field, which contribute to characterizing the field and distinguishing it from others.
In this paper, photon number distribution and second-order degree of coherence of a chaotic laser are analyzed and measured based on HBT scheme. The chaotic laser is composed of a distributed feedback laser diode with optical feedback in fiber external cavity configuration. The bandwidth of the chaotic laser that we obtain experimentally is 6.7 GHz. The photon number distribution of chaotic laser is fitted by Gaussian random distribution, Possionian distribution and Bose-Einstein distribution. With the increase of the mean photon number, the photon number distribution changes from Bose-Einstein distribution into Poissonian distribution and always accords with Gaussian random distribution well. The second-order coherence g(2)(0) drops gradually from 2 to 1. By changing the bias current (I = 1.0Ith-2.0Ith) and feedback strength (010%), we compare and illustrate different chaotic dynamics and g(2)(0). From low frequency fluctuation to coherence collapse, the chaotic laser shows bunching effect and fully chaotic field can be obtained at the broadest bandwidth. Furthermore, the physical explanation for sub-chaotic or weakening of bunching effect is provided. It is concluded that this method can well reveal photon statistics of chaotic laser and will open up an avenue to the research of chaos with quantum optics, which merges two important fields of modern physics and is extremely helpful for the high-speed remote chaotic communication.

2017, 66 (12): 120601.
doi: 10.7498/aps.66.120601

Abstract +

A whole-fiber methane sensor under high absorbance based on phase sensitive chirped laser dispersion spectroscopy is presented in this paper. The laser source of the sensor is a tunable distributed feedback diode laser with a frequency of 1653.7 nm. A telecom-based electro-optical intensity Mach-Zehnder modulator working in carrier suppression mode is adapted to modulate the single frequency laser beam for generating a dual-sideband spectrum beside the carrier wave. Unlike previous proposed phase sensitive chirped laser dispersion spectroscopy scheme, the beatnote signal generated by the two sidebands is detected experimentally. The refractive index fluctuation around the 23 transition of methane is measured by detecting the phase variation of the dual-sideband beatnote signal through using the heterodyne interferometric method. A lock-in amplifier is employed in the phase demodulation process. By connecting the refractive index (the real part of the complex refraction index) and the absorption coefficient (the imaginary part of the complex refraction index) via Kramers-Kroning relation, the gas concentration information is retrieved from the optical dispersion measurement. Absorption-based wavelength modulation spectroscopy measures the gas concentration encoded in the optical intensity based on Beer-Lambert's law. However, the signal sensitivity of wavelength modulation spectroscopy decreases, and the signal even decreases while the gas concentration is raised in high absorbance condition, which leads to an uncertainty in concentration measurement. Experimental results demonstrate that wavelength modulation spectroscopy has better performance in low absorbance condition. The detection limit is about 38.1 ppmm. However, because the sensitivity decreases in high absorbance conditions, the upper detection limit of wavelength modulation spectroscopy is only 1500 ppmm. The dynamic range is defined through dividing the upper detection limit by the detection limit. Therefore, the wavelength modulation spectroscopy obtains a linear measurement dynamic range of 16 dB. Nevertheless, under the same experimental condition, the phase sensitive chirped laser dispersion spectroscopy has a much larger linear measurement range from 47.3 ppmm to 174825 ppmm with a dynamic range higher than 35 dB. Absorption-based gas measurement technique such as wavelength modulation spectroscopy can achieve a low detection limit by using long optical path at the expense of lower upper limit concentration. Phase sensitive chirped laser dispersion spectroscopy appears to be effective in high absorbance condition, which may be caused by high concentration or long optical path. Furthermore, by combining phase sensitive chirped laser dispersion spectroscopy and long optical path technique such as multi pass cell in sensor design, large linear measurement dynamic range and low detection limit can be obtained at the same time.

## EDITOR'S SUGGESTION

2017, 66 (12): 120204.
doi: 10.7498/aps.66.120204

Abstract +

Using the improved element-free Galerkin (IEFG) method, in this paper we introduce the characteristic parameter r which can reflect the singular stress near the crack tip into the basic function of the improved moving least-squares (IMLS) approximation. Combining fracture theory with the IEFG method, we present an IEFG method of treating the elastic fracture problems, and analyze a numerical example of two-dimensional layered system of airport composite pavement with reflective crack.
In the IEFG method, the IMLS approximation is used to form the shape function. The IMLS approximation is presented from the moving least-squares (MLS) approximation, which is the basis of the element-free Galerkin (EFG) method. Compared with the MLS approximation, the IMLS approximation uses the orthonormal basis functions to obtain the shape function, which leads to the fact that the matrices for obtaining the undetermined coefficients are diagonal. Then the IMLS approximation can obtain the solutions of the undetermined coefficients directly without the inverse matrices. The IMLS approximation can overcome the disadvantages of the MLS approximation, in which the ill-conditional or singular matrices are formed sometimes. And it can also improve the computational efficiency of the MLS approximation.
Because of the advantages of the IMLS approximation, the IEFG method has greater computational efficiency than the EFG method which is based on the MLS approximation, and can obtain the solution for arbitrary node distribution, even though the EFG method cannot obtain the solution due to the ill-conditional or singular matrices in the MLS approximation.
Paving the asphalt concrete layer on the cement concrete pavement is an effective approach to improving the structure and service performance of an airport pavement, which is called airport composite pavement. The airport composite pavement has the advantages of rigid pavement and flexible pavement, but there are various forms of joints or cracks of cement concrete slab, which makes the crack reflect into the asphalt overlay easily under the plane load and environmental factors. Reflective crack is one of the main failure forms of the airport composite pavement. Therefore, it is of great theoretical significance and engineering application to study the generation and development mechanism of reflective crack of the airport composite pavement.
For the numerical methods of solving the fracture problems, introducing the characteristic parameter r which can reflect the singular stress near the crack tip into the basic function is a general approach. In this paper, we use this approach to obtain the IEFG method for fracture problems, and the layered system of airport composite pavement with reflective crack is considered. The numerical results of the displacements and stresses in the airport composite pavement are given. And at the tip of the crack, the stress is singular, which makes the crack of the airport composite pavement grow.
This paper provides a new method for solving the reflective crack problem of airport composite pavement.

2017, 66 (12): 120201.
doi: 10.7498/aps.66.120201

Abstract +

The centrality reflects the importance of a node in a complex network, which plays an important role in the propagation dynamics. Many researches in the field of node ranking estimation have revealed the characteristics of higher centrality in the structural dynamics and propagation dynamics. However, there are few reports about the effect of nodes with a relatively lower centrality on propagation process. In this paper, we focus on the effect of heterogeneous structural characteristics on propagation dynamics. First, we select four centrality measurements (i.e., degree, coreness, betweenness, and eigenvector) and initialize source nodes with the maximum and minimum centralities respectively. Then, based on the email propagation model and the SI model, the massive numbers of elaborate simulations are implemented in twelve scale-free networks. These networks include three networks generated by the Barabsi-Albert model, four synthetic networks compiled by the GLP (generalized linear preference) algorithm, and five benchmark networks. The simulation results contain two parts: one is the crossover phenomenon of two propagation processes, and the other is the correlation between the crossover point and the proportion of the initial source nodes. We present the crossover of two propagations by calculating the total infected nodes, the incremental infected nodes, and the average degree of the incremental infected nodes. The average degrees of the incremental infected nodes in both synthetic networks and benchmark networks show that there exist two kinds of diffusion modes (i.e., fan-shaped type and single-strand type). With the increase of the initial source nodes, the interaction between two modes results in the different dynamic changes of two propagations with respect to propagation speed, which may lead to the crossover of two propagations in terms of propagation scale in the propagation process. Specifically, the increase of the initial source nodes would suppress the propagation process in which nodes with the maximum centralities are portrayed as propagating sources. However, such an effect is not observed in the propagation process in which nodes with the minimum centralities are portrayed as propagating sources. Our further simulation indicates that the crossover points appear earlier as the proportion of the initial source nodes increases. And by employing the discrete-time method, we find that such a phenomenon can be triggered exactly by increasing the initial source nodes. This work reveals that the influence of the nodes with the minimum centralities should be taken into consideration because the initial infected nodes with a lower centrality will lead to a larger propagation scale if the initial proportion is high.

2017, 66 (12): 120203.
doi: 10.7498/aps.66.120203

Abstract +

This paper mainly uncovers the typical microscopic characteristics of Chinese capital market in three different stock price stages of rising, steady and falling based on the high frequency data of Shanghai composite index. Firstly, by analyzing the probability distribution of the Shanghai composite index in different time intervals, we clearly find that the logarithmic change of the index presents an obvious heavy tail feature as well as non-Gaussian Levy distribution, and the return series converges to a normal distribution with the increase of the time interval, which becomes more significant especially in the falling stage of stock prices. Secondly, by calculating the autocorrelation function, we observe that unlike the return rate, the fluctuation ratio of Shanghai composite index demonstrates remarkable long memory volatility with a periodicity of about 240 min, and the autocorrelation curve in falling stage is much higher than in rising and steady stages. Thirdly, in the multi-fractal structure, the volatility of return series has significant short-term and long-term differences among three different stages of rising, steady and falling due to the effects of time limitation and liquidity of investment. Finally, the macroscopic behavior of the Shanghai composite index is relatively consistent with that of the international mature stock market, however, the corresponding microscopic characteristics demonstrate significant differences due to the fact that the Chinese capital market is strongly dependent on the macroeconomic policy, investor sentiment, and liquidity levels. It is quite remarkable that the tail distribution of mature stock market is much fatter than that of Chinese stock market because of the special control and limit mechanism of stock prices in China, which finally causes the considerably lower amplitude of price fluctuation. Moreover, it is also found that the attenuation speed of the autocorrelation function in the Chinese capital market is obviously slower than that in the mature stock market, which suggests that the behaviors of investors in Chinese stock market are more likely to be influenced by the historic exchange information. At the same time, the periodicity of autocorrelation function is actually caused by the inertia recoil of investors, which further verifies the information asymmetry of Chinese stock market. Especially, by changing the starting values of the samples, we find that the periodicity of autocorrelation function still remains the same, which indicates that the periodicity characteristic of stock price is not dominated only by the intraday pattern of trading activity. Therefore, the investors should discover the underlying rules of high-frequency data and extract more useful knowledge in order to guide their investment decisions more effectively.

## EDITOR'S SUGGESTION

2017, 66 (12): 120302.
doi: 10.7498/aps.66.120302

Abstract +

Interference between independent photon sources is the key technique to realize complex quantum systems for more sophisticated applications such as multi-photon entanglement generation and quantum teleportation. Here, we report Hong-Ou-Mandel interference (HOMI) between two independent 1.55 m all-fiber photon pair sources over two 100 GHz dense wave division multiplexing (DWDM) channels, whose visibility reaches 53.2%8.4% (82.9%5.3%) without (with) back ground counts subtracted. In addition, we theoretically describe in detail the single photon spectral purity of the photon source generated in dispersion shifted fiber (DSF), simulate the influences of the pulse width and filter bandwidth on the purity, and obtain the optimized condition. The optimized pump pulse width is 8 ps and filter bandwidth is about 40 GHz or less. A home-made 1550.1 nm mode-locked fiber laser source, whose pulse width and repetition rate are 25 ps and 27.9 MHz respectively, acts as a pump of photon source. A tunable attenuator is used to adjust the pump power of the photon source, and the broad band background fluorescence photons are filtered out by cascade 100 GHz DWDM filters. The clean pump beam is divided into two equal parts by the 50 : 50 optical coupler to pump two 300 m DSFs (cooled by liquid nitrogen) to generate independent photon sources. Then the strong pump beam and noise photon from Raman scattering in orthogonal polarization are removed by 2 groups of 200 GHz DWDM filters and fiber polarization rotator and polarizer. Then two 100 GHz DWDMs are used for separating photons at correlated channel pairs. The relative delay between the two independent photons is adjusted by tunable fiber delay line. Photons from the same channels are combined in a second beam splitter for interference, and the other two photons are used as trigger signals. The two triggered photons are detected by two free running InGaAs avalanched single photon detectors (APD1, APD4, ID Quanta, ID220, 20% detection efficiency, 3 s dead time, dark count rate 4k cps), and the outputs of detectors APD1 and APD4 are used to trigger two single-photon detectors running in the gated mode (APD2, APD3, Qasky, Hefei, China, 100 MHz, free gating single photon detectors, 20% detection efficiency, dark count probability 410-5 per gate) for twophoton coincidence measurement. Detection output signals from APD2 and APD3 are sent to our coincidence count device (Pico quanta, TimeHarp 260, 1.6 ns coincidence window) for four-photon coincidence measurement. Before measuring the HOMI, we obtain a maximum-coincidence-to-accidental-coincidence ratio (CAR) of 131 by cooling the fiber in liquid nitrogen when the pump power is 23 W. There are a few remarks we want to point out.Firstly, the photon sources are not operated at the optimized pump pulse width for pure single photon generation, but narrow band 100 GHz filters are used in the experiments to increase the purity of the sources. Secondly, single photon detectors used in our experiment have lower detection efficiency and much higher dark counts than nano-wire single photon detectors, if we have high-performance nano-wire single photon detector, experimental results will be greatly improved due to the four-fold coincidences and dark coincidences scaling quadruplicate with the detection efficiency and dark count probability of a single detector. Thirdly, we use relatively high pump power for each DSF (0.12 mW) to reduce measurement time for photon coincidence, which will lead to a very poor raw visibility certainly. Finally, though only a 100 GHz channel pair is used in our experiment, we can use other channels for multiplexing such interference processes to improve the channel capacity in future quantum communication tasks theoretically. Our study shows greatly promising integrated optical elements for future scalable quantum information processing.

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

2017, 66 (12): 124202.
doi: 10.7498/aps.66.124202

Abstract +

Conical diffraction, a unique optical phenomenon in biaxial crystal, has important applications for the manipulation of particles. In this paper, a new model of annular Gaussian beam is constructed based on the Tovar's flat-topped multi-Gaussian laser beams. The conical diffraction of annular Gaussian beam is calculated using Belsky-Khapalyuk-Berry theory. The polarization characteristics of conical diffracted output beams under the annular Gaussian beam are theoretically calculated and experimentally demonstrated by means of the linearly polarized annular Gaussian beams with different polarization directions. It is found that the same azimuth angles of the inner and outer rings of the conical diffracted output beams have orthogonal polarization characteristics. A combined polarizer (CP) composed of eight polarizing segments with different specific pass axes of polarization is presented to simulate the polarization characteristic of the optical field of conical diffraction. Furthermore the calculations for output-field control of conical diffraction under the annular beam by using the proposed CP are compared with the experimental results. The results show that the intensities of both the inner and outer rings are periodically varied with CP azimuth angle. And when the azimuth angle of CP is 0, only the conical diffracted outer ring is remained, while only the inner ring of conical diffraction is remained for 180. This tunable conical diffracted field has important applications in optical tweezers and wavelength division multiplexing.

2017, 66 (12): 124203.
doi: 10.7498/aps.66.124203

Abstract +

Random numbers play an important role in many fields, including information security, testing and engineering practice. Especially in information security, generation of secure and reliable random numbers, they have a significant influence on national security, financial stability, trade secrets and personal privacy.
Generally, random number generators can be classified as two main types: pseudo random number generators and physical random number generators. Pseudo random numbers with high speed are generated by software algorithms, but the inherent periodicity will cause serious hidden dangers when they are used in information security. Random numbers based on physical entropy sources (such as electronic thermal noise, frequency jitter of oscillator, quantum randomness) can produce reliable random numbers. However, due to the limitation of traditional physical source bandwidth, their generation speeds are at a level of Mbit/s typically, which cannot meet the needs of the current high-speed and largecapacity communication.
In 2008, Uchida et al. (2008 Nat. Photon. 2 728) realized the physical random number of 1.7 Gbit/s by using a wideband chaotic laser for the first time. The emergence of wideband physical entropy sources such as chaotic laser greatly promote the rapid development of the physical random number generators. As far as we know, a semiconductor laser can generate wideband chaotic signals under external disturbances such as optical feedback, optical injection or photoelectric feedback. However, compared with the structures of other two lasers, the structure of the optical feedback semiconductor laser is simple and easy to integrate. Therefore, chaotic signals have received great attention to produce high-speed physical random number extracted from the optical feedback semiconductor laser. In the reported schemes, a variety of post-processing methods are used to improve the speed and randomness of random numbers. Besides, optimizing the chaotic entropy source can also improve the performance of random number.
So far, the influence of internal parameters on the dynamic characteristics of semiconductor lasers has attracted wide attention. The linewidth enhancement factor is one of the key parameters for a semiconductor laser. The values of linewidth enhancement factor are different, depending on the type of semiconductor laser. The existence of linewidth enhancement factor results in a large number of unstable dynamic characteristics of semiconductor lasers. Therefore, it is of great significance for studying the influence of the linewidth enhancement factor on performance of random numbers.
In this paper, we focus on the influence of the linewidth enhancement factor on the randomness of the obtained random numbers. The time delay characteristics and complexity are two important parameters to measure the quality of chaotic signals. The simulation results show that with the increase of the linewidth enhancement factor, the time delay characteristic peak of the chaotic signal from an optical feedback semiconductor laser decreases gradually, meanwhile, the maximum Lyapunov exponent of chaotic signal increases gradually. The randomness of random numbers, generated by the chaotic signal from the optical feedback semiconductor laser under different linewidth enhancement factors, is tested by NIST SP 800-22. The test results show that semiconductor laser with larger linewidth enhancement factor is chosen as a physical entropy source to generate random numbers with high quality.

2017, 66 (12): 124204.
doi: 10.7498/aps.66.124204

Abstract +

A key issue in developing a high-power laser driver, which can be used for inertial confinement fusion and laser produced plasma experiments, is to obtain uniform irradiation on the target surface, thus a number of spatial or temporal techniques have been proposed for laser beam smoothing. A scheme combining a lens array with the technique of smoothing by spectral dispersion (SSD) is being explored in the SG-II Laser Facility located in Shanghai Institute of Optics and Fine Mechanics. As the laser system involves a variety of optical elements, their influences have to be considered in the implementation of such a scheme. The Nd:glass amplifier is one of the most important parts of the system, and the phase-modulated laser beam will propagate through it along the long light path when SSD is employed. In this paper, the performance of uniform irradiation of the target pattern is studied based on two-dimensional simulations when the gain characteristic of the amplifier is taken into account. The major factors, such as the small signal gain profile of the amplifier, the amplification factor, the bandwidth of the phase-modulated laser beam and the difference between the central wavelength of the laser and the central wavelength of the amplifier gain curve, are analyzed in detail.
The numerical results show that when the central wavelength of the incident beam is different from the central wavelength of the amplifier gain curve, intensity distribution of the target pattern will be affected to a degree depending on the amplification factor; while these two wavelengths are very close to or identical with each other, variation in the intensity distribution is trivial. The symmetry of the phase-modulated laser spectrum will be destroyed due to the gain characteristic of the amplifier, especially when the bandwidth is relatively wide. However, the slight asymmetry does not result in significant influence on the spatial power spectrum nor uniformity of the target pattern, even in the case where the central wavelength of the incident beam is different from that of the amplifier gain curve. The reasons would be 1) the gain curve of the amplifier is actually quite flat within the laser bandwidth, and 2) with the technique of SSD, all spectral components contribute to the target intensity distribution within an average time. The analysis indicates that the performance of uniform irradiation of the target pattern depends mainly on the bandwidth of the phase-modulated laser beam. A wider bandwidth can always generate better irradiation when it is within a certain range, say no more than 0.3 nm, but beyond this range, the nonuniformity tends to remain at a level about 0.250.3. Multistage Nd:glass amplifiers will be employed in the practical laser driver, and the case investigated in this paper involves only one stage for simplicity. The conclusion obtained in this paper is important for implementing the technique of SSD in the laser system.

Propagation of stochastic electromagnetic high-order Bessel-Gaussian beams in the oceanic turbulence

2017, 66 (12): 124205.
doi: 10.7498/aps.66.124205

Abstract +

Recently, the laser beam propagation in the oceanic turbulence has become a hot research topic. In addition to the characteristics of free diffraction and self-reconstruction, the high-order Bessel-Gaussian beam is a kind of typical vortex beam because of the existence of a spiral phase factor with orbital angular momentum. Researchers have investigated the self-reconstruction property of the high-order Bessel-Gaussian beams in the free space, also carried out intensive researches on the transmission characteristics of high-order Bessel-Gaussian beam in the ABCD optical system and in the atmospheric turbulence. However, to the best of our knowledge, to date there has been no investigation on the propagation of this laser beam in the oceanic turbulence. In this paper, we will study the propagation characteristics of the random electromagnetic high-order Bessel-Gaussian beams in the oceanic turbulence, and discuss the variation of the normalized spectrum intensity, the spectral degree of polarization, and the spectral degree of coherence. By using the extended Huygens-Fresnel diffraction integral formula, the general expression for the cross spectral density matrix of the stochastic electromagnetic high-order Bessel-Gaussian beams propagating in the oceanic turbulence is obtained, and the statistical properties of the random electromagnetic high-order Bessel-Gaussian beams propagating in the seawater are investigated by numerical calculation. The numerical results show that the oceanic turbulence can affect the normalized spectral intensity distribution of the random electromagnetic beam. With the increase of the transmission distance, the center of the zero-order Bessel-Gaussian beam becomes depressed, and the center of the higher-order Bessel-Gaussian beam will become flat and then depressed. As the transmission distance increases far enough, regardless of the zero-order or higher-order, the intensity distribution will eventually evolve into the quasi Gaussian shaped distribution. The variation of the degree of polarization of each point on the x axis is related to the coherence length (xx，yy) and the oceanic turbulence parameters. The spectral coherence of the origin and any point on the x axis also changes with the increase of x, and the rate of dissipation of mean-square temperature T has influence on the spectral coherence. This research is of great value for applying the high-order Bessel-Gaussian beam to the optical communication, optical imaging and underwater exploration in the ocean.

2017, 66 (12): 124302.
doi: 10.7498/aps.66.124302

Abstract +

In the marine environment, when the line spectra of underwater target radiated signal are unknown or the continuous spectra are weak, it is extremely hard to accurately detect the underwater weak target. The line spectrum based method commonly requires spectrum information for detection, and the continuous spectrum based energy method is hard to achieve accurate detection in long distance. In this paper, an underwater radiated noise detection method based on generalized Duffing oscillator detection system is proposed. Firstly, a generalized Duffing oscillator detection system for non-periodic and non-stationary input signal is proposed through deducing the traditional Duffing oscillator detection system that is perturbed by periodic signal. And the proposed generalized Duffing oscillator detection system is able to detect the signals of targets without needing prior information. Secondly, when the target radiated signal (non-periodic and non-stationary signal) is input into the generalized Duffing oscillator, a special form of output phase space (a special state of motion) is discovered and the differences in output phase space among different input signals (periodic stationary signals, nonperiodic non-stationary signals and the target radiated signals) are analyzed. It is found that the special phase space has different form from the output phase spaces of other kinds of signals; accordingly the underwater targets can be detected through the representation of the difference between special phase space and ordinary phase space. Thirdly, a discrete distribution sequence calculation method based on phase space is proposed for the precise and efficient judgment of system motion. The proposed calculation method defines a similar-grid function, based on which, the distribution sequence calculation method of output phase space is deduced, and the distribution sequences of different kinds of output phase spaces are calculated. The method realizes an embedded expression of system output by using the statistical complexity, therefore achieving the embedded underwater target detection when the line spectra of underwater target radiated signal are unknown or the continuous spectra are weak. The analysis result indicates that the method is of low-computation. Finally, the experimental results in the sea are described and the lowest signalto-noise ratio (SNR) of the method is calculated to be -9.133 dB. Simulation and experimental results have shown that the proposed method can detect target successfully in a lower SNR than traditional detection method, and the real-time performance can meet the demand for underwater detection. The method in this paper provides new ideas and ways of thinking for underwater target detection, and has very important reference value for low SNR long-distance target detection under real condition.

2017, 66 (12): 124102.
doi: 10.7498/aps.66.124102

Abstract +

In recent years, the two-way parabolic equation method (2WPE) has been widely utilized for studying the tropospheric ground-wave propagation under the irregular terrain. This algorithm can deal with the influences of the irregular terrain characteristic and the different electromagnetic parameters of the surface structure on wave propagation. However, there are still some defects in 2WPE method. Firstly, the method considers the irregular terrain and obstacles as a whole, so it cannot deal with the situation where the medium parameters of obstacles and the ground are different. Secondly, its calculation precision is limited with the inclination of the undulating terrain: if there are obstacles the upper bound of the inclination is easily broken through. Therefore, in this paper, a novel two-way parabolic equation method is proposed for analyzing the radio wave propagation in obstacle environment. According to the principle of domain decomposition, the obstacle zones are divided into two domains in the new algorithm, and the two subdomains are calculated, respectively. Meanwhile, in order to avoid the calculation error caused by the abrupt truncation of the obstacle zone, the field at the upper boundary of obstacles is modified to ensure the continuity of tangential field. To further improve the accuracy of the new algorithm, according to the historical transmission paths, we exactly retrieve the phases of each forward and backward wave, especially when stepping in and out of the obstacles. Furthermore, the method of moment (MoM) is used to verify the calculation accuracy of the new algorithm in obstacle environment. Although the accuracy of the MoM is very high, it also requires a great deal of calculation resources: it can only be employed to compute the fields in short distance. To overcome the difficulty, we use the image principle in the obstacle environment and do not subdivide the ground into segments; therefore the verification accuracy can be improved. On this basis, to unify the source setting of the new algorithm and the MoM, the equivalent source model is used to set the initial field. Finally, through numerical experiments, the simulation results of both methods agree very well, so the effectiveness of the boundary correction and the phase correction which are presented in this paper are both verified. The accuracy and superiority of the new algorithm in obstacle environment are also demonstrated. To sum up, the novel two-way parabolic equation method can be used to accurately calculate the field of the space in the obstacle environment, and lays the foundation for the field calculation of radio wave propagation in real environment.

2017, 66 (12): 124201.
doi: 10.7498/aps.66.124201

Abstract +

To improve the performance of existing guided-mode resonance (GMR) anti-counterfeiting grating, a tri-color shift device based on a one-dimensional (1D) singly periodic rectangular structure and ZnS film is reported. By turning the azimuths, the proposed device exhibits tri-color shifts of blue, green, and red for both TE and TM polarizations simultaneously. As the natural light can be considered as a superposition of TE and TM polarizations, in order to achieve the azimuth-tuned tri-color shifts of blue, green, and red, the wavebands and magnitudes of the reflection peaks for TE and TM polarizations should be designed at three azimuths, that is, at the first azimuth, high reflectivity in blue band and low reflectivity in green and red band should be reached; at the second azimuth, high reflectivity in green band and low reflectivity in blue and red band should be reached; at the third azimuth, high reflectivity in red band and low reflectivity in blue and green band should be reached. Considering these design goals, the evaluation function is established. By making the rigorous coupled wave analysis, the 0th reflectivity of the device can be numerically solved, which is relative to the incident light parameters (, , , ), the structure parameters (f, T, dg, dc), as well as the refractive indices of all the regions (ni, nc, ns). There is no analytical relationship between these parameters and the 0th reflectivity. So genetic algorithm is used to optimize the evaluation function, and then the optimal parameters of the tri-color shift device are obtained. When T=431.5 nm, dg=124.2 nm, dc=13.1 nm, f=0.5, and =45, at azimuth angle 0, natural light has reflection peaks at 468 nm and 442 nm; at azimuth angle 58, natural light has reflection peaks at 557 nm and 521 nm; at azimuth angle 90, natural light has reflection peaks at 690 nm, 673 nm, 650 nm and 644 nm. As a result, the device exhibits blue, green and red color responses at 0, 58 and 90 azimuth, respectively. The research results are explained in physics. Furthermore, the influences of key parameters on the reflection peaks are investigated. It is found that the reflection peaks of blue, green and red light are red-shifted with the increase of device period, groove depth, coating thickness and the decrease of incident angle. When the period, depth, thickness, and the incident angle are changed by 4.6% ( 20 nm), 27.4% ( 34 nm), 100% ( 13.1 nm), and 11.1% ( 5) with respect to the original designs, respectively, the device can well keep the color-shift effects of blue, green and red. The results above are meaningful in the designing, manufacturing and testing of the device. Compared with the existing GMR anti-counterfeiting grating, the tri-color shift device has high anti-counterfeit and appreciative value because of the harder designing and richer visual effect. Moreover, the 1D simple periodical structure is good for the manufacture of the high-precision master masks, and the device can be massively produced at low cost by the traditional embossing and evaporating technique in the laser holography industry. This tri-color shift device breaks through the limit of bi-color shifting technology, and may have great applications in the field of the optically variable image security.

2017, 66 (12): 124301.
doi: 10.7498/aps.66.124301

Abstract +

The rotation of levitated object in the ultrasonic levitation experiment is a common phenomenon. This instability may give rise to many difficulties in locating and detecting the levitated object and even cause the experiment to fail. However, the relevant research of the rotation mechanism of levitated object is seldom carried out. In this work, the rotation mechanism of cylinder in a single-axis ultrasonic levitator is investigated experimentally and theoretically. In the ultrasonic levitation experiment, the cylinder begins to rotate about an axis along the vertical direction as it is levitated at the node between the emitter and reflector. The rotation speed of cylinder tends to a stable value due to the effect of the air resistance, and the final rotation direction is determined by its initial rotation state. Experimental results demonstrate that the rotation speed increases with the decreases of density and length-to-diameter ratio of the cylinder. In order to analyze the rotation mechanism, the finite element method is used to calculate the distribution of acoustic pressure field and the torque acting on the cylinder for each of three different cases. Numerical results reveal that the position offsets of the cylinder and the reflector as well as the tilt of the emitter can all result in the nonaxisymmetrical distribution of acoustic pressure field. Hence, a nonzero torque acting on the cylinder may be generated and the rotation state of the levitated cylinder is subsequently affected. The position offset of the cylinder can produce a torque driving itself to rotate and the torque increases with the increase of the deviation degree. A restoring torque suppressing the rotation of cylinder can be generated by deviating the reflector from the horizontal direction. The cylinder eventually keeps stationary state with its axis perpendicular to the offset direction of the reflector, showing good accordance with the experimental results. In addition, it is predicted that tilting the emitter can also offer a restoring torque which makes cylinder eventually static with its axis perpendicular to the plane through the axes of the emitter and the reflector. However, this restoring torque is approximately three orders of magnitude smaller than that generated by deviating the reflector. In the end, both experimental results and numerical simulations show that the rotation of the cylinder can be effectively suppressed under the disturbance of two fixed cylinders when the emitter and the reflector are coaxial. The cylinder eventually stays still and keeps coaxial with the two fixed cylinders.

2017, 66 (12): 124101.
doi: 10.7498/aps.66.124101

Abstract +

The transmission of 1.5 keV-electrons through a conical glass capillary is reported. This study aims to understand the so-called guiding effect for the negatively charged particles (e.g. electrons). The guiding mechanism is understood quite well with positively charged particles in particular highly charged ions, but not clear with electrons, i.e., even the basic scheme mediated by the existence of negative charge patches to guide the electrons is still somewhat controversial.
The study of the charging-up dynamics causing the electrons transport inside the capillary will shed light on this issue. In order to perform this, a data acquisition system has been setup to follow the time evolution of the twodimensional angular distribution of the transmitted electrons. The electrons are detected by the multi-channel plate (MCP) detector with a phosphor screen. The image from the phosphor screen is recorded by a charge-coupled device camera. The timing signals for the detected events are extracted from the back stack of the MCP detector and recorded by the data acquisition system, synchronized with the acquired images. The electron beam has a size of 0.5 mm0.5 mm and a divergence of less than 0.35. The inner diameter of the straight part of the capillary is 1.2 mm and the exit diameter is 225 m. A small conducting aperture of 0.3 mm in diameter is placed at the entrance of the capillary. Two-dimensional angular distribution of the transmitted electrons through conical glass capillary and its time evolution are measured. The results show that the transmission rate decreases and reaches to a constant value for the completely discharged glass capillary with time going by. The centroid of the angular distribution moves to an asymptotic value while the width remains unchanged. These transmission characteristics are different from those indicated in our previous work (2016 Acta Phys. Sin. 65 204103). The difference originates from the different manipulations of the capillary outer surface. A conducting layer is coated on the outer surface of the capillary and grounded in this work. This isolates various discharge/charge channels and forms a new stable discharge channel. The transmission rate as a function of the tilt angle shows that the allowed transmission occurs at the tilt angle limited by the geometrical factors, i.e., the geometrical opening angle given by the aspect ratio as well as the beam divergence. The transmission characteristics suggest that most likely there are formed no negative patches to facilitate the electron transmission through the glass capillary at this selected beam energy. It is different from that of highly charged ions, where the formation of the charge patches prohibits the close collisions between the following ions and guides them out of the capillary.

2017, 66 (12): 124206.
doi: 10.7498/aps.66.124206

Abstract +

In an optical fiber perimeter security system, due to the fact that a large quantity of samples are collected in the process of data acquisition, this heavy data burden inevitably degrades the efficiency and accuracy of intrusion recognition. Hence, it is urgent to remove the redundancy of the collected data records, which essentially requires to describe event features in a concise and proper way. In this paper, we propose a synthesized feature based intrusion recognition method, which is especially suitable to describing the fiber intrusion vibration signals with both wide bandwidth and high nonstationarity. Firstly, the all-phase filter bank characterized by large sidelobe attenuation and high flexibility of coefficient configuration, is employed to parallelly divide the input signal into multiple frequency channels, from which the power values can be accurately calculated. Secondly, the crossing rate of the input signal is combined with these power values to construct a synthetical feature vector, in which both the time-domain information and frequency-domain information are incorporated together. Finally, these synthetical feature vectors are fed into a radial-basis-function network based classifier to recognize 4 common intrusions (climbing, knocking, waggling and cutting). Essentially, the high efficiency of our proposed scheme lies in the parallel pipeline mode of the configurable filter bank and simple calculation of features, which facilitates speeding up the intrusion recognition. The high accuracy of our proposed scheme lies in two aspects: 1) the all-phase filter bank possesses small inter-channel interference, which helps to reduce the inter-coupling between output power values; 2) the synthesis of both frequency-domain information and time-domain information ensures the completeness of feature description. Experiments show that the sensing range of the proposed scheme can reach 2.25 km. Moreover, compared with the empirical mode decomposition based method, the proposed method not only improves the precision, but also significantly speeds up the recognition.

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

2017, 66 (12): 126301.
doi: 10.7498/aps.66.126301

Abstract +

Magnetic refrigeration technology is considered as a better alternative to traditional steam compression scheme, since it has many advantages such as environment friendly characteristic, more compact solid refrigerant, low cost, etc. The mechanical stability is of essential importance for serving as magnetic refrigerant materials which work under repeatedly thermal and magnetic cycles. Recent experiment reveals that the polycrystalline FeMnP1-xSix compounds are brittle, and even fracture of samples during post heat treatment is observed. Therefore, the improvement of the ductility of Fe2P-Type FeMn-based magnetocaloric materials becomes an important issue in practical application. So far, there are few studies of the mechanical properties of these compounds. Alloying is an effective method to improve the mechanical properties of single phase materials, and Ga or Ge could be a better choice to replace the Si element. In this paper, we study the mechanical properties of giant magnetocaloric FeMnP1-xTx (T=Si, Ga, Ge) compounds by the projector augmented wave method as implemented in VASP (Vienna ab initio simulation package) in the framework of density functional theory. It is found that the lattice parameter, total energy, magnetic moment, elastic constant and the electronic structure of FeMnP1-xGax compounds are similar to those of FeMnP1-xGex compounds, therefore, it is believed that the FeMnP1-xGax compounds are candidate refrigerant for room temperature magnetic refrigeration. The relatively large single crystalline elastic constants of FeMnP1-xTx (T=Si, Ga, Ge) compounds show that this family of compounds is mechanically stable. This ensures the long-term applicability of FeMnP1-xTx compounds in magnetic refrigeration facilities. For polycrystalline compounds, we calculate their shear moduli and bulk moduli by Hill averaging scheme. And according to Pugh criterion, the ductility or brittleness characteristics of FeMnP1-xTx (T=Si, Ga, Ge) compounds are discussed. All the FeMnP0.67T0.33 (T=Si, Ga, Ge) compounds are ductile, among them, FeMnP0.67Ga0.33 compound shows the best ductility, whereas the ductility of FeMnP0.67Si0.33 compound is the weakest. This result proves that substituting P with Ga could improve the ductility of this class of compound. The mechanical properties of polycrystalline FeMnP0.33T0.67 compounds are close to the ductile/brittle critical point. For FeMnP0.33T0.67 compounds, the T atoms just occupy the 2c sites of metalloid atom in Fe2P-type structure, therefore it is expected that the occupation disorders of P and T atoms at high T concentration could improve the ductility of the compounds according to the result of FeMnP0.67Ga0.33 compound. Finally, the self-consistent elastic constants of different compounds are understood from the calculated electronic density of states and force theorem.

2017, 66 (12): 126302.
doi: 10.7498/aps.66.126302

Abstract +

Using non-equilibrium Green's function method and keeping the zigzag carbon chains unchanged, we investigate the transmission rate of acoustic phonon and the reduced thermal conductance in the graphene nanoribbons with three cavities. The results show that the reduced thermal conductance approaches to 32kB2 T/(3h) in the limit T0 K. Due to the fact that only long wavelength acoustic phonons with zero cutoff frequency are excited at such low temperatures, the scattering influence on the long wavelength acoustic phonons by the dislocation distribution of three cavities in the graphene nanoribbons can be ignored and these phonons can go through the scattering region perfectly. As the temperature goes up, the reduced thermal conductance decreases. This is because the high-frequency phonons are excited and these high-frequency phonons are scattered easily by the scattering structures. With the further rise of temperature, acoustic phonon modes with the cutoff frequency greater than zero are excited, which leads to a rapid increase of the reduced thermal conductance. This study shows that in higher frequency region, the transmission spectra display complex peak-dip structures, which results from the fact that in higher frequency region, more phonon modes are excited and scattered in the middle scattering region with three cavities, and the scattering phonons are coupled with the incident phonons. When the three cavities are aligned perpendicularly to the edge of the graphene nanoribbons, the scattering from low-frequency phonons by the scattering structures is smallest, which leads to the fact that the reduced thermal conductance is largest at low temperatures; however, at high temperatures, the reduced thermal conductance is smallest when the three cavities is aligned perpendicularly to the edge of the graphene nanoribbons. This is because the scattering from high-frequency phonons by the scattering structures is biggest. These results show that the acoustic phonon transport and the reduced thermal conductance are dependent on the relative position of the three cavities. In addition, the dislocation distribution of the three cavities can only modulate obviously the high-temperature thermal conductance of the in-plane modes (IPMs). This is because the change of the relative position of the quantum dots can only modulate greatly the high-frequency phonon transmission rate and less modulate the low-frequency phonon transmission rate of the IPMs. However, the dislocation distribution of the three cavities can adjust obviously not only the high-temperature thermal conductance of the flexural phonon modes (FPMs), but also the low-temperature thermal conductance of the FPMs. This is because the change of the relative position of the three cavities can modulate greatly phonon transmission rates of flexural phonon modes in the low-frequency and high-frequency regions. These results provide an effective theoretical basis for designing the thermal transport quantum devices based on graphene nanoribbons.

2017, 66 (12): 126701.
doi: 10.7498/aps.66.126701

Abstract +

In this paper, we numerically solve the thermodynamic Bethe-ansatz coupled equations for a one-dimensional Hubbard model at finite temperature and obtain the second order thermodynamics properties, such as the specific heat, compressibility, and susceptibility. We find that these three quantities could embody the phase transitions of the system, from the vacuum state to the metallic state, from the metallic state to the Mott-insulating phase, from the Mott-insulating phase to the metallic state, and from the metallic state to the band-insulating phase. With the increase of temperature, the thermal fluctuation overwhelms the quantum fluctuations and the phase transition points disappear due to the destruction of the Mott-insulating phase. But in the case of the strong interaction strength, the Mott-insulating phase is robust, embodying the compressibility. Furthermore, we study the thermodynamic properties of the inhomogeneous Hubbard model with trapping potential. Making use of the Bethe-ansatz results from the homogeneous Hubbard model, we construct the chemical potential-functional theory (-BALDA) for the inhomogeneous Hubbard model instead of the commonly used density-functional theory, in order to solve the in-convergence problem of the Kohn-Sham equation in the case of the divergence appearing in the exchange-correlation potential. We further point out a multi-dimensional bisection method which changes the Kohn-Shan equation into a problem of finding the fixed points. Through -BALDA we numerically solve the one-dimensional homogeneous Hubbard model of trapping potential. The density profile and the local compressibility are obtained. We find that at a given interaction strength, the metallic phase and the Mott-insulating phase are destroyed and the density profile becomes a Guassian distribution with increasing temperature. To the metallic phase, Friedel oscillation caused by quantum fluctuations is still visible at low temperature. With increasing temperature, Friedel oscillation will disappear. This situation reflects the fact that the thermal fluctuation overwhelms the quantum fluctuations. For the Mott-insulating phase, the Mott-insulating plateau is robust at a certain temperature and only the boundary of the Mott-insulating plateau is destroyed. With increasing temperature, the Mott insulating plateau will be destroyed. And the change of the local compressibility provides the information about such a change. So we conclude that the thermal fluctuation destroys the original quantum phase. Through our analysis, we find that the -BALDA can be used to study the finite temperature properties for the system of the exchange-correlation potential divergence with high efficiency.

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

2017, 66 (12): 127301.
doi: 10.7498/aps.66.127301

Abstract +

In visual image processing, there is a three-Gauss model used to simulate the receptive field of retinal ganglion cells, which can realize image enhancement to a certain extent, such as image edge and information about details. However, in dealing with a large number of image data, it is necessary to manually adjust the parameters of the three-Gauss model in order to achieve better results, which is a very tedious and time-consuming process. According to this, in this paper we propose an adaptive three-Gauss model based on memristive cross array. Memristor, whose resistance is controlled by size, polarity and power supply time of the power supply, is a kind of non-volatile component. Moreover, if the voltage applied to both ends of memristor is removed, it can still keep the resistance value when the power is off. Many studies show that when voltage pulses with the different amplitudes and the same width are applied to both ends of the memristor, the resistance will change continuously. This principle is adopted to realize image storage. Therefore, it makes use of the characteristics of memristor in this paper. The proposed model is based on the traditional three-Gauss model and changes the model parameters by using the dynamic characteristics of memristive cross array according to the local characteristics of the image to be processed, in order to achieve the purpose of local optimization and make the whole image obtain better enhancement effect. First of all, according to the local brightness information of the image, the polarity and the width of the pulse voltage required by the memristor are determined. Then, the values of the model parameters corresponding to the memristance can be obtained. Finally, the local enhancement template will be available to realize the enhancement. In this paper, the color and gray images are selected. The qualitative and quantitative experimental results show that the proposed adaptive three-Gauss model based on memristive cross array can not only effectively enhance the edge contour of the image, but also greatly improve the image contrast and clarity. Moreover, it provides a new direction for the application of memristor to image processing.

2017, 66 (12): 127801.
doi: 10.7498/aps.66.127801

Abstract +

The transient changes of free electron density distribution and light field intensity during the interaction between the femtosecond Gaussian laser pulses and millimeter scale water droplets are studied. Based on the nonlinear Maxwell's equations and the ionization rate equation, a transient coupled model is proposed to describe the laser plasma produced in water droplet. The changes of electron density and light field with time are obtained by the finite element method.
The calculation results show that the laser induced breakdown threshold in the droplet is about 2 TW/cm2, one quarter of that in a boundaryless water medium under the same condition. We find that the region of plasma generated in the droplet will move along the laser direction at first, however, when the incident laser intensity becomes larger, it will move in the direction opposite to the laser beam propagation and the plasma shielded effect becomes more obvious. The laser beam converged by the droplet focuses outside the droplet, and its power density is five times larger than that of the incident laser. There happen the laser pulse duration compression and waveform distortion at the focus point due to the plasma absorption, and the absorption energy increases with the laser intensity increasing and reaches a saturation finally.
We expect the model and calculation results to be able to be used for the study of laser pulse propagation in cloud or rain, the precision control of droplet by laser or eye surgery by laser, and other laser technology applications.

2017, 66 (12): 127201.
doi: 10.7498/aps.66.127201

Abstract +

Spin-transfer effects induced by spin-polarized current in the spin valve structures present a platform for studying different static and dynamic magnetization states sustained or driven by current. Especially, it can excite some new magnetic states and cause magnetization reversal and precession, which offers some promising applications in data processing and microwave emission. However, most of researches so far have focused on the spin valve structure with parallel or perpendicular anisotropy. Compared with the spin valve structure with parallel or perpendicular anisotropy device, the spin valve structure with a tilted polarizer is also hopeful for its potential application in fast-switching and high-density magnetic recording. Moreover, the tilted polarizer provides a new way to control the spin torquedriven magnetization dynamics in spin valve structure. In this paper, the magnetization reversal and precession driven by the spin-transfer torque in spin valve structures with a perpendicular free layer and a tilted polarizer layer are investigated theoretically. By linearizing the Landau-Lifshitz-Gilbert equation including the spin-transfer torque, two coupled dynamically evolutive equations and new equilibrium directions are obtained. Performing stability analysis for all new equilibrium directions and taking [Co/Ni]4 multilayers as an illustrative example, we obtain the phase diagrams of magnetic states defined in parameter space spanned by external magnetic field and current density. Several magnetic states, including quasi-parallel stable states, quasi-antiparallel stable states, out-of-plane precession, and bistable states are distinguished in the phase diagrams. Through adjusting the magnitudes of current density and external magnetic field, the switching from stable states to precessional ones and the reversal between two stable states can be realized, and the reversal current increases with the external magnetic field increasing. Meanwhile, we portray the phase diagram of magnetic states defined in parameter space spanned by current density and the direction of tilted polarizer. In this case, the out-of-plane precession does not emerge as the current density and external magnetic field are relatively small. Affected by the directions of spin polarizer, the reversal current of magnetization is lowest when the direction of spin polarizer is parallel to the easy axis of free-layer, and is largest when the direction of spin polarizer is perpendicular to the easy axis of free-layer. Selecting the different directions of the polarized-layer magnetization provides an alternative way to improve the efficiency of current-driven microwave emitting and magnetization reversal. By solving temporal evolution equations numerically, the behaviors of different magnetic states are shown and the validities of the phase diagrams are confirmed.

2017, 66 (12): 127302.
doi: 10.7498/aps.66.127302

Abstract +

In this paper, we discuss the diffusion motion of carriers in the transistor channel in a terahertz frequency range, and propose an resistance-capacitance-inductance (RCL) model based on Boltzmann transport theory, and then put forward the rules to determine whether the diffusion part in the RCL model can be neglected for terahertz field-effect-transistor (FET) detectors. The traditional RCL model for FET detectors is based on classic kinetic theory. In this model only the drift and the scattering motion of the carrier density in transistor channel are considered, and the diffusion part is neglected without giving any explanation. To solve this problem, in this paper we adopt three steps: first, instead of classic kinetic theory, the equations of RCL transistor model including diffusion part are derived from Boltzmann transport equation, and by comparing the two models, the specific expression for the diffusion part is given. Second, the differences between the two models are calculated and simulated, including the conductivity in quasi-static mode and the current response in high frequency mode, with different gate voltages, temperatures and working frequencies. Third, combined with the 3 rules, the conditions to neglect the diffusion motion in the model are put forward. The results show that the diffusion motion of the carriers is caused by the inhomogeneity of the carrier density, affected by the gate voltage, the temperature and the changing speed of the carriers with respect to the local voltage. In quasi-static mode, the role of diffusion part will change with the gate voltage, and when the gate voltage equals threshold voltage (which is the best working point for transistor detector), the diffusion part cannot be neglected, for which the reason is that a larger gate voltage will lead to a smaller inhomogeneity of channel carrier density and then a weaker diffusion effect, thus the effect of diffusion conductance on the whole transistor conductance becomes smaller. For the terahertz-frequency working mode, the diffusion part will depend on temperature and frequency. With temperature increasing, the current responsivity difference caused by the diffusion part in the model slightly decreases; when the working frequency increases but below 1 THz, the diffusion part can be neglected; however, when the working frequency is above 1 THz, the transistor model should contain drift, scattering and diffusion part at the same time, for which the explanation is that when the temperature increases, the random thermal motion of the carrier becomes larger, thus the diffusion effect will be stronger; and if the frequency increases, the number of the carriers in one terminal of the channel will change faster, but due to the channel damping, the number of the carriers in another terminal will always be zero, thus the changing speed of the carrier density between the two terminals will be faster, then a larger inhomogeneity of carrier density and a stronger diffusion effect will appear. In conclusion, normally the transisitor works at the threshold gate voltage, and at this point, the diffusion effect in the channel will increase with working temperature and frequency increasing, thus the diffusion part in the model cannot be neglected. The results in this paper make a significant contribution to a more accurate terahertz transistor detector model.

2017, 66 (12): 127303.
doi: 10.7498/aps.66.127303

Abstract +

In this paper, the time-reversal (TR) symmetry broken quantum spin Hall (QSH) in Lieb lattice is investigated in the presence of both Rashba spin-orbit coupling (SOC) and uniform exchange field. The Lieb lattice has a simple cubic symmetry, and it has three different sites in each unit cell. The most distinctive feature of this model is that it contains only one Dirac-cone in the first Brillouin zone, where the upper dispersive band and the lower dispersive band touch the middle zero-energy band at M point and form a cone-like dispersion. The intrinsic SOC is essentially needed to open the full energy gap in the bulk. When the intrinsic SOC is nonzero, all the band structures are separated everywhere in the Brillouin zone and can be characterized by some topological invariants. The exact QSH first put forward by Kane and Mele in 2005 is characterized by the z2 number. The protection from the TR symmetry ensures the gapless crossing in the surface state in the bulk gap. In our model, the presence of the exchange field breaks the TR symmetry, which results in opening a small gap in the crossing point and the z2 topological order is not suitable for the system. This kind of state is a TR symmetry broken QSH, which is characterized by the spin Chern numbers. The spin Chern numbers have a much wider scope of application than z2 index. It is suitable for both TR symmetry system and the TR symmetry broken system. For Lieb lattice ribbons, the spin polarization and the wave-function distributions are obtained numerically. There exists a weak scattering between the counter-propagating states in the TR symmetry broken QSH, and the spin transport along the boundary with a low dissipation replaces the dissipationless spin current in a TR symmetry system. In experiment, such a system can be realized by the two-dimensional Fermi gases in optical lattice with Lieb symmetry. The above conclusions are expected to give theoretical guidance in the spin device and the quantum information.

2017, 66 (12): 127701.
doi: 10.7498/aps.66.127701

Abstract +

With the rapid development of the science and technology, the application of the high voltage power cable has become more and more extensive. Now, it is generally accepted that space charge has an important effect on the electrical properties of insulating material in a high voltage cable. The measurement of space charge is the research base for the behaviors and properties of space charge in the polymer dielectric. Actually, the pressure wave propagation (PWP) method and pulsed electroacoustic (PEA) method are two sophisticated methods of measuring the space charge. However, these two methods are based on a planar sample. For measuring the space charge in a real cable, it is necessary to need the correct and precise mathematical expressions for the PWP method and PEA method.
According to the theoretical analysis of the space charge distributions in the plate samples, measured by the pressure wave propagation method, we propose a physical model and its mathematical method of treating space charge distribution data measured in a coaxial geometry. In terms of Poisson equation, the influences of pressure waves on coaxial samples can be divided into two parts, namely, sample deformation and particle displacement. These two parts take into consideration the variations of the sample electric field, dielectric constant and density of space charge disturbed by pressure waves. Therefore, the voltage and current equations about the space charge distribution in the coaxial structure are found. The mathematical expression for the current measured indicates that compared with the current measured in the planar structure, which is proportional to the space charge distribution, the current signal measured in the coaxial structure should be further corrected.
This paper also shows the experimental results which are the induced current signals picked from the planar sample and coaxial sample respectively. The results indicate that the current measured in the planar sample is proportional to the space charge distribution. However, the current measured in the planar sample is related to the inner and outer diameter of the dielectric, which verifies the correctness of the mathematical expression.
Due to the influence of the coaxial structure of the high voltage cable, the pressure wave focusing effect is obvious as the pressure wave propagates along the axis, which causes the measurement signal to increase gradually with the propagation of sound wave. As a consequence, the electric field and the space charge density will change apparently. Due to the influence of the pressure wave focusing effect, the current and voltage signal will be amplified more obviously in cable, and the current measured by the PWP method shows the distribution of space charge density in cable.

###### ATOMIC AND MOLECULAR PHYSICS

2017, 66 (12): 123401.
doi: 10.7498/aps.66.123401

Abstract +

The effect of reagent vibrational excitation on the stereodynamical properties of H(2S)+CH+(X1+)C+(2P)+H2(X1g+)reaction is investigated by quasi-classical trajectory method on a globally smooth ab initio potential surface of the 2A' state at a collision energy of 500 meV. The reaction probability and the reaction cross-section are also studied. In the calculation, the vibrational levels of the reactant molecules are taken as v = 0, 1, 3, 5 and j = 0, respectively, where v is the vibrational quantum number and j is the rotational quantum number. The calculation results show that the reaction probability reaches a maximum when v = 1, and then decreases with the vibrational quantum number increasing. The integral cross-section decreases sharply with the increase of vibrational quantum number. The potential distribution P(r), the dihedral angle distribution P(r), and the polarization-dependent generalized differential cross sections are calculated. P(r) represents the relation between the reagent relative velocity k and the product rotational angular momentum j'. P(r) describes the correlation of k-k'-j', in which k' is the product reagent relative velocity. The peak of P(r) is at r = 90 and symmetric with respect to 90, which shows that the product rotational angular momentum vector is strongly aligned along the direction perpendicular to the relative velocity direction. The peak of P(r) distribution becomes increasingly obvious with the increase of the rotational quantum number. The dihedral angle distribution P(r) tends to be asymmetric with respect to the k-k' scattering plane (or about r= 180), directly reflecting the strong polarization of the product angular momentum for the title reaction. Each curve has two evident peaks at about r = 90 and r = 270, but the two peak intensities are obviously different, which suggests that j' is not only aligned, but also strongly orientated along the Y-axis of the center-of-mass frame. The peak at r= 90 is apparently stronger than that at r = 270, which indicates that j' tends to be oriented along the positive direction of Y-axis. In order to validate more information, we also plot the angular momentum polarization in the forms of polar plots r and r. The distribution of P(r; r) is well consistent with the distribution P(r) and also the distribution P(r) of the products at different vibrational quantum states. In addition, the polarization-dependent differential cross section is quite sensitive to the reagent vibrational excitation. Based on the obtained results, we find that the observed excess of the methylidyne cation CH+ is closely related to the reactant of vibrational excitation in interstellar chemistry.

2017, 66 (12): 123101.
doi: 10.7498/aps.66.123101

Abstract +

Energy levels of the core-excited high-spin Rydberg states (4,5,6L, L = S, P) in boron atom (ion) are calculated by the Rayleigh-Ritz variation method with using large-scale multi-configuration wave functions. The important orbital-spin angular momentum partial waves are selected based on the rule of configuration interaction. The computational convergence is discussed by the example of the contribution from each partial wave in the non-relativistic energy calculations of the high-spin state 1s2s2p2 5Pe in B+ ion. To saturate the wave functional space and improve the non-relativistic energy, the restricted variational method is used to calculate the restricted variational energy. Furthermore, the mass polarization effect and relativistic energy correction are included by using a first-order perturbation theory. The quantum electrodynamic effects and higher-order relativistic contributions to the energy levels are also calculated by the screened hydrogenic formula. Then, the accurate relativistic energy levels of these high-spin states of B atom (ion) are obtained by adding the non-relativistic energy and all corrections. The fine structure splitting of these high-spin states is also calculated by the Breit-Pauli operators in the first-order perturbation theory. Compared with other theoretical results, our calculation results are in good accordance with the experimental data.
The absorption oscillator strengths, emission oscillator strengths, absorption rates, emission rates, and transition wavelengths of the electric-dipole transitions between these high-spin states of B atom (ions) are systematically calculated by using the optimized wave functions. The oscillator strengths and transition rates are obtained in both the length and velocity gauges. By comparing the two gauge results of oscillator strength, we find that there is a good consistency between them when fl 0.3, and a reasonable consistency is obtained when fl 0.3. The accordance between the length and the velocity gauge results reflects that the calculated wave functions in this work are reasonably accurate. The calculated transition data are also compared with the corresponding experimental and other theoretical data. Good agreement is obtained except the wavelengths for two transitions: 1s2p4p 4Se1s2p3d 4P and 1s2p4d 4P1s2p3p 4Pe. The relative differences between our theoretical results and experimental data are 0.7% and 0.3%, respectively. They need to be verified by further theoretical and experimental studies. For some core-excited high-spin states, the related energy levels and transition data are reported for the first time. Our calculation results will provide valuable data for calculating the spectral lines in the relevant experiments.

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

2017, 66 (12): 125202.
doi: 10.7498/aps.66.125202

Abstract +

The radiation hydrodynamics code MULTI-2D, which was developed by Ramis et al. in 2009 (2009 Comput. Phys. Commun. 180 977) and adopted the single temperature fluid and unstructured lagrangian mesh, is modified into a radiation magnetohydrodynamics code MULTI2D-Z by adding the program module of evolution equation of magnetic field, and self-consistently considering the Lorentz force in the module of motion equation and the Ohmic heating in the module of energy equation. The newly developed module for magnetic field was validated to be reliable. The module is used to study the magnetic field diffusion process, and it is found that the diffusion is weakened due to the increasing of plasma temperature and density and the fluid convection, in which there is minus grads of velocity in radial direction. The new code MULTI2D-Z is used to simulate the formation process of dynamic hohlraum driven by tungsten wire-array Z-pinch at an 8 MA current level. The obtained results are that X-ray power and energy are, respectively, ～30 TW and ～300 kJ, radiation temperature in foam is ～120 eV, and the implosion trajectory of wire-array is also obtained. The calculated results reveal that the magnetic field is mainly distributed in the outside of tungsten plasma during the hohlraum formation. The foam expands due to the radiation heating from the shock wave created by the collision between wire-array plasma and the foam. The thermal radiation wave, which is characterized by radiation temperature, spreads towards the central axis faster than the plasma temperature. When the thermal radiation wave spreads to the central axis, the radiation temperature becomes comparatively uniform in space, and is almost equal to the plasma temperature except at the place of the shock wave. These results help the people to better understand the magnetic field diffusion and convection in Z-pinch, as well as the formation mechanism of dynamic hohlraum driven by wire-array Z-pinch. It is also indicated that the newly developed code MULTI2D-Z can be considered as a new tool for simulating Z-pinch and its applications, such as inertial confinement fusion and magnetically accelerated flyer plates.

## EDITOR'S SUGGESTION

2017, 66 (12): 125201.
doi: 10.7498/aps.66.125201

Abstract +

A green emission layer caused by lithium impurity is universally observed in plasma boundary region of Experimental Advanced Superconducting Tokamak (EAST) via a visible-light camera, where lithium coating is normally adopted as a routine technique of wall conditioning. In this article, in order to estimate the spatial distribution of green light intensity of this emission layer according to the given real parameter distributions of edge plasmas, a practicable method is proposed based on a collisional-radiative model. In this model, a finite number of energy levels of lithium are taken into account, and proper simplifications of convection-diffusion equations are made according to the order-of-magnitude analysis. We process the atomic data collected from the OPEN-ADAS database, and develop a corresponding program in Mathematica 10.4.1 to solve the simplified one-dimensional problem numerically. Estimation results are obtained respectively for the two sets of edge plasma profiles of EAST in L-mode and H-mode regimes, and both clearly show a good unimodal structure of the spatial distribution of green light intensity of this emission layer. These analyses actually provide the spatial distributions of lithium impurities at different energy levels, not only indicating the spatial distribution of the intensity of this emission layer induced by lithium impurity but also revealing the physical processes that lithium experiences in edge plasma. There are some different and common characteristics in the spatial distribution of the intensity of this emission layer in these two important cases. This emission layer is kept outside the last closed magnetic surface in both cases while it becomes thinner with a higher intensity peak in H-mode case. Besides, the sensitivity of this algorithm to the measurement error of edge plasma profile is also explored in this work. It is found that the relative errors of the numerical results obtained by our proposed method are comparable to those of edge plasma profiles. This work provides important theoretical references for developing a new practical technique of fast reconstructing edge plasma configurations in EAST based on the emission of lithium impurity, and may further contribute a lot to the studies of edge plasma behaviors when three-dimensional perturbation fields are adopted.

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

2017, 66 (12): 128201.
doi: 10.7498/aps.66.128201

Abstract +

In various energy conversion and storage devices, supercapacitors have been extensively used due to their high power densities, fast delivery rates, and exceptionally long cycle lives. However, the low specific capacitances and low energy densities of supercapacitors largely hinder widespread applications in large-scale energy conversion and storage systems. To improve the specific capacitances of the supercapacitors, the surface areas of the electrode materials should be made as large as possible to allow the capturing and releasing of particles (such as ions, molecules, or electric charges). Here in this work, we demonstrate an efficient approach to the large-scale production of Co3O4 mesoporous nanostructure supported by Ni foam via a simple hydrothermal synthesis followed by ambient annealing at 300 ℃ for 4 h. The designed and fabricated Co3O4 mesoporous nanostructures directly serve as binder- and conductive-agent-free electrodes for supercapacitors, which thus provide more chemical reaction sites, shorten the migration paths for electrons and ions, and improve the electrical conductivity. By taking advantage of the structural features and excellent electronic conductivity, the Co3O4 exhibits the ultrahigh specific capacitances (1.87 Fcm-2 (936 Fg-1) and 1.80 Fcm-2 (907 Fg-1) at current densities of 2.5 mAcm-2 and 5.5 mAcm-2, respectively), high rate capacitances (48.37% of the capacitance can be retained when the current density increases from 2.5 mAcm-2 to 100 mAcm-2) and excellent cycling stability (92.3% of the capacitance can be retained after 4000 charge/discharge cycles at a current density of 10 mAcm-2). The nanostructuring approach and utilizing a binder- and conductive-agent-free electrode can be readily extended to other electrochromic compounds of high-performance energy storage devices.

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

2017, 66 (12): 129101.
doi: 10.7498/aps.66.129101

Abstract +

With the system upgrading and construction demand for new generation global navigation satellite system (GNSS), the navigation signal modulation and multiplexing technology have made great progress. Up to now, many modulation modes for single signal component and many constant-envelope multiplexing methods for multiple signal components have been proposed, meanwhile the new signal structure continues to be presented. The satellite navigation signal code delay estimation error is the most critical factor that determines system service performance. Therefore, it is urgent to give an overall performance evaluation on code delay estimation error of GNSS signals with different modulation and multiplexing modes, and consequently provide a crucial selection basis for subsequent system application. The code delay estimation error is related to not only signal structure, but also receiver's receiving model and processing method of code tracking loop. The receiving models of new generation navigation receivers can be classified as two types. One is matched receiving model which means that the reference signal is the same as receiving signal, and the other is unmatched receiving model, where the reference signal is not the same as receiving signal. Recently, the unmatched receiving model has been extensively applied to the processing of binary offset carrier class signals.
Therefore, in this paper we propose an integrated evaluation method for code delay estimation error of navigation signals. Firstly, the equivalent model for the code tracking loop of navigation receivers is generalized and the current navigation receivers are classified as four types based on whether matched receiving or coherent processing is used. Because the code delay estimation error is dependent on the type, it is necessary to provide an evaluation method for each type. Then, on the assumed condition that the code delay estimation error is very small, the expressions of code delay estimation error for coherent processing and non-coherent processing under matched receiving model are respectively presented and the relationships between each other are discussed under various noise environments and the code loop interval going to zero. The expression of code delay estimation error for non-coherent processing under unmatched receiving model is derived and the relationship with coherent processing is discussed under the same condition as matched receiving model. Finally, the Ziv-Zakai bound of code delay estimation error is derived, which provides a perfect evaluation method when the code delay estimation error is not very small. The proposed method is expressed by power spectrum density of navigation signals, which provides important theoretical guidance for signal design and receiver development, and simultaneously brings great convenience to the evaluation of the signal. Simulation experiment attests to effective evaluation on the code delay estimation error of new generation typical navigation signals.

2017, 66 (12): 129501.
doi: 10.7498/aps.66.129501

Abstract +

Adaptive optics (AO) system which is widely used in astronomical observations can improve the image quality by the real-time measurement and correction of the wave-front. One of the main problems in the AO system is the poor quality of the image because of the system noises. The noises in AO system are additive noises. The main sources of the noises are the background noise, the photon noise, and the readout noise of charge-coupled device. The background noise is distributed evenly and is easy to process. The photon noise is dependent on the characteristics of the spot itself. Readout noise, which is Gaussian distribution with the mean value of 0 and the variance of 2, is the main noise source in AO system. In this paper, we focus on the readout noise and propose a new regularization model to remove additive noises from the AO system. In this model, the regularization parameters can be adaptively changed. A nonconvex regularization term is used to make the homogeneous region of the image smooth efficiently, while the integrity of the spot can be well restored. The properties of the regularization proposed are shown below. 1) The proposed nonconvex regularization term can act as the L0 norm which is sparser than L1 norm. 2) The proposed model can protect the edge of the spot from over smoothing. To prevent the edges from over smoothing, the regularization parameter must be an increasing function. Moreover, it converges to a constant so that it cannot affect the strong gradient of the image. 3) The regularization term proposed is nonconvex which is more sensible to the minor change of the image. Therefore, the edges of the image can be better preserved. Though the proposed model can well preserve the edges of the spot, it is difficult to resolve by traditional methods because of the nonconvexity. Split Bregman algorithm and augmented Lagrangian duality algorithm are used to solve this problem. We can obtain a denoised spot image as well as an edge indicator by using the proposed model. The visual and quantitative evaluations are used to value the restored images. The evaluating indicators are the peak signal-to-noise ratio and centroid detecting error which includes the root mean square and the peak valley value of the centroid deviation. The simulation and experimental results show the efficiency of this model in removing the additive noises from the AO system.