## Vol. 65, No. 19 (2016)

##### 2016-10-05

###### GENERAL

2016, 65 (19): 190301.
doi: 10.7498/aps.65.190301

Abstract +

When the optical signal is transmitted in the free space, it inevitably passes through the atmosphere. The atmospheric aerosol is one of the most important components of the atmosphere, which not only affects the regional climate, but also influences the transmission of the free space optical signal. However, the study on the relationship between the non-spherical aerosols and the parameters of the free space quantum communication channel has not been carried out so far. To investigate this relationship, the spectral distribution function of the aerosol and its extinction factor should be analyzed first. According to three nonspherical aerosol particles: cylindrical particles, ellipsoidal particles and Chebyshev particles, the equation between channel attenuation of the free space quantum communication and the degree of quantum entanglement can then be established. After that, the effects of the relative humidity of the atmosphere on the degree of quantum entanglement and the fidelity of quantum communication can be analyzed and simulated finally. The simulation results show that the channel attenuations of the free space quantum communication are sequenced in ascending order as cylindrical particles, ellipsoidal particles, and Chebyshev particles, and their influences on the degree of quantum entanglement have different changing trends. When the transmission time is fixed, with the increase of aspect ratio of ellipsoidal particles, the degree of quantum entanglement shows a growing trend, with the increase of aspect ratio of cylindrical particles, the degree of quantum entanglement shows descending trend. With the increase of Chebyshev particle equivalent radius, the degree of quantum entanglement also shows the descending trend. When the relative humidity of the atmosphere is 0.2(0.9), the degree of quantum entanglement and the fidelity of quantum communication will be 0.72(0.75) and 0.32(0.22), respectively. It can be seen that the nonspherical aerosol particles and the relative humidity of the atmosphere each have a significant effect on the function of the free space quantum communication system. Therefore, in a practical free space quantum communication system, the shape factor of nonspherical aerosol particle, orientating factor, equivalent radius and the relative humidity of the atmosphere cannot be ignored, in order to improve the effectiveness and reliability of the free space quantum communication, the different parameters of the communication system should be adjusted adaptively.

## EDITOR'S SUGGESTION

2016, 65 (19): 190501.
doi: 10.7498/aps.65.190501

Abstract +

Sample entropy, a complexity measure that quantifies the new pattern generation rate of time series, has been widely applied to physiological signal analysis. It can effectively reflect the pattern complexity of one-dimensional sequences, such as the information contained in amplitude or period features. However, the traditional method usually ignores the interaction between amplitude and period in time series, such as electroencephalogram (EEG) signals. To address this issue, in this study, we propose a new method to describe the pattern complexity of waveform in a two-dimensional space. In this method, the local peaks of the signals are first extracted, and the variation range and the duration time between the adjacent peaks are calculated as the instantaneous amplitude and period. Then the amplitude and period sequences are combined into a two-dimensional sequence to calculate the sample entropy based on the amplitude and period information. In addition, in order to avoid the influence of the different units in the two dimensions, we use the Jaccard distance to measure the similarity of the amplitude-period bi-vectors in the waveforms, which is different from the one-dimensional method. The Jaccard distance is defined as the ratio of the different area to the combined area of two rectangles containing the amplitude-period bi-vectors in the Cartesian coordinate system. To verify the effectiveness of the method, we construct five sets of simulative waveforms in which the numbers of patterns are completely equal in one-dimensional space of amplitude or period but the numbers in two-dimensional space are significantly different (P0.00001). Simulation results show that the two-dimensional sample entropy could effectively reflect the different complexities of the five signals (P0.00001), while the sample entropy in one-dimensional space of amplitude or period cannot do. The results indicate that compared with the one-dimensional sample entropy, the two-dimensional sample entropy is very effective to describe and distinguish the complexity of interactive patterns based on amplitude and period features in waveforms. The entropy is also used to analyze the resting state EEG signals between well-matched depression patient and healthy control groups. Signals in three separated frequency bands (Theta, Alpha, Beta) and ten brain regions (bilateral: frontal, central, parietal, temporal, occipital) are analyzed. Experimental results show that in the Alpha band and in the left parietal and occipital regions, the two-dimensional sample entropy in depression is significantly lower than that in the healthy group (P0.01), indicating the disability of depression patients in generation of various EEG patterns. These features might become potential biomarkers of depressions.

2016, 65 (19): 190502.
doi: 10.7498/aps.65.190502

Abstract +

To study the application of memristor in chaotic system, we employ the smooth continuous nonlinear flux-controlled memristor model and feedback control technique to design a hyperchaotic system based on the simplified Lorenz system. By using memristor as a positive feedback of the simplified Lorenz system, the dimensionless mathematical model is derived. The differences between the memristor-based chaotic system and ordinary chaotic system are then further studied. Firstly, the stable equilibrium and unstable equilibrium point sets of the system are analyzed theoretically, and it is found that the system has infinite equilibrium points including stable and unstable equilibrium points. The stable and unstable ranges of the system with different parameters are also determined. Theoretical analysis shows that the system has the same symmetry as the simplified Lorenz system. Thus the system has rich dynamical behaviors, such as limit cycle, chaotic attractor, and hyper-chaotic attractor. Secondly, by the methods of bifurcation diagram, Lyapunov exponent spectrum, Poincar section, and Spectral Entropy algorithm, the dynamical behaviors of the system are analyzed in detail. By calculating the Lyapunov exponent spectrum, the dynamical behaviors are studied and they change with system parameters and the initial conditions of memristor respectively. The maximum positive Lyapunov exponent of the memristor-based Lorenz hyperchaotic system is higher than that of the simplified Lorenz system, which indicates the memristor-based Lorenz hyperchaotic system is more complex. Further, we find all the complex dynamical behaviors to be coexisting with the infinite equilibrium sets, which is quite different from those of many ordinary hyper-chaotic systems. Meanwhile, we observe the attractors coexisting and state transition phenomenon in this system, caused by changing the initial conditions of the memristor. State transition phenomenon is then further studied by means of phase portraits and spectral entropy algorithm for the first time. Finally, by using operational amplifiers, diodes and other discrete components, we design an equivalent circuit of the smooth continuous nonlinear flux-controlled memristor model, and the equivalent circuit is used to design and realize the analog electronic circuit of the memristor-based Lorenz hyper-chaotic system. By using an analog oscilloscope, the phase portraits of hyper-chaotic attractor are observed clearly. The state transition phenomenon can also be seen using the oscilloscope. It is found that the circuit experimental results are in agreement with those of the theoretical analysis and numerical simulation. It verifies that the system is physically realizable, and lays a strong foundation for its applications in engineering. Next, we will try to investigate the chaotic secure communication based on this hyper-chaotic system.

2016, 65 (19): 190701.
doi: 10.7498/aps.65.190701

Abstract +

As a new optical detection technique,quartz enhanced photoacoustic spectroscopy (QEPAS) has been widely used in the field of trace gas detection,which has an outstanding performance because of its advantages of extremely high sensitivity,high selectivity and compact absorption detection module.The most important factor of the detection sensitivity for QEPAS sensor is the acoustic wave enhancement.For increasing the acoustic enhancement,great effort has been devoted to the investigations by increasing laser power,employing tube resonators and using custom-made acoustic transducers.However,less attention has been paid to the elliptical cavity enhancement photoacoustic spectroscopy.In this work,novel quartz enhanced photoacoustic spectroscopy based on an elliptical cavity is proposed,which employs two quartz tuning forks and an elliptical cavity to further enhance the acoustic wave.The analysis and optimization of the elliptical cavity are also demonstrated.
For the elliptical cavity QEPAS sensor,the acoustic enhancement properties can be influenced by resonant modes, coupling between laser and acoustic wave,and dimension of the cavity.Based on the Helmholtz wave equation,the acoustic modes and corresponding resonance frequency can be quantized.To further investigate the acoustic wave resonance inside the cavity,the model of the cavity is established in Comsol Multiphysics software with finite element method.The acoustic pressure,quality factor can be obtained numerically by the software.With the model,parameters of the spectrophone are investigated,including the resonant modes,laser incidence angle and dimension of the elliptical cavity.As a result,the (2,1) resonant mode is selected as the enhancement mode in the cavity,in which the maximum acoustic pressure is achieved at the ends of the long axis.By changing the incidence angle of the laser beam from 0 to 90,the performance of the sensor is analyzed,which indicates that the laser incidence angle has little influence on acoustic properties except for 30.This is due to the interaction of other resonant modes at this incidence angle.With the length of half-long axis varying from 4.8 mm to 5.2 mm,eccentricity from 0.5 to 0.8 and the cavity height from 0.4 mm to 0.8 mm,the resonance frequency,acoustic pressure and quality factor are studied.It reveals that there is an optimal length of half-long axis for a fixed eccentricity,and a relative large height is beneficial to enhancing the acoustic pressure.On the whole,a set of parameters is identified for the optimal sensor performance.
By optimizing and designing the spectrophone,the experiment is conducted,in which a laser (1578 nm) and H2S as the sample gas are used.The detection limit of H2S gas of 6.3 ppm is achieved and the corresponding Normalized noise equivalent absorption coefficient (NNEA) is 2.0210-9cm-1W/Hz1/2.Finally,several H2S detection results of other QEPAS methods are listed and compared for demonstrating the high detection sensitivity of the sensor.This work may contribute to the research of high sensitivity photoacoustic detection.

###### NUCLEAR PHYSICS

2016, 65 (19): 192101.
doi: 10.7498/aps.65.192101

Abstract +

Using shell model to calculate the nuclear systems in a large model space is an important method in the field of nuclear physics.On the basis of the nuclear shell model,a large symmetric non-orthonormal sparse Hamiltonian matrix is generated when adopting the generalized seniority method to truncate the many-body space.Calculating the energy eigenvalues and energy eigenvectors of the large symmetric non-orthonormal sparse Hamiltonian matrix is of indispensable steps before energies of nucleus are further calculated.In the mean time,some low-lying energy eigenvalues are always the focus of attention on the occasion of large scale shell model calculation.In this paper,by combining reorthogonalization Lanczos method with Cholesky decomposition method and Elementary transformation method,converting the generalized eigenvalue problems into the standard eigenvalue problems,and transforming the large standard eigenvalue problems into the small standard eigenvalue problems,we successfully calculate the eigenvalues and eigenvectors of large non-orthonormal sparse matrices with the help of computers with limited memory.The values obtained by using this method to calculate the small matrix agree with the exact values,which demonstrates that this method is accurate and can be used to calculate the energy eigenvalues and energy eigenvectors of large symmetric nonorthonormal sparse matrix.We take 116Sn (s=8,the number of unpaired particles,namely the generalized seniority) as an example in which there are active valence neutrons but inert protons at the magic number,and calculate ten of its lowest energy eigenvalues.Through calculation,we find that among these low-lying energy eigenvalues,the lowest energy eigenvalue converges fastest.A comparison between the calculation values and the experiment values shows that the difference between the calculated high-lying energy eigenvalue and its corresponding experimental one arrives at hundreds of keV,while for the low-lying energy eigenvalue,its calculation value can reach an accuracy of a few tens of keV.The results demonstrate that the Lanczos method is feasible in Matlab programming and shell model calculations. The significance of this research lies in the fact that this method will not only greatly help to calculate and obtain the low-lying energy eigenvalues of some medium-mass and heavy nuclei,but also possess great importance in calculating partial eigenvalues involved in large matrices in other theoretical researches and engineering designs.

###### ATOMIC AND MOLECULAR PHYSICS

2016, 65 (19): 193301.
doi: 10.7498/aps.65.193301

Abstract +

The ozone layer which absorbs harmful solar UV radiation is a necessary umbrella for human beings and biosphere. A large amount of alkyl halide including freon exhausted by human into the atmosphere poses a great threat to the ozone layer. Freon dissociates into the product of halogen radical, like Br and Cl, induced by UV sunlight radiation, which is found to be the main culprit for the destruction of atmospheric ozone. In this paper, time-of-flight (TOF) mass spectrometry and velocity map imaging technique are employed for investigating the multiphoton dissociation dynamics of Freon F114B2 (C2F4Br2) induced by femtosecond UV radiation at 267 nm. Fragment mass spectra of C2F4Br2 under UV radiation at 266 nm are obtained by TOF mass spectrometry. Three daughter ions C2F4Br+, C2F4+ and CF2Br+are discovered together with the parent ions C2F4Br2+. And three corresponding photodissociation mechanisms are concluded as follows: 1) C2F4Br2+C2F4Br++Br with single CBr bond breaking and direct production of Br radical; 2) C2F4Br2+C2F4++2Br with double CBr bonds breaking and production of two Br radical; 3) C2F4Br2+CF2Br++CF2Br with CC bond breaking. Velocity map images of the strongest daughter ion C2F4Br+with CBr breaking are measured by imaging apparatus. The kinetic energy distribution of C2F4Br+ ions is obtained from the measured velocity map images. And it can be well fitted by three Gaussian curves which describe normal distribution. It indicates that the production of the fragment C2F4Br+ stems from three different dissociation channels. Additional photodissociation dynamics is obtained by analyzing the angular distribution of the measured image. The values of anisotropy parameter are measured to be 0.1 (for the low energy channel), 0.8 (for the middle energy channel) and 1.4 (for the high energy channel) for the fragment C2F4Br+, respectively. The ratios of parallel transition to perpendicular transition are determined for three different channels. In addition, density functional theory calculations are also performed for further analysis and discussion. The optimized geometries of ground state and ionic state of C2F4Br2 are obtained and compared at the level of B3LYP/6-311G++(d, p). The calculated information about ionic states, including energy level and oscillator strength for the ionic excited states, are given.

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

2016, 65 (19): 194101.
doi: 10.7498/aps.65.194101

Abstract +

In order to solve the problems of rapidly recognizing the shapes of the tumour in the stomach, a new kind of capsule endoscopy with through-body radar is utilized for the first time. Finite difference time domain method is used to establish an electromagnetic simulation model of stomach. After being swallowed by a patient, the capsule which consists of the radar moves through esophagus and stomach. Finally it drains out of the body by the self peristalsis of the human GI tract. During this time, the radar is used to transmit accurate radar data of human stomach. Then we will carry out electromagnetic inverse scattering imaging by back projection algorithm with the radar data. The algorithm must consider the influence of various tissues in the human body: the attenuation of the signal strength of electromagnetic waves, the decrease in speed and the refraction due to the different permittivities between the different organs of the body. These factors will eventually lead to image offset, and even generating a virtual image. It is effective to refrain the displacement of image with modifying the time element of the imaging algorithm by iteration. It is shown that ultra-wideband radar built-in capsule endoscopy can track and locate targets in the human's stomach.

2016, 65 (19): 194201.
doi: 10.7498/aps.65.194201

Abstract +

In recent years,sparse representation theory has acquired considerable progress and has extensively been used in visual tracking.Most trackers used the sparse coefficients to merely calculate the position of the target according to the reconstruction error relative to sparse coefficients,and often neglected the information contained by representation residual matrix in representing step.Consequently,we present a novel sparse representation based tracker which takes representation residual matrix into consideration.First of all,at initialization of a new frame,we reconstruct the frame by singular value decomposition (SVD) to eliminate noise and useless information,which contributes a friendly frame for the following representation step.To obtain the compact representation of the target,we build L2-norm regularization according to the distance between the candidates wrapped in particle framework and the reconstruction calculated by dictionary templates and residual matrix.Additionally,we use the L1-norm constraint to restrict the sparse coefficients and the residual matrix of each candidate.Secondly,as the built optimization problem does not have closed-form solution,we design a method to compute the coefficients and the residual matrix iteratively.During each iteration,the coefficients are obtained by solving classical least absolute shrinkage and selectionator operator (LASSO) model,and the residual matrix is achieved by shrinkage operation.After solving the optimization problem,we compute the score of each candidate for evaluating the truth target with considering coefficients and residual matrix.The score is formulated as weighted reconstruction error which consists of dictionary templates,candidates,coefficients and residual matrix. The weight is the exponential value of absolute value of elements in residual matrix.Finally,for capturing the varying appearance of target in series,we update the dictionary template with assembled template,which is composed of residual matrix,selected candidate and dictionary template.In this paper,the template to be replaced is determined according to the score which is inversely proportional to the distance between the selected candidate and each dictionary template. Then we update the dictionary frame by frame during tracking process.Contributions of this work are threefold:1) the representation model captures holistic and local features of target and makes the tracker robust to varying illumination, shape transformation,and background clutter,profiting from preprocessing of SVD reconstruction,the model exhibits a more compact representation of target without disturbance of noisy variance;2) we employ a weight matrix to adjust reconstruction error in candidate evaluation step,as described above,the weight matrix strengthens the effect of error in residual matrix for evaluating candidates from which target is selected,it is noted that weights are all greater than one,which leads to reconstruction error expanding according to the error value of residual matrix,and keeps pixels where there is small error value believable for evaluation;and 3) we adopt an assembled template to update dictionary template and reconstruction of coefficients of selected candidate,which alleviates dictionary degradation and tracking drift problems and provides an accurate description of new appearance of target.In order to illustrate the performance of the proposed tracker,we enforce the algorithm on several challenging sequences and compare the proposed algorithm with five state-of-art methods,whose codes are all supplied by the authors.For complete illustration,both qualitative evaluation and quantitative evaluation are presented in experiment section.Through the experimental results,we could conclude that the proposed algorithm has a more favorable and robust performance than other state-of-art algorithms when dealing with kinds of situations during tracking.

2016, 65 (19): 194202.
doi: 10.7498/aps.65.194202

Abstract +

Degenerate correlated photon pairs (DCPPs) have been widely used in quantum information science,especially in the areas of quantum computation,quantum state control and precision measurement,which are typically generated in a (2) nonlinear crystal through the spontaneous parametric down-conversion.However,such a source is not compatible with optical fiber as large coupling losses occur when the pairs are launched into it,which restricts its direct application to quantum information processing system.More recently,DCPP generation from spontaneous four-wave mixing in (3) optical fiber has aroused strong interest,due to its advantages of compatibility with existing fiber networks and free of alignment.The process of generating DCPP in fiber can be described as follows:two pump photons at different frequencies p1 and p2 scatter through the (3) nonlinearity to create a pair of identical photons at the mean frequency c,such that p1+p2=2c.Because the collinear tensor component xxxx(3) in a Kerr nonlinear medium is 3 times as large as the tensor component xyxy(3),the co-polarized four-wave mixing is preferred,which means the two pump photons and new-born twin photons are both co-polarized.Therefore,it is very challenging to deterministically separate the fiber-based DCPP,since the twin photons share the same properties in all degrees of freedom:frequency,polarization and spatial.Sagnac fiber loop (SFL),composed of a piece of nonlinear fiber and 50/50 coupler,is presented as the splitter for DCPP based on the reversed Hong-Ou-Mandel quantum interference of counter-propagating DCPPs.The SFL can be configured as a total reflector,total transmitter or equally transmissive and reflective state,which sets the differential phases of counter-propagating DCPPs meeting at 50/50 coupler to be ,0 and -,respectively.In order to satisfy the differential phase requirement for completely splitting the DCPP,the SFL is always set to be equally transmissive and reflective state,however,the polarization-mode matching of counter-propagating DCPPs is not easily achieved due to the disturbance of fiber birefringence.According to the Jones matrix derivation of DCPP propagating in the SFL,the polarization mode of counter-propagating DCPPs when interference at 50/50 coupler is automatically matched,if the SFL is set as a total reflector or total transmitter.In experimental scheme,utilizing the SFL as a total reflector,the 1.1 nm bandwidth and 1544.53 nm central wavelength DCPPs are generated by two pulsed light beams pumping the 300 m dispersion-shifted fiber in the SFL.Using the two pieces of single mode fiber connecting the 300 m dispersion-shifted fiber and 50/50 coupler,whose length difference is fixed at 3.3 m,the differential phase of counter-propagating DCPPs highly dependent on the dispersion properties of single mode fiber is managed at 2 for fully distributing DCPPs into which degrades the fidelity of DCPP source.The measured ratio of coincidence to accidental-coincidence of DCPPs from one port is approximately 1.8:1,which indicates that the coincidence counts mainly originate from accidental coincidence counts and extra coincidence counts from photon bunching and there are not any DCPPs outputting from one port.Meanwhile,the ratio of best measured coincidence to accidental-coincidence of DCPPs from two ports reaches 47:1,when the average power of two pumps is fixed at 0.026 mW.The experimental results demonstrate that the high purity and fully spatial separation DCPPs are successfully prepared in optical fibers,which is a very useful tool for realizing various quantum information systems.How the spatial state of outputting DCPPs depends on the length difference between single-mode fiber and detuning wavelength is also discussed in detail.

2016, 65 (19): 194203.
doi: 10.7498/aps.65.194203

Abstract +

The output phase of the Sagnac interferometer has been measured with quantum balanced homodyne technique when coherent light and squeezed vacuum light are fed into the Sagnac interferometer simultaneously [Chen Kun et al., Acta Phys. Sin. 65 054203(2016)]. Nevertheless, there exist two deficiencies: 1) the phase sensitivity is related to the phase itself; 2) there are strict requirements for the phases of local oscillator light, coherent light and squeezed vacuum light.
For overcoming these deficiencies, an adaptive optimal measurement scheme is suggested for the phase estimation. Firstly, we calculate that the quantum Fisher information (QFI) of the squeezed vacuum and coherent state is sinh2r+||2e2r by treating them as a quantum pure state, for they satisfy a condition of the quantum pure state, namely ()=()2. The QFI is related to quantum Cramer-Rao lower bound which can be used to evaluate the performance of the estimator. Secondly, we make an analysis of positive operator-valued measure (POVM) and design a set of the optimal measurement operators for reaching the quantum Cramer-Rao lower bound, whereas the optimal measurement operators depend on the true value of the phase which is what we want to estimate. In order to solve the problem and estimate the parameter effectively, an adaptive method is suggested. We set an initial value of the phase parameter to obtain a set of measurement operators which are not optimal at the first step. And then the initial measurement operators are used for POVM and to obtain a conditional probability function, from which we can obtain a new value of the phase with maximum likelihood estimator. Therefore, the measurement operators and conditional probability function will be updated with the new value. As the measurement operators and conditional probability function are updated step by step, we can estimate the value adaptively. In fact, the results of the maximum likelihood estimator will converge at the true value of the phase parameter gradually, which is then proved with the theoretical analysis. All in all, an adaptive measurement method of estimating the phase parameter of the squeezed vacuum and coherent state in Sagnac interferometer is suggested, and is proved theoretically to be that the scheme will converge at the true value of the phase with a probability of 1 and can reach the quantum Cramer-Rao lower bound.

2016, 65 (19): 194204.
doi: 10.7498/aps.65.194204

Abstract +

The spontaneous emission field and spectrum of a two-level atom, located in an isotropic photonic crystal with dynamic band edges, are investigated by means of numeric calculation. The investigation is expected to help comprehend the characteristics of the atomic spontaneous emission in the dynamic photonic crystal, and provide a possible way to control dynamically the spontaneous emission in photonic crystal. The expression of the spontaneous radiation field is obtained without using the far-zone approximation and the Weisskopf-Wigner approximation, and expected to be applicable in other relevant researches. In the investigation, the spontaneous radiation field and spectrum are calculated when the band edge frequency is unmodulated, or modulated by a step function or triangle function. In the unmodulated situation, the radiation field intensity tends to a constant which is equal to the intensity of the localized field component. The radiation field pulse presents a wave packet behavior as propagation distance increases. The components of the radiation field correspond one-to-one to the peaks in the spontaneous radiation spectrum. When the band edge frequency is modulated by step function, the radiation field intensity tends to a steady-state value after the modulation has happened. And the steady-state intensity is affected by the time when the modulation happens. The components of the non-localized field and the frequency of the localized field after modulation depend on the atomic transition frequency and the band edge frequency, and are identical to those in the unmodulated situation with the same parameters. When the band edge frequency is modulated by a triangle function, the field intensity presents a decaying quasi-periodic oscillation after a long enough time. The modulation frequency determines the frequency of the oscillation, and influences the decay rate. The radiation energy becomes sharp peaks around a set of the discrete frequencies which are evenly spaced with the modulation frequency. The central frequency of these frequencies depends on the atomic transition frequency and the value range of the band edge frequency. The modulation initial phase affects the intensity of the radiation field emitted in an initial period of time.

2016, 65 (19): 194205.
doi: 10.7498/aps.65.194205

Abstract +

Whispering gallery mode (WGM) cavities due to their high quality factors, small mode volumes, and simple fabrications, have potential applications in photonic devices and ultrasensitive mass sensing. Cavity optomechanic systems based on WGM cavities have progressed enormously in recent years due to the fact that they reveal and explore fundamental quantum physics and pave the way for potential applications of optomechanical devices. However, WGM based cavity optomechanics still lies in a single optical mode coupled to a single mechanical mode. Here in this paper, in order to reveal more quantum phenomena and realize remarkable applications, we present a typical multimode cavity optomechanical system composed of two WGM cavities, of which one WGM cavity is an optomechanical cavity driven by a pump laser and a probe laser and the other cavity is an ordinary WGM cavity only driven with a pump laser. The two WGM cavities are coupled with each other via exchanging energy, and the coupling strength depends on the distance between the two cavities. With the standard method of quantum optics and the quantum Langevin equations, the coherent optical spectra are derived. The coherent optical propagation properties and the phenomenon of optomechanically induced transparency based slow-light effect are demonstrated theoretically via manipulating the coupling strength of the two cavities. The results based on the two-WGM cavity optomechanical system are also compared with those based on the single cavity optomechanical system, and the results indicate that the cavity-cavity coupling plays a key role in the system, which indicates a quantum channel, and influences the width of the transparency window. We further theoretically propose a mass sensor based on the double WGM cavity optomechanical system. To implement mass sensing, the first step is to determine the original frequency of the resonator. With adjusting the detuning parameters and the cavity-cavity coupling strength, a straightforward method to measure the resonance frequency of the WGM optomechanical resonator is proposed. The resonance frequency of the mechanical resonator can be determined from the probe transmission spectrum, and the coupling strength between the two cavities will enhance both the line width and the intensity, which will be beneficial to implementing mass sensing. The mass of external nanoparticles deposited onto the WGM optomechanical cavity can be measured conveniently by tracking the mechanical resonance frequency shifts due to the fact that mass changes in the probe transmission spectrum. Compared with those of single-cavity optomechanical mass sensors, the mass sensitivity and resolution are improved significantly due to the cavity-cavity coupling. This double WGM cavity optomechanical system provides a new platform for exploring the on-chip applications in optical storage and ultrahigh resolution sensing devices.

2016, 65 (19): 194206.
doi: 10.7498/aps.65.194206

Abstract +

In this paper, we present an experiment on a continuous-wave Nd:YVO4 Innoslab laser diode-pumped at 808 nm. The LD stack is composed of six bars, with the central wavelength fixed at 808 nm by adjusting the cooling water temperature. The emission from each diode laser bar is individually collimated by micro lens, which is coupled into a coupling system. The coupling system includes a planar waveguide, four cylindrical lenses and a spherical lens. The planar waveguide is used to shape the emitting beams of LD to obtain uniform distribution. The coupling system leads to a pump power loss of ~12%. By the coupling system, we obtain a homogeneous pumping line of ~0.4 mm22 mm coupled into the 0.3 at. % Nd:YVO4 (22 mm10 mm1 mm) crystal. The Nd:YVO4 crystal is a-cut with c axis along 22 mm direction. Indium foil is used for uniform thermal contact and cooling. The laser crystal is mounted between two water-cooled copper heat sinks with two large faces 22 mm10 mm. The heat conduction inside the laser crystal is quasionedimensional. The two 22 mm1 mm surfaces are polished and antireflectioncoated for the pump light and the laser light. Temperature of LD stack and laser crystal are controlled by cooling circulating water. The resonator consists of the input mirror (M1) and the output mirror (M2). M1 is a concave mirror with a radius of R1=500 mm, which is coated for high refection (HR) at 1064 nm and high transmission (HT) at 808 nm. The output mirror (M2) is a cylindrical mirror with a radius of R2=-350 mm, which is coated for HR at 1064 nm. M2 is cut and polished at one edge where the large beam exits. M1 and M2 constitute a stable resonator in vertical direction and off-axis unstable positive confocal resonator in the horizontal direction. In theory, the length of the resonator is L=(R1+R2)/2=75 mm. In fact, the length of the resonator is the same as the theoretical value. The equivalent transmission of the resonator is T=1-|R2/R1|=30%. At a pumping power of 462 W, a maximum power of 160 W continuous wave laser output is obtained, with the stability being 2.6%. Considering 88% of the coupling efficiency and 95% of absorbed efficiency, the optical-to-optical efficiency and slope efficiency are 41.5% and 47.7%, respectively. When the output power is 145 W, the beam quality M2 factors in the stable direction and unstable direction are 2.21 and 1.37, respectively. With the help of the ANSYS software, the temperature distribution in the crystal at the pumped power of 462 W is demonstrated. The temperature distributions are analogous to exponential decays in the Z-direction and parabola decay in the Y-direction, respectively. The maximum temperature difference is 71.6 K in our experiment. The thermal lens is negligible in the unstable direction because the temperature distribution is uniform. That is why the Innoslab laser is beneficial to the power scaling, as it keeps the power density constant, and enlarges the size of gain medium in the unstable direction to inject bigger power to obtain a higher power output, and maintain the constant beam quality.

2016, 65 (19): 194207.
doi: 10.7498/aps.65.194207

Abstract +

Optical chaos based on semiconductor laser (SL) has attracted much attention due to its potential application in various fields such as secure optical communication, chaotic radar, fast physical random bit generation, etc. By introducing external perturbations such as optical feedback, optical injection or optoelectronic feedback, SL can be driven into chaotic dynamic state. In general, an obvious time-delay signature (TDS) can be observed in a chaotic SL system with optical feedback, which is undesirable in some applications. So far, several schemes have been reported on the suppression of the TDS in chaotic SL systems, which are mostly based on external cavity feedback systems or mutually coupled systems. In this work, a novel scheme for suppressing TDS to generate multi-channel high-quality chaotic signals is proposed and numerically simulated based on a ring system composed of three unidirectionally polarization-rotated coupled 1550 nm vertical-cavity surface-emitting lasers (1550 nm-VCSELs). In this scheme, the output from the first 1550 nm-VCSEL passes through an optical circulator (OC), a Faraday rotator (FR) and a variable attenuator (VA), and then is injected into the second 1550 nm-VCSEL. The output from the second (third) 1550 nm-VCSEL passes through a similar path mentioned above, and then is injected into the third (first) 1550 nm-VCSEL. The polarization direction and the strength of injection light are controlled by the FR and VA, respectively. Adopting the spin flip model (SFM), the polarization-resolved dynamical characteristics of the three VCSELs in the ring system are analyzed. By the aid of self-correlation function (SF) and mutual information (MI), the influences of the coupled strength and frequency detuning on the TDS of polarization-resolved chaotic signal output from the three VCSELs are discussed. The results show that through selecting suitable coupling strength and frequency detuning, both the X-polarization component (X-PC) and Y-polarization component (Y-PC) in the three VCSELs can simultaneously be lased with comparative output powers, and the TDSs of these polarization components can also be effectively suppressed. Furthermore, we investigate the cross-correlation among the six-channel chaotic signals output from these VCSELs, and determine the region of coupled parameters for generating six-channel chaotic signals, within which satisfied is the weak cross-correlation between two signals from different VCSELs. Theoretically, the six-channel chaotic outputs can be used as physical entropy sources to generate six-channel random number sequences. By further merging the above two channel random bit sequences with weak cross-correlation, more channel random bit sequences with higher rate can be obtained. We hope this work can provide an effective guidance for multi-channel high-rate random bit generation.

2016, 65 (19): 194208.
doi: 10.7498/aps.65.194208

Abstract +

High-power ultrafast fiber lasers are important sources for a number of applications including material processing, pump source for optical parametric oscillator, and supercontinuum generation. Ultrafast thulium-doped fiber lasers, which extend the wavelength range of fiber lasers from 1.8 to 2.1 m, have rapidly developed in the last several years and the average output power of the ultrafast thulium-doped fiber amplifiers has reached a hundredwatt level. The broad and smooth gain spectrum of thulium-doped fiber makes it a well-suited gain medium for generating the ultrashort laser pulses and broad wavelength tunability. However, previous reports on ultrafast thulium-doped fiber lasers and amplifiers were related to non-PM fiber configuration. These ultrafast thulium-doped fiber lasers and amplifiers may suffer the environmental instability, which means that these fiber sources are sensitive to externally-induced changes, like significant temperature variations and mechanical perturbations which will influence the fiber birefringence property. An effective method to eliminate this environmental instability is to build an all-PM, thulium-doped all-fiber MOPA configuration where the light polarizes only along the slow or fast axis in the PM fiber and PM-fiber components. Here, we demonstrate a high-power all-polarization-maintaining picosecond thulium-doped all-fiber master-oscillator power-amplifier (MOPA) system. The linearly-polarized thulium-doped all-fiber MOPA yields 203 W of average output power at central wavelength of 1985 nm with a polarization extinction ratio of 15 dB. The pulse duration of 15 ps at 611.5 MHz repetition-rate results in a peak-power of 22 kW in the final thulium-doped fiber power amplifier. To the best of our knowledge, this is the highest average output power ever reported for a picosecond-pulsed thulium-doped all-fiber laser at 2 m wavelength. Furthermore, high-power linearly-polarized thulium-doped fiber laser with compact and simple design is greatly demanded for a variety of applications, such as coherent polarization beam combination, and frequency conversion in nonlinear crystals.

2016, 65 (19): 194209.
doi: 10.7498/aps.65.194209

Abstract +

High-power narrow-linewidth rare-earth-doped fiber lasers, which are well known for their high beam quality and high efficiency properties, have rapidly developed in the last decade, due to the needs of a vast range of applications such as nonlinear frequency conversion, and incoherent spectral beam combination to further scale up the total output power of fiber lasers. At the same time, many efforts have also been made to extend the operating wavelength of narrow-linewidth fiber laser toward the longer mid-infrared wavelength region, which was motivated by a large number of promising applications such as atmosphere monitoring, and pump source for mid-infrared optical parametric oscillator. In most cases, thulium-doped fiber lasers operate efficiently in a wavelength range of 1.8-2.1 m, which could be considered as being one of the most important sources of narrow-linewidth laser radiation that has been developed and intensively investigated in the last several years. Here, we demonstrate a high-power narrow-linewidth continuous-wave thulium-doped all-fiber laser based on master-oscillator power-amplifier (MOPA) configuration. The MOPA yields 342 W of narrow-linewidth laser output at the central wavelength of 2000.3 nm with a 3-dB spectral bandwidth of 90 pm. The beam quality factor is measured to be M2 of 1.15 at an output power of 300 W. No indication of stimulated Brillouin scattering could be observed at the highest output power level, and the output power is only currently limited by 793 nm available pump power. This kind of high-power narrow-linewidth thulium-doped all-fiber MOPA represents a promising achievement in the generation of high-power laser source via incoherent spectral beam combination.

2016, 65 (19): 194210.
doi: 10.7498/aps.65.194210

Abstract +

In this paper, a collimated femtosecond Gaussian beam with a central wavelength of 800 nm and a pulse duration of 50 fs is converted into a Bessel beam by an axicon with an apex angle of 140. By adjusting the femtosecond Gaussian beam incidence angle on the axicon, both anastigmatic and astigmatic femtosecond Bessel beams can be generated. Single- and double-core optical waveguides are fabricated in silica glass respectively by using anastigmatic and astigmatic femtosecond Bessel beams. Anastigmatic femtosecond Bessel beams with different single pulse energies (0.39 mJ and 0.47 mJ) are employed to fabricate the single-core optical waveguides in silica glass. The fabricated single-core waveguide's core diameter and refraction index change are found to be dependent on both the single pulse energy and pulse number used to fabricate the waveguide. By rotating the axicon, femtosecond Bessel beam with astigmatism is generated, which is used to fabricate double-core optical waveguides in silica glass. In the experiments 50 fs laser pulses with single pulse energy of 0.36 mJ are employed to fabricate the double-core optical waveguide. Experimental results show that when the rotation angle of the axicon is relatively small (1), i.e., the incidence angle of the femtosecond Gaussian beam on the axicon is 89, the distance between the two cores of the fabricated double-core waveguide is only 5.6 m. In this case the energy ratio of the coupled He-Ne laser between the two cores varies periodically as the waveguide's position changes towards one specific direction. When the axicon is rotated 3 and 5, the distances between the two cores increase respectively up to 9.1 m and 16.1 m, and no periodic variation of the coupled light energy ratio between the two cores is observed. It is inferred that the waveguides fabricated using the axicon with rotation angles of 3 and 5 are in fact optical waveguides with double parallel cores. According to the experimental results shown above, it is deduced that the double-core optical waveguide can be used as a highly sensitive differential displacement sensor, and the minimal detectable displacement is found to be less than 3 m. The light energy difference between the two cores is used to measure the displacement, so the displacement sensor made by double-core optical waveguide is a kind of differential detector with a higher signal-to-noise ratio than the frequently-used single-core waveguide displacement sensor. In addition, because the core zone of the double-core waveguide is composed of two cores separated by a distance which can be changed by adjusting the angle of the axicon before the fabrication process, the resulting larger core zone greatly facilitates the assembly process of the displacement sensor while the high detection sensitivity of the displacement is simultaneously achieved due to the using of the differential measurement method.

2016, 65 (19): 194211.
doi: 10.7498/aps.65.194211

Abstract +

The optical radiometric calibration method based on correlated photons generated by spontaneous parametric down-conversion (SPDC) is a promising method,because it is based on the basic physical phenomena and does not need radiometric traceability.At the present,the SPDC calibration technology is applicable for the photon-counting detector with a highest calibration accuracy of 0.18%.More and more researchers are making effort to improve its calibration accuracy and expand its applicable targets to analog detectors.Correlated photon circles have the high photon rate characteristic.The photon rates of signal and idle light can be improved significantly by using correlated photon circles in calibration.It has very important significance to study the time-correlation characteristic of correlated photon circles. In this paper,the spatial distribution of emission angle of the broadband (450-1000 nm) correlated photons generated by type-I spontaneous parametric down-conversion is presented through the theoretical calculations.The ZEMAX optical software is used to design the optical system which can receive the broadband correlated photon circles and remove the pump laser which is the main source of stray light.The 355 nm wavelength laser is used to pump -barium borate (BBO) crystal to generate the broadband correlated photon circles.A low-light-level CMOS camera is used to adjust and align the opt-mechanical system.Finally,the 430 nm-860 nm correlated photon circles are received by the optical system and detected by the low-light-level CMOS camera.An experimental measurement system is established to measure the time-correlation characteristics of 685 nm and 736.89 nm correlated photon circles.Using 1.0 mW continuous-wave laser to pump BBO crystal,a coincidence peak is observed evidently.The results show that the correlated photon circles generated by type-I SPDC have the characteristics of time-correlation and high photon rates.It can be conductive to improving optical radiometric calibration accuracy based on correlated photons and promoting the development and application in analog detector calibration.

2016, 65 (19): 194212.
doi: 10.7498/aps.65.194212

Abstract +

Due to the unique optical properties of low loss, low nonlinearity, high threshold and low latency, hollow core bandgap fibers are endowed with high expectations in the field of high power delivery, optical fiber communication, nonlinear optics, fiber sensors, etc. Fiber dispersion, as one of the basic transmission characteristics of optical fiber, makes the light pulse broadened during transmission, thus has adverse effects on high power pulse transmission system and high speed optical communication system. Therefore, it is significant to study the dispersion characteristics of the hollow core bandgap fiber for its applications in the field of high power pulse transmission and high speed communications. Because of the simple structure of measurement system, low cost, high accuracy and relatively short length of fiber (just needing a few meters long), interferometric technique is suitable for dispersion measurement of hollow core photonic bandgap fiber. The key to obtaining the dispersion results with interferometric technique is the phase extractiton from the interferogram. In order to meet the requirements of hollow core bandgap fiber for wide bandwidth, high efficiency and high accuracy dispersion measurement, a novel phase extraction method based on interferometry is proposed in this paper, by which the precision of dispersion measurement is improved through using the whole data-set in the interferogram. Combining with the determinations of the peak and center of symmetry points, the extraction of phase information can be implemented directly from the interferogram. The experimental results of measuring a standard single mode fiber indicate that the difference between the experimental measurement and theoretical simulation is just 0.6 psnm-1km-1, which proves that this proposed method possesses high accuracy and is suitable for the measurement of hollow core bandgap fiber. Consequently, according to the proposed phase extraction method, the measurement system based on Mach-Zehnder interferometer is set up and the dispersion measurement of a 19 cell hollow core bandgap fiber with a core diameter of 26 m is carried out. Experimental results indicate that the fundamental mode dispersion curve of the 19 cell hollow core photonic bandgap fiber in a wavelength range from 1400 nm to 1630 nm can be obtained. Moreover, four high order mode dispersion curves are obtained for the first time. The measurement results are in accordance with the simulation results. These findings are of significant importance for exploring the dispersion characteristics of hollow core photonic bandgap fibers, and also conducible to their applications in the fields of high power laser delivery, high capacity data communications, optical fiber nonlinear, etc.

2016, 65 (19): 194301.
doi: 10.7498/aps.65.194301

Abstract +

The influences of the interfacial properties on second-harmonic generation by primary circumferential ultrasonic guided wave (CUGW) propagation in a composite tube are investigated in this paper.Within a second-order perturbation approximation,the nonlinear effect of primary CUGW propagation may be treated as a second-order perturbation to its linear response.Due to the interfacial spring model,the properties of interface between the inner and outer circular tubes constituting the composite tube are characterized by the normal and tangential interfacial stiffness values.According to the technique of modal expansion analysis for waveguide excitation,the second-harmonic field of primary CUGW propagation can be decomposed into a series of double frequency CUGW modes.It is found that changes of the interfacial properties of composite tube will obviously influence the efficiency of second-harmonic generation by primary CUGW propagation.Specifically,for a given composite tube with a perfect interface,an appropriate fundamental and double frequency CUGW mode pair that satisfies the phase velocity matching condition can be chosen to enable the double frequency CUGW mode generated by the primary CUGW propagation to accumulate along the circumferential direction,and an obvious second-harmonic signal of primary CUGW propagation to be observed.When the changes of the interfacial properties of composite tube (versus the perfect interface with infinite interfacial stiffnesses) take place,the effect of second-harmonic generation by primary CUGW propagation will be influenced in the following aspects.Firstly, the changes of the interfacial properties in the case of perfect interface may provide different acoustic fields for the primary CUGW.This will influence the magnitude of the modal expansion coefficient of double frequency CUGW mode generated,because both the second-order bulk forcing source (due to the double frequency bulk driving force) and the second-order surface/interface forcing source (due to the quadratic term of expression of the first Piola-Kirchhoff stress tensor) in the governing equation of the double frequency CUGW are both proportional to the squared amplitude of the primary CUGW.Secondly,the second-order surface/interface forcing source in the said governing equation is directly associated with the interfacial stiffnesses.This will also lead to the change of the magnitude of the modal expansion coefficient of double frequency CUGW mode when the change of interfacial stiffnesses takes place.Thirdly,the change of the interfacial stiffnesses will influence the dispersion relation of CUGW propagation.The phase velocity matching conditions for the fundamental and double frequency CUGW mode pair,which are satisfied originally in the case of perfect interface,may not now be satisfied.This will remarkably influence the efficiency of second-harmonic generation by the primary CUGW propagation.It is found that when there is a clear difference between the phase velocities of the fundamental and double frequency CUGW mode pair (caused by the changes in the interfacial stiffnesses),the double frequency CUGW mode generated may not have a cumulative effect along the circumferential direction.In this case,the efficiency of second-harmonic generation by primary CUGW propagation will become more and more weak.Theoretical analyses and numerical simulations performed both demonstrate that the effect of second-harmonic generation by primary CUGW propagation is very sensitive to changes in the interfacial properties of composite tube, and that it can be used to accurately characterize the interfacial properties in composite tube structures.

2016, 65 (19): 194701.
doi: 10.7498/aps.65.194701

Abstract +

The laminar-turbulent transition has always been one of the most concerned and significant research topics. Receptivity is the first stage of the laminar-turbulent transition process in the boundary layer, and also plays a key role in the laminar-turbulent transition. However, previous studies for leading-edge receptivity mostly focused on the external sound disturbances, while it is seldom to see the relevant research on the leading-edge receptivity to free-stream turbulence in the boundary layer which is universal in the free stream. In view of this, direct numerical simulation is utilized in this paper to study the leading-edge receptivity to free-stream turbulence exciting the Tollmien-Schlichting (T-S) wave in the boundary layer. The high-order high-resolution compact finite difference schemes based on non-uniform meshes and fast Fourier transform are used in spatial discretization, and the fourth order modified Runge-Kutta scheme is used in temporal discretization to solve Navier-Stokes equations for direct numerical simulation. Perturbation waves with short wavelengths, whose wavelengths are approximately one-third of the disturbance wavelengths of free-stream turbulence, are excited in the boundary layer under the free-stream turbulence; and our numerical results show that the dispersion relations, growth rates and neutral stability curve of the group of the excited perturbation waves with different frequencies are in line with the solutions obtained from the linear stability theory. These obtained numerical results confirm that the group of the excited perturbation waves with different frequencies are a group of T-S waves with different frequencies and the interaction between leading-edge of flat plate and free-stream turbulence to excite unstable waves in the boundary layer is one of the receptivity mechanisms. Furthermore, it is found that the amplitudes of the excited T-S waves in the boundary layer increase linearly with increasing the amplitude of the free-stream turbulence; while the normal wave number and incident angle of free-stream turbulence are approximately 60 and 20, the leading-edge receptivity coefficient KI reaches a maximum; and the values of leading-edge receptivity coefficient KI

2016, 65 (19): 194702.
doi: 10.7498/aps.65.194702

Abstract +

The issue of fiber suspension flow has received great substantial attention in the last decades. In contrast with the abundant researches of normal size fiber suspensions flow, this paper is devoted to the small size fiber suspension composed of water and polyarmide fiber where Brownian motion plays an important role and thus cannot be neglected. The spatial distribution and orientation of fiber, streamwise mean velocity profile, turbulent kinetic energy, Reynolds stress and rheological property of fiber suspension in a turbulent channel flow are obtained and analyzed both numerically and experimentally. To simulate the small fiber suspension flow well, the well-known Reynolds averaged Navier-Stokes (N-S) equation governing the suspension flow is modified in consideration of the effect of fibers on base flow. The equation describing the probability density functions for fiber orientation is derived in view of the rotary Brownian diffusion. The general dynamic equation for fibers is reshaped in the effect of spatial Brownian diffusion. For the sake of the closure of the N-S equation, the turbulence kinetic energy and turbulence dissipation rate equations with fiber term are employed. The conditional finite difference method is adopted to discrete these partial differential equations. And the diffusion term and convective term are discretized by the central finite differences and the second-order upwind finite difference schemes, respectively. The second and fourth-order orientation tensors are integrated by the Simpson formula. Experiment is also performed to validate some numerical results. The results show that most fibers tend to align parallelly to the flow direction in the flow, especially in regions near the wall. Such a phenomenon is more obvious with the decreases of Reynolds number and fiber concentration, and with the increase of fiber aspect ratio. Fiber volume fraction distribution is non-uniform across the channel, and becomes more uniform with increasing Reynolds number, and with reducing fiber aspect ratio. The changes of fiber orientation distribution and spatial distribution are not sensitive to fiber aspect ratio for 5. Streamwise mean velocity profile in fiber suspension has a steeper slope than that in single phase flow, and the steepness increases as the fiber concentration and fiber aspect ratio increase, and as the Reynolds number decreases. The presence of fiber will reduce the turbulence kinetic energy and Reynolds stress. The effect of fiber on the turbulence suppression becomes more obvious with the increases of fiber concentration and aspect ratio, and with the decrease of Reynolds number. The first normal stress difference is less than 0.05 and much less than the shear stress. From the wall to the center of the channel, the shear stress increases while the first normal stress difference decreases. Both the shear stress and the first normal stress difference increase with increasing fiber concentration and aspect ratio. Shear stress increases while the first normal stress difference decreases with increasing Reynolds number. The effects of fiber concentration on the shear stress and the first normal stress difference are larger than the fiber aspect ratio.

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

## EDITOR'S SUGGESTION

2016, 65 (19): 196101.
doi: 10.7498/aps.65.196101

Abstract +

Graphene nanostructures are proposed as promising materials for nanoelectronics such as transistors, sensors, spin valves and photoelectric devices. Zigzag edge graphene nanostructures had attracted broad attention due to their unique electronic properties. Anisotropic hydrogen-plasma etching has been demonstrated as an efficient top-down fabrication technique for zigzag-edged graphene nanostructures with a sub-10 nm spacial resolution. This anisotropic etching works for monolayer, bilayer and multilayer graphene and the etching rate depends on substrate temperature with a maximum etching rate at arround 400 C. It has been also founded that the anisotropic etching is also affected by the surface roughness and charge impurities of the substrate. Atomically flat substrates with no charge impurities would be ideal for the anisotropic etching. So far the understanding of hydrogen-plasma anisotropic etching, e.g. whether hydrogen radicals or hydrogen ions dominate the etching process, remains unclear. In this work, we investigated the anisotropic etching of graphene under electrical field modulations. Bilayer graphene peeled off from grahpite on SiO2 substrate was used as the experimental object. 2 nm-Ti (adhesive layer) and 40 nm-Au electrodes was deposited by electronic beam evaporation for electrical contacts. Gate voltates were applied to the bilayer graphene samples to make them either positively or negitively charged. These charged samples were then subjected to the hydrogen anisotropic etching at 400 C under the plasma power of 60 W and gas pressure of 0.3 Torr. The etching rates were characterized by the sizes of the etched hexagonal holes. We found that the etching rate for bilayer graphene on SiO2 substrate depends strongly on the gate voltages applied. With gate voltages sweeping from the negative to the positive, etching rate shows obvious decrease. 45 times of etching rate decrease was seen when sweeping the gate voltages from -30 V (positively charged) to 30 V (negatively charged). This gate-dependent anisotropic etching suggests that hydrogen ions rather than radicals plays a key role during the anisotropic etching process since the negatively charged graphene could neutralize the hydrogen ions quickly thus make them unreactive. The present work provides a strategy for fabrication of graphene nanostructures by anisotropic etching with a controllable manner.

## EDITOR'S SUGGESTION

2016, 65 (19): 196201.
doi: 10.7498/aps.65.196201

Abstract +

In order to better understand the fracture mechanism of body-centered-cubic (BCC) metal, the multiscale quasi-continuum method (QC) is employed to analyze the nano-sized mode I cracks of three kinds of BCC metal materials, i.e., Ta, Fe and W. The plastic deformation near the crack tip and the brittle cleavage process are both investigated. The simulation result shows that there are different ductile-brittle behaviors in the cracks of different BCC materials. In the same loading range, the plastic deformation, such as dislocation nucleation and emission, stacking faults and twinning, is the main phenomenon for the crack of BCC-Ta. For the crack of BCC-Fe, plastic deformation and brittle cleavage are observed successively. At the initial stage, plastic deformation is dominant, which is similar to the crack of Ta. As loading increases, the crack begins to propagate, which differs from the crack of Ta. At first, the crack propagates along the initial direction [001], but then turns to [01] as the surface energy of {110} is lower than that of {01}. With the crack propagating, the crack tip is blunted by the plastic deformation, which is consistent with experimental results. As for BCC-W, the crack is found to propagate as brittle cleavage without plastic deformation at first. And the brittle cleavage is dominant all the time, which is a significant difference between W and the other two materials. In addition to the atomistic simulation, some theoretical calculations are also performed to analyze the ductile-brittle behaviors of the cracks. By an atomic slip model, the generalized stacking fault curves of BCC Ta, Fe and W are generated, which exhibit the unstable stacking fault energies of these materials. Based on the unstable stacking fault energy, two theoretical ductile-brittle criterions are analyzed. For the Rice-criterion, the result shows that the dislocation condition is met before cleavage for Ta and Fe, while for W the cleavage occurs before dislocation. For the ductile-brittle-parameter criterion, the result shows that Ta is the most ductile one in the three materials, followed by Fe, and W is the least ductile but the most brittle one. The analysis results of the two theoretical criterions both coincide well with the atomic simulation result, which well validates the simulation and fracture mechanisms.

2016, 65 (19): 196202.
doi: 10.7498/aps.65.196202

Abstract +

In order to explore the microscopic mechanism of mechanical properties in polyethylene/montmorillonite (PE/MMT) nanocomposite material,the molecular model and the molecule structure are simulated by simulation software,and the mechanisms of various complex phenomena of mechanical properties in PE/MMT nanocomposite material can be understood more in depth in the paper.To achieve this,the molecular model is developed under 423 K based on the molecular dynamics method and using the modules of Amorphous Cell as well,Forcite Tools and Reflex in the simulation software material studio includes polyethylene model,montmorillonite models without organization,organic montmorillonite model,and PE/MMT nanocomposites model.Then,microstructure and mechanical properties of PE/MMT nanocomposite material are analyzed by X-ray diffraction,radial distribution function and interaction energy test under universal force field,respectively.Some important findings emerge from the simulation results.First,after the molecular dynamic process of canonical ensemble (NVT) and constant-pressure,constant-temperature ensemble (NPT),the fluctuations in temperature and energy of polyethylene,montmorillonite without organization,organic montmorillonite,and PE/MMT nanocomposite material are all less than 5%.This implies that the low energy state is occupied and steady structures are formed in PE/MMT nanocomposite material.Second,the inter-layer spacing of organic montmorillonite is expanded to 20 due to cations of 18 alkyl three methyl ammonium chloride,which is increased by 79% compared with that of montmorillonite without organization.Meantime,the expansibility of PE/MMT nanocomposite material is obvious,and the density and volume of PE/MMT nanocomposite material are improved by -32% and 393% respectively,compared with those of organic montmorillonite.Third,when the mass fraction of organic montmorillonite reaches 4.0 wt%,the hydrogen bonding interaction obviously exists in PE/MMT nanocomposite material,and the interaction energy between polyethylene and montmorillonite layers has a maximum value of up to -390 kcal/mol,which leads to the stable structure of PE/MMT nanocomposite material and the significant improvement of the interfacial bonding between montmorillonite and polyethylene.Fourth,mechanical properties are significantly improved compared with that of polyethylene under elastic deformation,which is 4.0 wt% organic montmorillonite in PE/MMT nanocomposite material.Young's modulus,bulk modulus and shear modulus are increased by 38%,21% and 40%,respectively.Finally,the simulation results are compared with actual observed ones.The consistency between simulation results and actually observed ones can prove that the method of modeling PE/MMT nanocomposite material is correct and effective.Furthermore,when polyethylene chains enter into the layers of organic montmorillonite,it is verified that the PE/MMT nanocomposites can be formed and that the reason for the improvement of mechanical properties in PE/MMT nanocomposite material is the emergence of hydrogen bond.

2016, 65 (19): 196203.
doi: 10.7498/aps.65.196203

Abstract +

Plasticity behavior and phase transition of metal Fe subjected to shock loading have attracted considerable attention in shock physics community, in particular for underlying relationship between them. Experimental examinations and atomistic simulations on shocked Fe have displayed a three-wave structure: elastic wave, plastic wave and transformation wave. However, these studies are primarily limited to the one-dimensional planar case. Recently, owing to the rapid development of experimental techniques, investigating dynamic property of shocked metal has extended to the multi-dimensional loading conditions, such as cylindrical or spherical shocks. In this regard, fruitful findings are achieved, for example, twinning ratio in polycrystalline Fe under implosive compression is found to be much higher than that under planar shock, implying that the the complex stress state plays a critical role.
In this paper, we explore the effects of prestress on plasticity and phase transition of shocked polycrystalline iron. The imposed presstress normal to the impact direction in one-dimensional planar shocking represents the varying deviatoric stress, and does not nearly affect the principal stress. The utilized empirical potential for iron could describe the plasticity dislocation and phase transition very well. The simulations show that as the prestress increases, the shock speed at elastic stage and Hugoniot elastic limit increase, which is in accordance with the theoretical analyses based on shock wave theory and experimental measurement. Meanwhile the plastic wave speed increases more quickly and catches up with the transformation wave more easily, resulting in a steep shockwave front. Atomistic snapshots show that plasticity dislocation stemming from the grain boundary precedes phase transition, where most of BCC atoms are transformed into the HCP atoms and shear stress significantly decreases. Further observations from these images find that plastic zone becomes narrower with increasing prestress, representing a shorter plastic relaxation time, which accelerates the completion of phase transition. This rapid phase transition process is also indicated by quantitatively evaluating the ratio of transitioned closed packed atoms as a function of evolution time. The origin based on the atomistical prediction model of Fe phase transition is attributed to the fact that higher prestress gives rise to the larger von-Mises stress for easier dislocation emission while lower one cannot. But the final transformed atoms are independent of prestress. Additionally, the measured free surface velocity profiles from planar and cylindrical impact loading validate the simulations conducted here. These findings will help to understand experimentally the microscopically dynamic evolution of Fe, imposed by complex stress state.

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

2016, 65 (19): 197301.
doi: 10.7498/aps.65.197301

Abstract +

The nano-diamond has been a hot topic in the field of nano-science and nanotechnology for its optical properties. Much effort has been devoted to improving the fluorescence and Raman scattering intensity of nitrogen-vacancy (NV) center in nano-diamond by using plasmon resonance effect in sensing area. A combination of Ag nanoparticle and diamond can not only take advantage of the stability and biocompatibility of diamond, but also enhance the local electric field around NV center through the Ag nanoparticles, thereby speeding up the radiation of the fluorescent near the surface of the substrate, improving the strength and stability of the fluorescence, and greatly broadening the application areas of Raman spectroscopy. In this paper, we mix the nano-diamonds with Ag nanoparticles to improve the fluorescence and Raman scattering intensity on the basis of the localized surface plasmon resonance effect. The influences of Ag mass concentration on the Raman spectrum and fluorescence intensity are investigated. The results show that when the concentration of nano-Ag nanoparticles reaches up to 5 wt%, the light intensity becomes saturated, but the concentration further increases up to a value more than 7 wt% the light intensity begins to decline. Then the corresponding radiative transition rate and the fluorescence quantum efficiency are investigated, and based on these researches, influences and mechanism of surface plasmon resonance (SPR) enhancement are discussed thoroughly. We deduced that the fluorescence enhancement is mainly due to the enhanced surface plasmon field caused by transfer of surface plasmon resonance energy and the energy transfer between surface plasmon and excited state of NV centers. When the concentration of Ag nanoparticles reaches an appropriate value, a suitable distance between metal nanoparticles and diamond is obtained, thereby ensuring the strong local electric field forming on the metal surface, accelerating the emitting photons of diamond in the excited state, and also suppressing the transfer of non-radiative energy, eventually leading to the increase of diamond fluorescence emission intensity.

2016, 65 (19): 197302.
doi: 10.7498/aps.65.197302

Abstract +

GaN and its related nitride materials have been investigated for many years due to their extensive applications in semiconductor optoelectronics and microelectronics. The realization of p-GaN plays a key role in developing the GaN-based optoelectronic devices such as light-emittingdiodes, laser diodes and ultraviolet photodetectors. Furthermore, it is very significant to acuurately obtain the carrier concentration value of p-GaN layer for device design and fabrication. Usually the Hall measurements are employed to obtain the hole concentration of p-GaN layer. However, this method is not suitable for very thin samples, especially the p-GaN layer in the device structure, which is commonly very thin. Furthermore, the good Ohmic contact to p-GaN is not easy to realize. In consideration of the importance of p-GaN in determining the performance of GaN-based devices, it is necessary to find other new methods to measure or check the carrier concentration data of p-GaN. In this paper, a new method to estimate the carrier concentration of p-GaN by analyzing the current-voltage characteristic curve of p-GaN/n+-GaN diode is proposed. The main physical process is as follows: generally the carrrier concentration of p-GaN layer is far less than that of n+-GaN layer, and the depleted region is mainly located in the p-GaN. When the reversed bias voltage is very small, the diode shows conventional properties of p-n+ junction and the corresponding reversed current is very low since the p-GaN is not completely depleted. With the increase of reversed bias voltage, the depleted region of p-GaN also increases. Once the p-GaN is completely depleted, the case turns different. The diode will show Schottky junction properties and the corresponding reversed current increases obviously when the p-GaN is completely depleted under a certain reversed bias voltage since the ideal reversed current of Schottky junction is larger than that of p-n+ junction. The hole concentration could be derived according to the device physics if the bias voltage is discovered, which leads to the properties changing from the p-n+ junction to conventional Schottky junction. The simulation results confirm the idea, and the calculated p-GaN carrier concentration is almost equal to the originally assumed value. The proposed method is interesting and may be helpful to accelerate the research of p-GaN and related optoelectronic devices.

2016, 65 (19): 197501.
doi: 10.7498/aps.65.197501

Abstract +

Developing GaN based dilute magnetic semiconductors by making use of the preparation techniques for GaN materials,and combining the electrical and optical properties of existing GaN electronic devices with magnetic property will enable various novel spintronic devices to be made.The key enabler for the wide application of dilute magnetic semiconductors is room temperature ferromagnetism.Many research groups have reported numerous samples of GaN based dilute magnetic semiconductors with distinctively different magnetic properties.It may be argued that no consensus exists on the origin and control of ferromagnetism in these materials.There exists little work focusing on different doping modes for double-Mn doped GaN,GaN co-doped with Mn and non magnetic elements,and Mn doped GaN with vacancy defects,although such a doping method can significantly modify the electronic structures,magnetic and optical properties of these materials.Therefore,it is meaningful to study the effects of these different doping techniques on the electronic structure,magnetic and optical properties of Mn doped GaN so as to understand the magnetic exchange interaction in Mn doped GaN and improve its physical properties.In the calculation in this paper,the generalized gradient approximation (GGA+U) plane wave pseudopotential method under the framework of spin density functional theory is used.Models for the geometric structures of undoped wurtzite GaN supercell,three different doping modes of double Mn doped GaN, (Mn,Mg) co-doped GaN,and Mn-doped GaN with vacancy defects are constructed.The band structures,densities of states,energies and optical properties of these models are analyzed.The results show that the Curie temperature of the Mn doped GaN system can reach above room temperature.Compared with that of pure GaN,the volume of the Mn doped GaN system increases slightly.It is also discovered that the total energy and formation energy of the doped system increase with the Mn-Mn distance increasing,thereby lowering the stability of the system and making doping more difficult.Analysis reveals that co-doping the GaN with (Mn,Mg) can neither effectively increase the total magnetic moment of the doped system,nor improve the Curie temperature effect.The defects induced by Ga vacancies and N vacancies in the doped system hinder the stable ferromagnetic coupling from forming.In addition,the incorporation of Mn ions forms the spin polarized impurity band near the Fermi level.Due to the transitions between different electronic states in the spin polarized impurity band,the peak around 0.6868 eV in the imaginary part of the dielectric function and the peak near 1.25 eV in the optical absorption spectrum appear,respectively.This work offers a new insight into the understanding of the magnetic mechanisms and optical properties of Mn doped GaN,and will be conducible to improving its physical properties.

2016, 65 (19): 197701.
doi: 10.7498/aps.65.197701

Abstract +

In this paper, a method of designing tunable bandpass frequency selective surface via ceramics and ferrite material is proposed. The ferromagnetic resonance frequency can be tuned when magnetic field is applied. According to this property, the center-frequencies of the pass and stop band can be adjusted. The proposed model is composed of the ceramic part and ferrite part, and CST simulation under C band waveguide condition is employed in the research. For the ceramic part, five high-permittivity rectangular blocks are included. The aim is to achieve negative permittivity in broad band. The band-pass and band-stop properties of the frequency selective surface are clarfied based on the effective medium theory. The stop band originates from a similar Drude resonant electric monopole in the medium. The part of ferrite is composed of ten rectangular blocks. By adjusting the applied magnetic field, the ferromagnetic resonance and negative permeability are obtained at corresponding frequencies. Based on the double negative characteristics, the two parts are combined together to realize the pass band. For instance, when the magnetic field H0 is 1700 Oe, the ferromagnetic resonance appears at a frequency of 6.778 GHz. In this case, the center frequency of the pass band is at 6.758 GHz. By interacting with the electromagnetic wave, the electric resonance can take place in the ceramic blocks, and the ferromagnetic precession will appear in the ferrite blocks. The simulation results indicate that the pass band is switchable and tunable in a range of 6-8 GHz by changing the bias magnetic field. The distributions of electric and magnetic fields, and the parameters of perimittivity, permeability and impedance are obtained and discussed. Finally, the samples are fabricated and tested. The experimental results are basically consistent with the simulation results, indicating that the double negative passband can be adjusted via the applied magnetic field. This proposal provides a route to designing all-dielectric frequency selective surface and it can be used to design multi-band or tunable frequency selective surface.

2016, 65 (19): 197901.
doi: 10.7498/aps.65.197901

Abstract +

For laser ablation propulsion, the shielding effect of ablation plume on the incident laser is an essential factor affecting the propulsion performance. When the polymer doped metal is utilized as the propellant, the shielding effect would be more significant because the metal dopant is easily ionized. In order to study the shielding effect of ablation plume on the incident laser energy, a laser ablation model with taking into account the plume expansion, ionization and the shielding effect is built in the present work. For the polyoxymethylene doped aluminum particles irradiated by a laser with a fluence of 3-40 J/cm2, the specific impulse of laser ablation is calculated, and the consistency of the numerical results with the experimental data demonstrates the availability of the model. Furthermore, the effects of both the incompletely decomposed polymer chains and the plasma induced by laser ablation on the incident laser are considered. The time variations of electron number density distribution under different laser fluences are calculated based on the laser induced ionization model. Subsequently, the absorption coefficient distributions and the time variations of shielding coefficient under different laser fluences are obtained. The results show that at a low laser fluence (5 J/cm2), the electron number density is small, so the plume shielding effect is dominated by the laser energy absorption of the small polymer chains which are not completely decomposed. While at a high laser fluence (20 J/cm2), small polymer chains are almost completely decomposed into atoms even plasma, hence the shielding effect is dominated by the plasma since the electron number density in the plume increases up to 1020 m-3, and the complicated characteristic in the time variation of shielding coefficient appears. The quantitative analysis results obtained in the present work can be helpful for optimizing the performances of laser ablation propulsion.

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

2016, 65 (19): 198201.
doi: 10.7498/aps.65.198201

Abstract +

Much evidence shows that the appearance and instability of the spiral wave in cardiac tissue can be linked to a kind of heart disease. Therefore there needs a method of controlling spiral wave more safely and effectively. The intelligent modification of specific ion channel to achieve desired control is the future direction of gene therapy in heart disease. The key question that has to be answered is which ion channel is the best candidate for controlling spiral wave. Modern biological technology has been able to make the mutation of sodium channel gene to change its relaxation time constant. In this paper, we adopt the Luo-Rudy phase I model to investigate how to regulate the relaxation time constant of sodium channel gate to control spiral wave and spatiotemporal chaos in cardiac tissues. We suggest a control strategy which slows down the rate of sodium current activation and inactivation by increasing the relaxation time constant of the sodium activation gate by up to times while its fast inactivation gate is clamped to 0.77. Numerical simulation results show that a gradual increase of will cause the activation gate of sodium current to reach maximum more slowly, and its amplitude is gradually reduced, so that the amplitude and duration of the action potential of cardiomyocyte are gradually reduced. When the factor is large enough, the spiral wave and spatiotemporal chaos cannot propagate in the medium except planar wave with low frequency. The reason is that the excitabilities of medium and wave speed significantly decrease. Therefore, the spiral waves and spatiotemporal chaos can be effectively eliminated when the control time is properly selected and the factor is large enough. Spiral wave and spatiotemporal chaos disappear mainly due to conduction obstacle. In some cases, spiral wave can disappear through the transition from spiral wave to target wave or tip retraction. Spatiotemporal chaos disappears after spatiotemporal chaos has evolved into meandering spiral wave. When the parameters are chosen properly, the phenomenon that spiral wave evolves into a self-sustained target wave is also observed. The corresponding target wave source is the pair of spiral waves with opposite rotation directions. These results can provide useful information for gene therapy in heart disease.

2016, 65 (19): 198701.
doi: 10.7498/aps.65.198701

Abstract +

The super-resolution optical fluctuation imaging (SOFI) technique enhances image spatial resolution by evaluating the independent stochastic intensity fluctuations of emitters. In principle, it eliminates any noise uncorrelated temporally, and provides unlimited spatial resolution since the calculation of the nth-order cumulant followed by a deconvolution results in an image with n-fold resolution improvement in three dimensions. But in practice, due to limited data length, the statistical uncertainty of cumulants will affect the continuity and homogeneity of SOFI image, which results in the fact that the high order SOFI (typically over 3rd order) cannot improve spatial resolution significantly. Since the variance characterizes the statistical uncertainty of cumulant, we deduce its theoretical expression based on a single dataset. In traditional SOFI techniques, due to lack of statistical analysis of cumulant, there is no noise constraint condition of cumulant in the Lucy-Richardson deconvolution to prevent the algorithm from causing noise amplification. In this paper, based on the cumulant variance formula, we calculate the cumulant standard deviation in each pixel of SOFI image and introduce the results into the Lucy-Richardson algorithm as a DAMPAR to suppress the noise generation in such pixels. The simulation and experimental results show that under the same data length, the deconvolution optimization based on cumulant standard deviation significantly improves the uniformity and continuity of SOFI image. On the other hand, under the premise of identical image quality, this optimization technique can also greatly shorten the image frames to less than half the original, thus promoting the development of super-resolution imaging of living cells.

2016, 65 (19): 198901.
doi: 10.7498/aps.65.198901

Abstract +

Fluctuations of stock prices and their interactions network the corresponding entities in a stock market into a complex system.How a financial crisis affects the network structure,namely,the response of the structure to a financial shock,has received special attention from different fields.The response can reveal specific features of the crisis,which may shed light on the mechanism for its occurrence and provide further helpful information of the regulation of the financial system.
In the literature,there have appeared some pioneering studies on this topic.From return series of stock prices,one can calculate the cross-correlation coefficient between pairs of the entities.The cross-correlation matrix is then converted into networks according to different strategies,such as the threshold method in which an entity pair is linked only when the cross-correlation coefficient is larger than a certain value,and the planar maximally filtered graph method in which the constructed network can be embedded in a 2-dimensional surface.Some interesting findings are reported. However,there are still several essential problems to be solved.First,the previous work focused mainly on the clustering of entities and linking density of the network,while we are much more interested in the detailed changes of network structure.Second,in the planar maximally filtered graph approach,the number of links keeps constant,which means that different criterions are used in the procedures of constructing the networks before and during crisis.If we use the difference between the adjacency matrices as a measure of the structural changes,there will appear a large number of spurious changes.The real changes will be submerged in the artificial noises.The problem of artificial linkages exists also in the threshold-based method.Third,the records of stock prices form a multivariate time series,which may lead to a serious spurious estimation of correlations between the entities.Finally,the record series is limited in length.From the viewpoint of statistics,the estimated cross-correlation coefficients have usually unreasonably large values of confidence interval.
In the present paper,to reconstruct a reliable entity network,we use the time delay stability (TDS) method to extract dependent relationship from stock prices.If there exists an influence transferred from node A to node B,the transfer process will spend a certain time,called time delay.The method is based on a simple fact that though the transferred signals may vary,the time delay is determined by the intrinsic properties of the nodes and their link and consequently should keep constant,called time delay stability.What is more,spanning-tree is also constructed from the cross-correlation matrix,which is jointly used with the TDS to detect reliable links between the entities.Then we calculate the defferential networks,namely,the difference between the adjacency matrices corresponding to the scenarios before and in crisis durations,to measure quantitatively the structural changes of the entities network.
By using this method we consider the shocks of a total of 5 financial crises occurring in the period from 1994 to 2013.A total of 30 stocks that are used to construct the Do Jones index are considered.Interestingly,the influences of the financial crises share some features,for example in the crises the entities are tightly linked into dense clusters.At the same time,the influence of each financial crisis has its own features.For instance,the global financial crisis in 2008 led to the significant changes in the raw material related industries,in which the top three entities were the Aluminum Company of America,Exxon Mobil Corporation,and Chevron Corporation.While in the European Debt crisis in August 2011,the significantly shocked entities belong to the financial and banking industries,in which the entities Citygroup Inc.,Bank of America,and JPMorgan ChaseCoare were listed as the top three.
There exist various complex systems in diverse research fields.A complex system contains generally many elements that are networked by their complicated relationships.Monitoring the dynamical process of the elements and the edges produces a multivariate time series.Hence,reconstructing the network of the variables and monitoring the evolution of the network are the preliminary step to investigate the evolutionary behaviors of complex systems.Our procedure can be extended straightforwardly to the investigation of this problem.

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

2016, 65 (19): 199501.
doi: 10.7498/aps.65.199501

Abstract +

Astronomical telescopes with increasingly large apertures are required to upgrade the limit of diffraction and collect the light efficiently for the purpose of observing fainter and more remote objects with higher angular resolution. However, it is universally believed that traditional techniques of manufacturing, polishing and measuring large glass mirrors will soon face some practical challenges. Therefore, 10-m class or larger ground-based telescopes will need to employ arrays of several smaller segments to assemble into a large primary mirror. For a telescope with segmented mirrors, the piston errors between segments must be adjusted to nearly zero according to the requirements in order to be integrated into a single optical surface, which is known as co-phasing. One of the current co-phasing techniques, which has been successfully applied to Keck telescopes, employs an integration of edge sensors to detect the mirror shapes in real time with an optical phasing sensor to offer zero references for these sensors regularly. Another technique is demonstrated by use of a pyramid wavefront sensor (PWFS) to align and co-phase segmented mirrors in an active control close-loop with a single measurement. The co-phased best flat positions of segments are used as the zero references in order to measure the interaction matrix between the PWFS and the segmented mirrors. So it must be addressed that how the zero co-phasing reference is calibrated with high precision in a large capture range on the issues of co-phasing segmented mirrors. The current methods either lack accuracies, or just measure piston errors correctly in a small range. In order to solve the problem, a zero co-phasing reference calibration method based on dispersed interferogram is proposed. Specifically, the idea of the method is to define an appropriate cost function which is used to evaluate the piston errors between segments. Then it will be easy to determine the zero co-phasing reference position while all the cost function values are calculated based on the dispersed interferogram data with different piston errors inside the capture range. The proposed cost function is defined as the sum of the ratios of the second peak to the third peak of each of the columns of the two-dimensional dispersed interferogram, whose intensity distribution is along the dispersion direction. The precision and dynamic range of the method are analyzed theoretically and studied by simulations. Furthermore, the optical experiment is set up to demonstrate the efficacy of the method. In the experiment a scanning procedure is applied to one mirror and the dispersed interferograms between two mirrors with different piston errors are obtained. And then, the cost functions of these dispersed interferograms are computed through which the zero co-phasing reference position is located. The experimental results prove that the zero co-phasing reference between two mirrors can be calibrated within an accuracy of about 10 nm by making use of the proposed method. In addition, the novel method solves the problem of 2 ambiguity. Besides its sub-millimeter level wide capture range, this new co-phasing detecting method provides a helpful reference for relevant studies.