## Vol. 65, No. 4 (2016)

##### 2016-02-20

###### REVIEW

## EDITOR'S SUGGESTION

2016, 65 (4): 047201.
doi: 10.7498/aps.65.047201

Abstract +

VO2 is a metal oxide that has a thermally-induced phase-transition. In the vicinity of 341 K, VO2 undergoes a reversible transition from the high-temperature metal phase to the low-temperature insulator phase. Associated with the metal-insulator transition (MIT), there are drastic changes in its optical, electrical and magnetic characteristics. These make VO2 an attractive material for various applications, such as optical and/or electrical switches, smart glass, storage media, etc. Thus, the reversible metal-insulator phase transition in VO2 has long been a research hotspot. However, the metal-insulator transition mechanism in VO2 has been a subject of debate for several decades, and yet there is no unified explanation. This paper first describes changes of the crystal structure and the energy band structure during VO2 phase transition. With regard to the crystal structure, VO2 transforms from the low-temperature monoclinic phase VO2(M) into the high-temperature stable rutile phase VO2(R), and in some special cases, this phase transition process may also involve a metastable monoclinic VO2(B) phase and a tetragonal VO2(A) phase. In respect of the energy band structure, VO2 undergoes a transition from the low-temperature insulator phase into a high-temperature metal phase. In the band structure of low-temperature monoclinic phase, there is a band gap of about 0.7 eV between d// and * bands, and the Fermi level falls exactly into the band gap, which makes VO2 electronically insulating. In the band structure of high-temperature rutile phase, the Fermi level falls into the overlapping portion of the * and d// bands, which makes VO2 electronically metallic. Next, this paper summarizes the current research status of the physical mechanism underlying the VO2 MIT. Three kinds of theoretical perspectives, supported by corresponding experimental results, have been proposed so far, which includes electron-correlation-driven MIT, Peierls-like structure-driven MIT, and MIT driven by the interplay of both electron-correlation and Peierls-like structural phase transition. It is noted that recent reports mostly focus on the controversywhether VO2 is a Mott insulator, and whether the structural phase transition and the MIT accurately occur simultaneously in VO2. Finally, the paper points out the near-future development direction of the VO2 research.

###### GENERAL

2016, 65 (4): 040201.
doi: 10.7498/aps.65.040201

Abstract +

A generalized nonlinear Schrdinger equation is numerically studied using the split-step Fourier method. For a fixed external potential field and an initial pulse disturbance, the effects of the complex coefficients p and q in the nonlinear Schrdinger equation on the evolution of the wave field are investigated. From a large number of simulations, it is found that the evolution of the wave field remains similar for different signs of the real parts of p and q, and different values of the real part of p. The initial pulse consisting of the longest wavelength modes (in the smallest-|k| corner of the phase space) of the spectrum first suffers modulational instability. Collapse begins at t～0.1, followed by inverse cascade of the shortest wavelength modes to longer wavelength ones, so that the whole k space becomes turbulent. For p = 1+0.04i, and q = 1+0.6i, it is found that first modulational instability occurs in the longer wavelength regime and the wave energy is transferred to the larger |k| modes. Then the wave collapse appears with increasing wave energy. Next, the large-|k| modes condense into a smaller-|k| mode by inverse cascade before spreading to the center of the phase space, until a turbulent state occurs there. Finally, most of the wave energy is condensed to the neighborhoods of three modes.

2016, 65 (4): 040401.
doi: 10.7498/aps.65.040401

Abstract +

The AdS/CFT duality provides us a powerful guidance to study the strong-coupled conformal field theory by using its dual weak-coupled gravity. One of the interesting applications of the duality is to study high temperature superconductors, which are supposed to be a strongly coupled system. According to Ginzburg-Landau theory, a superconductor can be characterized by only two parameters, coherence length and the magnetic penetration length ; therefore, it is important to determine the two parameters. In this paper in the D=d+2-dimensional Lifshitz black hole, we analytically study the static fluctuation of the scalar field with nonzero spatial momentum along one spatial coordinate of the boundary, and investigate the perturbation of the gravitational system near the critical temperature Tc. Working in the probe limit (the gauge field and scalar field do not backreact on the original metric), we obtain the superconducting coherence length via AdS/CFT (anti-de Sitter/conformal field theory) correspondence, which is (1/Tc)(1-(T/Tc)-1/2. Moreover, in the probe limit (the magnetic field does not backreact to the background spacetime), we have calculated the diamagnetic current induced by a homogeneous external magnetic field perpendicular to the surface of the superconductor. Then, we obtain the magnetic penetration depth (Tc-T)-1/2, which agrees with the result in Ginzburg-Landau theory. And these results strongly support the idea that a superconductor can be described by a charged scalar field on the Lifshitz black hole via AdS/CFT (anti-de Sitter/conformal field theory) duality.

2016, 65 (4): 040501.
doi: 10.7498/aps.65.040501

Abstract +

Imaging through scattering media has been a focus in research because of its meaningful applications in many fields. Recently, it has been proposed that high quality images can be recovered after passing through stationary scattering media by using the single-pixel imaging system based on compressed sensing. No doubt, it is a very interesting discovery about compressed sensing. However, it is also reported that high quality image can be recovered only with stationary scattering media. Mostly, the scattering media will not remain stationary, for example, the properties of the fog will be dynamically changed when their is wind. Thus, in a dynamic case, the transmittance of the scattering media will be nonlinear over the time, which will make the measured data nonlinear and the reconstructed image quality decrease. In this paper, a novel algorithm of linear transformation for measured data (LTMD) is proposed to make the nonlinear attenuation factor gain a linear transformation after passing through the dynamic scattering media. The factor is proposed from the theoretical calculus based on compressed sensing, and this correction factor can help to eliminate the nonlinear errors caused by dynamic scattering media and make the measured data linear. So the transformed data will greatly upgrade the reconstructed image quality. Simulation results show that high peak singnal to noise ratio images can still be recovered even when the dynamic frequency reaches 300 times in the 900 times of sampling. In experiments, plastic films are used as scattering media, and the number of films can be changed during the sampling to simulate the dynamic state of scattering media. With LTMD, high quality image with a resolution of 64 48 is recovered after passing through dynamic plastic films while the recovered result without LTMD is still hard to be distinguished. The traditional reconstructed algorithms orthogonal matching pursuit, Tval3 and L1-magic are also used in the experiments, and the image is still hard to recover with any of the three traditional algorithms. In a word, the proposed LTMD algorithm uses the correction factor to make the affected nonlinear-measured data linear, so as to increase the reconstructed quality of the imaging system based on the compressed sensing even when passing through scattering media with highly dynamic frequency.

2016, 65 (4): 040502.
doi: 10.7498/aps.65.040502

Abstract +

A novel particle filter smoothing algorithm for non-linear state estimation is proposed. The key point of this algorithm is that the length of the interval of the particle filter smoothing can be dynamically computed by the difference between the particle and the signal observations, which effectively suppress the phenomenon of increasing error of the system state estimation caused by the particles' weight redistribution when using the fixed smoothing interval method. By considering the signal and the heat bath as an abstract universe based on the particle filter/resampling, a physical analogy is made between the particle filter and the abstract universe, which obeys the second law of thermodynamics. That is to say, when there is no new observation, no matter where the initial state is from, the entropy of the whole system will increase. However, with the coming of the observations this law can be violated. The particle filter behaves like a Maxwellian demon in this physical analogy, returning energy to the heat bath which thus causes entropy to decrease. This is possible due to the steady supply of new information. Then the length of the smoothing interval can be dynamically corrected based on the change of the entropy, so the weight assignments of the particles is optimized, and the performance of the particle filter can be improved. The estimation accuracy of the approach which is verified by simulations is better than the traditional smoothing methods with an affordable computation burden.

###### THE PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

2016, 65 (4): 041201.
doi: 10.7498/aps.65.041201

Abstract +

The study on the mass splittings of the mesons with the same structure but different spin-and orbit-quantum numbers is one of the important methods for checking the efficiency of potential models. In previous calculations for quark potential models, the splitting between - is easily obtained while that of the c-J/ is however too small to meet the experimental results. In this paper, the third term of the complete Breit quark potential in the momentum space is regularized twice by applying the form factor 2/(q2+2), and the other terms except the first term of the Coulombic potential and the seventh term of the constant potential are regularized once. The mass splittings are calculated by using these values. Our results indicate that the mass splittings of light mesons -, heavy mesons c-J/, b-(1s), and c0-c1-c2 can meet the experimental results with high accuracy only when the screen mass is expanded to the third-order polynomial with respect to the meson reduced mass r=mr mj/(mr+mj), while the masses of other mesons are improved greatly. An efficient quark potential model is thus described in this paper.

###### ATOMIC AND MOLECULAR PHYSICS

2016, 65 (4): 043701.
doi: 10.7498/aps.65.043701

Abstract +

For a quantum memory to be useful as a quantum repeater, a long coherence time is a crucial requirement. In recent years, the most commonly explored medium for quantum storage has been atomic gases. We report an experiment to realize a quantum memory based on an Rb atomic ensemble in a one-dimensional far-detuned optical lattice. A multimode 30 W continuous wave fiber laser was used to construct a travelling wave lattice with a period of 25 m. The Rb atoms were loaded into a magneto-optical-trap, which was then adjusted to optimize the polarization gradient cooling. To trap the cooled atoms, we turned on a laser which has a wavelength of 1064 nm and therefore is red-detuned from the resonance frequencies of D1 and D2 transitions of 87Rb atoms. By taking the short-distance time-of-flight image the temperature of the atoms was found to be about 20 K. This system will provide a foundation for future quantum information storage studies.

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

2016, 65 (4): 044101.
doi: 10.7498/aps.65.044101

Abstract +

An analytical model for double-layer shielding metallic enclosure with inner strip-shaped metallic plates is proposed for analyzing the shielding effectiveness of complex enclosures containing multiple spatial structures, based on the actual situation that the circuit systems in each spatial region are inevitably interfered by the electromagnetic penetration of those in adjacent spatial regions through slots, cables, and other transmission channels. The near-field electromagnetic interference of the external layer of the enclosure is represented by the equivalent electric dipoles, and the internal layer of it is regarded as the target point of shielding effectiveness, the analytical formulas of the internal layer's electromagnetic field then are derived based on Bethe's small aperture coupling theory and generalized Green's function. The model is employed to analyze the influences of some parameters of the strip-shaped metallic plate on the shielding effectiveness. It is shown that the position and direction of the strip-shaped metallic plate have obvious influence on the shielding effectiveness of the target point of the internal layer, embodied by the shielding values over some frequency ranges and different resonant modes, and at the same time the corresponding physical mechanisms are also given in detail. Comparison with the full wave simulation software CST has verified the model over a very broad frequency range, which provides a theoretical reference for the rapid calculation for shielding effectiveness of complex enclosures.

2016, 65 (4): 044102.
doi: 10.7498/aps.65.044102

Abstract +

In laser wake field acceleration, it is relatively easy to achieve and control electron injection by adopting a plasma density gradient. This scheme of plasma density gradient injection has been studied in recent years both theoretically and experimentally, but thus far theoretical studies have been done mostly by particle-in-cell simulations. In this paper the density gradient injection and acceleration of electrons are studied with a newly developed analytic approach. The energy threshold for electron injection versus plasma density gradient scale length is given. It is shown that in the plasma density gradient region, the energy threshold of electron injection becomes lower at later times after the driving laser pusle or when the gradient becomes sharper. Evolution of plasma wave's phase velocity and motion of the background electrons in the plasma density gradient are worked out in the linear plasma wave regime, i.e. the normalized laser intensity is a0～1. The energy, the location, and the timing of the injected electrons are obtained. Separatrices of test electrons in the gradient region are obtained by Hamiltonian theory. The influence of injection timing in the density gradient region on the succeeding acceleration in the homogeneous plasma density region is also discussed. It is indicated that whether the injected electrons may be accelerated efficiently or not in the homogeneous region depends on both the energy of the electrons and the phase of the plasma wave at the gradient-to-homogeneous turning point. The analytic results are confirmed by particle-in-cell simulations.

2016, 65 (4): 044103.
doi: 10.7498/aps.65.044103

Abstract +

In this paper, we propose how to generate the periodic bottle beam by using a partially coherent beam. Firstly, a spatially completely coherent beam is transformed into a partially coherent beam by a rotating ground glass. Secondly, after passing through the double-axicon system, the parallel beam is converted into two Bessel beams which have the same optical frequencies but different radial wave vectors. Finally, the partially coherent periodic bottle beam can be generated by two interfering Bessel beams. Based on the interference theory, an analytical expression can be obtained for calculating the distribution of light intensity in the image and spot diagrams in spectral degree of coherence for the optical field with 0.9. By doing this calculation, the proposed optical system can be made to generate a partially coherent periodic bottle beam with the oscillation period of 2.5 mm. Before further investigating the effect of field coherence on the periodic bottle beam, we may also calculate the distribution of light intensity in the images and spot diagrams in the spectral degree at 0.83, 0.7, 0.5 and 0.2, respectively. Results show that the intensity contrast ratio between the dark focus and the surrounding periodic regions can be reduced with the decrease of the spatial coherence degree. In this case, the period of the bottle beam and the central dark focus size will not be affected. We have also designed and carried out an experimental generation of the periodic bottle beam and measured its focusing properties. In the experiment, we can control the coherence in the incident field by controlling the size of the circular aperture located behind the rotating ground-glass disk. When the size of the circular aperture is 0.1 (or 0.2) mm, the value of the coherence degree of the incident optical field is 0.9 (or 0.83). The two different coherence degrees of the partially coherent bottle beam have been measured by CCD. Experimental results show that the obtained bottle beams are of the same period of 2.5 mm. The measured diameters of the two different coherence degrees of the central spots (maximum sizes of the dark spot) are both 15 m. Experimental results also show that the spectral degree of coherence cannot affect the shape and size of the periodic bottle beam except the contrast of it. Therefore, the experimental results agree well with the theoretical results.

2016, 65 (4): 044201.
doi: 10.7498/aps.65.044201

Abstract +

Polarization is one of the basic properties of electromagnetic waves and is valuable in communication, navigation and radar detecting. So it is important to control and manipulate polarization states of electromagnetic waves. In this paper, we design, fabricate and measure a broadband reflective metamaterial 90 polarization rotator which has a double-split-ring resonator (DSRR) structure, composed of two layers of dielectric and a metal plate ground. The explanation of the physical mechanism of the polarization rotator is presented according to the anisotropy media theory. Anisotropic metamaterials can cause a phase or amplitude difference between two crossed polarization waves, which can be used to manipulate the polarization states of the incident waves. The anisotropic polarization rotator behaves different for two orthogonal axes, and the surface current distributions of the DSRR are discussed to analyse the different characteristics of the structure along two orthogonal axes. The DSRR behaves as a dipole resonator that couples with the electric component along one axes and behaves as an LC resonance circuit that couples with the other electric component. Thus, almost an equal magnitude and a 180 phase difference can be generated between the two orthogonal electric components of the reflected waves. The polarization states of the reflected waves will be rotated by 90, when incident waves are polarized by 45 with respect to the symmetric axis of the rotator, and it will be retained when the incident waves are circularly polarized. Simulation results show that this device can work with the relative bandwidth of 90% from 5.5 to 14.5 GHz, of which the polarization conversion ratio is larger than 90%. The polarization conversion ratio will decrease as the incident angle increases, but this high polarization conversion ratio can be obtained at several frequencies. A 576-cell (2424) prototype of the polarization rotator has been fabricated using a printed circuit board method on the FR4 substrates and the experimental results agree well with that of the simulation. The polarization rotator has a simple geometry but more operating frequency bands, compared with the previous designs. It provides a route to broadband polarization rotation and has application values in polarization control, design of new antenna and stealth technology.

2016, 65 (4): 044202.
doi: 10.7498/aps.65.044202

Abstract +

According to the diffraction integral theory of vector field and the pupil filtering method with a discrete complex amplitude, we present a tunable pupil filter to achieve and manipulate the focused vector fields with ultra-long depth of focus. The filter consists of a polarization rotator with two /2 wave plates and a discrete complex amplitude filter with six zones. Amplitude transmissions of these zones are different and increase along the radial direction. And every two adjacent transmitted zones have the opposed phases 0 and . With optimized cylindrical polarization (0 =52) and discrete amplitude, the generalized cylindrical vector field can be tightly focused into a three-dimensional (3D) flat-top field with an extended depth of focus (～10 ) by a high numerical aperture lens. For the main outermost zone and the other five inner zones, we analyze the intensity distributions of the three polarized components and the total polarized component in the focal region. We find that the axially and azimuthally polarized components are the major contributors. The outermost zone offers the central field of the focused field while the other five zones affect the side lobe more obviously. Through adjusting the included angle between the double wave plates, we can change the polarization states of the incident vector field and alter the structures of the focused fields among the 3D flat-top focused field, needle-like field, tube-like field and the other fields with intermediate form. Result obtained is superior to that of the past research for the adjustable freedom between these forms, and it reveals the dynamic relation between the evolved vectorial form of incident field and the vector structure of the focused field. Our work paves a way to achieve the controlled dynamical focused field with a long depth of focus. The needle-like field, tube-like field and the well-matched 3D flat-top focused field will meet the demand of applications in optical microscope, optical micro-manipulating, optical micromachining and so on.

2016, 65 (4): 044203.
doi: 10.7498/aps.65.044203

Abstract +

The squeezed light at 1.5 m telecommunication band has been considered as an important resource of continuous variable (CV) practical fiber-based quantum information research because it is the lowest loss in fiber. A bright phase quadrature squeezed light for continuous variable at 1.5 m is demonstrated from a semi-monolithic degenerate optical parametric amplifier (DOPA) based on a periodically poled KTiOPO4 (PPKTP) crystal. The laser source is a continuous wave (CW) single-frequency fiber laser at 1.5 m, which is sent through a ring mode cleaner (MC) as a preliminary spatial and noise filter. And then the main portion of the output from the MC is used for external-enhanced second harmonic generation to obtain a CW single-frequency low noise laser at 780 nm that acts as the pump of the DOPA. The residual light of the output from the MC at 1.5 m is used as the injected signal light of the DOPA and the local oscillator (LO) of a balanced homodyne detector (BHD) system. The DOPA is built by using a type-I PPKTP crystal and a piezo-actuated output coupler and works in double-resonance case with a threshold power of 230 mW. When the DOPA is operating in the state of amplification, the output down-conversion field should be a bright phase quadrature squeezed light, where the relative phase between the pump and the injected signal is locked to 0. A 4.7 dB bright phase quadrature squeezed light is measured by the BHD system with the pump light of 110 mW and the injected signal of 3 mW, where the relative phase between the down-conversion field and the LO is locked to 0. Our measurement is limited by the optical losses and the detection efficiency. We have taken into account the detection efficiency of 86.6%, and the actual squeezing of the squeezed light being 6.3 dB. Moreover, because it is so crucial a process for CV quantum information system that the transmission and evolution of the CV squeezed states in the fiber may reappear in all information of the quantum states in the phase space, then the bright squeezed light is detected by a BHD system in the time domain, and its Wigner quasi-probability distribution function can be reconstructed by using a quantum tomographic technique. Furthermore, the bright squeezed state at 1.5 m is an ideal source for fiber-based long-distance quantum information because of its stability and bright mean field.

2016, 65 (4): 044204.
doi: 10.7498/aps.65.044204

Abstract +

Commercial and military applications of microwave and millimeter-wave sources in aerospace, radar, navigation, and communication system require high spectrum purity and low phase-noise oscillators. The optoelectronic oscillator (OEO) emerges as an excellent low noise source that has attracted great attention in recent years. In this paper, a novel technique is proposed for single-mode selection in an optoelectronic oscillator, which uses a microwave cavity as the mode selector. It consists of a pump laser and a feedback circuit including an intensity modulator, an optical fiber delay lines, a photodetector, an amplifier, a filter and two drilling cables. The drilling cable is fabricated by drilling open holes on a coaxial cable using a drilling machine. By changing the radius of the drilling holes, the designed reflection coefficient can be obtained. By simulation, the constructed microwave resonator that consists of a filter and two drilling cables has a higher Q value and only the modes that satisfy the oscillation conditions of the loop will be selected. The basic principle is analyzed theoretically and experimentally. By comparing with traditional structure of OEO, it is shown that the novel structure can effectively improve the side-mode suppression ratio. In addition, the stability of the oscillation frequency is easier to control than the parallel structure. In this experiment, the output of a 10 GHz single-mode signal with a side-mode suppression ratio of 72 dB and a phase noise of -122 dBc/Hz@10 kHz from the carrier is obtained. Meanwhile, phase-lock techniques are used to compensate the drift of cavity length. Then the radio frequency (RF) stability of the oscillation frequency is measured using an RF spectrum analyzer, and the RF stability over 3 hours for the OEO is less than 4 Hz. This scheme has the advantages of traditional OEO with low noise since no extra active devices are needed, and it suppresses the side-mode noise also effectively. In addition, this system is promising for the development of compact, high frequency, low cost and low noise OEOs.

2016, 65 (4): 044205.
doi: 10.7498/aps.65.044205

Abstract +

In this paper, we employ a new kind of quasi-boson approach and the mean field theory to study analytically the Hamiltonian of an array of cavities with a three-level atom embedded in each cavity in the process of two-photon resonant transition under the influence of a bosonic bath. The superfluid order parameter of the system is obtained analytically and then analyzed numerically to investigate the effects of dissipation on the quantum phase transition from the superfluid to the Mott-insulator phase. It is shown that when the two-photon resonance is achieved one can have the superfluid phase at (ZJ/)= (ZJ/)c' 0.34 in the related ideal case. Furthermore, the system while in the two-photon resonant process has a larger dissipation rate as compared with that in the one-photon resonant process, thus leading to the suppression of the long-range coherence time and enhancement of the critical hopping rate for restoring coherence.

Theoretical study on generating mid-infrared ultrashort pulse in mode-locked Er3+: ZBLAN fiber laser

2016, 65 (4): 044206.
doi: 10.7498/aps.65.044206

Abstract +

Fiber lasers show several advantages over other types of lasers. They are efficient, compact, and rugged since they require few bulk components and are virtually unaffected by the surrounding environment. Mode-locked mid-infrared (mid-IR) lasers are essential for a wide variety of applications. The promising applications of mode-locked fiber lasers at wavelengths near 3 m include combs generation (metrology), spectroscopic sensors, infrared countermeasures, laser surgery, high-efficient pump sources for longer-wavelength oscillators and mid-IR supercontinuum source pumping. Based on the nonlinear Schrdinger equation (NLSE), a theoretical model of passively mode-locked Er3+-doped fluoride fiber laser using a saturable absorber is set up. Some mechanisms for generating mid-IR ultrashort pulse in fiber lasers are investigated. When the dispersion of the cavity is managed properly, the numerical simulation mainly focuses on the evolution process of mid-IR ultrashort pulse in fluoride fiber oscillators. Influences of the intracavity net dispersion and the small-signal gain on the generation of mode-locked pulses are analyzed in detail. And the reasonable parameter windows are given. Just as the simulated results showed, for a case of 4 m Er3+-doped fluoride fiber, small-signal gain g0= 0.6 m-1 and unsaturated loss l0 = 0.7, the stable mode-locked pulses are achieved by tuning the net intracavity dispersion within a certain range from 0.72 ps2 to 0.83 ps2. As the net intracavity dispersion increases, the output pulse duration increases gradually, while the spectrum width (FWHM) and peak power decrease accordingly. In addition, for the case of 4 m Er3+-doped fluoride fiber, unsaturated loss l0 = 0.7 and net intracavity dispersion of 0.8 ps2, the stable mode-locked pulses can also be obtained by tuning the small-signal gain within a certain range from 0.55 to 0.70 m-1. As the small-signal gain increases, the output pulse duration, spectral width, and peak power increase gradually. This work may be beneficial to the design of experiments for achieving more narrow pulse duration, wide spectral width, and high peak power mid-infrared ultrashort pulse.

2016, 65 (4): 044207.
doi: 10.7498/aps.65.044207

Abstract +

The sum-frequency conversion efficiency is directly proportional to the product of two fundamental laser powers. Therefore, sum-frequency conversion efficiency is rather low when the fundamental beams pass through a nonlinear crystal only once. External resonant technique as an effective means of improving the powers of the fundamental light has been widely applied to the field of nonlinear frequency conversion. This technique can greatly improve the sum-frequency conversion efficiency and is particularly suitable for the situation in which the input power of the fundamental frequency lasers bas been limited. The implementation of high efficient sum-frequency generation in an external resonator requires that the fundamental frequency laser should be efficiently coupled to the external cavity. Therefore, the system needs to achieve impedance matching. In the part of theoretical analysis, first, we derive the enhancement factor when travelingwave cavity is resonant, and then, establish the theoretical models of doubly resonant and singly resonant sum-frequency generation in an external resonator respectively. The variation of enhancement factors as functions of reflectivity of the input couplers and power of the input fundamental light for doubly resonant and singly resonant sum-frequency systems is derived from Boyd-Kleinman theory in detail based on the theoretical models described in the text. The expressions of enhancement factors reflect the nonlinear correlation characteristics of two fundamental light beams in the process of sum-frequency generation. In the part of numerical simulation, firstly, we draw contour plots of output power as functions of reflectivity of the input couplers at two input frequencies in the doubly resonant sum-frequency system by theoretical simulation, and achieve an optimum reflectivity of the input couplers under the condition of different powers of input fundamental light. Secondly, we draw the contour plots of output power as functions of the reflectivity of the input coupler at the resonant frequency, and the input power of non-resonant frequency light in the singly resonant sum-frequency system by theoretical simulation, and achieve an optimum reflectivity of the input coupler at the resonant frequency. These optimum values enable the system to achieve impedance matching; consequently, the sum-frequency conversion efficiency is improved. Finally, this paper analyzes the influence of input power on the impedance matching, and shows that the optimal coupling mirror reflectivity of the resonant fundamental frequency will decrease with the increase of incident power of the other resonant or non-resonant fundamental frequency laser, otherwise, the resonant incident power of its own has less influence on the optimal coupling mirror reflectivity, whether the system undergoes doubly resonant or singly resonant sum-frequency. In addition, if the coupling mirror reflectivity exceeds the optimum value, the power of sum-frequency light will decrease rapidly, while if it is less than the optimum value, the power of sum-frequency light decreases relatively slowly. Therefore an input coupler that may yield over-coupling should be avoided. These results will have a certain guiding significance to related experiments.

2016, 65 (4): 044208.
doi: 10.7498/aps.65.044208

Abstract +

A series of Yb-doped silicate glasses with the composition of 60 SiO2-12 Al2O3-28 CaO-1.0 mol% Yb2O3 are prepared by a conventional melting method under normal processing conditions. These glasses are divided into two groups. One group experienced a total dose 3 kGy radiation under a Co60 radiation source, and the other group is pristine. The absorption spectra as well as the near-infrared (NIR) luminescence spectra of the glasses (pristine Ybc, irradiated Ybc, heat bleaching Ybc) are investigated. Theoretically, effects of gamma-ray radiation exposure would lead to the formation of color centers in the glass samples. Such radiation-induced color center defects cause a strong broad optical absorption band with widths from 300 to 900 nm, and its tail extends into the NIR region. In this experiment the absorption coefficient of the glass is measured by a ultraviolet-visible spectrophotometer named Lambda35, and the NIR spectrum is measured by a Zolix grating spectrometer named Omni-. Furthermore, a special test system is set up to test the NIR spectrum of the glass at high temperatures. Experimental results show that the absorption coefficient of the glass after irradiation increases significantly in the visible region. The absorption coefficients of the glasses (pristine Ybc, irradiated Ybc) at 400 nm are 0.93 cm-1 and 2.9 cm-1 respectively. With a certain temperature treatment, the absorption coefficient of the irradiated glass is 1.89 cm-1 at 400 nm. Compared with the absorption coefficient obtained before, it is decreased by 35%. The NIR intensities of the glasses (pristine Ybc, irradiated Ybc, heat bleaching Ybc) are 588, 261 and 436 (arbitrary units) respectively. It may be due to the color center defects produced by radiation, that have decomposed under a certain temperature treatment. As a result, this method greatly improve the optical performance of the glass. So thermal bleaching phenomenon will happen in the irradiated glass that experiences in a certain temperature treatment. Finally, results obtained in this paper may provide a theoretical basis for studying the anti-radiation of optical glasses.

2016, 65 (4): 044209.
doi: 10.7498/aps.65.044209

Abstract +

Residual stresses will be formed around the mitigated site after the damaged site is irradiated by 10.6 m CO2 laser. Using those mitigated sites can improve the damage resistance ability in optics, and once the reinitiating damage occurs, the damaged site will grow under the subsequence irradiation and large fracture may form around the mitigated site. In this study, the annealing temperatures 650, 750 and 850 ℃, and time durations 6, 8, 10 and 12 h are used to anneal the samples. The sample annealed at 750 ℃ is the main research object of this study, while the sample annealed at 650 ℃ or 850 ℃ is only treated for 10 h. The differences of damage growth morphology and velocity of mitigated site on fused silica treated under those annealing conditions are investigated when it is damaged once again. Results are also compared with the damage growth behaviors of the unannealed substrate and mitigated site. It is indicated that the damage growth data still fit to an exponential curve even for the unannealed mitigated site. However, for the unannealed mitigated site, a more serious and larger size of damage site will be formed when the reinitiating damage occurs. It is mainly attributed to the fast propagation of crack under the effect of residual stress around the mitigated site. This behavior can be effectively controlled by the annealing treatment. Results show that the crack propagation behavior can be avoided when the retardation of mitigated sites is controlled in the range of 25 nm; moreover, the damage growth velocity and coefficient will gradually decrease with the increase of the annealing duration and annealing temperatures. A notable result indicates that there is no difference between the mitigated site and substrate when the retardation of mitigated sites is controlled below 10 nm, especially for the samples treated at 750 ℃ for 12 h and 850 ℃ for 10 h. Moreover, the reported investigation indicates that the stresses can still improve the damage resistance ability in optics. This is the most desirable outcome of the annealing treatment. Thus, the investigation results can provide a reference on how to analyze the effect of stress on damage growth of mitigated site and optimize the annealing parameters.

2016, 65 (4): 044210.
doi: 10.7498/aps.65.044210

Abstract +

Distributed fiber optic sensors are studied extensively, for monitoring abnormal events in continuous space, due to the advantages of immunity to electrical interference, non-conductivity and light weight. Moreover, the position of abnormal events, such as intrusions, could be determined directly without additional measurements. Among the various techniques, Sagnac interferometers prove to be promising for providing high sensitivity and large dynamic range in detecting intrusions. Two interference light beams are used which are naturally of equal optical path length in static status. When an intrusion occurs along the sensing fiber, the two light beams arrive at the intrusion position in different time and thus cause different phase changes induced by the intrusion. Analysis of the phase difference signal can predict the intrusion position, as well as the existence of the intrusion. As a Faraday rotator mirror (FRM) connected in the far-end of sensing fiber, both beams travel twice to the intrusion position after being reflected by the FRM. The propagation time interval T between the two interactions corresponds to the distance between the intrusion position and the far-end of sensing fiber Lx, which is further extracted as the localization of intrusion. Previously, the auto-correlation algorithm deals with the phase difference signal in the time domain and the null-frequency algorithm is used in frequency domain to calculate the distance. However the poor localization performance usually can not meet the requirement in high-quality monitoring applications. To determine the position of an intrusion effectively and accurately, the localization algorithm which deals with the phase difference signal in cepstrum domain is proposed in this article. Inspired by the research on the pitch examination we first introduce the algorithm for intrusion localization. Through theoretical analysis, the phase difference signal can be regarded as the convolution of the original waveform of intrusion and the T-related transform function. By applying the fast Fourier transform to the logarithmic spectrum, the phase difference signal is changed into the cepstrum domain, where the original waveform of intrusion and the transform function behave differently and are separated. The propagation time interval T, as well as the distance Lx, can be directly acquired from the peak produced by the transform function. In addition, to overcome the roughness in localization resolution brought by down-sampling of the phase difference signal, the decimator factor is scanned from 30 to 50 for multi-resolution localization at an original sampling rate 4 million/s-1. Besides the basic peak, high order peaks also emerge in the cepstrum in high signal-noise-ratio condition, which can also be used for localization. Since the localizations from different decimator factor and different peaks spread around the actual distance, an average of all reasonable localizations is calculated as the ultimate localization result for the intrusion. Firstly in experiments, intrusions occurring at a position 40.498 km are produced for the verification of the algorithm. The localizations are 40.489, 40.515 and 40.487 km, with localization errors as small as 9, 17 and 11 m respectively. Intrusions at different positions are tested and also correctly localized. For comparison, the standard deviations of localization error are respectively 695 m and 118 m for the auto-correlation algorithm and the null frequency algorithm, which are 58 times and 10 times of the result 12 m, which is obtained by the proposed cepstrum algorithm. The performance suggests promise to achieve better localization in practical applications.

2016, 65 (4): 044211.
doi: 10.7498/aps.65.044211

Abstract +

Vacuum fluctuation at audio frequencies is very important and interesting in many research fields, such as the gravitational wave detection, ultra-weak magnetic field measurement, and the research of quantum metrology, etc. Since the generation of squeezed light in 1985, most of the squeezed light have been generated and measured at radio frequencies (～MHz) as there has not been much technical noise at higher frequencies. In the Michelson-interferometer-based gravitational wave detection, the detection band has frequencies from a few to tens of thousands Hz. Measuring vacuum noise at such low frequencies is a challenge since we have to stabilize and control all the audio noises and the interferences from a variety of mechanical and electronic noises, therefore a very high classical noise suppression is needed when the measurement time increases. In order to measure the squeezed light of low frequencies, the standard vacuum noise at audio frequencies must be measured. In this paper, a balanced homodyne detection system for measuring the low-frequency quantum vacuum noises is reported. It is not trivial to extend the detected frequency to very low analysis frequencies. Through a self-made self-subtraction balanced homodyne configuration, which can eliminate the DC component of each photocurrent from the photodiode and the classical common-mode technical noise, the standard vacuum noise has been detected. The linearity of the vacuum noise power has been validated by varying the local oscillator power, showing that the saturation power of light incidence is about 3.2 mW. When the incident-light power is 400 W, the standard vacuum noise is 11 dB higher than the electronic noise at 80 Hz. In the regime of about 80 Hz to 400 kHz, the linearity of the standard noise power as a function of incident laser power is verified. However, when the measurement is carried out at even lower frequencies, for example, 50 Hz, we may encounter some excess and non-stationary noises and find that the measured noise power is not proportional to the incident light power any more. These non-stationary noises are the main technical obstacle at low frequencies. The average common mode rejection ratio in the test frequency range from 10 Hz to 400 kHz is 55 dB and its maximum 63 dB at 100 Hz is obtained, implying a high suppression of the technical noise. This self-made homodyne vacuum noise detector can be widely used for precision measurement in quantum metrology and quantum optics.

2016, 65 (4): 044301.
doi: 10.7498/aps.65.044301

Abstract +

Due to accidental degeneracy, a semi-Dirac point is realized at the center of the Brillouin zone in a two-dimensional phononic crystal (PC) consisting of a square array of core-shell-structure elliptical cylinders in water. In the vicinity of the semi-Dirac point, the dispersion is linear along the X direction, but it is quadratic along the Y direction. The semi-Dirac point is formed by the degeneracy of dipole and quadrupole modes, through accurately adjusting the radius of the cores and shells, the two modes will coincide and the dispersion relation will become linear. It is worth to be emphasised that the frequency of the semi-Dirac point is very low in our designed PC, and this is exactly the special advantage of a three-component system. Since the dispersion relation is different in the vicinity of the semi-Dirac point, some new features may be seen. Firstly, the anisotropic transmission phenomenon is demonstrated. A PC slab is placed in a rectangular waveguide where the sound hard boundary conditions are used on the upper and lower walls; a plane wave impinges on the PC slab along the X direction at the semi-Dirac point frequency, and total transmission can be achieved, so that the sound energy transmissivity is also equal to one. In the meantime, the waves experience no spatial phase changes when they are transmitting through the PC slab; this behavior indicates that the PC can be equivalent to zero index medium along the X direction. However, when the plane wave is incident along the Y direction, the transmitted field is very weak, and the sound energy transmission is nearly zero. Secondly, the properties of the semi-Dirac point can be applied to design acoustic diode. The scatterers of the PC are arranged in triangular prism shapes and placed into a straight waveguide; when the wave is incident along the X direction, it can be transmitted through the PC slab and emerge in the right area, but when the waves is incident from the opposite direction, it will be totally reflected back. Therefore, the semi-Dirac point in PC provides a way to realize the acoustic diode. Finally, the unidirectional wave-front shape effect can also be observed in our considered system. We put a square sample with 16-by-16 coating rods into water medium. When a tightly focused Gaussian beam impinges on the PC sample along the X direction at the semi-Dirac point frequency, the outgoing wave will be modulated to a plan wave. Whereas, when the incident wave along the Y direction, the Gaussian beam will be totally reflected. In conclusion, the singular features of semi-Dirac point in PC will provides an advantageous means to manipulate acoustic waves and exploit new functional materials.

2016, 65 (4): 044302.
doi: 10.7498/aps.65.044302

Abstract +

By taking advantage of spread processing gain, the direct-sequence spread-spectrum (DSSS) for underwater acoustic (UWA) communication system can be carried out at low signal levels, which is the preferred method for high-quality UWA communication and remote UWA communication. However, phase fluctuation caused by complex marine environment seriously affects the performance of spread spectrum system, leading to the reduction of spread processing gain. Differential energy detector is proposed for DSSS UWA communication system in this paper, which has a good ability of anti-carrier phase fluctuation and multi-path interference by detecting the output energy of two correlators. Differential coding can avoid error propagation when determining the relationship between adjacent symbols. Differential energy detector combined with improved active average sound intensity detector is further proposed in this paper, which can get vector processing gain by updating the estimated azimuth so as to make the system operate stably at a low signal to noise ratio. Improved active average sound intensity detector also has the ability of anti-carrier phase fluctuation, and the feedback code bit information of differential energy detector can ensure that the processing gain of improved active average sound intensity detector is not affected by Doppler's accumulation. Simulation and Dalian sea test have verified the robustness of single vector differential energy detector algorithm. Using the single-vector differential energy detector, good performance is achieved for a signal-to-noise ratio as low as -18 dB based on at-sea data.

2016, 65 (4): 044303.
doi: 10.7498/aps.65.044303

Abstract +

Acoustic focusing effect with broad bandwidth based on the temperature gradient distribution is studied. The propagation paths of the acoustic waves can be controlled by the temperature gradient distribution generated by two heat sources, which is adopted to realize the acoustic focusing effect. This focusing effect arises from the continuous change of the acoustic refractive index induced by the change of temperature, and has no reflection energy loss. Therefore, the acoustic focusing effect has the advantages of broad bandwidth and high focusing performance. In addition, we have investigated the influences of the factors (incident frequency, temperature of heat source, spatial distribution of interface, position of heat source, attenuation coefficient of the medium, and asymmetric distribution of heat source temperature) on the acoustic focusing effect in detail, and verified the feasibility of the acoustic focusing system by using aerogel based on temperature gradient distribution in single medium.

2016, 65 (4): 044304.
doi: 10.7498/aps.65.044304

Abstract +

Acoustic cavitation bubble and its production extreme physics such as shockwaves and micro-jets on a solid wall have attracted great interest in the application of ultrasound (e.g., ultrasonic medical, ultrasonic cleaning, and ultrasonic machining). However, the prediction and control of micro-jets induced by ultrasonic field have been a very challenging work, due to the complicated mechanisms of collapsing of cavitation bubbles. In order to determine the interaction of micro-jet with the key parameters that influence the acoustic cavitation, the dynamics of bubble growth and collapse near a rigid boundary in water is investigated. Using the method of mirror image, a revised bubble dynamics equation in radial oscillation for a bubble near a plane rigid wall is derived from the double-bubble equation (the Doinikov equation). In the present equation, the gas inside the bubble is assumed to be the van der Waals gas, and the weak compressibility of the liquid is also assumed. The revised equation is then employed to simulate numerically the dynamical behaviors of a bubble, using the fourth-order Runge-Kutta method with variable step size adaptive control. Numerical simulations of the motion characteristics and collapse velocities of a bubble near a rigid boundary or a free boundary have been performed, under various conditions of initial bubble radius, spacing between the center of the bubble and the wall, acoustic pressure and ultrasonic frequency, in order to explain the effects of these key parameters on the acoustic cavitation intensity. It is shown that, compared with free boundary, the effect of rigid boundary on the bubble plays a significant role in suppressing the bubble oscillation. The intensity of bubble collapsing is reduced as the increase of the initial bubble radius and ultrasonic frequency, and increased by enlarging the spacing between the center of the bubble and the wall. There exists an optimal acoustic pressure (almost 3.5 times bigger than the ambient pressure), at which the collapse of a bubble near a rigid wall can be the most violent. Furthermore, the relationship between the collapse velocity of a bubble near a rigid boundary and its micro-jet is described. Results demonstrate that the velocity of micro-jet is dependent on that of bubble collapse, and it can be controlled by adjusting the velocity of bubble collapse indirectly. Calculation results of the micro-jet in this paper are compared with some numerical and experimental results given in the literature and good apparent trends between them are obtained. These results will give important implications for further understanding the dynamics of cavitation bubble on a solid wall induced by the ultrasonic field and its different requirements in engineering applications.

2016, 65 (4): 044305.
doi: 10.7498/aps.65.044305

Abstract +

Based on Huygens principle about the aspect of phased array, this paper presents a structure of cylindrical acoustic transducer consisting of circular ring piezoelectric transducer elements in radial vibration mode, which can be used to achieve the ultrasonic nondestructive test for the cylindrical scanning acoustic field in three-dimensional space. By analyzing the acoustic field of a single ring line source and a single element, the sound field distribution of the phased array is obtained for constructing circular ring acoustic focused field. By means of the phased array incentive mode, the phase difference of driving signals is generated and forms a regular time delay; with the accomplishment of sound field scanning in cylindrical three-dimensional space, the circular ring acoustic focused field can be controlled in real time.Theoretical analysis and finite element simulation results demonstrate that the size of the circular ring acoustic focused field can be controlled by the numbers of the excited array elements, which are 4, 8, 16 and 32 respectively in our work. We find that with more array element numbers, the circular ring acoustic field has better focused features. The radius size of the circular ring acoustic focused field can be controlled by the different locations of the focus positions which are 30 and 50 mm respectively in our work. And we find that as the distance between the focus positions and the center of piezoelectric wafer becomes longer, the radius of the circular ring acoustic focused field becomes bigger, and the position of the focus is equivalent to the radius of the circular ring acoustic focused field. The movement along the axial direction of circular ring acoustic focused field can be controlled by the angle of deflection, which are set as 0, 10 respectively in our work. And we find that the circular ring acoustic focused field is deflected in a corresponding deflection angle along the Z-axis, and the moving distance is FZ = F/sin . With the theoretical analysis and the experimental simulation, it can be shown that the structure of cylindrical acoustic transducer array presented in this paper could create an adjustable circular ring acoustic focused field and can potentially provide an acoustic field scan method in detection ultrasound, medical ultrasound and other areas of a cylindrical space.

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

2016, 65 (4): 045201.
doi: 10.7498/aps.65.045201

Abstract +

Electron cyclotron resonance ion source (ECRIS) for space propulsion requires to be compact and efficient. In this work, ECRIS, which generates magnetic field through permanent magnets, is compact and heats electrons by microwave in magnetic field to induce ionization collision and produce plasma. In ECRIS, magnetic field is crucial in gas discharge, plasma confinement and transport. Due to the complex interaction among the processes, including plasma generation, wave transmission and ion extraction, the effects of magnetic field on the performance of ECRIS are complex. In this paper, the effects of magnetic field topology on the performance of the ECRIS are studied experimentally. Argon is discharged by microwaves in four types of ion sources, different in the magnet positions and the ion beam extracted. The gas flow rate varies from 30 to 210 g/s, the microwave power from 10 to 20 W and the extracting voltage form 500 to 1500 V. The properties of the ion sources are analyzed by comparing their extracted ion beams, propellant utilization efficiency, discharge loss and stability. Results show that the maximum ion beam, the highest gas utilization efficiency and the minimum discharge loss are respectively 160 mA, 60%, and 120 WA-1. Each ion source presents more than one mode, determined by the microwave power and the gas flow rate, and affected by the extracting voltage. The microwave power and the gas flow rate at which the ion source mode changes relative to the position of the magnets. Finally, the influences of magnetic topology on the performance of the ion source are summarized and analyzed. It is concluded that inside this kind of ECRIS, the magnetic field featured by a wide electron cyclotron resonance (ECR) zone, and the narrow gap between the ECR zone and the screen grid will increase the extracted ion beam at the same level of the input power and the gas supply. But it is difficult to achieve high gas utilization efficiency in the ion source with such a structure. By keeping the ECR zone close to the power entrance, the gas inlet will significantly decrease the threshold for the power and gas consumption to sustain the high current mode. But the discharge loss in the ion source of such a structure is huge. Elaborate considerations should be taken to balance the magnitude of the extracted ion beam and the efficiency. These results may improve the understanding of the working process of this type of ECRIS and help the design processes.

2016, 65 (4): 045202.
doi: 10.7498/aps.65.045202

Abstract +

So far, the investigations of carbon nanotube (CNT) cathode have been focused on the field emission with low current and voltage. However, the properties of the intense pulsed emission of CNT cathode have not been discussed deeply and comprehensively. In this paper, the intense emission properties of velvet and CNT cathode are studied in various aspects, such as emission capability, cathode plasma expansion, cathode initialization, emission uniformity, operation stability, outgassing property, and so on. Three different CNT cathodes are made by using electrophoresis deposition, chemical vapor deposition and also CNT paper (or buckypaper) gluing. Results show that the emission capability of CNT arrays and CNT paper cathode is definitely better than the velvet cathode. At the same diode voltage (～300 kV), the amplitudes of diode current of CNT array and CNT paper are 2.75 and 3.1 kA respectively, which are bigger than that of the velvet cathode (～1 kA). The orientation of CNT should not affect the emission capability of CNT cathodes. And the small radius of the tube wall and the existence of defects are suggested to be the reasons for the emission of electrons from the body of the tubes. The threshold electric field strength of intense emission of CNTs is about two-thirds of velvet cathode. The onset delay time of CNT cathode is shorter than the velvet cathode by about 12-17 ns at the same electric field growth rate. The time-evolution processes of the plasma expansion velocity of CNT and velvet cathodes are similar, which could be divided into three phases (rapid rising, quick decreasing and stable phase). In summary, the plasma expansion velocity of CNT cathode is less than one fourth that of velvet at the end of the first phase. During the stable phase, which sustains until the end of the voltage pulse, both cathodes have the same plasma expansion velocity (7 cm/s). The emission uniformity of the cathode has been studied by analyzing the distributions of cathode plasma spots and Cherenkov radiation light, which are captured by the high speed frame camera. The emission uniformity of CNT cathode is much better than that of the velvet cathode. Especially, the cathode plasma spots on the whole surface of CNT array cathode are very dense and uniform. The peak outgassing pressure of the CNT paper cathode is 0.3 Pa, which is one fifth that of the velvet cathode; while the peak outgassing pressure of the CNT array cathode is 0.042 Pa, which is the lowest, and the outgassing pressure of the CNT cathode is related to the fabrication methods. Volatile such as epoxy should be avoided in the fabrication processes. This CNT cathode appears to be suitable for intense emission source and high-power microwave device applications.

2016, 65 (4): 045203.
doi: 10.7498/aps.65.045203

Abstract +

The shock wave driven by laser is an important tool for investigating equation of state and can provide the state of compressed matter. The X-ray source, generated by the short-pulse intense laser interaction with the solid target, has the properties of short pulse, small spot, high yield and tunable energy. Therefore the X-ray source is the first chosen as a backlighter for the diagnosis of dynamic process. The model of the X-ray radiography is established by Monte Carlo code Geant4. The density distribution in an object is obtained by hydrodynamic code Multi-1D and the laser parameters are obtained by the XGIII laser facility. Under the condition of one-dimensional density the object in the shape of rectangular solid, three evaluation criterions, root mean square, peak value and ratio of rise gradient, are defined for evaluating density results. The signal-to-noise, spatial resolution, and contrast of radiography results have been optimized. First, the signal-to-noise has been optimized and the optimization magnification is 5.6 with the photon yield 1012. Second, the spatial resolution according to different spot X-ray source has been simulated by designing resolution plate radiography. Third, in the condition of same magnification, the influence of source yield on radiography result has been analyzed. Fourth, the radiography results of different X-ray energy have been simulated. The optimization energy for radiography requests that the penetrability ratio is greater than 1.5 and the photon count in pixel after penetrating the compressed matter is greater than 3000. And the optimum criteria make sure that the radiography images simultaneously have high contrast and high signal-to-noise. The radiography of one-dimensional density object in the shape of cylinder has been simulated. The Abel inversion algorithm is established based on Radon inversion. The inversion result accords well with the designed density distribution in simulation at the request of the radius of X-ray source less than 5 m. The inversion result basically accords with the designed density distribution in simulation at the request of the radius of X-ray source less than 15 m. This work will contribute to the measurement experiments on the compressed matter achieved by laser-driven-shock and provide the reference for the optimization of radiography based on X-ray.

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

2016, 65 (4): 046101.
doi: 10.7498/aps.65.046101

Abstract +

Metallic glasses offer novel physical, chemical and mechanical properties and have promising potential applications. Recently, exploring the structure and deformation mechanism of metallic glasses according to the rheological mechanical behavior in the nominal elastic region has been the object of intensive research. Physically the mechanical analogues of fractional elements can be represented by self-similarity spring-dashpot fractal networks. In light of the fractal distribution features of the structural heterogeneities, a fractional differential rheological model is introduced to explore the viscoelastic a behavior of metallic glasses in this paper. To investigate the viscoelastic deformation mechanism, carefully designed nanoindentation tests at ambient temperature are proposed in this study. Three kinds of metallic glasses with different Poisson's ratio and glass transition temperature, which have the chemical compositions of Pd40Cu30Ni10P20, Zr48Cu34Pd2Al8Ag8, and (Fe0.432Co0.288B0.192Si0.048Nb0.04) 96Cr4 are selected as the model materials. Experimental and theoretical results clearly indicate that in the nominal elastic region, these metallic glasses exhibit linear viscoelasticity, implying a loading rate-dependent character. Based on the fractional calculus and Riemann-Liouville definition, experimental results are analyzed by the fractional-differential and integer order rheology models respectively. According to the stability of the fitting parameters, here we show that the fractional-differential Kelvin model, which consists of a spring and a fractional dashpot element, can fit the experimental viscoelastic deformation data of the investigated metallic glasses better than that with integer order rheological model. The extracted elastic modulis E1 of the spring in the fractional-differential Kelvin model are comparable to those of samples measured by traditional methods. Such a similarity can be well explained by the mechanical analogue of fractal model proposed for describing the distribution features of the structural heterogeneities in metallic glasses. The rheological parameters obtained here including viscosity index A and fractional order are capable of reflecting the rheological features and the flowing tendency of the above-mentioned metallic glasses. It is found that there exists a clear relationship between the rheological parameters and the reduced glass transition temperature as well as Poisson's ratio, which is helpful for understanding the correlation between plasticity and Poisson's ratio from the micro-structural point of view. The current work provides a rheological model-structure-property relation that may be applicable to a wide range of glassy materials.

2016, 65 (4): 046102.
doi: 10.7498/aps.65.046102

Abstract +

This investigation aims at the Zr-doping in -TiAl alloy systems in which Ti (or Al) atoms are partly replaced and the impurity concentrations are 1/54, 1/36, 1/24 and 1/16 (molar ratio), respectively. The structural, energy, plastic and electronic properties of the alloys are calculated and studied by using the first-principles method based on the density functional theory and other physical theory. From geometry optimization results it is shown that doping with Zr can change the structural symmetry of the -TiAl systems. These results also suggest that the cubic degree of Zr-doped -TiAl alloys can be increased due to the Zr-substitution. For instance, the cubic degrees of Ti12Al11Zr and Ti18Al17Zr systems are enhanced distinctly, which are positive for improving the mechanical properties of the alloys. The average formation energies obtained indicate that the Ti atom replaced by Zr can slightly decrease the formation energy of the system (0.003 eV/atom); while Zr substituting the Al atom can increase the formation energies of the systems (0.07 eV/atom). Accordingly, when Zr atoms are introduced in the -TiAl system, they tend to substitute Ti atoms, and can also substitute Al atoms with a certain possibility. Thus, various Zr-doped -TiAl regions can be produced in the system. The integral effects are of significance for improving the performance of the -TiAl based alloys by means of Zr-doping method. Comparing the axial ratios of Zr-doped -TiAl systems with that of pure -TiAl system, we find that Zr substituting Al atom can reduce the axial ratio of the Zr-doped alloys, which is responsible for the ductility of the materials. It should be mentioned that when the impurity concentration is in the range of 1.85 at%-6.25 at%, the doping effect will be most distinct and the axial ratio of the alloys is close to unity. It is expected that the Ti12Al11Zr system has a good ductility for its axial ratio equals to 1.007. The band structures of Zr-doped -TiAl systems show that they all have metallic conductivities. After Zr atom substitutes the Al atom in the -TiAl system, the intensity of covalent bond between Zr atom and its nearest neighbour Ti atoms in Ti12Al11Zr system reduces evidently and the bond length increases (0.032 ), which is indicated by the obtained overlap population (decrease by 0.21) and the densities of states in the Zr-doped and pure -TiAl systems. These results in the decrease of average intensity of Ti-Al(Zr) bonds and the increase of metallic bonds in Ti12Al11Zr system, which is an important factor for improving the ductility of -TiAl based alloys.

## EDITOR'S SUGGESTION

2016, 65 (4): 046201.
doi: 10.7498/aps.65.046201

Abstract +

The refractive index of Z-cut quartz under magnetically driven quasi-isentropic compression is researched by using the pulsed power generator CQ-4. Its velocities of interface between the aluminum panel and the window are measured by a four-channel dual laser heterodyne velocimeter, which is operated at an incident laser wavelength of 1550 nm. The history profile of magnetic pressure on the electrodes is obtained by a backward integration calculation of the aluminum/LiF interface velocity. And then the pressure history profile is used in the LS-DYNA simulation to get the true particle velocity of the aluminum/quartz interface. Combining with the apparent particle of aluminum/quartz interface which is obtained from experiments, a continuous index of refraction in Z-cut quartz has been obtained at up to a pressure of 14.55 GPa as the longitudinal stress is gradually increased to its elastic limit. The relation between the apparent particle and true particle velocities can be fitted by a polynomial, and the required derivative obtained by differentiation of that polynomial. Refractive index determined from the linear fitting parameters is n=1.087 ( 0.008)+0.4408 /0, which agrees well with the previous shock results. Results from polarizability analysis suggest that the temperature and loading path should have less effect on the refractive index of Z-cut quartz within its elastic limit.

2016, 65 (4): 046801.
doi: 10.7498/aps.65.046801

Abstract +

In this work, the relaxation dynamics of optically excited electrons and lattice in translucent gold nanofilms is measured with femtosecond transient reflection and transmission technique. In order to investigate the mechanisms of heat transfer in metal nanofilm theoretically, the two-temperature model and the Crude-model approximation are used to estimate the profile of decays and the temperature of electrons and lattice. Ultrafast relaxation dynamics of gold nanofilm 60 nm in thickness is different obviously in transient reflection and transmission measurements. Electron-lattice coupling effect in the transmission method is stronger and more sensitive than that in the reflection method under the same experimental conditions. Gradient change of temperature along the direction of film thickness and interface thermal resistance due to the boundary scattering should be responsible for the difference between them. Experimental data suggest that both transient reflection and transient transmission of translucent films should be considered together in the investigation on the mechanism of heat transfer. With increasing energy of pump laser pulse, the rise time is about 1.0 ps, and the electron-lattice relaxation time becomes longer.

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

2016, 65 (4): 047501.
doi: 10.7498/aps.65.047501

Abstract +

Vortex structures in a mesoscopic a superconducting ring, which is in the magnetic field generated by a circular electric current, are investigated based on the phenomenological Ginzburg-Landau (G-L) theory. Due to the axial symmetry of the system, the three-dimensional problem is reduced to a two-dimensional problem. We can mesh a two-dimensional sample into grids, and discretize the first G-L equation by using the finite-difference method. Then the eigenvalues and eigenfunctions will be evaluated numerically by solving the discrete equations. With the eigenvalues and eigenfunctions we further obtain the minimum free energy of the system and the corresponding superconducting wave function. We discuss the influences of the ring size and magnetic field distribution on two kinds of the vortex structures: giant vortex state (GVS) and multivortex state (MVS). Calculations show: 1) the GVS with axial symmetric wave function exists only in a small size superconducting ring, as the GVS is a state of single vortex line that only goes through the hole at the center of the superconducting ring and carries several magnetic flux quanta with it; 2) with the increase of the ring size, the diamagnetism of superconducting ring becomes stronger, and the critical magnetic field value of a giant vortex state increases, and the maximal number of giant vortexes that the superconducting ring can accommodate is also growing; furthermore, the entrance of a flux line will cause fluctuations of critical field values; 3) when the superconducting ring size is large enough, a GVS splits into a number of MVS. The MVS is an excited state and the GVS is mostly a ground state; 4) the free energy of the system changes with the magnetic field distribution, the magnetic field provided by a central small current loop can pass through the superconducting ring easily, and produce multivortices whose formations are diverse; if the magnetic field runs parallel to the plane of the superconducting ring, it is difficult to pass through the superconducting ring and form multivortices; 5) the vortex lines are naturally bent with the magnetic field lines and can pass through the same horizontal plane twice, so that one of the two vortex states seems to be an antivortex state; generally, the magnetic field lines can go through the hole of a superconducting ring easily but can hardly penetrate through the body of a superconducting ring, the structure of multivortices is similar to that of the magnetic field distribution in a superconducting ring. We also obtain a vortex structure with coexistences of giant vortex and multivortices. This study is of significance for the application of superconducting nanomaterials.

2016, 65 (4): 047701.
doi: 10.7498/aps.65.047701

Abstract +

Surface charge accumulation and decay behaviors of dielectric materials are the key factors restricting the development of high voltage direct current power equipment. For flat samples, the density of surface charges deposited by corona can be regarded as a linear change with the surface potential. For this reason, the behavior of surface charge decay can be directly related to that of surface potential. According to the corona charging process, the surface charge deposition and detrapping process, as well as the charge transport process in the bulk, we may establish a physical model dynamic response to the surface potential. Influences of grid voltage, relative permittivity, and bulk conductivity on the surface potential decay process can be obtained through calculating the surface potential decay behaviors of epoxy resin. The higher the grid voltage, the faster the surface potential decays. At the typical parameter value of epoxy resin (relative permittivity 3.93, bulk conductivity 10-14 S m-1), the normalized decay rate can be fitted by two straight lines in a log-log plot; moreover, the calculated results show a linear variation of power factors with the grid voltage, while the power function shows a relationship between the characteristic time and the grid voltage. The bigger the relative permittivity, the slower the surface potential decays. In the typical parameter area of epoxy resin (relative permittivity 3-4), the surface potential decay time constant increases from 1720 s to 2540 s, showing a linear variation. Also the bigger the bulk conductivity, the faster the surface potential decays. In the typical parameter area of epoxy resin (bulk conductivity 10-15-10-13 S m-1), the surface potential decay time constant decreases from 24760 s to 260 s, showing a power function relationship.

2016, 65 (4): 047801.
doi: 10.7498/aps.65.047801

Abstract +

Active manipulation of light in optical fibers has been extensively studied with great interest because of the structure simplicity, small footprint, low insertion loss and the compatibility with diverse fiber-optic systems. While graphene can be seen to exhibit a strong electro-optic effect originating from its gapless Dirac-fermionic band structure, there is no report on the electro-absorption properties of all-fiber graphene devices. Here a novel tunable graphene-based hollow optical fiber structure is designed with graphene coated on the inner wall of the fiber central core. Evanescent field of the guided mode propagating in the hollow optical fiber interacts with a monolayer or stacked multilayer graphene, which could modulate the intensity of the propagating mode via altering the chemical potential of the graphene by an external electric field. A full vector finite element method is adopted to analyse the influences of the chemical potential, the air-hole's radius and layers of graphene on the electro-optic modulation properties of the structure. Numerical simulation results show that by adjusting the chemical potential of graphene, the phase and on-off features of the fiber can be tuned correspondingly, as well as the position, magnitude and width of the loss peak and the sub-peak. However, the air-hole's radius and layers of graphene will only affect the loss variation, the magnitude and width of the loss peak and the sub-peak, but have no influence on the on-off point and the position of the loss peak and the sub-peak. In addition, the loss variation caused by N-layer graphene is N times that of the monolayer graphene. Since it is the dielectric constant of graphene that determines the effective refractive index and the loss of the fiber, the dielectric constant is only related to its chemical potential while independent of the air-hole's radius and the layers of graphene. Finally, an optimal electro-absorptive modulator based on the penta-layer graphene-coated hollow optical fiber is proposed for its advantage of ultra-compact footprint (5 mm 125 m), ultrawide optical bandwidth (580 nm), high extinction ratio (16 dB), high modulation bandwidth (64 MHz) and low insertion loss (1.23 dB), as well as a broad operational spectrum that ranges from 1180 to 1760 nm. Our results can provide theoretical references for the design and application of graphene-based tunable photonic fiber devices.

2016, 65 (4): 047802.
doi: 10.7498/aps.65.047802

Abstract +

As an important secondary explosive, cyclotrimethylenetrinitramine (RDX, C3H6O6N6) is extensively used in military and industrial applications due to its high energy density and low sensitivity to external stimulations. Considerable attention has been devoted to the study of the detonation initiation, with particular interest in the mechanism by which energy is transferred from a shock wave to the internal molecular vibrations so as to begin endothermic decomposition. During the whole process, phonons as the primary carriers of heat may play an important role. Experimentally, inelastic neutron scattering (INS) technique provides a means of studying the dynamics of motions of atoms and molecules in the crystal, especially in the low frequency region which contains most phonon lattice modes. In this work, neutron diffraction pattern of polycrystalline RDX under ambient condition has been measured and compared with the calculated results, showing reasonable agreement with and thus confirming the structure of RDX. Subsequently, the vibrational INS spectrum of RDX has been measured at T=10 K over the region of 10-104~cm-1 by using cold neutron triple-axis spectrometer. On the basis of the solid-state density functional calculations with the generalized gradient approximation (BLYP and BP functionals), it is possible to perform normal-mode analysis, which agrees with previous assignments. A total of 9 phonon lattice modes and 3 internal vibrations have been identified. Eight possible doorway modes may be predicted in the energy range between 100 and 148~cm-1, which arise from the combinations of phonon lattice modes 38.3, 40.3, 50.2, 61.5~cm-1 and fundamental vibrations 86.6, 88.6, 101.4~cm-1. The doorway modes are the proposed bridge by which the energy of initial shockwave can pass from the external degrees of freedom into those of the molecule. It is shown that all of these eight modes have fundamental vibrational components that consist of nitro-group deformation vibrations. This point is of particular importance and supports the theory that the initial bond broken in detonation is the NN bond. This work may shed light on the mechanism of detonation initiation from a microscopic viewpoint.

2016, 65 (4): 047901.
doi: 10.7498/aps.65.047901

Abstract +

Multicarrier multipactor, which is found in the wideband high power vacuum microwave passive components, potentially threatens the reliability of microwave systems in space and accelerator applications. The global threshold analysis of multicarrier multipactor is of vital importance for the risk assessment of high power vacuum devices. Till now, however, no effective solutions for the global threshold analysis of multicarrier multipactor have been proposed for practical microwave components with complex structures. In this paper, an efficient approach capable of evaluating the global threshold of multicarrier multipactor based on detectable level of multipactor test system is presented. Electromagnetic characteristics of the microwave device are theoretically related to the electron density by equivalently considering the distribution zone of electrons as a plasma medium. In order to obtain the global threshold using the optimization algorithm, such as the Monte Carlo method, we further propose an efficient approach capable of rapidly computing the fluctuation of number of electrons in the evolving process of a multicarrier multipactor based on the equivalency of half-sine-like segments for the acceleration of electrons. Analytical results comply with the tested thresholds. Different from the conventional equivalent power using the empirical rule, the proposed approach is based on the criterion of critical density of electrons and rapidly computing the fluctuation of number of electrons, providing an efficient method for the accurate global threshold analysis of multicarrier multipactor.

## EDITOR'S SUGGESTION

2016, 65 (4): 047902.
doi: 10.7498/aps.65.047902

Abstract +

Combining ultraviolet photoemission spectroscopy (UPS), X-ray photoemission spectroscopy and atomic force microscopy (AFM), we perform a systematic investigation on the correlation of energy level alignment, film growth and molecular orientation of 2, 7-dioctyl[1]benzothieno-[3, 2-b][1]benzothiophene (C8-BTBT) on Ni(100). The molecules lie down at the first layer and are partly devulcanized by the substrate. Chemical adsorption of reaction products of sulfur atoms on the Ni substrate and the evaporation of the hydrocarbon products into vacuum make the C/S ratio as low as 11.5 : 1 in the XPS of the initially deposited C8-BTBT film of 1-4 thickness, far less than the stoichiometric of 15 : 1. With the thickness increasing from 4 to 8 , there are sharp downward shifts of Evac, HOMO and core levels of C 1s, S 2p, and a sharp increase of C/S ratio, which can be ascribed to the change of molecular orientations from lying down at 4 to standing up at 8 . From 8 onward, the C/S ratio increases steadily till it reaches 15 : 1. The energy levels show relatively less changes when the thickness increases from 8 to 32 . When the thickness increases over 32 , the energy band starts bending downward apparently because of the charging effect during the photoelectron emission processes. The poor conductivity along the standing alkyl chain of C8-is the main cause for the charging. The standing up configurations of the C8-BTBT molecules are confirmed by the AFM investigation in which the heights of the upper layers of C8-BTBT are around 30 , close to the length of the long c-axis. AFM image also indicates that the molecules tend to grow into islands for larger thickness, which is consistent with the slower decrease of the (I/I0) of Ni 2p3/2 with the C8-BTBT film thickness. Our results suggest that a buffer layer be inserted between Ni and C8-BTBT and the thickness of the C8-BTBT film be controlled as thin as possible in related devices.

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

2016, 65 (4): 048101.
doi: 10.7498/aps.65.048101

Abstract +

The diameter monodispersity and the surface charge distribution of three imogolite-like nanotubes (not substituted (IMO), substituted by NH2 (IMO-NH2), substituted by F (IMO-F) are investigated using self-consistent periodic density functional theory, and the phenomenon of the monodispersity is explained qualitatively in terms of bond length. We assume that the axial length of the nanotube is constant and confirm it; the energetic minimum axial lengths of the three nanotubes increase in the sequence IMO_NH2 IMO IMO_F, and are respectively 8.61, 8.62 and 8.66 . Then the energies for different nanotubes and lamellar structures are calculated. A series of strain energy curves of IMO, IMO_NH2 and IMO_F are plotted based on calculations, and the results show that the energetic minimum diameters of these three nanotubes increase in the sequence of IMO IMO_NH2 IMO_F, and are respectively N= 9, 10 and 11. In order to explain the diameter monodispersity, we have calculated the bond lengths of SiO, AlO and AlOH three nanotubes and plotted the curves of length against diameter. Results show that the monodispersity can be attributed to the interaction between the energy increase resulting from the stretching of the SiO, AlO bonds in the inner wall, and the energy decreases caused by the shortening of the AlOH bond in the outer wall. In a word, with the increase of tube diameter, the SiO and AlO bonds increase while the AlOH bond decreases monotonically. Additionally, we have also calculated the Mulliken charge distributions of the three nanotubes with different diameter and analysed their surface charges. On this basis, we summarize the effect of diameter on surface charge. Results show that the main positive charges are accumulating on the outer surface while the negative charges are located on the inner region, and the outer surface charge increases gradually with the increase of the diameter of the nanotubes. The study indicates that the internal surface functional group has an effect on the axial length, diameter and surface charge of the imogolite-like nanotubes. We can control the nanotube diameter and surface charge distribution by changing different functional substitutes in the inner surface; it is significant in the molecular design and application of imogolite-like materials.

2016, 65 (4): 048102.
doi: 10.7498/aps.65.048102

Abstract +

The structure magnetism and ordering transition of the ferromagnetic shape memory alloy Mn2 -xNiGa1+xhave been systematically studied in this paper. With increasing Ga content, the structure of the parent phase Mn2 -xNiGa1+x is transformed from Hg2CuTi-type to Cu2MnAl-type Heusler alloy gradually. Its lattice constant increases first and then decreases, reaching its maximum at x=0.3. The sample displays both the primary phase of Heusler and the Ni2In-type hexagonal phase in precipitate form when x lies in the range of 0.3-0.8. The Curie temperature of the primary phase of Heusler alloy Mn2 -xNiGa1+x reduces gradually from 590 K for Mn2NiGa to about 220 K for Ga2MnNi with the decrease of the exchange interaction between 3d electrons in the transition metals. However, the variation of Curie temperature of Ni2In-type hexagonal phase is gentle. The separation of Curie temperatures between the Ni2In-type hexagonal phase and the primary phase of Heusler occurs when x lies in the range from 0.6 to 0.8. Substitution of Mn by Ga has a significant influence on the coupling interaction among various atoms, leading to first increasing and then decreasing of the saturated magnetization of Mn2 -xNiGa1+x at low temperatures. That is, the saturated magnetization will rise for x0.4 and drops sharply for x0.4. Results of differential scanning calorimeter show that the melting temperature decreases gradually as x increases. Meanwhile, the transition temperature from parent phase (B2) to Heusler phase decreases first and increases later.

2016, 65 (4): 048401.
doi: 10.7498/aps.65.048401

Abstract +

In this paper, we investigate the transmission mechanism and eddy-current loss of the contact-less power transmission (CPT) system in seawater environment. Contact-less power transfer could be achieved in the three following ways: magnetic coupling, magnetic resonance coupling, and microwave radiation. When the primary and secondary coils are in resonance, a channel of low resistance in the magnetic resonance coupling system is formed. Therefore, it is used for medium-distance power transmission and it has less restrictions on orientation, which means that it has wide applications in many scenarios. Moreover, contact-less power transfer is safer and more concealed than traditional plug power supply, especially in underwater vehicles. Firstly, the mathematical model based on the mutual inductance model is proposed for the CPT system in the air, then the frequency analysis of the CPT model as well as theoretical explanation of the splitting phenomenon is conducted, after that we consider the seawater effect on the mutual inductance coefficient. Secondly, we build a mathematical model of the eddy-current loss in seawater circumstance according to the Maxwell's equations, where we introduce an average magnetic induction in cross section, then derive an approximate formula through Taylor expansion, and analyze the relations between eddy-current loss and the physical parameters including coil radius, resonance frequency, transmission distance, and magnetic induction. According to the theoretical results, we optimize these physical parameters and then design a 754 kHz CPT system, thereafter we validate the CPT system both in the air and in seawater and find the difference between these two circumstances, and verify the relations between eddy-current loss and the physical parameters which are proposed in our theory. It can be learned from the experiment that when transmission distance is 50 mm and transmission power is 100 W in the air, the transmission efficiency is over 80%, and when transmission distance is 50 mm and transmission power is 100 W in seawater, the transmission efficiency is over 67%. Apparently, our magnetic-resonance-coupling-based CPT system has potentials serving as an underwater vehicle.

2016, 65 (4): 048701.
doi: 10.7498/aps.65.048701

Abstract +

In this paper, we propose a quantitative approach to analyze the influence of pupil truncation on the phase-only modulation laser beam shaping system, based on the near-field phase and the far-field metric functions. First, the relationship between near-field phase and pupil radius is studied by Lagrange multiplier method. Result indicates that both the peak-to-valley and the root-mean-square of the near-field phase increase approximately linearly with the pupil radius. Second, the influence of pupil radius on a beam shaping system is investigated. To quantify the performance of the beam shaping system, the correlation coefficient (C) and the mean square difference (MSD) are introduced as the metric functions. Then, by comparing the metric functions at different pupil radius, it is shown that the pupil radius influences the performance of focal beam shaping distinctly at the lower pupil radius, whereas the influence trails off, and both the C and the MSD get close to the theoretical limit as the pupil radius continuously increases. Third, the mathematical models of the C and the MSD are proposed to reveal the relationship among the metric functions, pupil radius and target intensity's size, as it is difficult to obtain the explicit expressions on the basis of metric functions' definition. And the three coefficients in each model are ascertained by surface fitting method based on the sampling data. In addition, SSE (sum of square due to error), RMSE (root mean square error) and R-square (coefficient of determination) are adopted to determine the fitting precision. For both the metric functions, the precision of SSE and RMSE can reach 10-2 and the R-square is shown to be more than 97%. The SSE, RMSE and R-square verify the proposed mathematical models. Finally, according to the models, we analyze when the influence of pupil truncation becomes negligible for the rectangle or circle target intensity. In practice, the size of target intensity is determined first. Sequentially, by combining the mathematical models and their first-order partial differentials, the changing regularity of metric functions with respect to pupil radius is studied. Meanwhile, the regularity helps us to find the beginning points for rectangle target and circle target intensities respectively. For the rectangle target intensity, when the pupil radius is 2.5 times that of the Gaussian waist radius, the metric functions become stable. The C with a value of 0.997 and the MSD with a value of 410-4 are both close to the theoretical limit. In the meantime, the influence of pupil truncation tends to be minimal as expected. For circle target intensity, when the pupil radius is 3 times that of the Gaussian waist radius, the first-order partial differentials of the C and the MSD decrease to about 10-3. This means that the metric functions begin to converge and that the influence of pupil truncation tends to be minimal at this point. Consequently, it is effective and meaningful to determine the best pupil radius using the proposed models in the article when designing a beam shaping system. Moreover, the models can also be used to evaluate the performance of a laser beam shaping system.

2016, 65 (4): 048801.
doi: 10.7498/aps.65.048801

Abstract +

To verify that the molybdenum metals exhibit similar catalysis characteristics as the related molybdenum compounds, i.e. molybdenum selenide (MoSe2) and molybdenum sulfide (MoS2) which have been well known as the high-performing catalysts for hydrogen evolution reactions, we may thus seek a low-cost, process-simplified, scalable, and highly-catalytic counterpart. We have grown periodic molybdenum (Mo) metal catalytic electrodes by employing self-assembled polystyrene (PS) spheres prepared by a sauna-like method as templates, followed by a reactive ion etching (RIE) process with oxygen gas and a double-layer deposition by low-temperature magnetron sputtering. By controlling the etching time of oxygen gas on PS spheres during the RIE process, the lateral and vertical feature sizes of Mo catalytic electrodes can be efficiently controlled, thereby having various surface area ratios. According to surface morphologies from atomic force microscopy, electrochemical linear sweep voltammetry, Tafel, and impendency measurements, we have found that the surface roughness and surface area ratios of Mo metal catalytic electrodes can be enhanced by prolonging the etching times of PS spheres, thereby reducing the charge transfer resistances and Tafel slopes, and then improving the hydrogen evolution reactions at the catalysts/electrolyte interfaces. We attribute this improvement to the fact that the Mo metal catalytic electrodes can efficiently form beneficial Schottky junctions with the electrolyte to enhance the carrier transportation, and the increased surface area ratios can improve the effective area of the Schottky junctions, thereby enhancing the carrier transportation at the catalysts/electrolyte interfaces. Tafel slope of the periodic molybdenum (Mo) metal catalytic electrodes in our work is as low as about 53.9 mV/dec, equivalent to highly catalytic materials MoS2 (55 mV/dec) and MoSe2 (105-120 mV/dec). The proposed periodic Mo catalytic electrodes, which combine a simple sauna-like self-assembly process with a double-layer Mo architecture is scalable and simple; and the surface area of periodic molybdenum (Mo) metal catalytic electrodes can also be flexibly controlled, so that the low-temperature magnetron sputtered Mo metal catalytic electrodes are cost-effective and highly compatible with various photovoltaic devices, highlighting the great potential to form high efficient monolithic solar-water-splitting devices.

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

2016, 65 (4): 049701.
doi: 10.7498/aps.65.049701

Abstract +

Rotation and tide are two important factors that have very important impacts on the stellar structure and evolution. Based on the observational data of Achernar, we have derived the inclined pressure structure in a single rotating star or as a member in the binaries. We have given the distributions of the physical quantities on the isobaric surface and these distributions are derived from the Legendre series of expansions. We have also found the relationship between all levels of perturbation potential functions (including rotational and tidal distortions) and the distributions of density and pressure under the condition of inclined pressure structure. In particular, the gravitational darkening with the models including the effects of rotation and tide is investigated. We have found that the critical ratio of equatorial radius to the polar radius is consistent with the observations in rotating binaries better than that in single rotating model. The reason is that the tidal force can make the polar radius shortened because the tidal force exerts an inward force to the two polar points. However, the theoretical angular velocity in binaries is smaller than that observed. It is also shown that the positive shear enhances the centrifugal force and decreases the mean effective gravitational acceleration and effective temperatures whereas the negative shear plays a role to strengthen the effective gravitational acceleration. Moreover, the solid body rotation has not been supported inside Achernar because magnetic fields have not been detected through observations. Furthermore, the theoretical angular velocity in rigid rotation is higher than the angular velocity observed. Achernar has a periodic variation of light curves due to mass outburst, which also supports differential rotation. A positive shear indicates that the mass in accretion disks is falling to Achernar and the Achernar is spun up to critical rotation according to current observations. By comparing the theoretical results with observations, it can be seen that when the theoretical spin angular velocity of Achernar is 4.65 10-5 s-1 and the positive shears / s are 0.7851, the temperature of the polar points is 16041 K and that of equatorial sphere is 12073 K. Relative errors between the theoretical values and observations are less than 3% and are listed in the text. This model is the best and is the most possible one for Achernar.