## Vol. 66, No. 22 (2017)

##### 2017-11-20

###### GENERAL

## EDITOR'S SUGGESTION

2017, 66 (22): 220202.
doi: 10.7498/aps.66.220202

Abstract +

The cladding mode of the in-fiber interference sensor relates to the externally sensing physical quantity, so the investigation of the cladding mode is very important for designing and improving the sensing performance of the sensor. By using the finite difference beam propagation method, the interference spectra of the sensors with different lengths and different core-to-core diameter ratios are simulated. Its spatial frequency spectrum is obtained through Fourier transform. The effective refractive index of the dominant cladding mode can be obtained through analyzing its spatial frequency spectrum. Its corresponding cladding mode order can be determined through substituting the values of the effective refractive index into the dispersion equation of sensing optical fiber. The simulation results show that the number and the order of the cladding modes both increase with sensing part fiber length increasing. The interference spectrum becomes dense according to the superposition of multi order cladding mode interferences. Its free spectral space of the sensor output interference spectrum becomes small. With the variations of the input fiber and sensing fiber core-to-core diameter ratio, the power distributions among the modes change obviously. The increase of core-to-core diameter ratio can increase the number and order of the cladding modes.

## EDITOR'S SUGGESTION

2017, 66 (22): 220203.
doi: 10.7498/aps.66.220203

Abstract +

Global optimization methods are becoming more and more important in aerodynamic shape optimization. A large number of proceeding data will be generated during design optimization, from which the implicit but valuable design knowledge can be extracted. The design knowledge can then be used to help the designers to acquire the effects of geometric variations on the aerodynamic performance changes. In this paper, we strive to extract the implicit design knowledge from proceeding data by a data mining method based on proper orthogonal decomposition (POD), by which the design knowledge more enriched and more visualized than those obtained from other data mining methods can be obtained. Proceeding data for data mining are ingathered from aerodynamic shape optimization of a transonic compressor rotor blade, NASA Rotor 37. The design optimization attempts to maximize the adiabatic efficiency of Rotor 37 under the operation condition near peak efficiency with the constrains of mass flow rate and total pressure ratio. The parallel synchronous particle swarm optimization method is employed to search for the optimization in the design space. The particles with improved adiabatic efficiency, while within the optimization constrain tolerances are picked up from the design optimization, which are then used for data mining. The geometric coordinates of the aerodynamic shape with respect to the ingathered particles are regarded as the snapshots. Then the POD modes of the aerodynamic shape can be obtained by singular value decomposition on the snapshots. The results show that the universal rules of geometry variations for the optimization maximizing the adiabatic efficiency of Rotor 37 can be directly visualized by the design knowledge extracted from the proceeding data by POD-based data mining technique. Furthermore, the optimization results are also verified by the design knowledge extracted by data mining.

2017, 66 (22): 220204.
doi: 10.7498/aps.66.220204

Abstract +

Long-term measurement of CO2 and its stable isotopes not only obtain the CO2 sources and sink information, but also determine the contributions of different emission sources to atmospheric CO2.Fourier transform infrared spectroscopy (FTIR) is an important technique which can provide highly precise remote sensing of column abundances of atmospheric trace gases.In the study,the stable isotopes of atmospheric CO2,13CO2 and 12CO2,are retrieved from the near-infrared solar absorption spectra collected by a ground-based high-resolution Fourier transform spectrometer. Three spectral windows of 13CO2 and two spectral windows of 12CO2 are chosen to retrieve the two species.The root mean square spectral fitting residuals are about 1.2%,2.3% and 1.2% for the three spectral windows of 13CO2,and about 0.64% and 0.60% for the two spectral windows of 12CO2,respectively.The small spectral fitting residuals indicate the high-quality spectral fitting.The mean retrieval errors are (1.180.27)% and (0.890.25)% for 13CO2 and 12CO2 during the experiment,respectively.The measurement precision of carbon isotopic ratio 13C for the observation system is estimated to be about 0.041 based on the Allan variance method,comparable to the precision of in situ FTIR measurement.Moreover,long time series of atmospheric 13C in one year from September 18,2015 to September 24,2016 is obtained.The results show that atmospheric 13C varies from -7.58 to -11.66,and the mean value is about (-9.50.57) over the duration of the experiment.Also,time series of carbon isotopic signature 13C has an obvious seasonal trend,with a minimum of (-9.350.47) in winter and a maximum of (-8.730.39) in summer. The further analysis suggests that the increase of emission from the fossil fuel burning due to heating may explain the depletion of heavy isotope 13CO2 in winter.Additionally,it is revealed that the variation range of atmospheric 13C observed in Hefei area is consistent with the reported values in Nanjing area based on in situ measurement,while 13C values in summer and winter are higher than the corresponding values detected in Beijing area as indicated in recent publications,which may result from the fact that the CO2 emissions from the fossil fuel combustion in Beijing are more than those in Hefei.The experimental results demonstrate the ability of the ground-based high-resolution FTIR to detect the stable isotopes of atmospheric CO2,13CO2 and 12CO2,and carbon isotopic ratio 13C with a high precision and accuracy.

2017, 66 (22): 220301.
doi: 10.7498/aps.66.220301

Abstract +

An impurity immersed in a superfluid can move without friction when its velocity is below a critical value. This phenomenon can be explained by the famous Landau criterion, according to which, the critical velocity is determined by the elementary excitation spectrum of the superfluid. Landau critical velocity has been measured in the isotropic superfluid, such as the liquid He-Ⅱ and the Bose-Einstein condensates of dilute atomic gases, where the onset of dissipation is due to the creation of roton and phonon, respectively. The recent realization of synthetic spin-orbit coupling in quantum gas opens up possibilities for the study of novel superfluidity with ultracold atoms. To date, a specific type of spin-orbit coupling, which is generated by a pair of Raman laser beams, has been achieved in a Bose-Einstein condensate of 87Rb experimentally. Remarkably, the excitation spectrum of this system is anisotropic and can be feasibly tuned by the external laser field. While the anisotropic dynamics has been observed experimentally, the critical velocity has not been measured so far. It is a conventional wisdom that in an anisotropic superfluid, the critical velocity is determined by the excitation spectrum in the moving direction of the impurity. However, this is not always the case. In this work, we investigate the motion of a point-like impurity in a spin-orbit-coupled condensate with the spin-dependent interatomic interaction. In the vicinity of the quantum phase transition between the plane-wave (PW) phase and the zero-momentum (ZM) phase, the onset of the dissipation is due to the emission of a phonon, and the Landau critical velocity vc depends on the anisotropic sound velocity. While the sound velocity varies smoothly across the PW-ZM phase transition, the critical velocity in the direction perpendicular to the axis of spin-orbit coupling exhibits a sudden jump at the phase boundary. The value of vc on the PW phase side of the transition is generally smaller than the one on the ZM phase side, and the jump amplitude of vc is an increasing function of the spin-dependent interaction strength. Beyond the critical velocity, the energy dissipation rate of the impurity is explicitly calculated via a perturbation approach. The discontinuity of vc at the phase boundary can be clearly seen from the dissipation curves, which can be measured through the heating of the condensate. Our prediction can be tested in the current experiments with ultracold atoms.

2017, 66 (22): 220501.
doi: 10.7498/aps.66.220501

Abstract +

Molecular motors in life activities of cell are known to operate efficiently.They could convert molecular-scale chemical energy into macroscopic-scale mechanical work with high efficiency.In order to acquire the transport mechanism of the molecular motor,the Brownian ratchet has been proposed to explore the property of directed transport and energy conversion.There are different kinds of Brownian ratchet models like flashing ratchets,rocking ratchets,and time-asymmetric ratchets and so on.Through investigating the performance of Brownian ratchet moving in periodic potential,the directed transport of ratchet could be explained,and the effective usage of ratchet energy for directed transport could also be improved.Recently,optimizing the transport of Brownian ratchet has aroused the interest of researchers.It is found that the viscous resistance could reinforce the directed transport of the Brownian particle in damping liquid.Meanwhile,a large number of conclusions indicate that the transport of Brownian ratchets would be enhanced if the asymmetry of the potential is changed.Those results show that the influences of the external potential and the damping force on the particle flow cannot be neglected.Hence in this paper,the effects of the potential structure and the temperature of heat bath on transport are discussed.
Furthermore,how to use the ratchet energy effectively has been investigated in recent years.When the Brownian motor operates with load,the input energy is reduced.More importantly,the energy transformation efficiency defined as the ratio of the useful work done against the load to the input energy is assumed to be a zero value in the absence of load.With the help of stochastic energetic theory proposed by Sekimoto,the Stokes efficiency has been used to explore the performance of the Brownian ratchet.So far,the numerical solution has been used extensively in most theoretical investigations.Nevertheless,in our work,the Stokes efficiency is discussed analytically for explaining the mechanism of directed transport.We consider the transport performance of the Brownian ratchet described by the Fokker Planck equation which is corresponding to the Langevin equation under time-varying external force and thermal noise.Mainly, the effects of potential asymmetry,external force,height of the barrier,and intensity of the thermal noise on transport are discussed in detail.It is found that the transport direction of Brownian ratchet will be reversed under the condition of appropriate potential structures,and the probability current can reach a maximal value by changing the asymmetry of potential.It is worthwhile to point out that the performance of directed transport of the ratchet can be improved when an appropriate amplitude of the external force is applied.Meanwhile,there is an optimal value of the barrier height at which the Stokes efficiency reaches a maximal value and the directed transport of ratchet is enhanced.Through our conclusions,the ratchets of different structures could be designed for improving the transport property of Brownian motor.And the results have helpful theoretical guidance not only in the aspect of medical delivery but also in the control of nano-devices.

2017, 66 (22): 220502.
doi: 10.7498/aps.66.220502

Abstract +

In the study of piezoelectric cantilever energy harvesting system, a bi-stable nonlinear cantilever with magnets added to the structure has a wider frequency band response and a higher energy output efficiency. Hence, the calculation accuracy of the magnetic force on which the potential function and dynamics of the system depend is essential to predicting the output response and energy harvesting effect. In this work, we use a shape function to describe the relation between the deflections of an arbitrary point and the free-end point on the beam, and then calculate the trace and deflection angle of the beam's free-end by integrating the entire slope of the cantilever beam. The magnetic force is consequently derived from the magnets' real-time relative positions and postures by using the magnetizing current method. With comprehensively considering the axial magnetic force and the lateral magnetic force, the simulation results demonstrate that when the displacement of the magnet at the end of the beam is large enough, the directions of axial and lateral magnetic force change from repulsive to attractive, which leads to a large veer of the resultant magnetic force across two quadrants. So, it means that a smaller interval between magnets may not cause a larger deflection of the beam, and the magnetic force existing as attractive force could diminish the well space of potential function (that is, the distance between two equilibrium positions of the system). The experimental data in this work are nicely consistent with the simulation results. And in this work, we also make a comparison of the simulation results with those from our method and existing method, showing that the accuracy of the proposed method is much higher than that from the existing calculation method, especially in the scenario where the magnet at the end of the beam is far from the horizontal axis.

2017, 66 (22): 220701.
doi: 10.7498/aps.66.220701

Abstract +

In practical applications such as mobile communication, radar and sonar, the effect of angular spread on the source energy can no longer be ignored due to multipath phenomena. Therefore, a spatially distributed source model is more realistic than the point source mode in these complex cases. A lot of direction-of-arrival (DOA) estimation methods for distributed sources have been published. Whereas researches concentrated on the complex circular signal case, the noncircular property of signal can be employed to further improve the estimation performance, which has received extensive attention recently. To date, several low-complexity DOA estimation algorithms for two-dimensional (2D) coherently distributed (CD) noncircular sources have been proposed. However, all these algorithms need obtain the approximate shift invariance relationship between the sub-arrays by applying the one-order Taylor series approximation to the generalized steering vectors, which may introduce additional errors and affect the estimation accuracy.
In this paper, a novel 2D DOA estimation algorithm based on the symmetric shift invariance relationship is proposed using the centro-symmetric three-dimensional (3D) linear arrays. Firstly, the extended array model is established by exploiting the noncircularity of the signal. Then, it is proved that the deterministic angular distribution function vector of the CD source has a symmetrical property for arbitrary centro-symmetric array, based on which the symmetric shift invariance relationships of extended generalized steering vectors are established in the three sub-arrays of 3D linear arrays. On the premise of such relationships, the center azimuth and elevation DOAs are obtained by the polynomial rooting method without spectral peak searching. Finally, the cost function implementing the parameter matching is constructed by the symmetric shift invariance relationship of the generalized steering vector of the whole array. Theoretical analysis and simulation experiment show that compared with the existing low-complexity algorithms, the proposed algorithm avoids the additional errors introduced by the Taylor series approximation, which allows it to achieve higher estimation accuracy with the small complexity cost. Moreover, the proposed algorithm can achieve omnidirectional angle estimation in the three-dimensional space.

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

2017, 66 (22): 224101.
doi: 10.7498/aps.66.224101

Abstract +

The electronic structure of a 3,4,9,10-perylene-tetracarboxylic-dianhydride (PTCDA) thin film is investigated in situ using synchrotron-based near edge X-ray absorption fine structure (NEXAFS) spectroscopy and resonant photoemission spectroscopy (RPES).The NEXAFS spectroscopy can monitor the electronic transitions from core level to unoccupied states.The C K-edge NEXAFS spectrum of the PTCDA thin film shows four distinct absorption peaks below 290 eV,which are attributed to the transitions from 1s core level of C-atoms in different chemical environments (perylene core C-atoms vs anhydride C-atoms) into lowest unoccupied molecular orbitals (LUMOs) with * symmetry. The RPES spectra are collected in the valence band region by sweeping photon energy across the C 1s * absorption edge.Three typical features of the C 1s signals excited by second-order harmonic X-ray,resonant photoemission and resonant Auger features are observed in RPES spectra,and are identified,relying on the development of kinetic energy of the emitted photoelectrons upon the change of incident photons energy.It is found that the C 1s signals excited by second-order harmonic X-ray are present at high kinetic energy side of spectrum.The kinetic energy of this feature shows photon energy dependence,that is,this feature shifts to higher kinetic energy by photon energy increasing twice.Resonant Auger peaks in RPES spectra are located on the low kinetic energy side with constant kinetic energy regardless the change of photon energy.The resonant Auger may originate from deeper molecular orbitals with binding energy large than 4.1 eV,suggesting that the resonant Auger decay process involved in deeper molecular orbitals occurs on a time scale comparable to C 1s core hole lifetime of 6 femtoseconds.Resonant enhancement of highest occupied molecular orbitals (HOMOs) derived valence band features or HOMO-1 and HOMO-2 derived resonant photoemission features in our case are lying between the C 1s signals and the resonant Auger signals.The Kinetic energy increases as the photon energy sweeps across the absorption edge,whereas their binding energy remains constant.In addition, the enhancements of two resonances show photon energy dependence that enhancement of HOMO-1 related resonance dominates over HOMO-2 related resonance at energies corresponding to perylene core C 1s to LUMOs transitions, whereas HOMO-2 related resonance becomes dominant at transitions from anhydride C 1s to LUMOs.This behavior can be related to the wavefunction character and symmetry of the frontier molecular orbitals.Clarifying each resonant feature in RPES spectra and their origin will pave the way for accurately determining the ultrafast charge transfer time at organic/electrode interfaces using synchrotron-based core hole clock technique implementation of RPES.

2017, 66 (22): 224201.
doi: 10.7498/aps.66.224201

Abstract +

Fourier ptychography (FP) is a newly developed imaging technology, which can reconstruct high-resolution (HR) wide-field image from a series of low-resolution (LR) images. The limitation of FP is its long acquisition and reconstruction time due to the numerous LR images that are needed and the low illumination intensity of light-emitting diodes (LEDs) which lead to long exposure time of imaging sensors. Many researches have been done to speed up FP. The available speeding-up methods with single LED illumination are still constrained by low illumination intensity of LED. Although multi-illumination methods can improve illumination intensity, they are time-consuming during spectrum decomposition. In this paper, we demonstrate a new efficient method, termed symmetric Fourier ptychography (SFP). For thin samples irrespective of phases, two center-symmetric illuminations generate the same intensity distribution, so that two center-symmetric LEDs used in FP can be lit up simultaneously and the illumination intensity is doubled. Spectra have central conjugate symmetry in Fourier domain so that only half of spectra need recovering, then, the processing time can be reduced by about 50%. Simulations are conducted with the Cameraman image as input amplitude. The LR images are generated based on the FP simulation process and then the LR images generated by LEDs from two center-symmetrical positions are summed. Furthermore, HR images are recovered by using FP reconstruction algorithms. It is found that root-mean-square-error of SFP is almost the same as that of traditional FP, which indicates that the SFP can achieve the same performance as that of traditional FP. Then, central conjugate symmetry is adopted in Fourier domain, where only half of spectra are recovered and the other half of spectra are obtained from conjugate symmetry. It proves that HR images can be recovered based on central conjugate symmetry in Fourier domain and 50% of processing time is saved. For imaging experiments of USAF target and biological samples, two LEDs of central symmetry are lit up simultaneously, and 113 LR images are gathered in contrast with 225 ones of traditional FP. It is also found that SFP can achieve the same resolution as that of the traditional FP. In the meantime, SFP can reduce about 50% LR images and save about 70% acquisition time without increasing the complexity of FP system and algorithms. In addition, SFP can be combined with other methods to further speed up the speed of FP, and its feasibility is proven by the experimental results of combination with adaptive Fourier ptychography. All results in this paper indicate that the proposed method has the potential to improve the application of FP in real-time imaging.

2017, 66 (22): 224202.
doi: 10.7498/aps.66.224202

Abstract +

Concave diffraction gratings (CDGs) have the advantages of being compact, time reliability, cost effective, and channel spacing accuracy. These devices can be used in the wavelength division multiplexing (WDM) systems and micro-spectrometer devices. However, comparing with arrayed waveguides gratings (AWGs), the development of traditional CDGs is far from satisfactory. Because the traditional CDGs need deeply etched facets and perfect grating profiles to reduce the insertion losses, which will increase the difficulty in etching process. In order to solve this problem, Bragg reflectors based CDGs (Bragg-CDGs) are proposed. This structure can greatly reduce the insertion loss, and reduce the difficulty in etching process. The performance of the Bragg-CDG is determined by both the reflection condition of the Bragg reflectors and the diffraction condition of the CDG. With the Bragg reflection condition determined, the diffraction condition of Bragg-CDG will have a major influence on the performance of device. For successive strips based Bragg-CDG, the number of Bragg periods per diffraction grating period is an important parameter of Bragg-CDG. The diffraction condition of concave gratings is closely related to this parameter. This parameter has an effect on the performance of Bragg-CDG, specially termed resolution, the free spectrum range, and the diffraction efficiency. The effect of the number of Bragg periods per diffraction grating period on the Bragg diffraction grating is studied by theoretical analysis. In addition, four Bragg-CDGs with different numbers of Bragg periods are studied using the finite-difference time domain method. The results show that with sizes of diffraction gratings fixed, the resolution of Bragg-CDG does not have a significant improvement by changing the number of Bragg periods per diffraction grating period; the total number of diffraction orders is proportional to the number of Bragg periods per diffraction grating period. The Bragg-CDG with a single Bragg period per grating period has a maximum diffraction efficiency, since it has the minimal number of diffraction orders; in addition, with the increase of the number of Bragg periods per diffraction grating period, the free spectrum range of the main diffraction order gradually decreases. This research can contribute to the development of the demultiplexer with the low insertion loss, the high resolution, and the wide operating waveband.

2017, 66 (22): 224501.
doi: 10.7498/aps.66.224501

Abstract +

The rapid development of social economy speeds up urbanization, but also brings urban traffic congestion and urban traffic problems, such as frequent accidents, energy consumption and environmental pollution. Road traffic, as a part of the most important components in city traffic, is a complex system problem. To solve the difficulties in current city development and people's production and living, and to promote the development of national economy and society greatly, we need to study the road traffic. In order to solve the problem of complex road traffic system influenced by many factors, a physics model of pseudo-fluid of macroscopic road traffic system is established in combination with the traditional Lighthill-Whitham-Richards physics model based on kinetic theory of granular flow. A coupling method of meshless particles with grid is adopted to solve the new traffic model, which is then applied to solving the typical traffic problems. In the new model, vehicles are likened to hard particles. Car-following is likened to collision interactions between particles. Driver driving affected by known road conditions is likened to the driving force exerted by external fluid in two-phase system consisting of fluid and particle, and the influence of vehicles in different lanes is likened to viscous effect between particles. Thus the pseudo-fluid model of road traffic system is deduced and established based on the kinetic theory of granular flow. Then, the traffic multiphase system model is established by adding pedestrians and other non-motorized vehicles to the particles with different attributes. The boundary model of road traffic system based on pipeline theory is established through comparing the boundary model of traffic lights, barricades and forbidden lane changes to wall boundary conditions. Therefore, a complex large traffic model with different initial and boundary conditions considering the complex factors of the system is established. The Smoothed discrete particle hydrodynamics (SDPH) is used to discretize the vehicle system model. A one-to-one correspondence between SDPH vehicles and real vehicles is established through adding the vehicle flow properties characterized by SDPH particles. Then the two-fluid model of road traffic system is solved by combining the finite volume method. Thus, a new simulation approach to solving the macroscopic model of traffic flow is established. Finally, the effects of mixed flow composed of motorized and non-motorized vehicles and vehicles merging on the road traffic are simulated by employing the established model and method. The real-time distribution of the vehicle on the road is obtained, and the variation of the vehicle flow density with time is analyzed. The simulation results are in good agreement with the measured values, which shows that the new model and method are effective and reliable, and they provide a new way of solving the road traffic problem.

2017, 66 (22): 224701.
doi: 10.7498/aps.66.224701

Abstract +

Considering the anharmonic vibrations and the interactions between electron and phonon of atoms, in this article we study the temperature dependence of Grneisen parameter, thermal expansion coefficient at low temperature and phonon relaxation time by using the theory and method of solid state physics. The influences of the anharmonic vibration of the atom on the above parameters are further discussed. The obtained results are as follows. 1) The thermal expansion coefficient of graphene is a negative value when the temperature drops below room temperature. The absolute value of the thermal expansion coefficient of graphene increases monotonically with the increase of temperature. The thermal expansion coefficient of graphene is-3.64×10-6 K-1 at room temperature. 2) The value of Grneisen parameter is zero in the harmonic approximation. If the anharmonic vibration is considered, the Grneisen parameter will increase slowly with the increase of temperature. Its value is between 1.40 and1.42 and the change is almost linear. And we find that the influence of the second anharmonic term is less than that of the first anharmonic term on Grneisen parameter. 3) The phonon relaxation time decreases with the increase of temperature. The rate changes rapidly at low temperature (T<10 K), then it changes very slowly. The phonon relaxation time is almost inversely proportional to temperature when the temperature is higher than 300 K.

2017, 66 (22): 224702.
doi: 10.7498/aps.66.224702

Abstract +

This paper performs a newly developed method, which combines the immersed boundary method (IBM) with multi-relaxation-time lattice Boltzmann flux solver (MRT-LBFS), for solving fluid-structure interaction problems. Finite volume discretization is used to solve the macroscopic governing equations with the flow variables defined at cell centers. Based on the multi-scale Chapman-Enskog expansion analysis, LBFS builds a relationship between the variables and fluxes in incompressible Navier-Stokes equations and density distribution functions in lattice Boltzmann equation. In order to ensure no-slip boundary condition, boundary condition-enforced immersed boundary method is used to treat the fluid-structure interface. The restoring force can be resolved by making a velocity correction in the flow field. The four-stage RungeKutta scheme is used to solve the motion equation of structure. Using the lattice model and immersed boundary method, fluid-structure coupling calculation can be implemented in a Cartesian grid, without generating the body-fitted mesh and using moving mesh technique. Therefore, the computational process is considerably simplified. In order to verify the validity and feasibility of IB-MRT-LBFS to solve fluid-structure interaction problems, both one-and two-degree of freedom vortex-induced vibrations (VIV) of a circular cylinder and two-degree of freedom VIV of two cylinders in a tandem arrangement are simulated by this proposal method. For a VIV cylinder system, the transverse vibration response is much stronger than the axial response. When the vibration occurs in the range of lock-in regime, the shedding vortex frequency of the wake is close to natural frequency of the cylinder so that resonance appears, consequently causing larger amplitude. For two VIV cylinders in a tandem arrangement, the dynamic behavior of each cylinder is significantly different from that of a single cylinder. The gap spacing between the two cylinder centers is a significant parameter which effects vibration characteristics and the spacing is fixed in the simulations of two tandem cylinders. With the effects of upstream cylinder wake, the axial and transverse amplitudes of downstream cylinder obviously increase with adding the reduced velocity. The downstream cylinder is delayed, coming into lock-in regime, and the range of lock-in regime is expanded under the effects of the wake of the upstream cylinder. As the reduced velocity is relatively large, the vibration response of the upstream cylinder is close to a single cylinder and the vibration response of the downstream cylinder is more intense than the upstream cylinder. Compared with the existing literature results, our result illustrates that IB-MRT-LBFS owns the ability to correctly predict the lock-in regime, dynamic response and the forces of vortex-induced vibrations of cylinders. And this method can accurately capture the wake structures.

2017, 66 (22): 224703.
doi: 10.7498/aps.66.224703

Abstract +

Junction temperature is an important factor affecting the reliabilities of semiconductor devices. Usually, the method of measuring the junction temperature is not tested on-line. However, due to the fact that neither contact thermal resistance nor thermal resistance varying with temperature is taken into account, there exists an error in the off-line measurement. A way to solve the problem of off-line measurement is to measure the junction temperature on-line. In this paper, we propose an electrical method of measuring the temperature rise of high-power bipolar transistor in the working condition. The measurement method is based on a good linear relationship between base-emitter voltage (Vbe) and temperature during the steady-state. Taking the model 2N3055 of bipolar high power transistor for example, in this paper we study the relationship between base-emitter voltage (Vbe) and temperature under the conditions of constant collector-emitter voltage (Vce) and collector-current (Ice). During the experiment, the device is placed in a thermostat. A voltage is applied to the device collector, a current is applied to the base, and the emitter is earthed. Before the device is measured, we set different temperatures and make sure that the equipment is in a steady state. In order to avoid the effect of self-heating, the pulse current is used in the experiment. The pulse width and the period are 500 μups and 1 ms, respectively.The research result shows that the base-emitter voltage (Vbe) decreases linearly with temperature increasing and the base-emitter current is changed below 4% when the temperature is in a range of 40 ℃-140 ℃. In this paper we also deduce the mathematical expressions for base-emitter voltage (Vbe) and temperature under a steady state. It is proved that the Vbe-temperatrue curve is linear and temperature error is less than 0.5 ℃ when the changes of base current value does not exceed 4%. Therefore, in this paper we deduce a new method of testing the junction temperature in the speeding up measurement experiment. By measuring any of the reference points on the calibration curve under certain experimental conditions, the junction temperature can be calculated quickly according to the proposed formula.Finally, the phase 11 is used to verify the proposed method. We measure the thermal resistance upper the case for the junction of model 2N3055 and the thermal resistance under the case for the junction of model 2SD1047. The measurement results of phase11are compared with the junction temperature calculated using the test formula. The results show that the error of junction temperature between the two methods is less than 0.7%, which is corresponding with the needs of practical application. It proves the correctness and feasibility of the method.

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

2017, 66 (22): 226801.
doi: 10.7498/aps.66.226801

Abstract +

The kesterite compound Cu2ZnSnS4(CZTS) is one of the most interesting materials for absorber layers of thin-film solar cells,not only because it is composed of earth abundant and non-toxic elements,but also owing to the fact that its absorption coefficient is high (on the order of 104 cm-1) and its optimal band gap is 1.5 eV for single-junction solar cells.
Plenty of methods are used to deposit the CZTS layer,such as evaporation,sputtering,spray-pyrolysis,sol-gel, pulsed laser deposition and electro-chemical deposition.Among these methods,sputtering is considered as one of the most viable deposition techniques for producing a large-scale panel of thin film solar cells with demonstrable productivity and easy adjustment.In this paper,Cu2ZnSnS4 thin films are prepared by in-situ annealing after being sputtered with a quaternary compound target.This technology can reduce the extrinsic defects in the thin film.It is desirable to control the growth of grain boundary,increase grain size and make the thin film more compact and smooth.
The in-situ annealing is a method which can heat a work piece fast to a certain temperature and maintain the temperature for some time after sputtering.As is well known,one of the major reasons for affecting CZTS device performance is the low open circuit voltage (Voc),and it is also a challenge to obtain a high value because there are a lot of defect states at the grain boundaries.The experiment shows that using the method of in-situ annealing after sputtering can obtain large size grains and smooth and compact surface.The obtained thin films are Cu-poor,Zn-rich and Sn-poor,which can restrain the Cu vacancies (VCu) and anti-site defects (CuZn,SnZn,and SnCu).The free carrier concentration (NA) increases with the increase of Zn content,while the open circuit voltage of CZTS solar cells increases with the increase of NA. In order to develop CZTS solar cells based on the thin films,the n-type CdS buffer layer (70 nm) is grown using chemical bath deposition,and intrinsic ZnO (70 nm) and ZnO:Al (250 nm) films are deposited by RF-magnetron sputtering.In the end,Ni-Al metal grids as the top electrode are prepared by thermal evaporation.The final solar cells with an active area of 0.25 cm2 are determined by mechanical scribing.The solar cell based the CZTS film with in-situ annealing has better-performance parameters,its open circuit voltage and short-circuit current density are 575 mV and 8.32 mA/cm2,respectively.The photoelectric conversion efficiency of 1.82% is achieved.In order to enhance the efficiency of device,it is important to minimize Cu/Zn disorder in CZTS film and control the element composition by optimizing high-temperature crystallization process.The relevant research work on reducing defects in the films,increasing the carrier collection and enhancing the Jsc is under way. This method not only avoids the contamination caused by the external annealing but also simplifies the preparation process of the thin film,which greatly saves the preparation time of the solar cell and is beneficial to industrial production.annealing is a method which can heat a work piece fast to a certain temperature and maintain the temperature for some time after sputtering.As is well known,one of the major reasons for affecting CZTS device performance is the low open circuit voltage (Voc),and it is also a challenge to obtain a high value because there are a lot of defect states at the grain boundaries.The experiment shows that using the method of in-situ annealing after sputtering can obtain large size grains and smooth and compact surface.The obtained thin films are Cu-poor,Zn-rich and Sn-poor,which can restrain the Cu vacancies (VCu) and anti-site defects (CuZn,SnZn,and SnCu).The free carrier concentration (NA) increases with the increase of Zn content,while the open circuit voltage of CZTS solar cells increases with the increase of NA.
In order to develop CZTS solar cells based on the thin films,the n-type CdS buffer layer (70 nm) is grown using chemical bath deposition,and intrinsic ZnO (70 nm) and ZnO:Al (250 nm) films are deposited by RF-magnetron sputtering.In the end,Ni-Al metal grids as the top electrode are prepared by thermal evaporation.The final solar cells with an active area of 0.25 cm2 are determined by mechanical scribing.The solar cell based the CZTS film with in-situ annealing has better-performance parameters,its open circuit voltage and short-circuit current density are 575 mV and 8.32 mA/cm2,respectively.The photoelectric conversion efficiency of 1.82% is achieved.In order to enhance the efficiency of device,it is important to minimize Cu/Zn disorder in CZTS film and control the element composition by optimizing high-temperature crystallization process.The relevant research work on reducing defects in the films,increasing the carrier collection and enhancing the Jsc is under way.
This method not only avoids the contamination caused by the external annealing but also simplifies the preparation process of the thin film,which greatly saves the preparation time of the solar cell and is beneficial to industrial production.

2017, 66 (22): 226101.
doi: 10.7498/aps.66.226101

Abstract +

Insertion devices are crucial parts of the third generation of synchrotron radiation facility and free electron laser devices. The use of insertion device can improve the brightness and coherence of synchrotron radiation light. Undulator, one kind of insertion device, is largely installed in the storage ring of Shanghai synchrotron radiation facility. The main part of undulator is the device of magnetic source which consists of periodically arranged permanent magnets with the same magnetic field strength. In order to keep the normal electronic trajectory, a stable magnetic intensity in undulator is required. The Sm2Co17 type permanent magnets with high intrinsic coercive force and good radiation stability are largely installed in the facility. However, the losses for magnetic properties of Sm2Co17 type permanent magnets can be induced by longperiod irradiation in undulator through beam loss or mis-steering. The reduction of magnetic field could affect the electron energy, direction and the movement trajectory and so on, which seriously affects the amount of synchrotron radiation light. Microstructure of Sm2Co17 type permanent magnet affects the macro magnetic properties and there is not any available report on the microstructure investigation of Sm2Co17 type permanent magnet after being irradiated. Therefore, in this work, the effect of irradiation on the microstructure evolution is investigated. The radiation fields of Sm2Co17 type permanent magnets and the main particles (neutron) that result in losing magnetic properties are first analyzed and confirmed by Monte Carlo code FLUKA calculation. Then, Sm2Co17 type permanent magnet samples are irradiated by Ar ions at different fluences to simulate neutron irradiation damage. Meanwhile, the microstructure evolutions of irradiated samples are characterized by transmission electron microscopy. Moreover, high resolution transmission electron microscopic images are taken at the peak of radiation damage field to further investigate the radiation damage. In the respect of macro magnetic properties, hysteresis loops are measured by vibrating sample magnetometer in order to study the change of saturated magnetization. The results indicate that the decrease of saturated magnetization value is related to the change of microstructure, which proves the speculation of previous investigations. The evolution of 2:17 phase transformed from single crystals into amorphous structure is a possible microscopic mechanism for irreversible loss for saturated magnetization of Sm2Co17.

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

2017, 66 (22): 227101.
doi: 10.7498/aps.66.227101

Abstract +

Polyimide (PI) and the functional graphene modified with nano-composite models of hydroxyl,carboxyl and amino groups are realized by a multi-scale modeling method.The influences of the functional graphenes with different functional groups on the microstructure,mechanical and thermodynamic performances of polyimide-based composite models are investigated by the molecular dynamics simulation.The cell parameters,solubility parameters,elastic coefficients, Young's moduli,shear moduli,and the values of glass-transition temperature (Tg) of polyimide-based composite models are calculated with the COMPASS force field.Moreover,the interaction energies and hydrogen bonds of composites are analyzed to explore the internal mechanisms for improving mechanical and thermodynamic properties.The results demonstrate that the density of PI matrix is 1.312 g·cm-3 and the solubility parameter of PI matrix is 21.84 J1/2·cm-3/2, which are in accord with the actual PI parameters.The Young's moduli of the composites increase obviously with the increase of the interaction energy between the PI matrix and the functional graphenes with hydroxyl,carboxyl and amino groups at 298 K and 1 atm.The Young's moduli of PI and PI/graphene with carboxyl groups are respectively 3.174 GPa and 4.946 GPa and the shear moduli are respectively 1.139 GPa and 1.816 GPa.Comparing with pure PI/graphene composite,the average hydrogen bonds increase obviously after graphene has been functionalized.Because the interaction between the functional graphene and PI matrix increases,the movement of PI molecular chain needs more energy,and the rigidity of the composite is enhanced.The Tg of the composite also relates to the interaction energy.It is also found that the Tg of the nano-composite effectively decreases by the hybrid functional graphene.The Tg of pure PI is 663.57 K,while the Tg values of PI/graphene and PI/graphene with carboxyl groups nanocomposites are 559.30 K and 601.61 K,respectively.Moreover,the density and interaction energy of hydrogen bonds of the PGCOOH are 784.81 kcal/mol and 1.396 g/cm3,respectively,which are the largest among their counterparts of the composite systems.The elastic coefficients show that the PGCOOH is more uniform than that other composites.All of these indicate that the graphene with carboxyl group can greatly enhance the interaction between graphene and PI,improve the mechanical properties and adjust the Tg value of the PI matrix.The chemical modification of interaction energy in matrix is deemed to be of benefit to the improvement in composite performance,and the interaction energy calculation is considered to be an effective method of predicting the structures and performances of new composites.

2017, 66 (22): 227301.
doi: 10.7498/aps.66.227301

Abstract +

Plasmon in quantum dot system is one of the most notable research topics in the field of optoelectronics. With the development of nanotechnology, plasmon in nano-structure has received considerable attention due to its potential applications in future natural science areas. To better understand the quantum effect and the properties of plasmon, in this paper we use the linear response theory and the tight-binding approximation to investigate the collective response of charge in a twodimensional square quantum dot system. The results show that when the frequency of the external field equals the frequency of the plasmon, there are strong charge collective oscillations in the quantum dot system, accompanied by great energy absorption and near-field enhancement. Owing to the quantization of plasmon, the collective charge oscillations in a two-dimensional square quantum dot system are found at different frequencies. The number of quantum modes of plasmon increases with the size and electron number of square quantum dots increasing, this behaviour of quantum mode of plasmon is similar to the one of phonon. The reasons for this behaviour are as follows. First, with the increase of quantum dot size, there are more energy levels around the fermi energy, and the electrons can jump from more energy levels to the outside of fermi circle, so there are more collective excitation frequencies (i.e., more quantum modes of plasmon) in a larger size system. Second, with the increase of electron number in quantum dots, there are more energy levels occupied by electrons, so there are more quantum modes of plasmon too. Furthermore, the size dependence of plasmon shows that with the increase of quantum dot size, the frequency interval between two neighbouring modes of plasmon is smaller, and the discrete modes of plasmon will gradually display quasi-continuous characteristic and transform gradually into the classical continuous modes of plasmon, and the frequency spectrum of plasmon turns into the classical dispersion relation. Such a characteristic is in accord with Bohr's correspondence principle, implying that the quantum plasmon and classical plasmon are gradually unified in a macroscopic size. The dependence of plasmon on the size and electron number of quantum dots also show that with the increase of the quantum dot size, the frequencies of the plasmon is red-shifted and the excitation intensity of the plasmon increases; with the increase of the electron number in quantum dot, the frequency of the plasmon is blue-shifted and the excitation intensity of the plasmon increases.

2017, 66 (22): 227302.
doi: 10.7498/aps.66.227302

Abstract +

Surface plasmon polariton (SPP) is a kind of highly confined surface-wave mode associated with collective electron charge oscillation. A remarkable feature of the SPP is its highly sensitive response to change in permittivity or refractive index of the material in the vicinity of the metal surface, and it can be used as a high sensitive sensor. Long-range surface plasmon polariton (LRSPP) is a low-loss surface wave supported by symmetric structure, such as symmetric insulator-metal-insulator (IMI) slab. In most of previous investigations, only the properties of the eigenmodes of LRSPPs are analyzed. In this paper, however, we investigate the phenomena associated with the excitations of LRSPPs which cannot be explained by the eigenmode theory. Double-electrode structures are studied in this paper. For simplicity, we assume that the structures are symmetric if no coupler is introduced. When the coupler is introduced, however, this system can have interesting new properties. The influence of the parameters of the structure on the LRSPP is discussed in detail, and the enhancement effect of the LRSPP excited by the attenuated total reflectance (ATR) method is found. The research on the parameters is based on the reflectivity and the field enhancement calculated by the characteristic matrix technique. Taking the coupler into consideration, there are six media in the double-electrode structure excited by ATR. It turns out that the LRSPP can have new properties other than those of eigenmodes supported by symmetric structures without couplers. This is due to the asymmetry brought by the coupler in the ATR method, thus it is possible to enhance the wanted mode while suppress the other mode. The asymmetry brought by the coupler in the ATR method leads to new and interesting phenomena. If the distance between the coupler and the closer metal film (denoted by s) and that between the two metal films (denoted by t) are properly chosen, the long-range mode will be enhanced while the other mode will be suppressed. It should be emphasized that s is a crucial parameter. When s is small, the long-range mode is suppressed and the other mode is enhanced; when s is large, the energy focuses more on the long-range mode. However, when s is too large, the exciting efficiency is very low. It is found that the appropriate parameters in the ATR-mothod-exciting double electrode structure are s=350 nm, t=(1)/4λ, where λ is the wavelength of the source light in vacuum and is taken to be 546.1 nm, and the thickness of each metal Ag film is taken to be 36 nm. These parameters are important for future experiments to observe this kind of phenomenon.It is also found that both the field enhancement factor and its sensitivity to the refractivity of the output-end medium are very high in LRSPP case, which is possible to be used as a biological or chemical sensor. The asymmetry brought by the coupler in the ATR method makes LRSPP have new and interesting features, one of which is the enhancement of the long-range mode. The present research has heuristic significance for studying the long-range surface plasmon in asymmetric excitation configuration.

2017, 66 (22): 227801.
doi: 10.7498/aps.66.227801

Abstract +

In order to study the relation between spectral response and absorptivity of GaAs photocathode, two kinds of GaAs photocathodes are prepared by molecular beam epitaxy (MBE) and metal-organic chemical vapor deposition (MOCVD), respectively. The samples grown by the MBE include varying doping GaAs photocathodes with different values of emission layer thickness from A to E. The thickness of GaAs emission layer is 1.6 μm or 2 μm. The Al component is 0.5 or 0.63. The samples grown by the MOCVD include varying doping or various component GaAs photocathodes with different values of emission layer thickness and different window layer components from F to J. The thickness values of GaAs emission layer are 1.4 μm, 1.6 μm or 1.8 μm, respectively. The Al component is 0.7 or varies from 0.9 to 0. The doping concentration of the GaAs emission layer is divided into 8 sections between 1×1018 cm-3 and 1×1019 cm-3. The experimental spectral response curves for all samples are obtained by the optical spectrum analyzer. And the experimental reflectivity and transmittivity curves are measured by the ultraviolet visible near infrared spectrohootometer. Based on the law of energy conservation, the absorptivity curves are obtained according to the experimental reflectivity and transmittivity. In the same coordinate system, both the curves are obtained by unitary processing according to the max. A similar surface barrier can be given by dividing the normalized absorptivity by the normalized spectral response, and those are termed the similar I barrier and the similar Ⅱ barrier, respectively. The results indicate that for both the GaAs photocathodes, the experimental spectral response curves both tend to move to the infrared band compared with the experimental absorptivity curves. The average energy differences between absorptivity and spectral response are calculated to be 0.3101 eV for the MBE sample, and 0.3025 eV for the MOCVD sample, respectively. The red-shifts of the photocathodes grown by MBE are a bit bigger than those of the photocathodes grown by MOCVD. In the shortwave region, the absorptivity is very large, but the spectral response cuts off nearby 500 nm. In the visible wavelength region, the peak position of the spectral response curve shifts toward the infrared band for several hundred meV in comparison with the absorptivity curve. In the near infrared region, a red shift of several meV appears at the cut-off position of the spectral response curve in comparison with the absorptivity curve. The results have the guiding significance for improving the photoemission performance of wide-spectrum GaAs photocathode by optimizing the optical performance.

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

2017, 66 (22): 228401.
doi: 10.7498/aps.66.228401

Abstract +

The popularity of various portable electronics and biological health monitoring devices, such as pedometers, pulse oximeters, mobile telephones, wearable watches, has greatly changed our lifestyles and brought significant convenience to us. Energy harvesting has been a key technology for the self-powered mobile terminals, because there are many defects such as limited lifetime, large size, low energy density and environmentally unfriendly feature for the traditional chemical batteries. Lots of devices used for the energy harvesting of the human movement have been reported. However, some problems such as poor efficiency, low output power and low sensitivity need further studying. In this work, we demonstrate a novel magnetically levitated electromagnetic-triboelectric generator. The device size is φ4.8 cm×2.4 cm, and its weight is 80 g. The device uses the magnetically levitation structure as the core components, and the structure contains four magnets to form a magnetic array, in which three cylindrical magnets are placed around a bigger magnet. And two coils with polyvinyl-acetal enameled copper wires of 70 μm areplaced at the top and bottom of the device, respectively. Then two silica gel thin films with inverted tetrahedron patterned on the surface are integrated inside the structure. Then, we analyze the motion feature with the Maxwell simulation software, and discuss output characteristics of the two energy harvest units theoretically. The device possesses a high sensitivity, wide frequency response and high output performance. The dynamic response characteristics are analyzed in this paper.The frequency response range of the device is from 2 Hz to 20 Hz. The wider frequency response means that it can harvest more energy from complicated external environment. Furthermore, we analyze the output signal at low frequency, which has more than one wave crest after an environment perturbation. The triboelectric units can deliver peak output voltages of 70 V and 71 V, respectively, and the electromagnetic units each can deliver a peak output voltage of 10 V. In addition, the triboelectric units can produce peak output powers of 0.12 mW and 0.13 mW, respectively, under a loading resistance of 10 MΩ, while the electromagnetic units produce peak output powers of 36 mW and 38 mW, respectively, under a loading resistance of 1 kΩ. We discuss the energy output and energy conversion efficiency of the device, which are 750.89 μJ and 18%, respectively. Then we use the hybridized generator to charge a capacitor of 33 μF, the output voltage of which can reach 8 V in 2 seconds. Furthermore, the hybridized generator can power a pedometer continuously, which can work steadily and display movement data. This work has a significant step toward human mechanical energy harvesting and potential application in self-powered wearable devices.

2017, 66 (22): 228501.
doi: 10.7498/aps.66.228501

Abstract +

Polymer-based visible-near infrared photodetectors have attracted considerable attention in the recent years due to their unique advantages of low cost of fabrication, compatibility with lightweight/flexible electronics, and wide material sources. Current researches mainly focus on high performence visble-near infrared photovoltaic detector based on narrow bandgap polymer. Device structure of the photodetector is ITO/PEDOT:PSS/photosensitive layer/Ca/Al. The weak light (0.4 mW/cm2, 800 nm) and reverse bias (-2 V) induce insignificant differences in photocurrent among the devices. Current values of 1.69×10-4 A/cm2, 7.96×10-5 A/cm2 and 6.98×10-5 A/cm2 are obtained with photosensitive layer thickness values of 100, 200 and 300 nm, respectively. However, the dark current density-voltage characteristics of the detectors with various thickness values of the photosensitive layer show that reverse bias (-2 V) induces significant differences in current among the devices. Current values of 1.35×10-6 A/cm2, 1.13×10-7 A/cm2 and 2.98×10-8 A/cm2 are obtained with photosensitive layer thickness values of 100 nm, 200 nm and 300 nm, respectively. Meanwhile, all detectors possess high rectification ratios over 105(±2 V), indicating good diode rectification characteristics. Photosensitivity measurements show that detection spectral regions of the detectors are extended from 380 nm to 960 nm. The values of detectivity (D*) of detectors with various thickness values of photosensitive layers are investigated, and the obtained values of D* of tested detectors are found to be very stable in a range from 400 nm to 860 nm, and the average D* value for the 300 nm thick device in this spectral range is as high as 6.89×1012 Jones. The latter compares well with values obtained with silicon detectors. In a range from 800 nm to 900 nm, the estimated detectivities of the 300 nm and 200 nm thick detectors are slightly higher than those obtained with InGaAs devices. Through analyzing energy band diagrams of the polymer photodetectors under reverse voltage bias it could be argued that the relatively weak electric field in the thicker device is the origin of the lower noise current density. The capacitance characteristics of polymer based detectors at high frequency (100 kHz) are examined through capacitance-voltage curves, and the resulting data show that capacitances of all devices at reverse and even small positive voltage are constant. This indicates that the device photosensitive layers are fully depleted and fast signal detections are theoretically possible. The time responses of detectors under near-infrared stimulation are also examined. The output signal appears to rise and fall periodically according to the input signal, suggesting a good repeatability. The rise and fall times for the devices are recorded to be ~5 μs and ~50 μs, indicating that the polymer photodetectors have quick response capabilities.

###### SPECIAL TOPIC—Topological classical waves

## EDITOR'S SUGGESTION

2017, 66 (22): 220201.
doi: 10.7498/aps.66.220201

Abstract +

The well-known Su-Schrieffer-Heeger (SSH) model predicts that a chain of sites with alternating coupling constant exhibits two topological distinct phases, and at the truncated edge of the topological nontrivial phase there exists topologically protected edge modes. Such modes are named zero-energy modes as their eigenvalues are located exactly at the midgaps of the corresponding bandstructures. The previous publications have reported a variety of photonic realizations of the SSH model, however, all of these studies have been restricted in the systems of time-reversal-symmetry (TRS), and thus the important question how the breaking of TRS affects the topological edge modes has not been explored. In this work, to the best of our knowledge, we study for the first time the topological zero-energy modes in the systems where the TRS is broken. The system used here is semiconductor microcavities supporting exciton-polariton quasi-particle, in which the interplay between the spin-orbit coupling stemming from the TE-TM energy splitting and the Zeeman effect causes the TRS to break. We first study the topological edge modes occurring at the edge of one-dimensional microcavity array that has alternative coupling strengths between adjacent microcavity, and, by rigorously solving the Schrdinger-like equations (see Eq.(1) or Eq.(2) in the main text), we find that the eigen-energies of topological zero-energy modes are no longer pinned at the midgap position:rather, with the increasing of the spin-orbit coupling, they gradually shift from the original midgap position, with the spin-down edge modes moving toward the lower band while the spin-up edge modes moving towards the upper band. Interestingly enough, the mode profiles of these edge modes remain almost unchanged even they are approaching the bulk transmission bands, which is in sharp contrast to the conventional defect modes that have an origin of bifurcation from the Bloch mode of the upper or lower bands. We also study the edge modes in the two-dimensional microcavity square array, and find that the topological zero modes acquire mobility along the truncated edge due to the coupling from the adjacent arrays. Importantly, owing to the breaking of the TRS, a pair of counterpropagating edge modes, of which one has a momentum k and the other has -k, is no longer of energy degeneracy; as a result the scattering between the forward-and backward-propagating modes is greatly suppressed. Thus, we propose the concept of the one-dimensional topological zero-energy modes that are propagating along the two-dimensional lattice edge, with extremely weak backscattering even on the collisions of the topological zero-energy modes with structural defects or disorder.

2017, 66 (22): 220302.
doi: 10.7498/aps.66.220302

Abstract +

Dirac Fermion, as one of the basic particles in the particle physics, nowadays have been widely used to describe the electronic states with the behavior of Dirac fermion in the topological electronics. These exotic electronic states are called Dirac point, which exhibited as a linear crossing point in the band structure. Usually Dirac point is the topological phase transition point and thus viewed as the mother state of various topological states. As an analogue of topological electronics, topological photonics, also attracted a great deal of interest due to its potential application. One of the key topic in topological photonics is to realize photonic bands with Dirac point. In this review, we briefly introduce the progress of Dirac point in the photonic system and focus on the realization method of Dirac point in photonic crystal by take advantage of lattice symmetry. We also discuss Weyl point in the photonic crystal as an extension of the Dirac point.

2017, 66 (22): 224102.
doi: 10.7498/aps.66.224102

Abstract +

We found that core-shell gyromagnetic photonic crystal of two-dimensional triangular lattice exhibit topological phases. In a certain parameters and magnetic field, those phases could be a conventional insulator phase, a quantum spin Hall phase, and a quantum anomalous Hall phase. Different from the structure of Ref[1], phase transitions in our core-shell structure does not involve changes of space symmetry, which depend on parameters of our structure and the broken of time reverse symmetry. Our result shows the variety of topological phase transitions in photonic crystals.

2017, 66 (22): 224203.
doi: 10.7498/aps.66.224203

Abstract +

Recently, artificial bandgap materials (such as photonic crystals and phononic crystals) have been becoming the research hotspot of the next generation intelligent materials, because of its extremely designable, tunable and controllable capacity of classical waves. On the other hand, topological material phase, originally proposed and first demonstrated in Fermionic electronic systems, has been proposed in more and more Bosonic systems. In this review paper, we first focus on some of the representative photonic/phononic topological models, and four common types of topological photonic system are discussed:1) photonic/phononic quantum Hall effect with broken time-reversal symmetry; 2) photonic topological insulator and the associated pseudo-time-reversal symmetry protected mechanism; 3) time/space periodically modulated photonic Floquet topological insulator; 4) a summary and outlook including a brief introduction of Zak phase in one-dimensional systems and Weyl point in three-dimensional systems. Finally, the underlying Dirac model is analyzed.

2017, 66 (22): 224301.
doi: 10.7498/aps.66.224301

Abstract +

We design a two-dimensional acoustic crystal (AC) to obtain topologically protected edge states for sound waves. The AC is composed of a triangular array of a complex unit cell consisting of two identical triangle-shaped steel rods arranged in air. The steel rods are placed on the vertices of the hexagonal unit cell so that the whole lattice possesses the C6v symmetry. We show that by simply rotating all triangular rods around their respective centers by 180 degrees, a topological phase transition can be achieved, and more importantly, such a transition is accomplished with no need of changing the fill ratios or changing the positions of the rods. Interestingly, the achieved topologically nontrivial band gap has a very large frequency width, which is really beneficial to future applications. The topological properties of the AC are rooted in the spatial symmetries of the eigenstates. It is well known that there are two doubly-degenerate eigenstates at the point for a C6v point group, and they are usually called the p and d states in electronic system. By utilizing the spatial symmetries of the p and d states in the AC, we can construct the pseudo-time reversal symmetry which renders the Kramers doubling in this classical system. We find pseudospin states in the interface between topologically trivial and nontrivial ACs, where anticlockwise (clockwise) rotational behaviors of time-averaged Poynting vectors correspond to the pseudospin-up (pseudospin-down) orientations of the edge states, respectively. These phenomena are very similar to the real spin states of quantum spin Hall effect in electronic systems. We also develop an effective Hamiltonian for the associated bands to characterize the topological properties of the AC around the Brillouin zone center by the kp perturbation method. We calculate the spin Chern numbers of the ACs, and reveal the inherent link between the band inversion and the topological phase transition. With full-wave simulations, we demonstrate the one-way propagation of sound waves along the interface between topologically distinct ACs, and demonstrate the robustness of the edge states against different types of defects including bends, cavity and disorder. Our design provides a new way to realize acoustic topological effects in a wide frequency range spanning from infrasound to ultrasound. Potential applications and acoustic devices based on our design are expected, so that people can manipulate and transport sound waves in a more efficient way.

2017, 66 (22): 224502.
doi: 10.7498/aps.66.224502

Abstract +

Topological phase is a new degree of freedom to describe the state of matter in condensed matter physics. One could predict the existence of the interface state between two topological different phononic crystals. The band structures of phononic crystal depend on the characteristics of their composite and their combination, such as geometry, filling fraction, and stiffness. However, after the phononic crystal is fabricated out, it is relatively difficult to tune their band structure and its topology. In order to broaden the application scope of phononic crystals, different kinds of tunable phononic crystals have been proposed. One method to achieve this tunability is to introduce nonlinearity into the phononic crystals. Granular crystals is one type of tunable nonlinear material, whose nonlinearity stems from nonlinear Hertzian contact. By changing the static precompression, the dispersion of granular crystals can be tuned. In this paper, by combining topology with nonlinear we create a new type of interface state switch without changing the experimental setup. Based on the Su-Schrieffer-Heeger (SSH) model–an example of a one dimensional (1D) topological insulator, we present a 1D nonlinear granular crystal, to realize the topological transition by precompression. First, we construct a 1D mechanical structure, which is made up of nonlinear granular crystal and linear phononic crystal. The 1D nonlinear granular crystal is simplified as a “mass-spring” model with tunable elastic constant and invariable elastic constant. By calculating the band topology–the Zak phase, we found that the Zak phase of the two bands can switch from π to 0. There exist a critical precompression F0, when F F0 the Zak phase of the band is π, when F > F0 the Zak phase is 0. The granular crystal vary from nontrivial bandgap to trivial one as precompression gradually increase. This effect enables us to design interface state switch at the interface between granular crystals with trivial and nontrivial band gap. Furthermore, when F F0, we find that the localization of interface state decreases as the applied precompression increases. Thus, we investigate existence of the interface state under different precompression and found that the interface state can be controlled freely. We anticipate these results to enable the creation of novel tunable acoustic devices.

2017, 66 (22): 226601.
doi: 10.7498/aps.66.226601

Abstract +

The combination of topology and physics is a new field of physics development in recent decades. It is not only active in quantum field theory and high energy physics, but also widely exists in condensed matter physics, including quantum (anomalous, spin) Hall effect and topological insulators (superconductors) etc. Phonon, as the main carrier of heat transport in the crystal, recently, due to the discovery of various phonon devices, phonons has been widely concerned by scientist. In this paper, we introduce the topological properties of phonons and the phonon hall effect. We have reviewed the related physical research progress of phonon hall effect, phonon valley hall effect and so on, which are generated by breaking the time reversal symmetry, spatial inversion symmetry, both breaking the time and spatial inversion symmetry. Finally, the application of topology in other acoustic systems is briefly introduced, and the future development direction is discussed too.

2017, 66 (22): 227802.
doi: 10.7498/aps.66.227802

Abstract +

Topological insulators have aroused much research interest in condensed matter physics in recent years. Topological protected edge states can propagate unidirectionally and backscattering free along the boundaries of the topological insulators' which will be important for future electronic devices for its immunity to defects. Topology is dependent only on the symmetry of lattice of the system rather than its specific wave form. Thus, based on the analogy between electronics and photons, photonic topological insulator has also been demonstrated both theoretically and experimentally. Graphene, composed of a monolayer of carbon atoms in honeycomb lattice, exhibits unusual properties due to its intriguing band diagram. Many types of graphene allotropes have been proposed theoretically. However, due to fabrication difficulties, most of graphene allotropes are unavailable. Here, we propose to study two dimensional (2D) photonic crystal (PC) with complex lattices, similar to that of graphene allotrope. The complex PC structure provides more degrees of freedom in manipulating its symmetry.Interface states can also exist in the interface region between two PCs, if they have different topological properties. Without any surface decoration, deterministic interface states can be created when bulk photonic band inversion can be induced and are demonstrated theoretically and experimentally in 2D PCs with square lattice. By controlling the parameters of PCs, their bulk photonic band properties are engineered and topological phase transition occurs. By inverting the bulk photonic band properties, interface states exist in the common band gaps for two PC systems in the gapped region. Similarly, we proceed to complex honeycomb lattice of PCs. By lowering its original C6v symmetry to C3v, C3, C2v and even C2 symmetry, the degeneracies of valley Dirac dispersion at the corners of Brillouin zone are lifted. Photonic band inversion occurs in all four symmetries and the deterministic interface states are numerically realized in the interface region between two PCs. Unidirectional propagation of interface state immune to backscattering along the interface channels is demonstrated if a source with proper optical vortex index is utilized. Due to its easy fabrication, PC is a perfect platform to explore the topological properties of complex lattice and these acquired topological optical states can be of benefit to the control the propagation of light in the photonic waveguide.

2017, 66 (22): 227803.
doi: 10.7498/aps.66.227803

Abstract +

Quantum spin Hall effect (QSHE) of electrons has improved the development of condensed matter researchnowadays, which describesone kind of spin-dependent quantum transport behavior in solid state. Recently, a variety of theoretical and experimental work has revealed that Maxwell equations, which is formulated 150 years ago and ultimately describeproperties of light, can exhibit an intrinsic quantum spin Hall effect of light. The evanescent wave supported on the interface among different media behaves strong spin-momentum locking. With the rapid development of new optics materials, metamaterials, we can not only adjust the optical parameters of media arbitrarily, but also introduce a lot of complex spin-orbit interaction mechanism. Based on metamaterials, the essential physical mechanism behind quantum spin Hall effect of light can be understood deeply and verified easily. The purpose of this review is to give a brief introduction to quantum spin Hall effect of light in metamaterials. These include, for example, the physical essence of QSHE of light, the topological interface mode between permittivity negative and permeability negative metamaterials, QSHE in topological circuits.

2017, 66 (22): 227804.
doi: 10.7498/aps.66.227804

Abstract +

We report a new topological phononic crystal in a ring-waveguide acoustic system. In the previous reports on topological phononic crystals, there are two types of topological phases:quantum Hall phase and quantum spin Hall phase. A key point in achieving quantum Hall insulator is to break the time-reversal (TR) symmetry, and for quantum spin Hall insulator, the construction of pseudo-spin is necessary. We build such pseudo-spin states under particular crystalline symmetry (C6v) and then break the degeneracy of the pseudo-spin states by introducing airflow to the ring. We study the topology evolution by changing both the geometric parameters of the unit cell and the strength of the applied airflow. We find that the system exhibits three phases:quantum spin Hall phase, conventional insulator phase and a new quantum anomalous Hall phase.The quantum anomalous Hall phase is first observed in phononics and cannot be simply classified by the Chern number or Z2 index since it results from TR-broken quantum spin Hall phase. We develop a tight-binding model to capture the essential physics of the topological phase transition. The analytical calculation based on the tight-binding model shows that the spin Chern number is a topological invariant to classify the bandgap. The quantum anomalous Hall insulator has a spin Chern number C±=(1,0) indicating the edge state is pseudo-spin orientation dependent and robust against TR-broken impurities.We also perform finite-element numerical simulations to verify the topological differences of the bandgaps. At the interface between a conventional insulator and a quantum anomalous Hall insulator, pseudo-spin dependent one-way propagation interface states are clearly observed, which are strikingly deferent from chiral edge states resulting from quantum Hall insulator and pairs of helical edge states resulting from quantum spin Hall insulator. Moreover, our pseudo-spin dependent edge state is robust against TR-broken impurities, which also sheds lights on spintronic devices.

2017, 66 (22): 228101.
doi: 10.7498/aps.66.228101

Abstract +

Phononic crystals possess Dirac linear dispersion bands. In the vicinity of Dirac cones, phononic crystals exhibit topological properties which have good application prospects in control of acoustic waves. Up to now, the topological edge states of phononic crystals, based on the band structures arising from the Bragg scattering, cannot realize low-frequency sound waves by the topologically protected one-way edge transmission. In this paper, by introducing the space-coiling structure, a space-coiling phononic metamaterial with C3v symmetry is designed. At the K (K') points of the Brillouin zone, the bands linearly cross to a subwavelength Dirac degenerated cones. With a rotation of the acoustic metamaterials, the mirror symmetry will be broken and the Dirac degenerated cones will be reopened, leading to subwavelength topological phase transition and subwavelength topological valley-spin states. Lastly, along the topological interface between acoustic metamaterials with different topological valley-spin states, we successfully observe the phononic topologically valley-spin transmission. The subwavelength Dirac conical dispersion and the subwavelength topological valley-spin state breakthrough the limitation of the geometric dimension of the phononic topological insulator, and provide a theoretical basis for the application of the phononic topologically robust transmission in a subwavelength scale.