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GENERAL

Analytical solution of three-dimensional Fourier transform frequency spectrum for three-level potassium atomic gas
Zhao Chao-Ying, Tan Wei-Han
2020, 69 (2): 020201. doi: 10.7498/aps.69.20190964
Abstract +
With the development of laser technology in the field of optics, ultra-fast optics has become an important research field. Compared with the traditional technology, ultrafast optics can be realized not only under shorter pulse function, but also on a smaller scale, which can more quickly reflect the dynamic process. We present an analytical calculation of the full three-dimensional (3D) coherent spectrum with a finite duration two-dimensional (2D) Gaussian pulse envelope. Our starting point is the solution of the optical Bloch equations for three-level potassium atomic gas in the 3D time domain by using the projection-slice theorem, error function and Fourier-shift theorem of 3D Fourier transform. These principles are used to calculate and simplify the third-order polarization equation generated by the device, and the analytical calculation of three-dimensional Fourier transform frequency spectrum at T = 0 is obtained. We simulate the analytic solution by using mathematics software. By comparing the simulations with the experimental results, with the homogeneous line-width fixed, we can obtain the relationship among the in-homogeneous broadening, the correlation diagonal coefficients and the three-dimensional spectrum characteristics, which can be identified quantitatively by fitting the slices of three-dimensional Fourier transform spectrum peaks in an appropriate direction. The results show that the three-dimensional Fourier transform spectrum will extend along the diagonal direction with the increasing of the in-homogeneous broadening, and the spectrogram progressively becomes a circle with the increasing of the diagonal correlation coefficient, and the amplitude also gradually turns smaller. According to the analytical solution, we give a complete two-dimensional spectrum of the T = 0 interface. The results can be fit to the experimental 3D coherent spectrum for arbitrary inhomogeneity.

GENERAL

Two-dimensional wave equation solved by generalized alternating flux based local discontinuous Galerkin method
Zhang Rong-Pei, Wang Di, Yu Xi-Jun, Wen Xue-Bing
2020, 69 (2): 020202. doi: 10.7498/aps.69.20190613
Abstract +
The wave propagation is often carried out in complex geological structures. Solving the wave propagation problem effectively in inhomogeneous medium is of great interest and has many applications in physics and engineering. In this paper, the local discontinuous Galekin (LDG) method is applied to the numerical solution of the second-order wave equation. Firstly, the auxiliary variables are introduced, and the second-order wave equations are written as a system of first-order partial differential equations. Then the discontinuous Galerkin format is applied to the corresponding linearized wave equations and adjoint equations. We consider the triangulation in this paper. In order to ensure that the discrete format satisfies the energy conservation, the generalized alternating flux is chosen on the element boundary. We proves that the LDG method satisfies the energy conservation. The exponential integral factor method is used in time discretization. In order to improve the computational efficiency, the Krylov subspace method is used to approximate the product of the exponential matrix and the vector. Numerical examples with exact solutions are given in numerical experiments. The numerical results verify the numerical precision and energy conservation of the LDG method. In addition, the calculation of inhomogeneous medium and complex computational regions are considered. The results show that the LDG method is suitable for simulation of complex structures and propagation in multi-scale structured medium.

INVITED REVIEW

Superconductivity in topological materials
Gu Kai-Yuan, Luo Tian-Chuang, Ge Jun, Wang Jian
2020, 69 (2): 020301. doi: 10.7498/aps.69.20191627
Abstract +
In recent years, by introducing topological invariants into condensed matter systems, new phases of mater are revealed. Of these new phases, the topological insulator, topological semimetal and topological superconductor are the most important. They are called topological materials due to nontrivial topological parameters. Topological superconductors hold Majorana zero modes at the edges, satisfying non-abelian statistics, which makes them major candidate for realizing topological quantum computation. Besides exploring intrinsic topological superconductor, a promising way to realize topological superconductor is to induce superconductivity into other kinds of topological materials. Up to now, experimentalists have developed some techniques, such as gating, doping, high pressure, interface effect and hard point contact to introduce superconductivity into various topological materials, and also they have studied the topological properties of the induced superconductivity. In this review, we summarize the representative researches on intrinsic topological superconductor candidates and induced superconductivities in topological insulators and semimetals. The advantages and disadvantages of different techniques are discussed. Besides, the potential evidences of topological superconductors are analyzed. In the end, the outlook of this actively pursued research field is given.

GENERAL

Dynamic analysis of rumor-spread-delaying model based on rumor-refuting mechanism
Zhu Lin-He, Li Ling
2020, 69 (2): 020501. doi: 10.7498/aps.69.20191503
Abstract +
In this paper, we establish a susceptible-infected-removed (SIR) rumor spreading model based on the influence of rumor-refuting mechanism and time delay on internet rumor spreading. The threshold R0 of rumor spreading is obtained by using the spectral radius method of regenerative matrix; the conditions for the existence of rumor prevailing equilibrium point are given according to the quadratic function characteristics; the local stability of rumor-free equilibrium point and rumor prevailing equilibrium point are established by using eigenvalue theory and Routh-Hurwitz criterion; and the criterion for the occurrence of Hopf bifurcation is also established. The numerical simulation results show that the information about refuting rumors, released by the government and the media, can accelerate the convergence rate of rumors and reduce the maximum density of rumor-spreaders.

GENERAL

Electrical properties of an arbitrary m×n rectangular network
Tan Zhi-Zhong, Tan Zhen
2020, 69 (2): 020502. doi: 10.7498/aps.69.20191303
Abstract +
The development of natural science raises many complex new problems and requires people to find the basic method to resolve them. It was found that many problems could be resolved by building the resistor network model. In 1845, the German scientist Kirchhoff set up the node current law and the circuit voltage law.Since then the basic theory of electric circuit has been established. At present, three general theories for studying large-scale resistor networks have been developed, for example, In 2000 Cserti [Am. J. Phys. 2000, 68 , 896] set up the Green function technique to evaluate the resistance of infinite lattices. In 2004 Wu [J. Phys. A: Math. Gen. 2014, 37 , 6653] formulated a Laplacian matrix method and calculated the resistance of arbitrary finite and infinite lattices by using the eigenvalues and eigenvectors. In 2011 Tan [Resistance Network Model (Xi’an: Xidian University Press) 2011, pp16–216] proposed the recursion-transform (RT) method which depends on the one matrix along one directions and avoids the trouble of the Laplacian method that depends on two matrices along two directions. Among them, only two theories can calculate both finite and infinite networks. One is Wu's Laplacian matrix method and the other is Tan's RT method. However, there is only one way to compute a resistor network with arbitrary boundary, that is, the Tan's RT method.Potential distribution problem in arbitrary rectangular circuit network has always been a problem of scientific research. In this paper, we develop the RT-I theory of resistor networks to calculate the arbitrary m × n circuit network model. We study the potential distribution and the equivalent resistance of a class of m × n rectangular network with an arbitrary boundary, a profound problem that has not been resolved so far, because previous research depends on the boundary conditions of rules or a zero-resistance boundary condition. Other methods, such as Green function technique and Laplacian method to calculate potential function are difficult and also impossible to study the resistor network with arbitrary boundary. Potential function problem is an important research subject in natural science and engineering technology, for example, the solution of Laplace's equation is one of research work. In this paper, we present an analytical expression of the node potential function of m × n rectangular resistor network with an arbitrary boundary, and also obtainan equivalent resistance formula between any two nodes, and the results in some special cases as well. In the comparative study of different results, a new mathematical identity and several interesting inferences are discovered.

ATOMIC AND MOLECULAR PHYSICS

Density functional theory calculation of spectrum and excitation properties of mer-Alq3
Peng Jie, Zhang Si-Jie, Wang Ke, Dove Martin
2020, 69 (2): 023101. doi: 10.7498/aps.69.20191453
Abstract +
Meridional tris(8-hydroxyquinoline)aluminum (III) (mer-Alq3) is an organometallic semiconductor material with phenomenal photo-electric properties. In order to understand the molecular luminescence properties of mer-Alq3, the density functional theoretical (B3LYP) method with 6-31G* basis set is employed to calculate its structure, infrared spectrum and Raman spectrum and the frontier molecular orbital of its ground state. The UV-vis absorption and the excited state characteristics are investigated by the time-dependent density functional theory (TD-DFT) method. The results show that the calculated spectral characteristics are in good agreement with the experimental data. The electron cloud of the highest occupied molecular orbital (HOMO) is located mostly on the phenoxide ring, whereas that of the lowest unoccupied molecular orbital (LUMO) sits on the pyridine ring. The absorption peaks of the UV-visible absorption spectrum are located in the visible and ultraviolet region. S0→S2 is attributed to the superposition of the π-π* local excitation in the direction from benzene ring to pyridine ring and the n-π* local excitation in the direction from oxygen atom to pyridine ring. The π-π* local excitation from benzene ring to pyridine ring is S0→S4. The superposition of π-n local excitation from benzene to carbon and n-n local excitation from oxygen to carbon are excited by S0→S11. S0→S14 is charge-transfer excitation and contributed by the superposition of π-π* in the direction from benzene ring to pyridine ring and n-π* in the direction from oxygen atom to pyridine ring. This work is significant for understanding the basic properties of mer-Alq3 and the mechanisms of electron excitations. It provides a deeper insight into the luminescence mechanism of mer-Alq3, thus playing a guidance role in further improving the luminescence efficiency and regulating the spectral range of the light-emitting mer-Alq3.

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

Analytical algorithem of stretcher dispersion in chirp pulse amplification laser system
Wang Nan, Ruan Shuang-Chen
2020, 69 (2): 024201. doi: 10.7498/aps.69.20191587
Abstract +
Dispersion control is one of many key techniques in ultrashort laser pulse generation and its applications. By controlling the optical path of wavelength in the laser pulse to generate relative time delay, the pulse width of laser can be changed. The stretcher is the optical scheme to broaden the pulse width in chirp pulse amplification. By using ray trace, the pulse stretch time can be evaluated. However, due to the complicated formula of optical path in stretcher, it is difficult to obtain an analytical expression of high-order dispersion by using direct derivative. In this case, the present numerical methods are commonly used and error would be introduced into the optical system design and optimization inevitably. In this paper we introduce an analytical algorithm of stretcher dispersion. By summarizing the characteristic of stretcher formula, four fundamental functions are introduced to help to calculate the analytical derivative. By substituting the separate terms of the expressions step by step, analytical calculation of stretcher dispersion can be realized. In this paper, the ray trace of Martinez stretcher is first introduced to achieve similar phase expressions to them of existing Offner stretcher, then accurate high order dispersion results are attained by using analytical method, finally the calculation results by using the analytical method and numerical method are compared with each other. The algorithm introduced into this paper for calculating the dispersion is practical and hopeful in designing the chirp pulse amplification laser systems.

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

Mode control of electrically injected semiconductor laser with parity-time symmetry
Wang Xue-You, Wang Yu-Fei, Zheng Wan-Hua
2020, 69 (2): 024202. doi: 10.7498/aps.69.20191351
Abstract +
The non-Hermitian description is of great significance for open systems, and the Hamiltonian which satisfies parity-time symmetry can make the energy have real eigenvalue within a certain range. The properties of parity-time symmetry have bright application prospects in optical systems. For semiconductor lasers, the parity-time symmetry can be constructed by adjusting the level of electrical injection to help achieve better mode control. Electric injection is easier to realize than optical pump when the device size is small and the structure is complex. Therefore, we hope to analyze the characteristics of the laser that satisfies the parity-time symmetry condition under the condition of electric injection. In this paper, we simulate the effects of different set loss values on parity-time symmetry. It is found that with the increase of set loss value, the imaginary part of the refractive index of the gain cavity corresponding to the parity-time symmetry breaking point so-called exceptional point will decrease, and the imaginary part of the characteristic frequency corresponding to the exceptional point will also decrease. We also simulate the effect of structural size ratio of gain region and loss region on parity-time symmetry. On condition that the total cavity length and the imaginary part of the refractive index of the loss region remain unchanged, as the gain cavity becomes longer and the loss cavity becomes shorter, the imaginary part of the refractive index of the gain cavity corresponding to the exceptional point will increase, and the imaginary part of the characteristic frequency corresponding to the exceptional point will also increase. And we qualitatively explain the above phenomenon through the coupled mode equations. Through experiments, metal organic chemical vapor deposition (MOCVD) and standard lithography techniques are used to fabricate asymmetric ridge lasers. Under thermoelectric cooler (TEC) refrigeration and by controlling the injection level of the gain area, the doubled mode spacing and halved mode number of ridge waveguide are found for the first time due to the parity-time symmetry breaking under the condition of electric injection. We believe that the study of parity-time symmetry in ridge laser under the condition of electric injection will be of great help in implementing the mode control.

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

Spatiotemporal evolution and spectral character of second harmonic generation in optical microresonator
Xu Xin, Jin Xue-Ying, Hu Xiao-Hong, Huang Xin-Ning
2020, 69 (2): 024203. doi: 10.7498/aps.69.20191294
Abstract +
With the consideration of the second and the third order nonlinear effect, the Lugiato-Lefeve equation which describes the field evolution of the fundamental frequency wave and the second harmonic wave is introduced. Based on the Lugiato-Lefeve equation, the generation of the second harmonic wave in the SiN microresonator is analyzed, and the effect of the each parameter on the dual field is studied. Simulation results indicate that the stable field of the fundamental frequency wave is of flat top pulse, and the field of the second harmonic wave is of sinusoidal distribution. When the detuning parameter increases, the power of the dual wave inside the microresonator oscillates, and the stable power weakens, the stable light field is periodically varied. Moreover, the chaos emerges as detuning parameter becomes large. The stable field can be generated in the microresonator with the weak pump power. However, because of the high pump power, the dispersion and nonlinear effect are enhanced, resulting in the periodic light field. Furthermore, the oscillation of the dual power curve is aggravated, as the pump power increases. In addition, the turning patterns can be observed by choosing the special dimension of microresonator. Theoretical analysis results are significant for studying the generation of the second harmonic wave in the microresonator.

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

Interaction between spatiotemporal collinear self-decelerating Airy elegant-Laguerre-Gaussian wave packets in free space
Zhang Xia-Ping
2020, 69 (2): 024204. doi: 10.7498/aps.69.20191272
Abstract +
Based on the (3+1)-dimensional free-space Schrödinger equation, the analytical solutions to the equation for the propagating properties of two three-dimensional collinear self-decelerating Airy-elegant-Laguerre-Gaussian(AELG) light beams in free space are investigated. The different mode numbers, the mode index for each of the collinear beams, weight factor of combined beam, and initial phase difference will affect the profiles of the wave packets, and thus giving the method to control the spatiotemporal profiles during propagation. The spatiotemporal profiles will rotate if none of the mode parameters are equal to zero, and there are vortices in the center of the phase distribution curve. If the mode parameters are positive numbers, the profiles of the beams will rotate in a helical clockwise direction. Otherwise, if the mode parameters are negative numbers,they will rotate in a helical anticlockwise direction during propagation. The wave packets will also rotate when the relative phase is varied. However, the rotation principles of these two rotation characteristics are completely different. The spatiotemporal hollow self-decelerating AELG wave packets can be attained if the mode numbers of the collinear AiELG wave packets are the same. Multi-ring structure evolves into single-ring structure along radial direction with their propagation distance increasing during propagation, which makes the hollow part expand continuously.
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