Generation of arbitrary radially polarized array beams by modulating the correlation structure

We demonstrate a convenient approach for simultaneously manipulating the amplitude and polarization of light beams by means of the modulation of the correlation structure. As an illustration, we constructed a periodic correlation structure that can generate an arbitrary radially polarized array (RPA) beam of a radial or rectangular symmetry array in the focal plane from a radially polarized (RP) beam. The physical realizability conditions for such source and the far-field beam condition are derived. It is illustrated that the beamlet shape and the state of polarization (SOP) can be effectively controlled by the initial correlation structure and the coherence width. Furthermore, by designing the source correlation structure, a tunable OK-shaped RPA beam and an optical cage are demonstrated, which can find widespread applications in non-destructive manipulation of particles and living biological cells. The arbitrariness in the design of correlation structure prompted us to find more convenient approaches for controlling the statistics of light beams in terms of amplitude and polarization

The reversibility of the Goos-H\"anchen shift near the band-crossing structure of one-dimemsional photonic crystals containing left-handed metamaterials

We perform a theoretical investigation on the Goos-H\"achen (GH) shift in one-dimensional photonic crystals (1DPCs) containing left-handed metamaterials (LHMs). We find an unusal effect of the GH shift near the photonic band-crossing structure, which is located at the condition, $-k_{z}^{(A)}d_{A}=k_{z}^{(B)}d_{B}=m\pi$ $(m=1,2,3...)$, under the inclined incident angle, here A denotes the LHM layer and B denotes the dielectric layer. Above the frequency of the band-crossing point (BCP), the GH shift changes from negative to positive as the incident angle increases, while the GH shift changes reversely below the BCP frequency. This effect is explained in terms of the phase property of the band-crossing structure.Comment: 4 pages, 5 figure

Electronic Band gaps and transport properties inside graphene superlattices with one-dimensional periodic squared potentials

The electronic transport properties and band structures for the graphene-based one-dimensional (1D) superlattices with periodic squared potentials are investigated. It is found that a new Dirac point is formed, which is exactly located at the energy which corresponds to the zero (volume) averaged wavenumber inside the 1D periodic potentials. The location of such a new Dirac point is robust against variations in the lattice constants, and it is only dependent on the ratio of potential widths. The zero-averaged wavenumber gap associated with the new Dirac point is insensitive to both the lattice constant and the structural disorder, and the defect mode in the zero-averaged wavenumber gap is weakly dependent on the insident angles of carriers.Comment: 7 figure

General decay for a viscoelastic wave equation with dynamic boundary conditions and a time-varying delay

The goal of this paper is to study a nonlinear viscoelastic wave equation with strong damping, time-varying delay and dynamical boundary condition. By introducing suitable energy and Lyapunov functionals, under suitable assumptions, we then prove a general decay result of the energy, from which the usual exponential and polynomial decay rates are only special cases

Fidelity, purity and entanglement of two-mode spatially Gaussian-entangled light fields in Turbulence Atmosphere

In this paper, we investigate the propagation of two-mode spatially Gaussian-entangled quantum light fields passing through the turbulence atmosphere. From the propagation formula of the two-mode wave function in the position representation, we have derived the analytical expressions for the fidelity, purity and logarithmic negativity (entanglement) of the resulting quantum state after the long-distance atmospheric transportation. Based on the derived formulae, the effects of the atmospheric turbulences on the evolutions of quantum properties of the resulting two-mode quantum state are discussed in detail under different input parameters of the initial two-mode quantum state. The results show that the maximal distributing distance of quantum entanglement is strongly dependent on the atmospheric conditions: when the atmospheric turbulence becomes stronger and stronger, the maximal distance becomes shorter and shorter, and both the fidelity and purity decrease quicker and quicker as functions of propagating distances. Under a certain atmospheric condition, with the increasing of the input entanglement of the initial two-mode spatially Gaussian-entangled quantum state, the maximal distributing distance for preserving the entanglement gradually increases and always has a saturated (upper) limitation, and both the evolutions of the fidelity and purity are affected by the input parameters of the initial two-mode quantum state, Finally the optimal parameters of the input two-mode quantum state with the fixed input entanglement are discussed in order to obtain the optimal transfer distribution of the quantum entanglement over a long distance under a certain atmosphere. Our theoretical results are very helpful for building the distribution of the quantum entanglement via free-space atmosphere link.Comment: 16 pages, 5 figure

Well-posedness and general decay of solution for a transmission problem with viscoelastic term and delay

In this paper, we consider a transmission problem in a bounded domain with a viscoelastic term and a delay term. Under appropriate hypothesis on the relaxation function and the relationship between the weight of the damping and the weight of the delay, we prove the well-posedness result by using Faedo-Galerkin method. By introducing suitable Lyaponov functionals, we establish a general decay result, from which the exponential and polynomial types of decay are only special cases

Laser Driven Ultra-compact Undulator for Synchrotron Radiation

Laser wakefield accelerators have emerged as a promising candidate for compact synchrotron radiation and even x-ray free electron lasers. Today, to make the electrons emit electromagnetic radiation, the trajectories of laser wakefield accelerated electrons are deflected by transverse wakefield, counter-propagating laser field or external permanent magnet insertion device. Here, we propose a novel type of undulator which has a few hundred microns of period and tens of Tesla of magnetic field. The undulator consists of a bifilar capacitor-coil target which sustains strong discharge current that generates helical magnetic field around the coil axis when irradiated by a high energy laser. Coupling this undulator with state-of-the-art laser wakefield accelerators can, simultaneously, produce ultra-bright quasi-monochromatic x-rays with tunable energy ranging 5-250 keV and optimize the free electron laser parameter and gain length compared with permanent magnet based undulator. This concept may pave a path toward ultra-compact synchrotron radiation and even x-ray free electron lasers.Comment: 12 pages, 7 figure

Langer Modification, Quantization condition and Barrier Penetration in Quantum Mechanics

The WKB approximation plays an essential role in the development of quantum mechanics and various important results have been obtained from it. In this paper, we introduce another method, {\it the so-called uniform asymptotic approximations}, which is an analytical approximation method to calculate the wave functions of the Schr\"odinger-like equations, and is applicable to various problems, including cases with poles (singularities) and multiple turning points. An distinguished feature of the method is that in each order of the approximations the upper bounds of the errors are given explicitly. By properly choosing the freedom introduced in the method, the errors can be minimized, which significantly improves the accuracy of the calculations. A byproduct of the method is to provide a very clear explanation of the Langer modification encountered in the studies of the hydrogen atom and harmonic oscillator. To further test our method, we calculate (analytically) the wave functions for several exactly solvable potentials of the Schr\"odinger equation, and then obtain the transmission coefficients of particles over potential barriers, as well as the quantization conditions for bound states. We find that such obtained results agree with the exact ones extremely well. Possible applications of the method to other fields are also discussed.Comment: revtex4-1, 1 figures, and 1 table. Published in Universe 6 (2020) 9

New Insight into Collimated Plasmon Beam: Nondiffracting versus Linear Focusing

We worked out a new group of collimated plasmon beams by the means of in-plane diffraction with symmetric phase modulation. As the phase type changes from 1.8 to 1.0, the beam undergoes an interesting evolution from focusing to a straight line. Upon this, an intuitive diagram was proposed to elucidate the beam nature and answer the question whether they are nondiffracting or linear focusing. Based on this diagram, we further achieved a highly designable scheme to modulate the beam intensity (e.g., 'lossless' plasmon). Our finding holds remarkable generality and flexibility in beam engineering and would inspire more intriguing photonic designs

Performance of Network-Assisted Full-Duplex for Cell-Free Massive MIMO

Network assisted full-duplex (NAFD) is a spatial-division duplex technique for future wireless networks with cell-free massive multiple-input multiple-output (CF massive MIMO) network, where a large number of remote antenna units (RAUs), either using half-duplex or full-duplex, jointly support truly flexible duplex including time-division duplex, frequency-division duplex and full duplex on demand of uplink and downlink traffic by using network MIMO methods. With NAFD, bi-directional data rates of the wireless network could be increased and end-to-end delay could be reduced. In this paper, the spectral efficiency of NAFD communications in CF massive MIMO network with imperfect channel state information (CSI) is investigated under spatial correlated channels. Based on large dimensional random matrix theory, the deterministic equivalents for the uplink sum-rate with minimum-mean-square-error (MMSE) receiver as well as the downlink sum-rate with zero-forcing (ZF) and regularized zero-forcing (RZF) beamforming are derived. Numerical results show that under various environmental settings, the deterministic equivalents are accurate in both a large-scale system and system with a finite number of antennas. It is also shown that with the downlink-to-uplink interference cancellation, the uplink spectral efficiency of CF massive MIMO with NAFD could be improved. The spectral efficiencies of NAFD with different duplex configurations such as in-band full-duplex, and half-duplex are compared. With the same total numbers of transmit and receive antennas, NAFD with half-duplex RAUs offers a higher spectral efficiency. To alleviate the uplink-to-downlink interference, a novel genetic algorithm based user scheduling strategy (GAS) is proposed. Simulation results show that the achievable downlink sum-rate by using the GAS is greatly improved compared to that by using the random user scheduling