Dedekind整环上的不可分解扭模

We give a direct proof to the classification of all indecomposable torsion modules over a Dedekind ring. As an application, we classify all indecomposable locally-nilpotent modules over the polynomial algebra with one variable over a field.     

A new high-order discontinuous Galerkin spectral finite element method for Lagrangian gas dynamics in two-dimensions

This paper presents a new high-order cell-centered Lagrangian scheme for two-dimensional compressible flow. The scheme uses a fully Lagrangian form of the gas dynamics equations, which is a weakly hyperbolic system of conservation laws. The system of equations is discretized in the Lagrangian space by discontinuous Galerkin method using a spectral basis. The vertex velocities and the numerical fluxes through the cell interfaces are computed consistently in the Eulerian space by virtue of an improved nodal solver. The nodal solver uses the HLLC approximate Riemann solver to compute the velocities of the vertex. The time marching is implemented by a class of TVD Runge–Kutta type methods. A new HWENO (Hermite WENO) reconstruction algorithm is developed and used as limiters for RKDG methods to maintain compactness of RKDG methods. The scheme is conservative for the mass, momentum and total energy. It can maintain high-order accuracy both in space and time, obey the geometrical conservation law, and achieve at least second order accuracy on quadrilateral meshes. Results of some numerical tests are presented to demonstrate the accuracy and the robustness of the scheme.     

Structural and optical properties of waveguides in YbVO4 crystals formed by 3.0 MeV Cu-ions implantation

We report on the structural and optical characterization of waveguides formed in YbVO₄ crystals by Cu²⁺-ion implantation with an energy of 3.0 MeV and doses of 3.0×10¹⁴-1.0×10¹⁵ ions/cm². The damage properties are determined by RBS/Channeling measurements with the help of simulation code RUMP. The m-line method is used to characterize the dark-mode spectroscopy in the planar waveguides. According to the reconstructed refractive index profile of the waveguide cross section, a numerical simulation is carried out to investigate the confinement of the light in the waveguides based on the beam propagation method.     

Propagation properties of Lorentz beam in uniaxial crystals orthogonal to the optical axis

The properties of Lorentz beams propagating in uniaxial crystals orthogonal to the optical axis are studied. The diffraction field components and effective beam sizes of the Lorentz beams are derived in analytical forms. Numerical results show that, upon propagating in uniaxial crystals, a Lorentz beam loses its initial Lorentz type distribution. Also, after propagating for sufficient distances, the transverse components would finally convert into a specific four-petal profile with an axial shadow, which may find applications in the optical trapping of particles. It also shows that the Lorentz beam parameters w_0x, w_0y and the ratios of refractive indices have strong influences on the diffraction field components and on the effective beam sizes when propagating in uniaxial crystals.     

Properties of a vector soliton laser passively mode-locked by a fiber-based semiconductor saturable absorber operating in transmission

We experimentally demonstrate a passively mode-locked fiber laser employing a fiber-based semiconductor saturable absorber (SSA) operating in transmission. Polarization rotation locked vector solitons are observed in the laser. Due to the intrinsic dynamic feature of the laser, period-doubling of these vector solitons has also been observed. Furthermore, extra spectral sidebands are formed on the optical spectrum, caused by the energy exchange between the two orthogonal polarization components of the vector solitons. By careful reduction of the pump power together with fine adjustment to the cavity birefringence, period-one state can further be obtained. Additionally, the phase noise properties of the vector soliton fiber laser have also been characterized experimentally and analytically.     

A full-duplex radio-over-fiber system based on dual quadrupling-frequency

We proposed and simulatedly demonstrated a novel full-duplex radio-over-fiber system using an external modulator and an optical interleaver to generate dual quadrupling-frequency optical millimeter waves for carrying two base station downstream data and wavelength reuse for uplink connection. The simulation results reveal that the power penalties for the downstream and upstream signals of both base stations are less than 0.8 dB. In this new scheme, the configuration of the both base stations is simplified further because there is no additional laser at two base stations. The frequency of local oscillator signal is reduced due to frequency quadrupling. The cost of the new system is largely reduced.     

60 GHz Radio over Fiber Technology for Wireless Access by employing Narrow-Angle PSK Modulation

This paper investigates two key techniques used in 60 GHz Radio over Fiber (RoF) technology for wireless access, namely, the generation of 60 GHz signals and the distribution of 60 GHz local oscillator (LO). In the proposed model, a 60 GHz PSK signal is generated by a heterodyne of two subcarriers with narrow-angle PSK (NA-PSK) modulation, whose phase shift is equal to one half that of a normal PSK signal. Then we use a 60 GHz mixer to frequency mix two PSK signals in two different bands, 60 GHz and baseband. By doing this, the modulation information can be fully eliminated, resulting in a 60 GHz LO. In the wireless terminal, coherent demodulation is realized by a self-mixing of the transmitted 60 GHz PSK signal and LO. Thus no millimeter-wave (mm-wave) band oscillator is needed in the wireless terminal.     

Impact of geometry on the TM photonic band gaps of photonic crystals and quasicrystals

Here we demonstrate a novel quantitative procedure to pursue statistical studies on the geometric properties of photonic crystals and photonic quasicrystals (PQCs) which consist of separate dielectric particles. The geometric properties are quantified and correlated to the size of the photonic band gap (PBG) for wide permittivity range using three characteristic parameters: shape anisotropy, size distribution, and feature-feature distribution. Our concept brings statistical analysis to the photonic crystal research and offers the possibility to predict the PBG from a morphological analysis.     

Fractional spin textures in the frustrated magnet SrCr(9p)Ga(12-9p)O₁₉

We consider the archetypal frustrated antiferromagnet SrCr(9p)Ga(12-9p)O?? in its well-known spin-liquid state, and demonstrate that a Cr(3+) spin S=3/2 ion in direct proximity to a pair of vacancies (in disordered p<1 samples) is cloaked by a spatially extended spin texture that encodes the correlations of the parent spin liquid. In this spin-liquid regime, our analytic theory predicts that the combined object has a magnetic response identical to a classical spin of length S/2=3/4, which dominates over the small intrinsic susceptibility of the pure system. This fractional-spin texture leaves an unmistakable imprint on the measured ?1Ga nuclear magnetic resonance line shapes, which we compute using Monte Carlo simulations and compare with experimental data.     

Exact solutions for a type of electron pairing model with spin-orbit interactions and Zeeman coupling

A type of electron pairing model with spin-orbit interactions or Zeeman coupling is solved exactly in the framework of the Richardson ansatz. Based on the exact solutions for the case with spin-orbit interactions, it is shown rigorously that the pairing symmetry is of the p + ip wave and the ground state possesses time-reversal symmetry, regardless of the strength of the pairing interaction. Intriguingly, how Majorana fermions can emerge in the system is also elaborated. Exact results are illustrated for two systems, respectively, with spin-orbit interactions and Zeeman coupling.