Global solution curves for a class of elliptic systems

We study curves of positive solutions for a system of elliptic equations of Hamiltonian type on a unit ball. We give conditions for all positive solutions to lie on global solution curves, allowing us to use the analysis similar to the case of one equation, as developed in P. Korman, Y. Li and T. Ouyang [An exact multiplicity result for a class of semilinear equations, Commun. PDE 22 (1997), pp. 661–684.] (see also T. Ouyang and J. Shi [Exact multiplicity of positive solutions for a class of semilinear problems, II, J. Diff. Eqns. 158(1) (1999), pp. 94–151].). As an application, we obtain some non-degeneracy and uniqueness results. For the one-dimensional case we also prove the positivity for the linearized problem, resulting in more detailed results.     

液晶填充碲酸盐光子晶体光纤偏振旋转器

提出一种液晶填充碲酸盐玻璃的柚子型光子晶体光纤偏振旋转器,利用全矢量有限元法,对液晶填充碲酸盐玻璃的柚子型光子晶体光纤的偏振旋转特性进行数值模拟,并分析了光纤结构参数、环境温度、工作波长等对光纤偏振旋转特性的影响.研究结果表明:此种偏振旋转器具有较高的旋转效率、较低的工作串扰和较短的旋转长度,在工作波长为1.55μm、偏振角度为45°时,其值分别达到99.947%、-32.84dB和197μm;另外,随着光纤薄壁厚度的增加,旋转长度随之升高,随着工作波长的变大,旋转长度随之降低,随着温度的增加,旋转长度随之升高.这种新型的光子晶体光纤为偏振旋转器的研发提供了参考.     

Switchable dual-wavelength Erbium-doped fiber ring laser with cascaded fiber Bragg gratings

We have experimentally shown wavelength mode switching in a dual-wavelength Erbium-doped single cavity fiber laser where the initial two wavelengths of 1 nm spacing are determined by the cascaded reflection type short-period fiber Bragg gratings having two different centre wavelengths of 1550.5 and 1551.5 nm. The lasing mode depends on the polarization in the ring cavity to migrate from one wavelength to another or operates in both modes in a polarization beam splitter output. To effectively control the polarization in the ring cavity, the polarization controllers were positioned before and after the polarization beam splitter. This method of wavelength switching provides a simple way of mode tuning in dual-wavelength fiber lasers.     

The H2+ molecular ion: Low-lying states

Matching for a wavefunction the WKB expansion at large distances and Taylor expansion at small distances leads to a compact, few-parametric uniform approximation found in Turbiner and Olivares-Pilon (2011). The ten low-lying eigenstates of H₂⁺ of the quantum numbers (n,m,Λ,±)$(n,m,\Lambda ,\pm )$  with n=m=0$n=m=0$ at Λ=0,1,2$\Lambda =0,1,2$, with n=1$n=1$, m=0$m=0$ and n=0$n=0$, m=1$m=1$ at Λ=0$\Lambda =0$ of both parities are explored for all interproton distances R$R$. For all these states this approximation provides the relative accuracy ?10⁻⁵$?10^{-5}$ (not less than 5 s.d.) locally, for any real coordinate x$x$ in eigenfunctions, when for total energy E(R)$E\left(R\right)$ it gives 10-11 s.d. for R∈[0,50]$R\in [0,50]$  a.u. Corrections to the approximation are evaluated in the specially-designed, convergent perturbation theory. Separation constants are found with not less than 8 s.d. The oscillator strength for the electric dipole transitions E1$E1$ is calculated with not less than 6 s.d. A dramatic dip in the E1$E1$ oscillator strength f_{1sσg−3pσu}$f_{1s{\sigma }_g-3p{\sigma }_u}$ at R∼R_eq$R\sim R_{eq}$ is observed. The magnetic dipole and electric quadrupole transitions are calculated for the first time with not less than 6 s.d. in oscillator strength. For two lowest states (0,0,0,±)$(0,0,0,\pm )$ (or, equivalently, 1sσ_g$1s{\sigma }_g$ and 2pσ_u$2p{\sigma }_u$ states) the potential curves are checked and confirmed in the Lagrange mesh method within 12 s.d. Based on them the Energy Gap between 1sσ_g$1s{\sigma }_g$ and 2pσ_u$2p{\sigma }_u$ potential curves is approximated with modified Pade Re^−R[Pade(8/7)](R)$R{e}^{-R}\left[Pade(8/7)\right]\left(R\right)$ with not less than 4-5 figures at R∈[0,40]$R\in [0,40]$ a.u. Sum of potential curves E_1sσg+E_2pσu$E_{1s{\sigma }_g}+E_{2p{\sigma }_u}$ is approximated by Pade 1/R[Pade(5/8)](R)$1/R\left[Pade(5/8)\right]\left(R\right)$ in R∈[0,40]$R\in [0,40]$ a.u. with not less than 3-4 figures.     

倾斜光纤光栅谱特性

基于倾斜光纤光栅耦合模理论,采用数值分析法研究了前后向导模耦合时倾斜角度和调制深度对倾斜光纤光栅反射谱的影响,以及导模和辐射模耦合时针对不同的入射光偏振态在倾斜角度、调制深度、光栅长度等不同时倾斜光纤光栅透射谱(或反射谱)的特性.研究结果表明,在前后向导模耦合时,不同偏振态入射光的光谱几乎相同;而对于辐射模耦合,由于反射谱的包络受消光系数的调制,而不同偏振态入射光的消光系数不同,并且倾斜角度越大不同偏振态的入射光的消光系数差别越大,故在研究辐射模耦合时需要将偏振态予以考虑.     

保参数方向的形状可调过渡曲线与曲面

针对保参数方向构造过渡曲线曲面方法的不足, 构造了任意参数曲线曲面间既保持参数方向又具有形状可调性的C¹与C²连续过渡曲线曲面。首先,基于2类带1个自由参数的调配函数,分别构造满足C¹与C²连续的过渡曲线,并讨论基于能量优化模型的最佳过渡曲线构造问题;然后,将所提出的方法推广到过渡曲面的构造。 实例结果表明,2被过渡曲线曲面为任意参数曲线曲面时,利用该方法构造的过渡曲线曲面不仅与2被过渡曲线曲面的参数方向保持一致,而且可利用所带的自由参数对其形状进行调整。通过能量优化模型确定自由参数的取值,可获得尽可能光顺的过渡曲线曲面。 所提方法弥补了保参数方向构造过渡曲线曲面方法的不足,是一种实用的过渡曲线曲面构造方法。     

Hypercrosslinked polystyrene: A polymer in a non‐classical physical state

Deformation and relaxation properties of hypercrosslinked polystyrene networks have been studied by thermomechanical method at a uniaxial compression using individual spherical beads of the polymer. The networks examined were prepared by postcrosslinking of highly swollen beads of a styrene‐0.3% DVB copolymer with 0.3–0.75 mole of monochlorodimethyl ether, which results in the introduction of 0.6–1.5 methylene bridges between each two polystyrene phenyl rings. The polymers obtained are shown to belong neither to typical glassy materials, nor to typical elastomers. Though no characteristic plateau of rubberlike elasticity was observed on the deformation curves of the beads, the polymers exhibit two fundamentally important features of the rubberlike state: The deformations are large (up to 30–40% of the initial diameter) and reversible. Relaxation of residual deformations, however, requires prolonged heating of the sample, or a cycle of swelling and drying. The deformation can start in the temperature range from −70 to +150°C depending on pressure applied. The crosslinking degree in the range from 40–100% and higher does not affect noticeably the behavior of the hypercrosslinked polystyrene. Nature of the high mobility of the hypercrosslinked network is discussed. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2324–2333, 1999     

Potential energy curves for the X~1Σ_g~ , B~1△_g and B′~1Σ_g~ states of C_2 using MRCI and approximate CI methods

The potential energy curves for the X1Σ g , B1△g and B′1Σ g states of C2 have been studied by using MRC and approximate CI methods, and are benchmarked against the calculations of full configuration in teraction (FCI). The results obtained by MRCI method agree with the FCI very well, and even are accu rate enough to compare other approximate methods as benchmark, when the calculations of FCI ar not feasible. The approximate CI methods mentioned in this paper are reliable for treating chemica problems.     

Quantum theory for plasmon-assisted local field enhancement

We applied quantum theory for nonlocal response and plasmon-assisted field enhancement near a small metallic nanoscale antenna in the limit of weak incoming fields. A simple asymmetric bio-inspired design of the nanoantenna for polarization-resolved measurement is proposed. The spatial field intensity distribution was calculated for different field frequencies and polarizations. We have shown that the proposed design the antenna allows us to resolve the polarization of incoming photons.