New splitting methods for two-dimensional evolutionary equations

New second- and third-order splitting methods are proposed for evolutionary-type partial differential equations in a two-dimensional space. These methods are derived on the basis of diagonally implicit methods applied to the numerical analysis of stiff ordinary differential equations. The splitting methods are found to be absolutely unconditionally stable. Test calculations are presented.     

Propagation of torsional waves in a prestretched compound hollow circular cylinder

The propagation of torsional waves in a prestressed compound (bi-layered) hollow circular cylinder is in vestigated within the frame work of a piecewise homogeneous body model, with the use of a three-dimensional linerized theory of elastic waves in initially stressed bodies. The elasticity relations for components of the compound cylinder are obtained from the Murnaghan potential. Numerical investigations are performed for bronze and steel. According to the results obtained, the effect of variations in the geometric (the ratio between the thickness of the cylinder and its inner radius) and mechanical parameters on the dispersion curves are analyzed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 1, pp. 103–116, January–February, 2008.     

Ag:Bi2O3复合膜的线性和非线性光学性质

从实验和理论两个方面，探讨了金属Ag不同掺杂浓度对Ag:Bi₂O₃复合膜线性和非线性光学性质的影响. 用吸收光谱研究了Ag浓度与Ag:Bi₂O₃复合膜表面等离子体共振带之间的关系；用皮秒Z-扫描技术研究了共振和非共振情况下(激发光波长分别为532nm和1064nm)，金属Ag浓度与复合膜三阶非线性极化率的关系. 基于表面等离子体共振理论和局域场增强理论对复合膜进行了分析，得到了不同Ag浓度时Ag:Bi₂O₃复合膜的三阶非线性效应，研究了激发波长和金属浓度对复合膜线性和非线性光学性质的影响. 结果表明，等离子体共振增强和合适的金属掺杂浓度使得三阶极化率增强二个量级，在Ag浓度为35％左右和接近等离子体共振频率(相应吸收带位于560nm—622nm)的532nm激发时，χ⁽³⁾具有最大值2.4×10^-9esu. 关键词： 金属纳米颗粒 复合膜 三阶非线性 表面等离子体共振     

对超短脉冲强激光在大气通道中产生的三次谐波偏振特性及白光光谱调制特性的研究

研究了超短脉冲强激光在大气中传输产生电离通道后辐射的三次谐波强度随激光偏振的变化.此外，还研究了产生的白光辐射在短波长上的有规律的谱调制，分析了白光谱调制的产生机理. 关键词： 超短脉冲激光 大气通道 超连续辐射 三次谐波     

三新戊氧基溴硼亚酞菁薄膜材料的三阶非线性光学特性

通过单光束Z扫描技术 ,在波长为 1.0 6 4μm和 5 32nm、脉宽为 38ps条件下研究了一种新的酞菁相关化合物三新戊氧基溴硼亚酞菁薄膜材料的三阶非线性光学特性。观察到在 1.0 6 4μm(离强吸收带很远 )下的双光子吸收和在 5 32nm下的反饱和吸收现象 ,并计算出了相应的非线性吸收系数。在 1.0 6 4μm下的非共振三阶非线性极化率和在 5 32nm下的共振三阶非线性极化率 χ(3 ) 分别为 6 .1× 10 - 1 2 esu和 6 .7× 10 - 1 0 esu ,显著大于相关酞菁的值。这些结果表明三新戊氧基溴硼亚酞菁薄膜材料在非线性光学方面具有潜在的应用前景。     

Organometallic materials for nonlinear optics

Almost three decades ago, the field of nonlinear optics evolved with the discovery of lasers. In the beginning, nonlinear optical (NLO) phenomena were investigated in inorganic materials, leading to the development of traditional NLO materials such as lithium niobate, potassium titanyl phosphate, quartz and gallium arsenide. In the 1970s, the importance of organic materials was realized because of the promise of large NLO responses, high laser damage thresholds, fast optical responses, architectural flexibility and ease of fabrication. Following work with organic materials, the scrutiny of organometallics also began recently. In organometallics, the metal-ligand bonding is expected to display large molecular hyperpolarizability because of the transfer of electron density between the metal atom and the conjugated ligand system. In organometallics, the diversity of central metals, oxidation states and ligands fosters in optimization of the charge-transfer interactions. Keeping this in view, second- and third-order NLO properties of organometallics have been reviewed here, highlighting new materials that are emerging. Organometallics may have a wide range of applications in opto-electronics including integrated optics, optical switching, telecommunications, bistability and modulation.     

MULTIPLE POSITIVE SOLUTIONS OF SINGULAR THIRD-ORDER PERIODIC BOUNDARY VALUE PROBLEM

This paper deals with the singular nonlinear third-order periodic boundary value problem u‘‘‘ ρ^3u = f(t,u), 0 ≤ t ≤ 2π, with u^(i)(0) = u^(i)(2π), i = 0,1,2, where ρ ∈ (0, 1 /√3) and f is singular at t = 0, t = 1 and u = 0. Under suitable weaker conditions than those of [1], it is proved by constructing a special cone in C[0, 2π] and employing the fixed point index theory that the problem has at least one or at least two positive solutions.     

LARGE AND EXTREMELY FAST THIRD-ORDER NON-LINEARITY OF Ag NANOPARTICLES EMBEDDED INTO A CsxO SEMICONDUCTOR MATRIX

The third-order optical nonlinearity of Ag-O-Cs thin films, where Ag nanoparticles are embedded into a Cs_xO semiconductor matrix, was measured by the femtosecond optical Kerr technique. The third-order nonlinear optical susceptibility, χ⁽³⁾, of the thin films was estimated to be 1.1×10^-9 esu at the incident wavelength of 820 nm. The response time, i.e. the full width at half-maximum of the Kerr signal, is as fast as 114 fs only. The intrinsic third-order optical nonlinearity can be attributed to the intraband transition of electrons from the occupied state near the Fermi level to the unoccupied state. It is suggested that such a nonlinearity is further enhanced by the local field effect that is present in the metallic nanoparticles composite thin films.     

Effects of walk-off on cross-phase modulation induced modulation instability in an optical fibre with high-order dispersion

This paper investigates the effects of walk-off among optical pulses on cross-phase modulation induced modulation instability in the normal dispersion region of an optical fibre with high-order dispersion. The results indicate that, in the case of high-order dispersion, the walk-off effect takes on new characteristics and will influence considerably the shape, position and especially the number of the spectral regions of the gain spectra of modulation instability. Not only the group-velocity mismatch, but also the difference of the third-order dispersion of two optical waves will alter the gain spectra of modulation instability but in different ways. Depending on the values of the walk-off parameters, the number of the spectral regions may increase from two to at most four, and the spectral shape and position may change too.     

带电荷C60分子的电子结构及其非线性光学性质

应用Su-Schrieffer-Heeget(SSH)模型研究带电荷C₆₀分子的结构和电子结构.分析所带电荷量对结构的影响,计算带不同电荷数时C₆₀分子的电子结构,进一步对三阶非线性光学极化率进行了研究.