Scattering on plasmonic nanostructures arrays modeled with a surface integral formulation

The surface integral formulation is a flexible, multiscale and accurate tool to simulate light scattering on nanostructures. Its generalization to periodic arrays is introduced in this paper. The general electromagnetic scattering problem is reduced to a discretizated model using the Method of Moments on the surface of the scatterers in the unit cell. The study of the resonances of an array of bowtie antennas illustrates the main features of the method. When placed into an array, the bowtie antennas show additional resonances compared to those of an individual antenna. Using the surface integral formulation, we are able to investigate both near-field and far-field properties of these resonances, with a high level of accuracy.     

基于复合腔的波长可调谐连续橙红色激光器

设计并研制了一种基于复合腔结构的波长可调谐、瓦级连续输出的橙红色激光器.该激光器是由半导体激光侧泵Nd∶GdVO_4晶体产生p-偏振1 062.9nm基频光的谐振腔和使用周期性极化晶体MgO∶PPLN(三个极化周期为29.0μm、29.8μm和30.8μm)的单共振光学参量振荡器组成.在两个谐振腔的重叠区域,利用Ⅱ类临界相位匹配KTP晶体对s-偏振信号光与p-偏振1 062.9nm基频光进行腔内和频.通过对MgO∶PPLN晶体进行三个不同极化周期的调谐和30℃~200℃范围内的温度调谐,在三个波段(613.4~619.2nm@29.0μm、620.2~628.9nm@29.8μm和634.4~649.1nm@30.8μm)获得了波长可调谐的橙红色激光连续输出,并在相应波段(3 980.0~3 758.5nm@29.0μm、3 714.2~3 438.3nm@29.8μm和3 278.0~2 940.2nm@30.8μm)获得了波长可调谐的中红外闲频光的连续输出.在30℃最低调谐温度,通过改变晶体的极化周期,在613.4nm、620.2nm和634.4nm处测得最大连续输出功率分别为1.52 W、2.21 W和3.03 W,对应的三束闲频光最大连续输出功率分别为2.36 W@3 980.0nm、3.17 W@3 714.2nm和4.13 W@3 278.0nm.     

周期变截面波导中的多缺陷态*

设计了一种具有对称结构的多缺陷周期变截面波导,并在其Bragg禁带中实现了多缺陷态的产生。研究表明,通过调整缺陷的个数和长度可实现对缺陷态数目的选择和缺陷态中心频率的调谐。另外,改变重复周期个数可对缺陷态的带宽进行调节。通过对各缺陷态的声场分布进一步分析,我们发现声压沿波导中心轴呈对称或反对称分布。对称缺陷态的最大声能量总是向长度较小的缺陷处偏移,而反对称缺陷态则相反,总是向长度较大的缺陷处偏移。利用这种偏移特性可实现对多缺陷态的声场调控。这不仅使我们对声缺陷态的认识更加深入,更有利于功能型声波导器件的发展与应用。     

Compton散射下等离子体中电子相轨道的演化

用KMR模型研究了等离子体中多光子非线性Compton散射下电子相轨道的演化,发现电子与光子进行能量交换后,只有未被俘获电子的相轨道才能从周期性向非周期性、随机型演化,其演化剧烈程度随电子吸收光子数的增大而加剧,随电子与光子碰撞非弹性成分和碰撞前初始速度的增大而迅速减弱,但低于强激光场中的剧烈程度。当电子被光场俘获时,这种演化过程结束并做稳定的运动,光子不再为电子提供能量。     

Periodic Solutions of a Class of Duffing Differential Equations

In this work we study the existence of new periodic solutions for the well knwon class of Duffing differential equation of the form $x^{\prime\prime}+ c x^{\prime}+ a(t) x +b(t) x^3 = h(t)$, where $c$ is a real parameter, $a(t)$, $b(t)$ and $h(t)$ are continuous $T$--periodic functions. Our results are proved using three different results on the averaging theory of first order.     

Asymptotic approximations for Bloch waves and topological mode steering in a planar array of Neumann scatterers

We study the canonical problem of wave scattering by periodic arrays, either of infinite or finite extent, of Neumann scatterers in the plane; the characteristic lengthscale of the scatterers is considered small relative to the lattice period. We utilise the method of matched asymptotic expansions, together with Fourier series representations, to create an efficient and accurate numerical approach for finding the dispersion curves associated with Floquet–Bloch waves through an infinite array of scatterers. The approach lends itself to direct scattering problems for finite arrays and we illustrate the flexibility of these asymptotic representations on topical examples from topological wave physics.     

Undercompressive shocks for nonstrictly hyperbolic conservation laws

We study 2×2 systems of hyperbolic conservation laws near an umbilic point. These systems have Undercompressive shock wave solutions, i.e., solutions whose viscous profiles are represented by saddle connections in an associated family of planar vector fields. Previous studies near umbilic points have assumed that the flux function is a quadratic polynomial, in which case saddle connections lie on invariant lines. We drop this assumption and study saddle connections using Golubitsky-Schaeffer equilibrium bifurcation theory and the Melnikov integral, which detects the breaking of heteroclinic orbits. The resulting information is used to construct solutions of Riemann problems.     

Sound attenuation of a periodic array of micro-perforated tube mufflers

The wave propagation in a periodic array of micro-perforated tube mufflers is investigated theoretically, numerically and experimentally. Because of the high acoustic resistance and low mass reactance due to the sub-millimeter perforation, the micro-perforated muffler can provide considerable sound attenuation of duct noise. Multiple mufflers are often used to enhance attenuation performance. When mufflers are distributed periodically in a duct, the periodic structure produces special dispersion characteristics in the overall sound transmission loss. The Bloch wave theory and the transfer matrix method are used to study the wave propagation in periodic micro-perforated tube mufflers and the dispersion characteristics of periodic micro-perforated mufflers are examined. The results predicted by the theory are compared with finite element method simulation and experimental results. The results indicate that the periodic structure can influence the performance of micro-perforated mufflers. With different periodic distances, the combination of the periodic structure and the micro-perforated tube muffler can contribute to the control of lower frequency noise with a broader frequency range or improvement of the peak transmission loss around the resonant frequency.     

Instability of two-phase flows: A lower bound on the dimension of the global attractor of the Cahn-Hilliard-Navier-Stokes system

We consider a model for the flow of a mixture of two viscous and incompressible fluids in a two or three dimensional channel-like domain. The model consists of the Navier-Stokes equations governing the fluid velocity coupled with a convective Cahn-Hilliard equation for the relative density of atoms of one of the fluids. We prove the instability of certain stationary solutions for such a system endowed with periodic boundary conditions on elongated domains (0,2π/α₀)×(0,2π) or (0,2π/α₀)×(0,2π)×(0,2π/β₀) for a special class of periodic body forces, provided that α₀ and β₀ are small enough. As a consequence, we deduce a lower bound for the Hausdorff dimension of the global attractor.     

经典轨道的封闭性和径向Schr?dinger方程的因式分解

研究表明,保证经典轨道具有封闭性的Bertrand定理可以进一步推广,在适当的角动量下,仍存在着非椭圆的闭合轨道．对于屏蔽Coulomb场,可获得广义Runge-Lenz矢量．这种轨道封闭性与径向Schr?dinger方程因式分解相对应．