A singularly perturbed Dirichlet problem for the Laplace operator in a periodically perforated domain. A functional analytic approach

Let Ω be a sufficiently regular bounded connected open subset of such that 0 ∈ Ω and that is connected. Then we take q₁₁, … ,q_nn ∈ ]0,+ ∞ [and . If ε is a small positive number, then we define the periodically perforated domain , where {e₁, … ,e_n} is the canonical basis of . For ε small and positive, we introduce a particular Dirichlet problem for the Laplace operator in the set . Namely, we consider a Dirichlet condition on the boundary of the set p + εΩ, together with a periodicity condition. Then we show real analytic continuation properties of the solution and of the corresponding energy integral as functionals of the pair of ε and of the Dirichlet datum on p + ε?Ω, around a degenerate pair with ε = 0. Copyright © 2011 John Wiley & Sons, Ltd.     

分段小信号近似方法研究准相位匹配倍频效率

从PPLN波导微结构出发分析准相位匹配倍频过程中的相位补偿机理,以极化畴为单元,通过耦合波方程计算极化畴内产生的二次谐波电场,通过电场相干叠加计算倍频效率。分别在小信号近似和基频光高消耗情况下计算准相位匹配倍频效率,结果显示：倍频效率小于5％时,两种情况下的计算结果吻合得很好;随着转换效率增大,小信号近似不再适用,需要在基频光高消耗情形下计算倍频效率。研究了基频光功率密度与准相位匹配倍频效率的关系,定性分析了极化周期存在误差时,误差对倍频效率的影响。     

A method for calculating the lyapunov exponent spectrum of a periodically excited non-autonomous dynamical system

The relation between the Lyapunov exponent spectrum of a periodically excited non-autonomous dynamical system and the Lyapunov exponent spectrum of the corresponding autonomous system is given and the validity of the relation is verified theoretically and computationally. A direct method for calculating the Lyapunov exponent spectrum of non-autonomous dynamical systems is suggested in this paper, which makes it more convenient to calculate the Lyapunov exponent spectrum of the dynamical system periodically excited. Following the definition of the Lyapunov dimensionD _L ^(A) of the autonomous system, the definition of the Lyapunov dimensionD _L of the non-autonomous dynamical system is also given, and the difference between them is the integer 1, namely,D _L ^(A) −D_L=1. For a quasi-periodically excited dynamical system, similar conclusions are formed. Project supported by the National Natural Science Foundation of China (No. 19772027), the Science Foundation of Shanghai Municipal Commission of Education (99A01) and the Science Foundation of Shanghai Municipal Commission of Science and Technology (No. 98JC14032).     

The Contact Problem for an Elastic Orthotropic Plate Supported by Periodically Located Bars of Equal Resistance

The contact problem of the plane theory of elasticity is studied for an elastic orthotropic half-plane supported by periodically located (infinitely many) stringers of equal resistance. Using the methods of the theory of a complex variable, the problem is reduced to the Keldysh-Sedov type problem for a circle. The solution of the problem is constructed.     

Magnetoelastic shear body waves in periodically inhomodeneous media

The shapes of magnetoelastic shear body waves in periodically inhomogeneous magnetostrictive dielectric media are studied with emphasis on wave shapes in the neighborhood of the zones of interaction of elastic and magnetostatic waves __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 10, pp. 13–20, October 2006.     

周期极化铌酸锂制作与应用

详细介绍了一种波长转换效率很高的周期极化铌酸锂(PPLN)的原理、制作及应用。周期极化铌酸锂以其有效非线性系数大于常用块状晶体一个数量级的特点得到迅速发展，PPLN可通过外加电场极化法、质子交换法等方法制备。近年来其制备工艺和光光转化效率有了很大的提高。周期极化铌酸锂可用于固体激光倍频。半导体激光直接倍频光参量振荡和放大等方面。使用PPLN与否。很大程度上已经成为传统非线性激光光源能否继续发展的决定性因素。     

The Fabrication and SHG Test of QPM Periodically Poled KTiOPO4

The Quasi-phase-matching periodically poled flux-grown KTP by high electrical field method is researched. A 8×5×1mm3, Λ=9.0μm PPKTP wafer is successfully fabricated for the first order QPM SHG. The interactive length of the sample is about 3mm. The SHG scheme of Nd:YAG at 1064nm tested that the output power of cw 532nm green light is 0.2mw at room temperature with fundamental power of 1.2w. The normalized conversion efficiency is about 0.09% (W·cm)-1.     

Time and Energy Characteristics of Radiation at <Emphasis Type="Italic">Q</Emphasis>-switched Self-Frequency Conversion

The results of a theoretical study of quasi-phase matched processes at self-frequency conversion in the Q-switched regime are presented. A scheme containing a periodically poled active nonlinear crystal and an acousto-optical modulator inserted inside the cavity is considered. Solutions of the set of equations describing such scheme are obtained by numerical methods. The time dynamics of the self-frequency doubling, self-frequency summing, and self-parametric frequency conversion processes are studied in detail. The energy characteristics of the radiation are also calculated and compared with those in the stationary regime.     

Drift and Diffusion in Periodically Driven Renewal Processes

We consider the drift and diffusion properties of periodically driven renewal processes. These processes are defined by a periodically time dependent waiting time distribution, which governs the interval between subsequent events. We show that the growth of the cumulants of the number of events is asymptotically periodic and develop a theory which relates these periodic growth coefficients to the waiting time distribution defining the periodic renewal process. The first two coefficients, which are the mean frequency and effective diffusion coefficient of the number of events are considered in greater detail. They may be used to quantify stochastic synchronization.     

周期极化LiNbO3晶体中电极布置对反转畴扩张的影响

利用外加电场极化的方法,分别研究了三种不同方式布置的极化电极对C向切割LiNbO_{3< /sub>晶体极化反转畴扩张的影响.实验结果表明在相同极化条件下，当极化电极长度方向与六边 形反转畴一对边呈90°和0°角时，极化扩张速度分别为0.089μm/ms和0.011μm/ms.实验结果揭示，为了有效地控制极化占空比，在制备一维准相位匹配LiNbO3晶体时应 避免极化电极与六边形反转畴壁中一对边呈90°的情况. 关键词： 周期极化 极化扩张 准相位匹配}