Theoretical analysis of optical coupling properties of the waveguide grating with novel rectangular structure

For the waveguide grating photocoupler with novel structure [Yu XQ, Zhang X, Wong KS, Xu GB, Xu XG, Ren Y, et al. A fabrication of coupling grating in the polymeric waveguide by using two-photon initiated photopolymerization. Mater Lett 2004;58:3879–83. [1]; Yu XQ, Zhang X, Xu GB, Zhao HP, He W, Shao ZS, et al. Fabrication of grating waveguide and coupling grating using two-photon initiated photopolymerization. Chem J Chin Univ 2004;25(10):1931–3 (in Chinese). [2]], the electric fields of the TE guided wave and the TE radiating wave are obtained by solving the Helmholtz equation in the spatial rectangular coordinates. And then the relations between the loss coefficient and the different structure parameters of the waveguide and grating are analyzed by using the mode coupling theories, and their corresponding numerical simulation results are given. In the end the result obtained for this novel structure and that for conventional rectangle structure are compared, and the difference and the sameness are obtained.     

轴向反馈式虚阴极振荡器辐射微波模式的远场测定

 采用远场测量法测量了虚阴极振荡器波导口的微波辐射方向图及虚阴极振荡器波导口处接上TM₀₁-TE₁₁模式转换器时的微波辐射方向图,接收喇叭口面与微波辐射口之间的距离为1.00 m,满足远场条件。结果表明：两种情况下的辐射主模式分别为TM₀₁模式和TE₁₁模式,从而证实了在实验装置轴对称的条件下,轴向虚阴极振荡器的微波辐射主模式确为理论所预期的TM₂模式。对辐射模式的分析表明,TM₀₁模式纯度约为90%,TE₁₁模式的辐射功率为TM₀₁模式的5%左右;TE₂₁,TE₀₁和TM₁₁模式三者的总辐射功率较TM₀₁模式低一个量级以上,微波辐射功率大于300 MW,辐射频率为4.6 GHz左右,微波脉宽大于40 ns。     

A priori tests of a stochastic mode reduction strategy

Several a priori tests of a systematic stochastic mode reduction procedure recently devised by the authors [Proc. Natl. Acad. Sci. 96 (1999) 14687; Commun. Pure Appl. Math. 54 (2001) 891] are developed here. In this procedure, reduced stochastic equations for a smaller collections of resolved variables are derived systematically for complex nonlinear systems with many degrees of freedom and a large collection of unresolved variables. While the above approach is mathematically rigorous in the limit when the ratio of correlation times between the resolved and the unresolved variables is arbitrary small, it is shown here on a systematic hierarchy of models that this ratio can be surprisingly big. Typically, the systematic reduced stochastic modeling yields quantitatively realistic dynamics for ratios as large as 1/2. The examples studied here vary from instructive stochastic triad models to prototype complex systems with many degrees of freedom utilizing the truncated Burgers–Hopf equations as a nonlinear heat bath. Systematic quantitative tests for the stochastic modeling procedure are developed here which involve the stationary distribution and the two-time correlations for the second and fourth moments including the resolved variables and the energy in the resolved variables. In an important illustrative example presented here, the nonlinear original system involves 102 degrees of freedom and the reduced stochastic model predicted by the theory for two resolved variables involves both nonlinear interaction and multiplicative noises. Even for large value of the correlation time ratio of the order of 1/2, the reduced stochastic model with two degrees of freedom captures the essentially nonlinear and non-Gaussian statistics of the original nonlinear systems with 102 modes extremely well. Furthermore, it is shown here that the standard regression fitting of the second-order correlations alone fails to reproduce the nonlinear stochastic dynamics in this example.     

增益介质的色散对锁模激光器输出脉宽和啁啾的影响

利用时间域内各光学元件的传播矩阵,在考虑了增益介质的色散后,对锁模激光器输出的脉宽和啁啾做了理论方面的推导,并做了相关的数值模拟,结果表明:当不考虑增益介质的色散时,其输出脉宽啁啾值为零;而考虑了增益介质的色散后,啁啾值随色散值的增加先增加而后降低,且存在一个最大值,脉宽随色散值的增加而增加.     

Thermal buckling and post-buckling of pinned–fixed Euler–Bernoulli beams on an elastic foundation

In this article, both thermal buckling and post-buckling of pinned–fixed beams resting on an elastic foundation are investigated. Based on the accurate geometrically non-linear theory for Euler–Bernoulli beams, considering both linear and non-linear elastic foundation effects, governing equations for large static deformations of the beam subjected to uniform temperature rise are derived. Due to the large deformation of the beam, the constraint forces of elastic foundation in both longitudinal and transverse directions are taken into account. The boundary value problem for the non-linear ordinary differential equations is solved effectively by using the shooting method. Characteristic curves of critical buckling temperature versus elastic foundation stiffness parameter corresponding to the first, the second, and the third buckling mode shapes are plotted. From the numerical results it can be found that the buckling load-elastic foundation stiffness curves have no intersection when the value of linear foundation stiffness parameter is less than 3000, which is different from the behaviors of symmetrically supported (pinned–pinned and fixed–fixed) beams. As we expect that the non-linear foundation stiffness parameter has no sharp influence on the critical buckling temperature and it has a slight effect on the post-buckling temperature compared with the linear one.     

Incremental dynamic mode decomposition: A reduced-model learner operating at the low-data limit

The present work aims at proposing a new methodology for learning reduced models from a small amount of data. It is based on the fact that discrete models, or their transfer function counterparts, have a low rank and then they can be expressed very efficiently using few terms of a tensor decomposition. An efficient procedure is proposed as well as a way for extending it to nonlinear settings while keeping limited the impact of data noise. The proposed methodology is then validated by considering a nonlinear elastic problem and constructing the model relating tractions and displacements at the observation points.     

LiNbO3质子交换波导及其退火效应

采用质子交换技术,以苯甲酸为交换源,实验研究X-切LiNbO₃质子交换平面波导及其退火效应。利用棱镜耦合器测出波导模折射率。采用费米函数,由模折射率确定出波导折射率分布随退火时间的变化关系,给出了分布参数和曲线.     

基于宽度可调节的线缺陷平板型光子晶体的空气槽微腔

研究了一种空气槽光子晶体微腔,这种腔是由在平板型光子晶体上引入一条宽度可以调节的线缺陷空气槽形成的.腔模的电场被强烈局限在空气槽中,由于介电常量的不连续性,电场得到很大的提高,同时模体积被大大地降低.数值模拟与分析了微腔的能带结构和场分布,考虑到腔模的谐振频率和对称性,发现一阶偶膜同时具有较高的品质因子和较小的模体积;应用有限时域差分法,得到腔模的品质因子可以高达10⁶,模体积仅为0.02(λ/n)³.计算了一阶偶模谐振波长随空气槽宽度以及空气孔半径的变化,发现随着宽度的增加,波长越来越短.而随着空气孔半径的增加,波长近似线性地减小;当空气孔半径为170 nm时,可以获得最高的腔品质因子.     

New generalized computations of quasi-planar waveguides characteristics

An efficient hybrid field solution to the general multilayer substrates transmission line problems with full shielded and half open cross-sectional geometry is presented by using the waveguide modes coupling and decoupling procedure in the spectral domain. Modal transverse transmission lines corresponding to the LSE and LSM modes are taken into account so that the Green's elements for the edge conditions can be derived by a simple iterative method. In this paper, we analyze not only the propagation constants and characteristic impedances but also the available transmission power capacity and power distribution of most commonly used structures. Normalized eigenmode power levels characterizing the propagation features are computed.