Curvature investigation in tapered fibers and its application to sensing and mode conversion

Non-adiabatic tapered fibers are basic photonic components used in a wide range of applications. Here we investigate a way to increase their utility through the controllable bending of one of their tapered sections. The experiments carried out explain, for the first time, the mechanics of this approach showing how these tapers can be used to build more sensitive sensors. Their use as highly efficient mode converters is also discussed.     

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.     

一种新型的二元光学器件——多位相光束分束器的制作

本文报道了用于多光束分束器的反射式16位相值二元光学器件的制作。该二元光学器件把一束光束分成5×5光束阵列。测量的衍射效率为76.16%,接近理论设计值79.68%。该二元光学器件的有效孔径为10mm×10mm。     

改善液晶光阀投影光学系统偏振特性的理论设计方法

定量分析了液晶光阀投影光学系统中影响系统对比度的主要因素，利用矢量方法建立三维空间数学模型对光线进行追迹，并利用琼斯矩阵和矢量光学的原理分析了偏振器件--主要是波片--和各种光学薄膜对光学系统性能的影响。给出了在一定假设条件下的对没有波片的光学系统和插入波征后的光学系统的仿真计算结果。两组数据比较表明在光路中插入合适相位差的波片可以显著提高系统对比度等性能。     

薄膜偏振分光镜的研究

概述薄膜偏振分光镜的研究现状及其主要特点，重点分析薄膜偏振分光镜的设计原理,并利用等效折射率的方法计算中心波长的反射率．     

A computational strategy for multiscale systems with applications to Lorenz 96 model

Numerical schemes for systems with multiple spatio-temporal scales are investigated. The multiscale schemes use asymptotic results for this type of systems which guarantee the existence of an effective dynamics for some suitably defined modes varying slowly on the largest scales. The multiscale schemes are analyzed in general, then illustrated on a specific example of a moderately large deterministic system displaying chaotic behavior due to Lorenz. Issues like consistency, accuracy, and efficiency are discussed in detail. The role of possible hidden slow variables as well as additional effects arising on the diffusive time-scale are also investigated. As a byproduct we obtain a rather complete characterization of the effective dynamics in Lorenz model.     

输入输出共轴的三弯曲型TM01-TE11模式转换器

 通过采用相位重匹配技术，设计了一种输入输出共轴的三弯曲型TM₀₁-TE₁₁模式转换器，该转换器由三段常曲率弯曲波导和两段直波导组成。用模式耦合理论建立了该类模式转换器的数值计算和优化设计方法，并设计了一个中心频率为7.0 GHz的模式转换器。该转换器的TM₀₁-TE₁₁转换效率在中心频率上大于99％，在6.5~7.5 GHz的频率范围内大于90％。应用时域有限差分法和有限元方法对所设计的模式转换器进行了仿真，仿真结果验证了设计理论和设计结果。     

改进型迈克耳孙干涉仪

采用分光梭镜代替迈克耳孙干涉仪中的分束镜和补偿板，不仅消除了杂散光斑，且简化了仪器的结构．     

Convergence rate of the best-r-point-average estimator for the maximizer of a nonparametric regression function

The best-r-point-average (BRPA) estimator of the maximizer of a regression function, proposed in Changchien (in: M.T. Chao, P.E. Cheng (Eds.), Proceedings of the 1990 Taipei Symposium in Statistics, June 28–30, 1990, pp. 63–78) has certain merits over the estimators derived through the estimation of the regression function. Some of the properties of the BRPA estimator have been studied in Chen et al. (J. Multivariate Anal. 57 (1996) 191) and Bai and Huang (Sankhya: Indian J. Statist. Ser. A. 61 (Pt. 2) (1999) 208–217). In this article, we further study the properties of the BRPA estimator and give its convergence rate under some quite general conditions. Simulation results are presented for the illustration of the convergence rate. Some comparisons with existing estimators such as the Müller estimator are provided.     

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.