Central limit theorem for integrated square error of kernel estimators of spherical density

LetX ₁,…,X _n be iid observations of a random variableX with probability density functionf(x) on the q-dimensional unit sphere Ω_q in R^q+1,q ⩾ 1. Let be a kernel estimator off(x). In this paper we establish a central limit theorem for integrated square error off _n under some mild conditions.     

Performance of Single-Hop WDM LANs Supporting Real-Time Services

Optical wavelength division multiplexing (WDM) local area networks are capable of fulfilling the enormous bandwidth demands of present and future applications. Up to now, the WDM LAN world is primarily dominated by the passive-star coupler (PSC) based architectures, for which many medium access control (MAC) protocols have been proposed. However, an arrayed waveguide grating multiplexer (AWGM)-based single-hop WDM network seems to be a very promising alternative. One of the most critical issues in designing next generation photonic LANs is the support of real-time services for applications with different time constraints. In this paper, different basic access protocols for the PSC as well as AWGM-based single-hop WDM LANs are considered and their performance in supporting real-time traffic is analyzed by means of extensive computer simulations. For evaluation of real-time performance, packet drop rates and deadline missing rates are taken as performance measures. Furthermore, new real-time message scheduling schemes are proposed which improve the performance of protocols accommodating mixed traffic. They can be differentiated between message scheduling at the source nodes transmit queues and scheduling based upon control information from a control channel. It is shown that both types of priority scheduling significantly improve the overall real-time performance.     

Partial subdifferentials, derivates and Rademacher's Theorem

In this paper, we present new partial subdifferentiation formulas in nonsmooth analysis, based upon the study of two directional derivatives. Simple applications of these formulas include a new elementary proof of Rademacher's Theorem in , as well as some results on Gâteaux and Fréchet differentiability for locally Lipschitz functions in a separable Hilbert space.

RÉSUMÉ. Dans cet article, nous présentons de nouvelles formules de sousdifférentiation partielle en analyse nonlisse, basées sur l'étude de deux dérivées directionnelles. Une simple application de ces formules nous permet d'obtenir une nouvelle preuve élémentaire du théorème de Rademacher dans , ainsi que certains résultats sur la différentiabilité Gâteaux ou Fréchet des fonctions localement Lipschitz sur un espace de Hilbert séparable.

     

Exact analysis of cascaded second-order nonlinearity in rotated Ti:LiNbO3 Couplers

The effects of anisotropic coupling on the nonlinear behavior of different LiNbO₃ waveguides and couplers employing cascaded second-order nonlinearity are analyzed and the importance of leaky mode effect is shown. A set of practical coupling structures made of both symmetric and asymmetric waveguides is investigated and their performance is compared. The home-made computer-code, based on coupled wave theory and anisotropic mode propagation in the complex domain, allows an exact electromagnetic investigation of devices, taking into account both guided and leaky propagation in structures which exhibit losses, the generated second harmonic wave having leaky nature. As an example, for the well-investigated slab three layer waveguide, by taking into account the leaky nature of the generated second harmonic, the modal mismatch = 333 m^–1 is obtained at the azimuthal angle _m 61.9 (between the crystal optical c-axis and the propagation direction) while the angle found via the conventional approach is _m 63.5. Moreover, the calculated second harmonic wave exhibits an attenuation equal to 7.44 × 10^–1dB/cm that strongly influences the whole cascaded second-order phenomenon. The simulation results, for those structures in which it is possible to neglect the hybrid and leaky nature of the propagation modes, are compared with the literature data and an excellent agreement is found.     

Computer aided design of inverted strip dielectric waveguide millimeter wave ring-resonator and coupler

A computer aided design technique has been developed for the design of millimeter-wave ring resonator and hybrid-ring coupler using inverted strip dielectric waveguides. The scattering matrix analysis for hybrid-ring coupler has also been developed. Numerical results for these components at f₀=80 GHZ with 3-dB coupling have been presented along with the variation of width, spacing, and radii with frequency.This work was supported by the faculty research committee of the University of North Dakota under research grant no. 1813/0909/2027 and partially funded by E.F. Johnson Co., Waseca, Minnesota, under grant no. 9009/8183.     

Social utility functions for strategic decisions in probabilistic voting models

This paper studies societies which have probabilistic voting that is smooth, scalable and unbiased. Its results establish that, in such societies, the decisions of vote-seeking candidates who start at a common location (such as the status quo for the society's policies and/or the same allocation of campaign resources) contain implicit rationality properties. In particular, it shows that in every such society there exist social utility functions which simultaneously rationalize the directional Nash behavior of candidates, the stationary electoral equilibria, and the non-degenerate local electoral equilibria which can occur at these locations. This is shown to be true both for unconstrained and for constrained sets of possible candidate locations. An example of such a utility function (which occurs in every one of the societies under consideration) is also provided.     

一种新型SOI Mach-Zehnder干涉型电光调制器的设计

在超紧缩双曲锥形3dB多模干涉耦合器的基础上,设计了一种新的Silicon-on-insulator (SOI) Mach-Zehnder干涉型电光调制器.与传统的Y分支器相比,双曲锥形3dB耦合器的制作容差大,而长度缩短了近30%,使得整个器件的尺寸大幅减小.调制区采用横向注入的PIN结构,模拟结果表明:当外加偏压为0.86V时,器件的调制深度最大,此时注入电流为13.2mA,对应的器件功耗为11.4mW.     

Compact Branched Optical Waveguides Using High-Index-Contrast Stacked Structure

We have developed a novel branched optical waveguide using a stacked directional coupler, which consists of two Si₃N₄ core layers (each 0.3 μm thick) stacked with a thin (0.2 μm) SiO₂ film in between. Using this stacked high-index-contrast system, the size of the multiple branched waveguides can be dramatically reduced compared with the conventional Y-shaped branches. A four-branch optical waveguide is designed and fabricated, and good performance of distribution power of 25 ± 4% to each branch has been achieved.     

Threshold characteristic of intracavity optical parametric oscillator pumped by all-solid-state Q-switched laser

We derive the threshold pump intensity for a singly resonant intracavity optical parametric oscillator (IOPO)based on a temporal coupled field model.Particular attention is Paid to the dependence of the intracavity singly resonant OPO(SRO)threshold intensity on the signal wave output coupling.Meanwhile,a Nd:YAG laser pumped KTiOPO4(KTP)IOPO for eye-safe laser output is studied experimentally.The experiment is performed with four signal wave output reflectivities of 60%,70%,80%,and 90%,respectively.The measured values are in good agreement with the theoretical results.With an output coupler reflectivity of 80%,a peak power of 70 kW at 1572 nm has been obtained at a repetition rate of 3.5 kHz.The pulse width is 4.9 ns.Such investigation is helpful to identifying suitable operational regime of low pump intensity.     

两平行长周期光栅耦合器型上下话路滤波器的研究

以两平行长周期光栅耦合器的通用模型为依据，全面分析了两光栅完全对准和存在纵向偏离时器件性能的稳定性. 在此基础上深入研究光栅调制强度、环境折射率以及光纤包层厚度等因素的影响，确定出实现100%上下话路滤波效率的条件. 初步的实验结果表明，不需要对光纤包层进行处理，利用两平行长周期光栅耦合器完全可以实现有效的上下话路.这为进一步简化制作工艺提供了依据. 关键词： 长周期光纤光栅 光纤耦合器 上下话路滤波器