Diffractive optics: Design, realization, and applications

This paper presents methods for designing and recording optimal computer-generated diffractive optical elements. The design method is based on an analytic ray-tracing procedure for minimizing aberrations. The recording involves computer-generated masks and multiple lithographic processes in order to form reflective and transmissive multilevel, surface relief-phase, diffractive elements. As a result, the elements can have high diffraction efficiencies over a broad range of incidence angles. Even generalized diffractive elements that operate with highly uniform diffraction efficiency and polychromatic radiation can be designed and recorded by optimizing the shape and height of the relief gratings. To illustrate the effectiveness of the diffractive optical elements, they have been incorporated into a number of applications, involving visible as well as infra-red radiation. Some that deal with coordinate transformation, beam shaping, and polarization control are briefly reviewed.     

在类比系统中研究引力和黑洞的性质

引力和量子力学的融合是理解时空起源和引力本质的重要问题,也是一个长期悬而未决的基础物理学根本问题。理论物理学家们对此提出了诸多理论猜想,也做出了许多预言。然而一些相关的预言涉及的效应极其微弱,因此难以通过实验观测加以证实。通过类比引力系统,人们可以将这些引力效应转化为实验室可测可控系统的一些效应。对这些类比系统的研究一方面可以帮助人们更深入地理解引力的性质本身,另一方面也可以为其他相关领域的研究提供启发和新的思路。文章将以几个具体的类比系统为例简要介绍类比引力研究的历史和最近的一些研究进展。     

Semiparametric random coefficient regression models

Linear regression models with random coefficients express the idea that each individual sampled may have a different linear response function. Technically speaking, random coefficient regression encompasses a rich variety of submodels. These include deconvolution or affine-mixture models as well as certain classical linear regression models that have heteroscedastic errors, or errors-in-variables, or random effects. This paper studies minimum distance estimates for the coefficient distributions in a general, semiparametric, random coefficient regression model. The analysis yields goodness-of-fit tests for the semiparametric model, prediction regions for future responses, and confidence regions for the distribution of the random coefficients.This research was supported in part by NSF Grant DMS 9001710.     

The Coloring Ideal and Coloring Complex of a Graph

Let G be a simple graph on d vertices. We define a monomial ideal K in the Stanley-Reisner ring A of the order complex of the Boolean algebra on d atoms. The monomials in K are in one-to-one correspondence with the proper colorings of G. In particular, the Hilbert polynomial of K equals the chromatic polynomial of G.The ideal K is generated by square-free monomials, so A/K is the Stanley-Reisner ring of a simplicial complex C. The h-vector of C is a certain transformation of the tail T(n) = n ^d – (n) of the chromatic polynomial of G. The combinatorial structure of the complex C is described explicitly and it is shown that the Euler characteristic of C equals the number of acyclic orientations of G.     

像面滤波技术在无透镜傅里叶变换数字全息中的应用

无透镜傅里叶变换数字全息波前重建主要采用全息图的一次快速傅里叶变换方法,重建图像不能充分占有重建平面.本文基于像平面滤波技术,提出对物体局部区域光波场进行放大重建并让重建图像布满重建平面的方法,给出具有精细结构物体的数字全息波前重建实例.此外,将数字全息光波场重建视为具有方形出射光瞳的光学系统的相干光成像过程,导出了物体放大图像的分辨率与光学系统相关参量的关系,并通过实验给予证明.     

Temperature Dependence of In-plane Resistivity and Inverse Hall Angle in NLED Holographic Model

In the strange metal phase of the high-Tc cuprates, it is challenging to explain the linear temperature dependence of the in-plane resistivity and the quadratic temperature dependence of the inverse Hall angle. In this paper, we investigate the temperature dependence of the in-plane resistivity and inverse Hall angle in the nonlinear electrodynamics holographic model developed in our recent work. Maxwell electrodynamics and Born-Infeld electrodynamics are considered. Both cases support a wide spectrum of temperature scalings in parameter space. For Maxwell electrodynamics, the T-linear in-plane resistivity generally dominates at low temperatures and survives into higher temperatures in a narrow strip-like manner. Meanwhile, the T-quadratic inverse Hall angle dominates at high temperatures and extends down to lower temperatures. The overlap between the T-linear in-plane resistivity and the T-quadratic inverse Hall angle, if occurs, would generally present in the intermediate temperate regime. The Born-Infeld case with a 0 is quite similar to the Maxwell case. For the Born-Infeld case with a 0, there can be a constraint on the charge density and magnetic field. Moreover, the overlap can occur for strong charge density.     

Modulation Characteristics of Tunable Quantum-Well Heterolasers at the Radiation Frequency Tuning

The influence of the tuning of the radiation frequency of quantum-well heterolasers within the limits of their amplification band on the output laser radiation parameters at different frequencies of pump-current modulation has been numerically simulated using two optical models of an active medium under the assumption that the excess of the invariable component of the pump current over its threshold value at any point of the amplification band is constant. It has been established that the amplitude-detuning characteristics of the lasers studied are linear at high current-modulation frequencies and nonlinear at medium ones. The behavior of the nonlinear spectral response of a laser diode is explained by its multiresonance structure and is mainly determined by the ratio between the pump-current modulation frequency and the maximum resonance frequency of the laser. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 4, pp. 473–478, July–August, 2005.     

关于2×2矩阵代数保立方幂等的单射

刻画了2×2全矩阵代数保立方幂等映射,利用保立方幂等映射象与原象矩阵对应元素相等这个特点计算出相应的结果,得出特征不等于2,3,5域上2×2全矩阵代数保立方幂等单射的一个具体的刻画.