III–V based-semiconductor photonic crystals

Three-dimensional (3D) and two-dimensional (2D) photonic crystals based on III–V semiconductors are described. On the 3D photonic crystals, the development of complete photonic crystals at optical wavelengths and their applications to ultrasmall optical integrated circuits including 3D sharp bend waveguide are described. On the 2D photonic crystals, two-unique device and/or phenomena are demonstrated.     

Integrated squared error of kernel-type estimator of distribution function

Let X ₁ ,...,X _n be a random sample drawn from distribution function F(x) with density function f(x) and suppose we want to estimate X(x). It is already shown that kernel estimator of F(x) is better than usual empirical distribution function in the sense of mean integrated squared error. In this paper we derive integrated squared error of kernel estimator and compare the error with that of the empirical distribution function. It is shown that the superiority of kernel estimators is not necessarily true in the sense of integrated squared error.     

Integrated Image Associative Memory and Its Optical Implementation

We present the concept of integrated processing to combine intuitive processing of neural networks with logical processing of the conventional digital computer. We investigate a way to embody the concept in the neural network system by introducing external constraints in terms of external input. The effect of the external input is analyzed using the generalized projection method. The concept of integrated processing is applied to an image associative memory system, and the system is optically implemented for high-speed parallel processing incorporating it with the computer. The experimental result is presented to illustrate the effectiveness of the external input to control the output of the image associative memory.     

Measuring the efficiency of trigonometric series estimates of a density

Some types of density estimators, particularly those based on trigonometric series, converge reasonably quickly to their limit except in the neighbourhood of one or two singularities. In this situation the mean integrated square error, the traditional measure of the efficiency of a density estimator, is an unsatisfactory measure. The notion of partial mean integrated square error is introduced and used to compare the performance of trigonometric series estimators. The results lead to consideration of some new estimators which have excellent properties from the points of view of both efficiency and ease of computation.     

Integrated Density of States For Random Metrics on Manifolds

We study ergodic random Schrödinger operators on a coveringmanifold, where the randomness enters both via the potentialand the metric. We prove measurability of the random operators,almost sure constancy of their spectral properties, the existenceof a self-averaging integrated density of states and a Pastur–ubintype trace formula. 2000 Mathematics Subjects Classification35J10, 58J35, 82B44.     

Modeling and Simulation of Saturation Gain of IR Integrated Photonic Amplifiers

IR integrated photonic amplifiers at 1.55m operation will have good foreground in optical phasedarray radars for splitters and signal processing. The saturation gain characteristics of IR integrated photonic waveguide amplifiers (taken Er³⁺Yb³⁺ co-doped phosphate glass waveguide amplifiers as an example) are studied theoretically. For the homemade laser glass materials the calculated saturation intensities are 2.22kw /cm² for signal and 10.15kw/cm² for pump. The effects of absorption saturation of signal and pump lights on the gain of amplifiers are discussed.     

Integrated optical cross strip polarizer concept

Passing across an abrupt junction from a thick vertically bimodal waveguide to a thinner single mode segment, guided light can undergo complete destructive interference, provided that the geometry and the phases of the modes in the initial segment are properly adjusted. We propose to employ this effect to realize a simple polarizer configuration, using a strip that is etched from a planar waveguide. A beam of light is made to pass the strip perpendicularly. The light enters from the single mode waveguide outside the strip into the strip segment, which is configured to support two modes. At the end of the strip, apart from reflections, the amount of power that is guided in the following lower segment depends on the local phases of the two modes. These phases are different for TE and TM light, hence we may expect a polarization dependent power transfer, resulting in polarizer performance for a properly selected geometry. The paper describes in detail the modeling of the device in terms of rigorous mode expansion. Design guidelines and tolerance requirements for geometric and material parameters are discussed. For typical Si₃N₄/SiO₂ materials, our calculations predict a peak performance of 34 dB polarization discrimination and 0.3 dB insertion loss for a device with a total length of about 12 m that selects TE polarization at a wavelength of 1.3 m.     

Local Power Properties of Kernel Based Goodness of Fit Tests

If (X_i, i ) is a strictly stationary process with marginal density function f, we are interested in testing the hypothesis H₀: {f=f₀}, where f₀ is given. We consider different test statistics based on integrated quadratic forms measuring the proximity between f_n, a kernel estimator of f, and f₀, or between f_n and its expected value computed under H₀. We study the asymptotic local power properties of the testing procedures under local alternatives. This study generalizes to the multidimensional case in a context of dependence the corresponding one made by P. J. Bickel and M. Rosenblatt in 1973 (Ann. Statist.1, 1071–1095).     

Hölder Regularity of Integrated Density of States for the Almost Mathieu Operator in a Perturbative Regime

Consider the Almost Mathieu operator H = cos 2(k +)+ on the lattice. It is shown that for large , the integrated density of states is Hölder continuous of exponent < . This result gives a precise version in the perturbative regime of recent work by M. Goldstein and W. Schlag on Hölder regularity of the integrated density of states for 1D quasi-periodic lattice Schrödinger operators, assuming positivity of the Lyapunov exponent (and proven by different means). Our approach provides also a new way to control Green's functions, in the spirit of the author's work in KAM theory. It is by no means restricted to the cosine-potential and extends to band operators.     

一种用于光机热集成分析的新方法——干涉图插值法

Zernike多项式是光机热集成分析中实现光、机、热各分析软件之间数据传递的重要工具。许多光学元件表面形状并不满足Zernike多项式的正交性条件，使有限元分析不能精确拟合光学元件表面变形及变形产生的各项像差。讨论影响Zernike正交性的几个因素，详细介绍将有限元分析得到的光学表面变形数据导入光学分析软件的一种新方法——干涉图插值法。该方法避开Zernike多项式拟合，在去除镜面刚体位移后将镜面畸变精确地表示成干涉图数据，直接生成数据接口。