Designing and fabricating diffractive optical elements with a complex profile by interference

We demonstrate a novel (to our knowledge) method for the design and the fabrication of diffractive optical elements (DOEs) with an arbitrary complex phase profile based on interference. The DOEs are designed to modulate the complex light wave by the analytical formulas, and an asymmetric holographic DOE with cubic phase modulation is fabricated by a two-step exposure technique. The desired Airy beams are produced experimentally, which demonstrates the validity of this method. It is a simple approach with a low cost for the design and the fabrication of DOEs with a large area and arbitrary phase distribution.     

Self-processing solgel material for one-step fabrication of micrometer-period sinusoidal phase gratings using the Lloyd's mirror scheme

A novel self-processing silica-zirconia hybrid solgel material has been developed and employed in one-step fabrication of micrometer-period sinusoidal phase gratings. In the process, the gratings with a sinusoidal profile were corrugated on the surface of the solgel film by UV exposure using the Lloyd's mirror setup. No further development or etching step is needed to reveal the sinusoidal profile because the corrugation is formed due to the self-processing property of the solgel material, which is robust enough to be used as an end product. The period, amplitude, diffraction efficiency of the +/-1 order, and surface roughness of one of the fabricated gratings are 0.99 microm, 330 nm, 30.56%, and 1.27 nm, respectively. The new self-processing material is practical and promising for fabrication of micro-optical elements.     

厚胶光刻非线性畸变的校正

利用厚胶光刻技术制作大深度微结构元件是一种有效的途径,但厚胶光刻过程中的非线性畸变对光刻面形质量的严重影响限制了该技术的应用,基于此,提出了一种对掩模透射率函数进行校正的方法。分析空间像形成及其在光刻胶内传递、曝光、显影等过程中非线性因素的影响,利用模拟退火算法对掩模透射率函数进行校正,以提高光刻面形质量,并以凹面柱透镜为例,给出了校正前后的显影轮廓模拟结果,其校正后浮雕面形的体积偏差仅为2.63%。该方法在有效改善面形质量的同时,并没有引起掩模的设计、制作难度及费用增加,这对于设计、制作高质量的微结构元件有重要意义。     

Analog micro-optics fabrication by use of a two-dimensional binary phase-grating mask

The utilization of phase-mask technology for the fabrication of an analog micro-optics profile with a thick photoresist was investigated. A two-dimensional phase-grating mask with pi phase depth can produce a desired analog variation of exposure intensity, which allows one to vary the thickness of an analog photoresist after its exposure by a photolithographic stepper and development of the photoresist. A two-dimensional phase-grating mask of square pixels was simulated, designed, and fabricated. The fabrication of analog micro-optics in a thick SPR-220 photoresist by use of this phase mask was also demonstrated.     

二元光学元件制作误差分析与模拟

从标量衍射理论出发，首先从理论上计算出多台阶二元化学元件发生深度误差时衍射效率的解析式，然后以４台阶和８台阶闪耀光栅为例，对二元光学元件套刻制作中的主要误差及其这些误差之间的相互影响进行了系统的分析和计算机模拟研究，模拟结果给实际制作提供了重要理论指导和实验参数。     

Large-angle scattering of heavy ions: (I). General structure of elastic cross section

Closed-form expressions are derived for the differential cross section of elastic heavy-ion scattering at large angles. The derivation is based on the general form of the elastic partial-wave S-matrix in real l-space. By a generalization of analytic techniques developed in earlier work, it is shown that the large-angle scattering cross section has a universal structure involving combinations of Bessel functions and the Fourier transforms of the rapidly varying parts of the S-matrix, irrespective of their dynamical origin. Anomalous large-angle scattering is attributed to deviations of the S-matrix from its “normal strong-absorption profile”, and general conditions for backward-angle enhancement are given. Our model-independent formulation provides the framework for an “inductive” method of analyzing experimental angular distributions and excitation functions aimed at identifying, as uniquely as possible, the dynamical mechanisms that operate in large-angle heavy-ion scattering. Extensions of the formalism to inelastic scattering and transfer reactions, and applications of the analytic method, will be described in subsequent papers.     

Gradient Profile Estimation Using Exponential Cubic Spline Smoothing in a Bayesian Framework

Attaining reliable gradient profiles is of utmost relevance for many physical systems. In many situations, the estimation of the gradient is inaccurate due to noise. It is common practice to first estimate the underlying system and then compute the gradient profile by taking the subsequent analytic derivative of the estimated system. The underlying system is often estimated by fitting or smoothing the data using other techniques. Taking the subsequent analytic derivative of an estimated function can be ill-posed. This becomes worse as the noise in the system increases. As a result, the uncertainty generated in the gradient estimate increases. In this paper, a theoretical framework for a method to estimate the gradient profile of discrete noisy data is presented. The method was developed within a Bayesian framework. Comprehensive numerical experiments were conducted on synthetic data at different levels of noise. The accuracy of the proposed method was quantified. Our findings suggest that the proposed gradient profile estimation method outperforms the state-of-the-art methods.     

Bounds for effective parameters of heterogeneous media by analytic continuation

We give a mathematical formulation of a method for obtaining bounds on effective parameters developed by D. Bergman and G. W. Milton. This method, in contrast to others used before, does not rely on a variational principle, but exploits the properties of the effective parameter as an analytic function of the component parameters. The method is at present restricted to two-component media.     

全息光栅制作中光栅掩模形状随曝光量及干涉场条纹对比度的变化规律

为了在光栅制作中对光栅掩模占宽比及槽深加以控制,结合光刻胶在显影过程中的非线性特性,建立了光栅掩模槽形演化的数学模型,由此分析和模拟曝光量、条纹对比度对光栅槽形的影响。结果表明:在显影条件确定时,光栅掩模占宽比随光刻胶曝光量的增大而减小,条纹对比度减小,则不仅使光栅占宽比减小,同时也是使光栅槽深减小的主要原因,这样做的前提是预先通过实验和计算确定出一个曝光量上限Ec。该方法能够反映光栅掩模形状的演化规律,为全息光栅参数预测和工艺控制提供依据。     

Design and fabrication of double-chirped mirrors

We present an analytic design method for the reproducible fabrication of double-chirped mirrors to achieve simultaneously a high reflectivity and dispersion compensation over an extended bandwidth compared with those of standard quarter-wave Bragg mirrors. The mirrors are fabricated by ion beam sputtering. Use of these mirrors in a Ti:sapphire laser leads to 6.5-fs pulses directly out of the laser. The method can also be applied to the design of chirped-fiber gratings and general optical filters.     

一种大F数微透镜阵列的制备方法

针对大F数(大于10)微透镜阵列难以制备的现状,提出了一种制备大F数微透镜阵列的方法.首先采用传统光刻胶热熔法及刻蚀技术制作出成形的微透镜阵列,再将一层具有较高粘滞系数的光刻胶均匀地涂覆在该微透镜阵列上,在光刻胶的粘滞作用以及烘烤过程中光刻胶自身表面张力的共同作用下,微透镜阵列的F数得到提高.采用该方法制备的二氧化硅微透镜阵列的F数达40,与传统大F数微透镜阵列的加工方法相比,该方法简便易行、制备的微透镜阵列面形良好,且只需调节光刻胶的粘滞系数,即可获得F数不同的微透镜阵列.     

A new surface-tension formulation for multi-phase SPH using a reproducing divergence approximation

In this paper, we propose a new surface-tension formulation for multi-phase smoothed particle hydrodynamics (SPH). To obtain a stable and accurate scheme for surface curvature, a new reproducing divergence approximation without the need for a matrix inversion is derived. Furthermore, we introduce a density-weighted color-gradient formulation to reflect the reality of an asymmetrically distributed surface-tension force. We validate our method with analytic solutions and demonstrate convergence for different cases. Furthermore, we show that our formulation can handle phase interfaces with density and viscosity ratios of up to 1000 and 100, respectively. Finally, complex three-dimensional simulations including breakup of an interface demonstrate the capabilities of our method.     

Haldane Gap in One-Dimensional Spin Chains

One-dimensional antiferromagnetic spin chains (S = 1) are quantized by means of the Gaus sian effective potential method for the O(3) nonlinear a model. The critical line-separating the missive phase with Haldane gap and massless phase is found in an analytic form. The spin correlation function is discussed via the sine-Gordon formulation as well.     

Techniques for formation of the surface profile of diffractive optical elements

We give a review of the findings of an investigation into a photolithographical method of fabricating diffractive optical elements (DOEs), based on the use of only one photomask with two transmittance gradations. The binarization of the continuous transmission function of the diffractive element is conducted using a technology of half-toning of continuous-tone images and the exposure of the light-sensitive medium is performed using an incoherent spatial filtration in combination with a conventional photolithographical process. We analyze how the DOE diffractive efficiency depends on photomask parameters, binarization methods and fabrication errors. Comparison of the characteristics of the method proposed with the well-known multilevel method is made. Peculiarities of fabricating DOEs with continuous phase profile resulting from the projection, contact, and X-ray lithography are discussed. The results of experimental research are given. A possibility of fabricating DOEs with an 80% diffractive efficiency using only one photomask is demonstrated.     

Computationally simple,analytic, closed form solution of the Coulomb self-interaction problem in Kohn–Sham density functional theory

We have developed and tested in terms of atomic calculations an exact, analytic and computationally simple procedure for determining the functional derivative of the exchange energy with respect to the density in the implementation of the Kohn–Sham formulation of density functional theory (KS-DFT), providing an analytic, closed-form solution of the self-interaction problem in KS-DFT. We demonstrate the efficacy of our method through ground-state calculations of the exchange potential and energy for atomic He and Be atoms, and comparisons with experiment and the results obtained within the optimized effective potential (OEP) method.     

Sample-inverted reflow technique for fabrication of a revolved-hyperboloid microlens array in hybrid solgel glass

We propose a novel fabrication method, which is referred to as the sample-inverted reflow technique, to fabricate a refractive microlens array (MLA) with a revolved-hyperboloid profile in a solgel material. The fabricated solgel MLA demonstrates an excellent smooth profile with a fabrication error much less than the difference between the revolved hyperboloid and the spherical surface. In an application of coupling a laser diode (LD) to a single-mode fiber (SMF), we propose a two-MLA coupling scheme in which two revolved-hyperboloid MLAs are used between the LD and the SMF. In this configuration the coupling efficiency achieves 81.7% (-0.88 dB).     

Propagation of laser beams through inhomogeneous media

The propagation of gaussian beams in media with an arbitrary gain and/or dispersion profile is discussed using a variational method. Simple analytic formulae are derived and applied to the spin-flip laser which has a gaussian gain profile. The results are a significant improvement on the quadratic-gain approximation.     

稳态自洽密度分布的三参量解族

本文利用严格的解析方法求得了激光等离子体中稳态自洽密度分布的三参量解族。讨论几种特殊情况,指出Lee等人给出的平台型密度分布只是其中的一种特殊情况。 关键词：     

Axially Symmetric Compact Range Reflectors: Application of the Analytic Regularization Method

An axially symmetric compact range reflector with a blended rolled edge was analyzed and optimized in a rigorous formulation of the diffraction problem. The corresponding boundary-value diffraction problem is solved with the analytic regularization method, which reduces the problem to an operator equation of the second kind, thus guaranteeing a numerically stable and effective solution. The distribution of the surface density and the fields at the aperture and in the near-field zone were obtained and analyzed for different types of the reflector-edge curvature. In addition, a “blending function” was used that esures an infinitely smooth contour across the junction between the paraboloid part of the reflector and its rolled edge. The procedure for determining the optimal edge is carried out in the rigorous formulation of the diffraction problem by minimizing the deviation from a plane wave.     

Modeling of graded index waveguide fabricated by ion exchange on Er3+ doped glass

A general numerical tool,based on thermal diffusion equation and full-vectorial eigen-mode equation,has been presented for the systematic analysis of graded index channel waveguide fabricated by ion exchange on Er3+ doped glass.Finite difference method with full-vectorial formulation(FV-FDM) is applied to solving the full-vectorial modes of graded index channel waveguide for the first time.The coupled difference equations based on magnetic fields in FV-FDM are derived from the Taylor series expansion and accurate formulation of boundary conditions.Hybrid nature of vectorial guided modes for both pump(980 nm) and signal light(1550 nm) are demonstrated by the simulation.Results show that the fabrication parameters of ion exchange,such as channel opening width and time ratio of second step to first step in ion exchange,have large influence on the properties of waveguide.By optimizing the fabrication parameters,maintenance of monomode for signal light and improvement of the gain dynamics can be achieved in Er3+ doped waveguide amplifier(EDWA) fabricated by ion exchange technique.This theoretical model is significant for the design and fabrication of EDWA with ion exchange technique.Furthermore,a single polarization EDWA,which operates at wavelength from 1528 nm to 1541 nm for HE polarization,is numerically designed.