基于白光干涉的光学球面半径测量研究

光学球面曲率半径是决定光学球面光学特性的重要参量,通过测量光学球面的曲率半径，可以审核光学元件设计制造质量。在基于白光干涉理论基础上，将莫尔光栅位移测量系统及CCD数字图像采集处理系统集成到迈克尔逊干涉仪上，利用CCD数字图像处理技术，构建了光学球面曲率半径自动测量系统。该测量系统对于大曲率半径的光学球面测量精度较高；对于半径R＝71.2037mm的光学球面,其测量标准误差σR＝0.4723mm。实验结果表明：设计的光学球面自动测量系统可以对大曲率半径光学球面实现高精度测量。     

Capacitance coefficients of two spheres

Compact and exact expressions are obtained for the capacitance coefficients C_aa, C_bb and C_ab of two conducting spheres of radii a and b, for any distance c between the sphere centres. The results are equivalent to those of Maxwell, Russell and Jeffery, but enable rapid calculation of the coefficients in the limit of close approach, which is otherwise computationally difficult. Erroneous results published by several authors are corrected.     

The single photon superradiance from the eigenmode analysis

Using the eigenmode analysis of the scalar photon theory, I compute the probability of the atoms remaining excited and the probability for the atoms remaining in the initial quantum state of a system of two-level atoms cloud in a sphere initially prepared to radiate in the forward direction, i.e., the single photon superradiance problem. The convergence in the results obtained for increasingly larger radii for the sphere suggests that the asymptotic limits for these quantities are obtained for a sphere with a radius equal to six times the resonant wavelength. I predict the maximal value of the probability of secondary excited states from large spheres at 17.1%.     

GaAs,GaP和GaAsxP1-x合金能带的计算

使用分区变分法计算了GaAs,GaP和GaAs_xP_1-x合金的能带。鉴于原胞内包含不同的原子,依据实际原子的大小,对不同原子球选用了不同的半径。晶体势用相应原子势的迭加势来计算。考虑到组成晶体时原子势场由于电子成键而产生畸变,因而在球外成键区选用了一些调整参数来调整势场,然后再用解析表式来逼近这种调整原子势。适当地选择调整参数使算得的能带同已知的实验值接近。对GaAs和GaP已算得了同实验结果符合的能带结构。使用所得的调整原子势进一步计算了GaAs_xP_1-x合金的能带。 关键词：     

自洽LMTO方法计算半导体αSn、CdTe的电子结构

本文将自洽LMTO能带方法应用到半导体开结构情况,如αSn(金刚石结构)、CdTe(闪锌矿结构)。我们采用了空球模型,每个球有一个球对称势,并使用优选法确定出原子球及空球半径的尺寸,计算了它们的能带结构,给出的数据与实验结果能较好地符合。它预示出局域密度泛函能带方法应用到开结构材料的前景。     

Acoustic scattering from two spheres,one with a small radius

The scattering of a plane acoustic wave from an acoustically penetrable or impenetrable (soft or hard) sphere separated at a distance from another sphere, also penetrable or impenetrable (soft or hard), of acoustically small radius, is examined. The penetrable spheres and the surrounding medium are fluids or fluidlike; i.e., they do not support shear waves. Separation of variables, in conjunction with translational addition theorems for spherical wave functions, is used. Analytical expressions are obtained for the scattered pressure field and the scattering cross sections. Numerical results are given for penetrable and impenetrable spheres, showing the influence of the small sphere on the scattering cross sections of the other sphere. Published in Russian in Akusticheskiĭ Zhurnal, 2007, Vol. 53, No. 1, pp. 38–49. The text was submitted by the authors in English.     

Radius-dependent binding or repelling forces exerted on metal nano-sphere clusters by infrared-induced plasmonic resonance

The force exerted on metal nano-particles is investigated numerically when the particles are in contact to form a cluster and are illuminated by a light of their fundamental plasmonic resonance frequency. For touching spheres, the mode of resonance changes drastically from those of separate spheres, and the resonance typically appears in the infrared wavelength range. For silver and gold two-sphere clusters, i.e. homo-dimers, of various radii, the magnitudes and the directions of the exerted forces are analyzed. It is found that the field enhancement in the gap region between the spheres depends largely on the sphere radius, and the force on the fundamental resonance exhibits binding only for small spheres; the greatest binding force is observed for radii of 40–60 nm; and the force turns to repelling when the radius becomes greater than approximately 100–150 nm as the field in the gap region becomes weaker.     

Computation of scattering from N spheres using multipole reexpansion

A computational technique for the solution of problems of wave scattering from multiple spheres is developed. This technique, based on the T-matrix method, uses the theory for the translation and reexpansion of multipole solutions of the Helmholtz equation for fast and exact recursive computation of the matrix elements. The spheres can have prescribed radii, impedances, and locations. Results are validated by comparison with boundary element calculations, and by convergence analyses. The method is much faster than numerical methods based on discretization of space, or of the sphere surfaces. An even faster method is presented for the case when the spheres are aligned coaxially.     

Multipolar corrections to the Clausius-Mossotti formula for the effective dielectric constant of a polydisperse suspension of spheres

We study multipolar corrections to the Clausius-Mossotti formula for the effective dielectric constant of a polydisperse suspension of spheres with identical uniform dielectric constant embedded in a uniform background. The first few moments of the spectral density occurring in the Bergman representation are evaluated exactly to second order in the volume fraction. We present numerical results for a log-normal distribution of sphere radii.     

Exact wave functions for concentric two-electron systems

We show that the exact solution of the Schrödinger equation for two electrons confined to two distinct concentric rings or spheres can be found in closed form for particular values of the ring or sphere radii. In the case of rings, we report exact polynomial and irrational solutions. In the case of spheres, we report exact polynomial solutions for the ground and excited states of S symmetry.     

Normal modes and quality factors of spherical dielectric resonators: I — shielded dielectric sphere

Electromagnetic theoretic analysis of shielded homogeneous and isotropic dielectric spheres has been made. Characteristic equations for the TE and TM modes have been derived. Dielectric spheres of radii of the order of μm size are found suitable for the optical frequency region whereas for the microwave region radii of the order of mm size are found suitable. Parameters suitable for their application in the optical and microwave frequency ranges have been used to compute the frequencies corresponding to the normal modes for the TE and TM modes. Expressions for the quality factors for realistic resonators, i.e., for a dielectric sphere with a non-zero conductivity and a metal shield with a finite conductivity have also been derived for the TE and TM modes. Computations of the quality factors have been made for resonators with parameters suitable for the optical and the microwave regions.     

Effective dielectric constant of dilute polydisperse suspensions of spheres

We study the effective dielectric constant of a dilute, polydisperse suspension of spheres embedded in a uniform background. We consider a frequency region where the dipole polarizability of individual spheres exhibits a resonance. We evaluate the effective dielectric constant to second order in the volume fraction employing the dipole approximation, which in previous work has been shown to be applicable in resonance. We apply our results to suspensions of spheres with identical and uniform dielectric constant, assuming a log-normal distribution of sphere radii.     

含有偏心球形微粒介质球的有效介电常量

对于处在均匀外电场中含有偏心球形微粒的介质球,利用分离变量法求出球内外的电场,给出了球外电偶极矩和电四极矩的近似表达式.首次引入含有偏心球形微粒介质球的有效介电常量,它不同于同心多层介质球的等效介电常量,不仅与介质球内的介质有关,而且与球外介质有关.数值结果显示了有效介电量数随偏心距和球外介质介电常量的变化情况.     

A kinetic model for droplet growth in the transition regime

A variant of the moment expansion method, used in an earlier paper to describe the flow of a gas toward an absorbing sphere, is applied to a more realistic model of a droplet condensing from a supersaturated vapor. In the simplest version a spherical droplet absorbs all incoming vapor molecules, but spontaneously emits molecules with a Maxwellian distribution at the droplet temperature and with the corresponding saturated vapor density. From a solution of the stationary linearized Boltzmann equation with these boundary conditions we obtain expressions for the heat and mass currents toward the sphere as a function of the supersaturation and the temperature difference between the droplet and the vapor at infinity. For small droplet radii the known free flow limit is obtained in a natural way. From the calculated expressions for the heat and mass current we derive evolution equations for the radius and temperature of the droplet. The temperature evolves more rapidly and can thus be eliminated adiabatically; the resulting growth curve for the radius shows a sharp transition from a kinetically controlled regime for small radii to a regime dominated by heat conduction for large radii. The effect of incomplete absorption at the surface is also studied. The actual calculations are carried out for Maxwell molecules, with parameters corresponding to argon at 0.65T _c and 100% supersaturation.     

Scattering of electromagnetic waves by a bi-isotropic sphere

The scattering of a plane electromagnetic wave at a bi-isotropic sphere is studied, and exact analytical representations are obtained for the fields inside and outside the sphere. Expressions corresponding to Rayleigh scattering can be used to find the effective values of the material parameters of a heterogeneous composite medium consisting of small bi-isotropic spheres randomly disseminated throughout a homogeneous dielectric.V. D. Kuznetsov Siberian Institute of Physics and Technology, Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 108–112, October, 1994.     

Assessing the Exact Muffin-Tin Orbitals method for the Bain path of metals

Abstract

We scrutinise the muffin-tin approximation and the screening within the framework of the Exact Muffin-Tin Orbitals method in the case of cubic and tetragonal crystal symmetries. Systematic total energy calculations are carried out for the Bain path including the body-centred cubic and face-centred cubic structures for a set of simple and transition metals. The present converged results in terms of potential sphere radius (S) and hard sphere radius (b) are in good agreement with previous theoretical calculations. We demonstrate that for all structures considered here, potential sphere radii around and slightly larger than the average Wigner–Seitz radius (w) yield accurate total energy results whereas S values smaller than w give large errors. It is shown that for converged total energies hard spheres with radii b = 0.7–0.8w should be used for an efficient screening within real space clusters consisting typically of 70–90 lattice sites. The less efficient convergence of the total energy in the case of small hard spheres is ascribed to the delocalisation of the screened spherical waves, which leads to inaccurate interstitial overlap matrix. The above conclusions are not significantly affected by the volume of the system.     

Structure and thermodynamics of the classical one-component plasma

An exact solution of the mean spherical approximation for charged hard spheres in a neutralizing background is used to calculate various static properties of the classical one-component plasma in the strong coupling regime. The expressions involved are simple and analytic, and involve the charged hard sphere diameter as the only unknown parameter, which we determine using an approximate scaling property of the direct correlation function. Results obtained for structural correlation functions and various thermodynamic quantities are in very good agreement with the Monte Carlo simulation data.     

Statistical geometry of hard sphere systems: exact relations for first-order phase transitions in multicomponent systems

Statistical geometry provides exact relations between the thermophysical properties of hard sphere systems and various geometric quantities. Utilizing recently derived relations that describe multicomponent hard sphere systems, we derive two new expressions which place rigorous constraints on the behaviour of geometric quantities across a first-order phase transition. Some implications of these constraints for a binary mixture of additive hard spheres are discussed.