On the Development of Controllable Sources of Single-Photon States with an Orbital Angular Momentum on the Basis of Spontaneous Parametric Down-Conversion of Light

Methods for beam shaping with nonzero orbital angular momentum are studied using diffraction optical elements with the purpose of developing a source of single-photon states based on spontaneous parametric down-conversion of light in the LiNbO₃ crystal in the cavity resonator. The probability of the coincidence of the number of photocounts in detecting signal and idle fields under pumping by a beam with the orbital angular momentum is simulated.     

First- and second-order statistics of partially coherent, high-numerical-aperture optical fields

The intensity probability distribution as well as the cross-spectral density of partially coherent optical fields generated through high-numerical-aperture illuminations are analyzed, and novel effects, not apparent in paraxial optical fields, are described. It is shown that the intensity probability distribution significantly differs from what can be expected from a small-angle analysis, and the number of degrees of freedom for the distribution is higher. It is further shown that the cross-spectral density of a high-angle optical field is a function of the coordinate difference along the propagation direction of the field.     

4f光学系统中滤波函数角位移补偿的研究

实验中4f光学系统的输入函数载体与滤波函数载体往往存在着一定的角位移,而这个角位移的存在影响了4f光学系统的精确滤波。将空间光调制器(SLM)作为4f光学系统的输入和滤波函数的载体,利用光栅衍射理论和傅里叶变换理论,提出了一种测量该角位移的方法。滤波函数旋转角位移值的大小可以补偿输入和滤波函数载体间存在的角位移。滤波实验证明了方法的有效性和必要性。     

基片衍射对会聚激光驻波场中原子波包几率密度演化的影响

针对激光会聚铬原子沉积实验,运用标量衍射理论,通过数值模拟研究了基片衍射对会聚激光驻波场中原子波包几率密度演化的影响。结果显示基片衍射的影响会随激光中轴线与基片沉积表面距离b0的变化而变化。相对于非衍射情况,衍射效应会提高激光驻波场中会聚平面内原子波包几率密度分布的中心值,同时减小其半峰全宽。当参量b0=－0.2w0(w0为高斯光束的束腰半径)时,原子波包几率密度的会聚平面和基片沉积表面完全重合。此处,衍射时原子波包几率密度分布的中心值为1.26,其半峰全宽为5.62 nm,两者分别为非衍射时的1.1倍和0.94倍。     

利用光电检测技术分析光栅衍射

本文利用光电检测技术对光盘光栅的衍射特性进行研究.实现了对分光范围、衍射光强分布、衍射叠级、自由光谱范围、衍射角与衍射光波长的线性度、角分辨率和光栅常数等光栅参数的观测和计算.该实验结果与衍射理论结果一致.该方法在一定程度上弥补传统光栅实验的不足,有利于增进本科生对大学光学中衍射光栅的认识.     

晶体X射线劳厄衍射分束特性研究

本文基于X射线衍射动力学分析了劳厄晶体的分束特性,模拟了晶体吸收和入射光角发散对于透射光和衍射光摇摆曲线的影响,定量给出晶体衍射面内角调节范围和晶体加工厚度对于劳厄衍射分束比的调制.在实验中,采用分析晶体和分束晶体的消色散配置限制入射光角发散的影响,实现300μm厚Si(220)晶体面内角调节劳厄衍射分束的精确测量,并得到300μm, 400μm和500μm厚度Si晶体分束比的调节范围,实现了透射光和衍射光强度的定量调制.     

Exact equations for radiative transfer of energy and momentum in free electromagnetic fields

In a recent paper a new theory of radiative energy transfer in free electromagnetic fields was formulated. The basic quantities in this theory are the so-called angular components of the average electromagnetic energy density and of the average Poynting vector. In the present paper it is shown that these angular components obey differential equations that may be considered to be rigorous equations for the radiative transfer of energy and of momentum in free electromagnetic fields.     

A finite difference method of solving anisotropic scattering problems

A new method of solving radiative transfer problems is described including a comparison of its speed with that of the doubling method, and a discussion of its accuracy and suitability for computations involving variable optical properties. The method uses a discretization in angle to produce a coupled set of first-order differential equations which are integrated between discrete depth points to produce a set of recursion relations for symmetric and anti-symmetric angular sums of the radiation field at alternate depth points. The formulation given here includes depth-dependent anisotropic scattering, absorption, and internal sources, and allows arbitrary combinations of specular and non-Lambertian diffuse reflection at either or both boundaries. The method is shown to be faster than the doubling method when the number of depth points and angular quadrature points is identical. Numerical tests of the method show that it can return accurate emergent intensities even for large optical depths. The method is also shown to conserve flux to machine accuracy in conservative atmospheres. Finally, several checks are made that demonstrate that the new method can compute accurate radiation fields in atmospheres with variable optical properties.     

Nonlinear optical response of an atom in the field of femtosecond laser pulses with near-atomic intensity

A theory of the nonresonant response of a single atom in a state with arbitrary magnitude and direction of the angular momentum of an atomic electron with respect to the polarization vector of the acting electromagnetic field has been developed. It has been shown that the atomic response current has a tensor structure and depends both on the direction of the angular momentum of the atom and on the polarization vector of the external field. The tensor character of the response is due to the effects of the anisotropy of probability density distribution of the atomic electron as compared to the case of the free atom. The selection rules for the axisymmetric problem of the atom in the field have been analyzed. The manifestation of the selection rules in the angular spectra of photoelectrons has been demonstrated. The probability of the ionization of the atom has been analyzed as a function of the amplitude and duration of the pulse. It has been shown that the width of the generation spectrum is a nonlinear function of the field strength and is saturated in the region of nearly atomic fields. Methods for controlling the parameters of the atomic response spectrum have been proposed on the basis of the use of a sequence of laser pulses with various time profiles, carrier frequencies, and polarization states. It has been shown that the generation of terahertz radiation is possible in the preionization regime, where the generation mechanism is attributed to atomic nonlinearity.     

Diffraction of stochastic electromagnetic fields by a hole in a thin film with real optical properties

The classical Kirchhoff theory of diffraction is extended to the case of real optical properties of a screen and its finite thickness. A spectral power density of diffracted electromagnetic fields by a hole in a thin film with real optical properties was calculated. The problem was solved by use of the vector Green theorems and related Green function of the boundary value problem. A spectral and spatial selectivity of the considered system was demonstrated. Diffracted patterns were calculated for the coherent and incoherent incident fields in case of holes array in a screen of perfect conductivity.     

相位光栅分离双波长宽角度光线的理论分析

使用衍射光栅的分色分光方式一般以平行光入射情况为讨论基础,对于非平行光入射的情况讨论较少.本文基于菲涅尔衍射理论和角谱理论,将球面波与平面波的衍射波场联系起来,从而在传播函数中引入角度参量,结合分数泰伯效应的理论基础,推导出双波长宽角度入射光线经相位光栅衍射后的波场分布函数,并对推导出的函数进行数值模拟,得到像面不同位置衍射波场分布.与平行光入射时的标准波场分布相比较,得到宽角度入射时的衍射波场的横向展宽量和偏移量.通过调节光栅台阶的宽度,改变衍射场的展宽和偏移,使各个单一波长的衍射波场宽度小于光栅周期的一半,从而减少双波长光衍射波场的混叠.同时本文给出波场宽度与光栅台阶宽度的变化关系,选取光栅面上多个位置作为台阶宽度的计算点,并对整个光栅的台阶宽度进行曲线拟合,得到可以使双波长宽角度入射光实现良好空间分离的光栅参量.该结果可用于各类宽角度入射光线的光谱分离场合,如双波长成像、液晶显示和液晶投影等.     

Angular momentum density of a Gaussian vortex beam

The Gaussian vortex beam is assumed to be linearly polarized.The analytical expression of the electric field of a linearly polarized Gaussian vortex beam propagating in free space is derived by using the vectorial Rayleigh-Sommerfeld integral formulae.The propagating magnetic field of the linearly polarized Gaussian vortex beam is presented by taking the curl of the electric field.By employing the electromagnetic field of the linearly polarized Gaussian vortex beam beyond the paraxial approximation,the analytical expression of the angular momentum density of the linearly polarized Gaussian vortex beam is derived.The three components of the angular momentum density of a linearly polarized Gaussian vortex beam are demonstrated in the reference plane.The effects of the linearly polarized angle and the topological charge on the three components of the angular momentum density are investigated.To acquire the more longitudinal angular momentum density requires such an optimal choice that the linearly polarized angle is set to be zero and the topological charge increases.This research is useful to the optical trapping,the optical guiding,and the optical manipulation.     

氢原子中电子概率密度的可视化研究

针对量子物理中氢原子电子概率密度抽象、不易理解的特点,本文给出了氢原子中电子概率密度分布函数,包括径向分布和角向分布函数.利用Matlab强大的绘图功能对其分布规律进行可视化研究.结果表明,该方法直观形象地揭示了氢原子中电子概率分布情况,为物理教学提供了新手段.     

Visualizing the Fractional Orbital Angular Momentum

This paper proposes a novel approach to visualize the fractional orbital angular amentum (OAM) flow of light fields at the example of the Lommel tornado wave (LoTW) along the propagation direction in free space. The novel approach that is based on the transverse intensity distributions of the LoTWs can be used to identify and quantify the fractional OAM. The energy that is continuously distributed flexibly is controlled via the asymmetry factor and topological charge. Furthermore, the OAM density on concentric rings and chiral paths is employed to demonstrate convincingly as a manifestation of the energy flow. Such beams are anticipated to find potential applications in optical communication and optical micromanipulation.     

Electromagnetically induced grating in double quantum dot system using spontaneously generated coherence

A model of electromagnetically induced grating (EIG) assisted by the spontaneously generated coherence (SGC) in the ladder-plus-Y double quantum dot (DQD) system is proposed. Using the density matrix theory, the amplitude and phase of the transmission function are studied. It is shown that the transmission is enhanced by the presence of SGC, and the resultant diffraction intensity can increase by controlling the phase. The SGC-assisted EIG controlled by two, three, and four coupling optical fields are studied respectively. Remarkably, we find that the system acquires a huge diffraction intensity when the wetting layer-quantum dot (WL-QD) field is high in the case of four coupling fields.     

Complete far-field asymptotic series for free fields

The closed form of the complete far-field asymptotic series is provided for the scalar and electromagnetic monochromatic fields in free space whose angular spectrum is smooth over the sphere of directions. The first few terms of this series are also shown to give corrections to the Fraunhofer diffraction formula. The application of this series is illustrated with two examples corresponding to a highly focused radially polarized field and to the scalar diffraction from a circular aperture.     

Microscopic study of ~7Li-nucleus potential

A microscopic approach is employed to study the optical potential for the 7Li-nucleus interaction system without any free parameters.It is obtained by folding the microscopic optical potentials of the constituent nucleons of 7Li over their density distributions.We employ an isospin-dependent nucleon microscopic optical potential,which is based on the Skyrme nucleon-nucleon effective interaction and derived using the Green's function method,as the nucleon optical potential.The harmonic oscillator shell model is used to describe the internal wave function of 7Li and obtain the nucleon density distribution.The 7Li microscopic optical potential is used to predict the reaction cross-sections and elastic scattering angular distributions for the target range from 27Al to 208Pb and energy range below 450 MeV.Generally,the results can reproduce the measured data reasonably well.In addition,the microscopic optical potential is comparable to a global phenomenological optical potential by fitting the presently existing measured data.     

Transient stationary waves and angular momentum

We report new transient stationary spherical waves generated by the time evolution of wave functions with angular momentum. In the study the 3D problem of the sudden release of a particle which initially was inside a spherical trap, the exact solution for the particle's time evolution is described by expected traveling incoming and outgoing spherical waves. However, unexpected transient stationary spherical waves are also present. The traveling waves have amplitudes describing diffraction in time, in a way similar to the optical diffraction by a single slit. In striking contrast with the similar 1D problem, the angular momentum generates unexpected transient stationary spherical waves which have their main contribution at points inside the sphere but only for very short times.     

Scale free distribution in an analytical approach

In order to explain the scale free feature of complex networks, we introduce an analytical approach for investigating the degree distribution. We represent the degree distribution by the probability density function, where the correspondence between them is given approximately by the transformation from discrete number, degree, to a continuous variable. We find that arbitrary representations of the degree distribution as the probability density function are reduced to a specific form which obeys scale free. Our result provides one explanation for the ubiquity of scale free networks.     

The optical near-field speckles and their first order statistics on the basis of the integral equations of electromagnetic field

Speckle fields are the random light wave distributions produced when the light fields are scattered from random surfaces or a random medium. They appear in many optical phenomena that are related to light propagations[1,2] and have found wide appli-cations in a variety of scientific and technical fields. The examples of the recent impor-tant applications of speckles include the analysis of the movement of the granules[3], the three-dimensional imaging for the microstructures of metal nanocryst…