Calculation of the Coulomb electrostatic potential created by a uniformly charged square on its plane: Exact mathematical formulas

We calculate exactly the Coulomb electrostatic potential created by a uniformly charged square on its plane. The chosen solution method leads to certain types of integral expressions which involve combinations of products of error functions and power functions. These type of integrals that should be solved are not standard ones, therefore, the integration formulas we derive in the process may be deemed of mathematical interest on their own right. Use of these formulas enables us to derive an exact analytic expression for the Coulomb electrostatic potential created by a uniformly charged square at an arbitrary point on its plane.     

一种新型透射式自聚焦光栅的设计及理论研究

结合普通透射光栅的分光特性和菲涅耳波带片的聚焦特性,提出一种应用于软X射线波段的新型透射式自聚焦光栅。根据菲涅耳衍射理论,对其衍射特性进行理论推导,证明该新型光栅存在一个与光栅平面垂直的焦平面,不同波长的光波聚焦于该焦平面的不同位置。在焦平面上,焦点位置随光子能量的变化是线性的,即能实现光子能量的线性测量。通过解析推导,得到在沿着焦平面和垂直于焦平面两个方向上光斑的展宽模式,发现该新型光栅在沿着焦平面的光斑展宽模式不同于普通光栅。根据基尔霍夫衍射公式,设置实用化参数,对其衍射模式进行了详细的数值模拟研究,并讨论了相应的测谱范围和谱分辨率。     

Quantum lithography with classical light

We show how to achieve subwavelength diffraction and imaging with classical light, previously thought to require quantum fields. By correlating wave vector and frequency in a narrow band, multiphoton detection process that uses Doppleron-type resonances, we show how to achieve arbitrary focal and image plane patterning with classical laser light at submultiples of the Rayleigh limit, with high efficiency, visibility, and spatial coherence. A frequency-selective measurement process thus allows one to simulate, semiclassically, the path-number correlations that distinguish a quantum entangled field.     

Focusing for laser hole drilling

The power intensity distribution of a laser beam across the focal plane is important for producing good hole geometry. To examine the power intensity distribution in the region of the image plane of a practical lens, a diffraction integral method is employed. Lens aberration is accounted for by the intensity of the appropriate phase changes. In the analysis, a free-running pulsed multimode solid-state laser is considered and the lens is assumed to have aberrations. Since an on-axis object is examined, only spherical aberration is taken into account.     

基于衍射光栅的CCD相机标定方法

提出一种基于1维线衍射光栅的CCD相机光电响应特性标定方法,该方法利用衍射光栅对入射光束的分束特性,在远场焦平面内形成一系列衍射子光斑,采取有效的方法对多组衍射子光斑峰值测量数据进行融合,得到测量灰度值及通过理论计算得到的理论灰度值,拟合两组数据从而完成对CCD光电响应特性的标定.根据实验室现有的激光源与聚焦光学系统的...     

Modelling diffraction during ray tracing using the concept of energy flow lines

The ray-tracing with diffraction on facets (RTDF) model is suitable for rapid computation of scattering on faceted dielectric objects such as ice crystals. It combines ray tracing with diffraction on flat facets. The model calculates diffraction using an approximation for the far-field direction of the Poynting vector. In this paper, an estimate based on an approximation by Prosser for the electric and magnetic fields describing diffraction at a slit is used to calculate energy flow lines and their far-field deflection angles. Best-fit formulas describing the dependence of the far-field deflection angle on the size parameter, angle of incidence and the position of the flow line in the plane of the slit are derived and incorporated into the RTDF model. Phase functions for hexagonal columns are presented and compared with an analytic technique, the separation of variables method, and geometric optics with projected area diffraction.     

Coherent light scattering from a two-dimensional Mott insulator

We experimentally demonstrate coherent light scattering from an atomic Mott insulator in a two-dimensional lattice. The far-field diffraction pattern of small clouds of a few hundred atoms was imaged while simultaneously laser cooling the atoms with the probe beams. We describe the position of the diffraction peaks and the scaling of the peak parameters by a simple analytic model. In contrast to Bragg scattering, scattering from a single plane yields diffraction peaks for any incidence angle. We demonstrate the feasibility of detecting spin correlations via light scattering by artificially creating a one-dimensional antiferromagnetic order as a density wave and observing the appearance of additional diffraction peaks.     

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。     

傅里叶变换系统的光线矩阵分析方法

本文应用光线矩阵方法,分析一般的非对称系统,导出了该系统的傅里叶变换条件;考虑到定位误差,文中给出了计算夫琅和费和傅里叶变换有效区域和物理焦深区的公式;并得出了在不同波面入射光波的情况下,谱面移动量的计算公式,最后给出了二个应用实例。     

Narrowing effect of focused polychromatic laser with small Fresnel number

Starting from Huygens-Fresnel diffraction integral, the field representation of focused polychromatic laser beams is derived. Intensity distributions of the focused polychromatic laser are investigated with different Fresnel number and bandwidth at focal plane. It is found that the width of transverse intensity distribution of the focused polychromatic laser decreases with increasing the bandwidth at the focal plane and zero local time, and the transverse intensity presents more obvious narrowing effects with smaller Fresnel number. A physical explanation for the narrowing effects is given based on a simplified expression.     

红外光学透镜焦距测量

采用CO₂激光器作为光源,热释电摄像机作为探测器,采集了单缝衍射图像.根据单缝衍射原理,测量了不同焦距的一组红外光学锗透镜的单色焦距,给出了实测结果.讨论了影响测试的主要误差因素.通过计算采样数据的调制传递函数,精确确定被测透镜焦平面的位置.介绍了图像采集系统长度尺寸的精确标定方法.     

亚微米局域空心光束的产生及其在单原子囚禁与冷却中的应用理论研究

提出了一种采用单模光纤、环形二元相位板和微透镜组成的光束整形系统产生亚微米局域空心光束的方案. 根据瑞利-索莫菲衍射积分公式, 数值计算了微透镜焦平面附近的场分布, 详细研究了空心光束的暗斑尺寸与单模光纤模场半径和微透镜焦距的关系. 数值计算结果表明: 在微透镜焦平面附近光场分布近似对称, 在焦点处场强近似为零, 周围场强逐渐增大, 形成半径约为0.4 μm的三维封闭的球形空心光场区域, 即亚微米局域空心光束. 当局域空心光束为蓝失谐时, 光场中的原子将被囚禁在光场最弱处. 若加上抽运光, 原子将受到蓝失谐局域空心光束与抽运光共同激发的强度梯度Sisyphus冷却. 本文利用该方案产生的亚微米局域空心光束构建单原子的囚禁与冷却器件, 并以单个⁸⁷Rb原子为例, 利用Mont-Carlo方法研究亚微米局域空心光束中单原子囚禁与强度梯度冷却的动力学过程, 结果表明利用该器件可以获得温度在5.8 μK量级的超冷单原子.     

Fast profile measurement of micrometer-sized tapered fibers with better than 50-nm accuracy

The forward scattering of light illuminating a transparent dielectric cylinder, such as a tapered fiber, from the side can be understood as interference of the diffracted, reflected, and transmitted light. Additionally, light can be resonantly coupled into the fiber if a multiple of the wavelength matches the circumference. Using a suitable laser setup with a novel evaluation algorithm allows us to quickly extract the fiber radius from the complex diffraction pattern, obtaining an accuracy of better than 50 nm. We demonstrate experimentally our method, which is noncontact and allows one to simultaneously measure the profile of a several-centimeter-long fiber waist with a diameter near the diffraction limit.     

Pade spectroscopy of structural correlation functions: Application to liquid gallium

We propose the new method of fluid structure investigation based on numerical analytic continuation of structural correlation functions with Pade approximants. The method particularly allows extracting hidden structural features of disordered condensed matter systems from experimental diffraction data. The method has been applied to investigate the local order of liquid gallium, which has a non-trivial structure in both the liquid and solid states. Processing the correlation functions obtained from molecular dynamic simulations, we show the method proposed reveals non-trivial structural features of liquid gallium such as the spectrum of length-scales and the existence of different types of local clusters in the liquid.     

Modelling of Threshold and Extraction Efficiency in Pr3+ ZBLAN Upconversion Fibre Lasers Using Two-Photon Pumping

We model the steady-state threshold and extracted power of a two-photon incoherently pumped upconversion fibre laser. Our threshold analysis is entirely analytic, and along with this derivation we obtain an analytic threshold cutback formula. This takes a particularly simple form when the ground state pump absorption follows exponential absorption. We also numerically simulate the extracted laser power. The experiment which we simulate is upconversion in Pr³⁺ doped ZBLAN fibre lasing at 491 nm and pumped with 1017 nm and 835 nm diode lasers. Our formulas and simulations are mutually consistent and agree with the experiment to within 10%.     

Nonlinear sharpening of holographically processed sub-microstructures

Wavelength dispersion of a computer-generated hologram causes spatial broadening of the focal spot in holographic femtosecond laser processing. From the paraxial approximation, we theoretically derived that the spatial broadening is proportional to only the diffraction position, defined as the distance from the optical axis. We performed experiments under the large-dispersion condition to analyze the influence of the diffraction position on the processed structure. In the processing experiment, a high-numerical-aperture lens and a laser energy near the threshold energy were used to fabricate sub-microstructures. We found a nonlinear dependence of the broadening of the processed structures on the diffraction position, and the degree of broadening was much smaller than the predicted value because of the nonlinear properties of the laser processing.     

Fresnel phase retrieval method using an annular lens array on an SLM

Wavefront aberrations play a major role when focusing an ultrashort laser pulse to a high-quality focal spot. Here, we report a novel method to measure and correct wavefront aberrations of a 30-fs pulsed laser beam. The method only requires a programmable liquid-crystal spatial light modulator and a camera. Wavefront retrieval is based on pupil segmentation with an annular lens array, which allows us to determine the local phase that minimizes focusing errors due to wavefront aberrations. Our method provides accurate results even when implemented with low dynamic range cameras and polychromatic beams. Finally, the retrieved phase is added to a diffractive lens codified onto the spatial light modulator to experimentally demonstrate near-diffraction-limited femtosecond beam focusing without refractive components.     

Digital in-line holography with a sub-picosecond laser beam

The diffraction of an ultrashort pulsed laser beam by an opaque particle is studied. The case of a pulse with a Gaussian spectrum is investigated analytically by using the steepest descent method. This analytical solution allows us to calculate the intensity distribution of the diffraction field. This result enables to determine the optimal fractional orders Fourier transform to reconstruct digital in-line particle hologram.     

Excitation of the isomeric 229mTh nuclear state via an electronic bridge process in 229Th+

We consider the excitation of the nuclear transition 229gTh-229mTh near 7.6 eV in singly ionized thorium via an electronic bridge process. The process relies on the excitation of the electron shell by two laser photons whose sum frequency is equal to the nuclear transition frequency. This scheme allows us to determine the nuclear transition frequency with high accuracy. Based on calculations of the electronic level structure of Th+ which combine the configuration-interaction method and many-body perturbation theory, we estimate that a nuclear excitation rate in the range of 10 s?1 can be obtained using conventional laser sources.