Reflection and transmission of Gaussian beam from a uniaxial crystal slab

We investigate the characteristics of Gaussian beams reflected and transmitted from a uniaxial crystal slab with an arbitrary orientation of its optical axis. The formulas of the total electric and magnetic fields inside and outside the slab are derived by use of Maxwell's equations and by matching the boundary conditions at the interfaces. Numerical simulations are presented and the field values as well as the power densities are computed. Negative refractions are demonstrated when the beam is transmitted through a uniaxial crystal slab. Beam splitting of the reflected beam is observed and is explained by the resonant transmission for plane waves. Dependences of the lateral shift on the incident angle and beam width are discussed. Negative and positive lateral shifts are observed due to the spatial anisotropic properties.

Double refraction and reflection of sequential crystal interfaces with arbitrary orientation of the optic axis and application to optimum design

The general formulation of double refraction or internal double reflection for any directions of incidence and arbitrary orientation of the optic axis in a uniaxial crystal is analysed in terms of Huygens' principle. Then double refraction and double reflection along the sequential interfaces in a crystal are discussed. On this basis, if the parameters of the interface are chosen appropriately, the range of angular separation between the ordinary ray and extraordinary ray can be much greater, It is useful for crystal element design. Finally, as an example, an optimum design of the Output end interface for a 2 x 2 electro-optic switch is given.

Propagation properties of beams generated by Gaussian mirror resonator in uniaxial crystals

Based on the paraxial vectorial theory of beams propagating in uniaxially anisotropic media, we have derived the analytical propagation equations of beams generated by Gaussian mirror resonator (GMR) in uniaxial crystals, and given the typical numerical example to illustrate our analytical results. Due to the anisotropy crystals, the ordinary and extraordinary beams originated by incident beams generated by GMR propagate with different diffraction lengths, thus the linear polarization state and axial symmetry of the incident beams generated by GMR do not remain during propagating in crystals. (c) 2006 Elsevier GmbH. All rights reserved.

高阶群速度色散引起的高斯超短脉冲宽度的展宽和形变

基于动量守恒和光参变过程中的三波耦合波方程, 和负单轴非线性光学晶体CsLiB6O10的色散方程, 研究了在光参变效应中超短激光脉冲由于群速度色散引起的展宽和形变。数值模拟显示, 在超短脉冲波形为双曲正割形和无啁啾调制时, 高阶群速度色散引起的超短脉冲为50 fs时, 晶体长度为10 mm, 紫外光213 nm作为基波入射时的脉冲展宽是波长为532 nm绿光在同等条件下的1.6倍。脉冲展宽程度与入射波长和晶体长度有关, 波长越短和晶体长度越长则脉冲展宽和波形变化越严重,高阶色散引起的超短高斯脉冲展宽, 将

参变过程中的群速延迟对晶体匹配长度的影响

基于能量守恒和三波耦合波方程, 建立了超短脉冲在参变过程中二次谐波产生时的I类和II类相位匹配条件、基波与谐波之间的群速延迟时间、以及群速失配对晶体长度限制的理论基础。以负单轴非线性光学晶体CsLiB6O10为例, 分析和数值计算了超短脉冲宽度为100 fs时, 谐波的群速匹配长度随基波波长变化的规律。研究结果表明在I类相位匹配条件下, 基波波长为642 nm时, 群速延迟最小, 相应的群速匹配晶体长度最长为19.1 mm;在II类相位匹配条件下, 基波波长为767 nm, 群速延迟最小, 群速匹配长度最

反射率对入射角扫描测定单轴晶体的折射率

通过分析波矢沿任意方向的单轴晶体的折射率,在光轴位于入射面内时,给出了入射光分别为s光和p光的反射率拟合函数。利用改进的反射率扫描仪,测量了CaCO3晶体的s光和p光反射率随入射角变化情况,由理论拟合获得单轴晶体的两个主折射率,分别为no=1.6559和ne=1.4851。这种方法不需要对样品进行加工,其精度达到0.0001。另外,对于晶体光轴未知的情况,采用改进的布儒斯特技术分别测出三个晶体表面的布儒斯特角,由此可以确定光轴的方向。

Crystal structure and drawing-induced polymorphism in poly(aryl ether ether ketone). IV

A new crystal modification induced by strain and denoted as form II exists alongside the dominant form I structure in the uniaxially oriented poly(ether ether ketone) (PEEK) and the related polymers. The crystal structure of form II for PEEK is also found to possess a two-chain orthorhombic packing with unit cell parameters of a equal to 0.475 nm, b equal to 1.060 nm, and c equal to 1.086 nm. More extended and flattened chain conformation of form II relative to that of form I is expected to account for an 8% increase in c-axis dimension, which is attributed to the extensional deformation fixed in situ through strain-induced crystallization during uniaxial drawing. Annealing experiments suggest that form II is thermodynamically metastable and can be transformed into more stable form I by chain relaxation and reorganization at elevated temperature without external tension. This strain-induced polymorphism exists universally in the poly(aryl ether ketone) family. (C) 1999 John Wiley & Sons, Inc.

The crystal structure and drawing-induced polymorphism in poly(aryl ether ketone)s .2. Poly(ether ether ketone ketone), PEEKK

The crystal structure, morphology and polymorphism induced by uniaxial drawing of poly(ether ether ketone ketone) [PEEKK] have been studied by transmission electron microscopy (TEM), electron diffraction (ED) and wide angle X-ray diffraction (WAXD). On the basis of WAXD and ED patterns,the crystal structure of unoriented PEEKK is determined to have two-chain orthorhombic packing with unit cell parameters of a 0.772 nm, b = 0.600 nm, c = 1.004 nm (form I), A stress-induced crystal modification (form II) is identified and found to possess a two-chain orthorhombic lattice with unit cell dimensions of a = 0.461 nm, b = 1.074 nm, c = 1.080 nm. The 7.5% increase in c-axis dimension for form II is attributed to an overextended chain conformation, arising from extensional deformation during uniaxial drawing and fixed ''in-situ'' through strain-induced crystallization. The average ether-ketone bridge bond angles in form II crystal are determined to be 148.9 degrees by using standard bond lengths. The crystal morphology of PEEKK bears a great similarity to that of PEEK. The crystals grow in the form of spherulites and have the b-axis of unit cell radial. The effects of draw rate on strain-induced crystallization and induction of form II structure are also discussed.

The crystal structure and drawing-induced polymorphism in poly(aryl ether ketone)s .1. Poly(oxybiphenyl-4-4'-diyloxy-1,4-phenylenecarbonyl-1,3-phenylenecarbonyl-1,4-phenylene)

Crystal structure and polymorphism induced by uniaxial drawing of a poly(aryl ether ketone) [PEDEKmK] prepared from 1,3-bis(4-fluorobenzoyl)benzene and biphenyl-4,4'-diol have been investigated by means of transmission electron microscopy (TEM), electron diffraction (ED), wide-angle X-ray diffraction (WAXD), and differential scanning calorimetry (DSC) techniques. The melting and recrystallization process in the temperature range of 250-260 degrees C, far below the next melting temperature (306 degrees C), was identified and found to be responsible for the remarkable changes in lamellar morphology. Based on WAXD and ED patterns, it was found that crystal structure of isotropic-crystalline PEDEKmK obtained under different crystallization conditions (melt-crystallization, cold-crystallization, solvent-induced crystallization, melting-recrystallization, and crystallization from solution) keeps the same mode of packing, i.e., a two-chain orthorhombic unit cell with the dimensions a = 0.784 nm, b = 0.600 nm, and c = 4.745 nm (form I). A second crystal modification (form II) can be induced by uniaxial drawing above the glass transition temperature, and always coexists with form I. This form also possesses an orthorhombic unit cell but with different dimensions, i.e., a = 0.470 nm, b = 1.054 nm, c = 5.064 nm. The 0.32 nm longer c-axis of form II as compared with form I is attributed to an overextended chain conformation due to the expansion of ether and ketone bridge bond angles during uniaxial drawing. The temperature dependence of WAXD patterns for the drawn PEDEKmK suggests that form II can be transformed into the more stable form I by relaxation of overextended chains and relief of internal stress at elevated temperature in absence of external tension.

Influence of Local Magnetic Fields on P-Doped Si Floating Zone Melting Crystal Growth in Microgravity

A two-dimensional axisymmetric numerical model is presented to study the influence of local magnetic fields on P-doped Si floating zone melting crystal growth in microgravity. The model is developed based on the finite difference method in a boundary-fitted curvilinear coordinate system. Extensive numerical simulations are carried out, and parameters studied include the curved growth interface shape and the magnetic field configurations. Computed results show that the local magnetic field is more effective in reducing the impurity concentration nonuniformity at the growth interface in comparison with the longitudinal magnetic field. Moreover, the curved growth interface causes more serious impurity concentration nonuniformity at the growth interface than the case with a planar growth interface.

DPIV and Interferometry Technique for Velocity Field and Concentration Fields Measurement in Crystal Growth

The property of crystal depends seriously on the solution concentration distribution near the growth surface of a crystal. However, the concentration distributions are affected by the diffusion and convection of the solution. In the present experiment, the two methods of optical measurement are used to obtained velocity field and concentration field of NaClO₃ solution. The convection patterns in sodium chlorate (NaClO₃) crystal growth are measured by Digital Particle image Velocimetry (DPIV) technology. The 2-dimentional velocity distributions in the solution of NaClO3 are obtained from experiments. And concentration field are obtained by a Mach-Zehnder interferometer with a phase shift servo system. Interference patterns were recorded directly by a computer via a CCD camera. The evolution of velocity field and concentration field from dissolution to crystallization are visualized clearly. The structures of velocity fields were compared with that of concentration field.

Effect of non-uniform magnetic field on crystal growth by floating-zone method in microgravity

The magnetic damping effect of the non-uniform magnetic field on the floating-zone crystal growth process in microgravity is studied by numerical simulation. The results show that the non-uniform magnetic field with designed configuration can effectively reduce the flow near the free surface and then in the melt zone. At the same time, the designed magnetic field can improve the impurity concentration non-uniformity along the solidification interface. The primary principles of the magnetic field configuration design are also discussed.

Depth dependence of nanohardness in a CuAlNi single crystal shape memory alloy

Instrumented nanoindentation was employed to study the depth dependence of nanohardness in a CuAlNi single crystal shape memory alloy that exhibits shape memory effect (SME). A Berkovich indenter and a cube comer indenter were used in this study, and the

The Uniaxial Tensile Deformation of Ni Nanowire: Atomic-Scale Computer Simulations

The mechanical deformations of nickel nanowire subjected to uniaxial tensile strain at 300 K are simulated by using molecular dynamics with the quantum corrected Sutten-Chen many-body force field. We have used common neighbor analysis method to investigate the structural evolution of Ni nanowire during the elongation process. For the strain rate of 0.1%/ps, the elastic limit is up to about 11% strain with the yield stress of 8.6 GPa. At the elastic stage, the deformation is carried mainly through the uniform elongation of the distances between the layers (perpendicular to the Z-axis) while the atomic structure remains basically unchanged. With further strain, the slips in the {111} planes start to take place in order to accommodate the applied strain to carry the deformation partially, and subsequently the neck forms. The atomic rearrangements in the neck region result in a zigzag change in the stress-strain curve; the atomic structures beyond the region, however, have no significant changes. With the strain close to the point of the breaking, we observe the formation of a one-atom thick necklace in Ni nanowire. The strain rates have no significant effect on the deformation mechanism, but have some influence on the yield stress, the elastic limit, and the fracture strain of the nanowire.

Concentration distribution in solution crystal growth: effect of moving interface conditions

The linear diffusion-reaction theory with finite interface kinetics is employed to describe the dissolution and the growth processes. The results show that it is imperative to consider the effect of the moving interfaces on the concentration distribution at the growth interface for some cases. For small aspect ratio and small gravity magnitude, the dissolution and the growth interfaces must be treated as the moving boundaries within an angle range of 0 degrees < gamma < 50 degrees in this work. For large aspect ratio or large gravity magnitude, the effect of the moving interfaces on the concentration distribution at the growth interface can be neglected except for gamma < - 50 degrees.