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。

Liquid crystal based continuous phase retarder: From optically neutral to a quarter waveplate in 200 microseconds

Liquid crystal variable phase retarders have been incorporated into prototype devices for optical communications system applications, both as endless polarization controllers 1,2,3, and as holographic beam steerers 4. Nematic liquid crystals allow continuous control of the degree of retardation induced at relatively slow switching speeds, while ferroelectric liquid crystal based devices allow fast (sub millisecond) switching, but only between two bistable states. The flexoelectro-optic effect 5,6 in short-pitch chiral nematic liquid crystals allows both fast switching of the optic axis and continuous, electric field dependent control of the degree of rotation of the optic axis. A novel geometry for the flexoelectro-optic effect is presented here, in which the helical axis of the chiral nematic is perpendicular to the cell walls (grandjean texture) and the electric field is applied in the plane of the cell. This facilitates deflection of the optic axis of the uniaxial negatively birefringent material from lying along the direction of propagation to having some component in the polarization plane of the light. The device is therefore optically neutral at zero field for telecommunications wavelengths (1550nm), and allows a continuously variable degree of phase excursion to be induced, up to 2π/3 radians achieved so far in a 40μm thick cell. The retardation has been shown both to appear, on application of the field, and disappear on removal, at speeds of 100-500 μs. The direction of deflection of the optic axis is also dependent on the direction of the field, allowing the possibility, in a converging electrode "cartwheel cell", of endless rotation of the liquid crystal waveplate at a higher rate than achievable through dielectric coupling to plain nematic materials.

Effect of Molecular Flexibility on the Nematic-to-Isotropic Phase Transition for Highly Biaxial Molecular Non-Symmetric Liquid Crystal Dimers

In this work, a study of the nematic (N)-isotropic (I) phase transition has been made in a series of odd non-symmetric liquid crystal dimers, the alpha-(4-cyanobiphenyl-4'-yloxy)-omega-(1-pyrenimine-benzylidene-4'-oxy) alkanes, by means of accurate calorimetric and dielectric measurements. These materials are potential candidates to present the elusive biaxial nematic (N-B) phase, as they exhibit both molecular biaxiality and flexibility. According to the theory, the uniaxial nematic (N-U)-isotropic (I) phase transition is first-order in nature, whereas the N-B-I phase transition is second-order. Thus, a fine analysis of the critical behavior of the N-I phase transition would allow us to determine the presence or not of the biaxial nematic phase and understand how the molecular biaxiality and flexibility of these compounds influences the critical behavior of the N-I phase transition.

I. Anisotropy and crystal structure of ferromagnetic thin films. II. Investigations into magnetic microstructure by Lorentz microscopy

The induced magnetic uniaxial anisotropy of Ni-Fe alloy films has been shown to be related to the crystal structure of the film. By use of electron diffraction, the crystal structure or vacuum-deposited films was determined over the composition range 5% to 85% Ni, with substrate temperature during deposition at various temperatures in the range 25° to 500° C. The phase diagram determined in this way has boundaries which are in fair agreement with the equilibrium boundaries for bulk material above 400°C. The (α+ ɤ) mixture phase disappears below 100°C.

The measurement of uniaxial anisotropy field for 25% Ni-Fe alloy films deposited at temperatures in the range -80°C to 375°C has been carried out. Comparison of the crystal structure phase diagram with the present data and those published by Wilts indicates that the anisotropy is strongly sensitive to crystal structure. Others have proposed pair ordering as an important source of anisotropy because of an apparent peak in the anisotropy energy at about 50% Ni composition. The present work shows no such peak, and leads to the conclusion that pair ordering cannot be a dominant contributor.

Width of the 180° domain wall in 76% Ni-Fe alloy films as a function of film thickness up to 1800 Å was measured using the defocused mode of Lorentz microscopy. For the thinner films, the measured wall widths are in good agreement with earlier data obtained by Fuchs. For films thicker than 800 Å, the wall width increases with film thickness to about 9000 Å at 1800 Å film thickness. Similar measurements for polycrystalline Co films with thickness from 200 to 1500 Å have been made. The wall width increases from 3000 Å at 400 Å film thickness to about 6000 Å at 1500 Å film thickness. The wall widths for Ni-Fe and Co films are much greater than predicted by present theories. The validity of the classical determination of wall width is discussed, and the comparison of the present data with theoretical results is given.

Finally, an experimental study of ripple by Lorentz microscopy in Ni-Fe alloy films has been carried out. The following should be noted: (1) the only practical way to determine experimentally a meaningful wavelength is to find a well-defined ripple periodicity by visual inspection of a photomicrograph. (2) The average wavelength is of the order of 1µ. This value is in reasonable agreement with the main wavelength predicted by the theories developed by others. The dependence of wavelength on substrate deposition temperature, alloy composition and the external magnetic field has been also studied and the results are compared with theoretical predictions. (3) The experimental fact that the ripple structure could not be observed in completely epitaxial films gives confirmation that the ripple results from the randomness of crystallite orientation. Furthermore, the experimental observation that the ripple disappeared in the range 71 and 75% Ni supports the theory that the ripple amplitude is directly dependent on the crystalline anisotropy. An attempt to experimentally determine the order of magnitude of the ripple angle was carried out. The measured angle was about 0.02 rad. The discrepancy between the experimental data and the theoretical prediction is serious. The accurate experimental determination of ripple angle is an unsolved problem.

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.

Texture changes during uniaxial compression of Mg-3AI-1Zn

The mechanical anisotropy of wrought Mg alloys is very high. For example the yield stress of extruded Mg-3Al-1Zn tested in tension can be as high as twice that obtained in compression [1]. To solve the problems this creates for product design it is necessary to understand the sensitivity of texture to processing parameters. Uniaxial compression tests at different temperatures were performed on cylindrical samples of an extruded Mg-3Al-1Zn bar. The texture
during this deformation changes from a situation where all crystal c-axes are nearly perpendicular to the sample axis to one where the c-axes are all nearly parallel to this axis. Compression was stopped at different strains to examine the rate of this texture change. Textures were examined using EBSD measurements. It was found that different mechanisms operate depending on the temperature of deformation and that a variety of textures can be created. Also it was seen that an annealing treatment performed after compression has an influence on the texture. Afterwards the samples were subjected to another uniaxial compression test to examine the influence of texture on room temperature properties.

Orientation dependence of the deformation microstructure in a Fe-30Ni-Nb model austenitic steel subjected to hot uniaxial compression

The present work was aimed at a detailed investigation of the orientation dependence of the microstructure characteristics in a Fe-30Ni-Nb austenitic model steel subjected to hot uniaxial compression at 1198 K (925 °C) at a strain rate of 1 s−1 to several strain levels up to 1.0. The quantification of the substructure evolution as a function of strain was performed for the stable 〈011〉 oriented grains. Other grain orientations were also investigated in detail at a strain of 0.2. The 〈110〉 oriented grains contained self-screening arrays of “microbands” (MBs) aligned with high Schmid factor {111} slip planes. The MB crystallographic alignment was largely maintained up to a strain of 1.0, which suggests that the corresponding boundaries kept continuously rearranging themselves during straining and did not follow the sample shape change. The mean MB spacing decreased and misorientation angle increased with strain towards saturation, indicating the operation of the “repolygonization” dynamic recovery mechanism. The non-〈011〉 oriented grains displayed a strong tendency to split during deformation into deformation bands having alternating orientations and being mutually rotated by large angles. The bands were separated by transition regions comprising arrays of closely spaced, extended sub-boundaries collectively accommodating large misorientations across very small distances.