Beam-splitting and recombining of free-electron-laser extreme-ultraviolet radiation

The design of systems for the splitting of the radiation from a free-electron-laser (FEL) in the extreme-ultraviolet spectral region is presented. Systems for the beam-splitting of the FEL radiation are important, both for having the light available simultaneously to several experiments, and for the division and recombination of the beam (pump-probe techniques). We present systems with a grazing-incidence plane grating, which is illuminated by the single FEL beam and gives several output beams (the zero order and the diffracted orders). The grating gives intrinsically a time stretching of the diffracted beam, so time-compensated configurations are used. Systems for the splitting of the primary beam in two secondary beams and for the splitting and recombining from two beams with variable delay are presented. PACS 41.60.Cr; 42.79.Dj; 42.79.Fm     

Common path interferometer based on the modified Michelson configuration using a reflective grating

A common-path interferometer using the modified Michelson system with a reflective grating is proposed for quantitative phase imaging. The frequency spectrum of the object beam is split into two beams using a beam splitter. One beam is diffracted into +1, 0, and −1 orders by the reflective grating to act as an object beam, and the other beam is low-filtered and diffracted by a pinhole mirror to act as a reference beam. Three phase-shifted interferograms can be simultaneously captured using the proposed interferometer, and the specimen phase can then be reconstructed from the three interferograms. Experiments are carried out to prove the precision, real-time ability, and stability of the proposed method.     

Intensity distribution and focal depth of axicon illuminated by Gaussian Schell-model beam

In view of second-order coherence theory, the generalized diffractive axicon illuminated by partially coherent Gaussian Schell-model (GSM) beams is analyzed. An analytical equation for focal depth of axicon without aperture illuminated by spatial partially coherent GSM beam is derived. We showed that the off-axis images can be evaluated by using the method of stationary phase at any correlation state, hence we demonstrated that the intensity distribution of diffracted beam is a superposition of Bessel Beams of various orders. We also showed that the diffracted beam is nondiffractive only on the boundaries of the focal depth.     

环形光束锥形衍射出射光场偏振特性及光场调控

环形光束的锥形衍射效应对于微粒的操控具有重要的应用价值.本文建立了环状高斯光束的锥形衍射模型,并基于Berry理论给出了线偏振态下环形光束锥形衍射出射光场的计算公式.理论仿真了环状光锥形衍射出射光场的偏振特性,得出环光锥形衍射出射光场的内、外亮环具有相互正交的偏振分布特性.搭建了线偏振态下环状高斯光锥形衍射的实验系统,实验验证了出射光场的偏振特性.针对环形光束锥形衍射出射光场具备的偏振特性,设计了一种组合偏振片,理论和实验研究了该组合偏振片对环光锥形衍射出射光场的调控.结果表明,随着组合偏振片方位角的变化,锥形衍射出射光场的内、外环强度发生周期性的变化.     

Transformation of optical-vortex beams by holograms with embedded phase singularity

Spatial characteristics of diffracted beams produced by the “fork” holograms from incident circular Laguerre-Gaussian modes are studied theoretically. The complex amplitude distribution of a diffracted beam is described by models of the Kummer beam or of the hypergeometric-Gaussian beam. Physically, in most cases its structure is formed under the influence of the divergent spherical wave originating from the discontinuity caused by the hologram’s groove bifurcation. Presence of this wave is manifested by the ripple structure in the near-field beam pattern and by the power-law amplitude decay at the beam periphery. Conditions when the divergent wave is not excited are discussed.The diffracted beam carries a screw wavefront dislocation (optical vortex) whose order equals to algebraic sum of the incident beam azimuthal index and the topological charge of the singularity imparted by the hologram. The input beam singularity can be healed when the above sum is zero. In such cases the diffracted beam can provide better energy concentration in the central intensity peak than the Gaussian beam whose initial distribution coincides with the Gaussian envelope of the incident beam. Applications are possible for generation of optical-vortex beams with prescribed properties and for analyzing the optical-vortex beams in problems of information processing.     

Effects of misalignments in the optical vortex transformation performed by holograms with embedded phase singularity

Spatial characteristics of diffracted beams produced by a “fork” hologram from an incident circular Laguerre-Gaussian beam whose axis differs from the hologram optical axis are studied theoretically. General analytical representations for the complex amplitude distribution of a diffracted beam are derived in terms of superposition of Kummer beams or hypergeometric-Gaussian beams. The diffracted beam structure is determined by combination of the “proper” topological charge m of the incident vortex beam and the topological charge l of the singularity “imparted” by the hologram. Evolution of the diffracted beam structure is studied in detail for several combinations of m and l and for various incident beam displacements with respect to the optical axis of the hologram. Variations of the intensity and phase distribution due to the incident beam misalignment are investigated and possible applications for the purposeful optical vortex beam generation and optical measurements are discussed.     

Theoretical conversion of the hypergeometric-Gaussian beams family into a high-order spiraling Bessel beams by a curved fork-shaped hologram

Based on the process of the Fresnel diffraction, the possibility of generating a new type of laser beams family by illuminating a curved fork-shaped hologram, with an input hypergeometric-Gaussian beams family of orders n and m is studied in this paper. The theoretical and the numerical results showed that, at the output plane, a high order spiraling Bessel vortex beam is produced. This vortex beam is divergence or non-divergence depending upon the waist position of the input hypergeometric-Gaussian beams, regarding the plane where the curved fork-shaped hologram is situated. Analytical expressions of the amplitude and the intensity distribution of the diffracted wave field are calculated and deduced using the stationary phase method. The actual work generalizes also the Fresnel diffraction study of some subfamilies of the hypergeometric-Gaussian beams family, such as: fundamental Gaussian, hollow Gaussian, modified quadratic Bessel–Gaussian and elegant Laguerre–Gaussian beams.     

Propagation of truncated modified Laguerre–Gaussian beams

By expanding the circ function into a finite sum of complex Gaussian functions and applying the Collins formula, the propagation of hard-edge diffracted modified Laguerre–Gaussian beams (MLGBs) through a paraxial ABCD system is studied, and the approximate closed-form propagation expression of hard-edge diffracted MLGBs is obtained. The transverse intensity distribution of the MLGB carrying finite power can be characterized by a single bright and symmetric ring during propagation when the aperture radius is very large. Starting from the definition of the generalized truncated second-order moments, the beam quality factor of MLGBs through a hard-edged circular aperture is investigated in a cylindrical coordinate system, which turns out to be dependent on the truncated radius and the beam orders.     

用频谱分析法测量声光驻波调制器的调制度

从调制的基本概念出发，指出声光驻波调制器件为宽带频率调制型。讨论了调制度概念的成立条件和适用范围。理论上求出其成立条件为ｖ＜０．９（ｖ＝２πＬ△ｕ／λ为衍射光强Ｉ（θ，ｔ）中的自变量）。鉴于一般驻波型声光器件都是含有一定的行波成份，但行波声场和驻波声场在拉曼－奈斯衍射范围内衍射角均遵从ｓｉｎθｍｉ＝土ｍλ／，故两者在空间上是无法分开的。文中给出了从频域上测量调制度Ｍ的一种新方法。并给出了零级和一般衍射光的测量值。     

基于二维光栅分光的同步移相干涉测量技术

为了干涉测量的抗振目的,提出了一种新的同步移相干涉测量方案并搭建了实验装置。整个测量系统在迈克耳孙偏振移相干涉仪的基础上,利用一个正交的二维光栅产生对称分光,选取对于理想光栅衍射效率一致的(±1,±1)级衍射光作为测量分光路,使之分别通过偏振方向依次相差45°的一个偏振片组,从而分别形成0°、90°、180°和270°相移的四幅移相干涉图,按照传统的四步移相算法,对被测波面进行了复原。分析了光强畸变和移相误差对系统的测量误差的影响。利用该系统测量一球面系统,结果与在ZYGO干涉仪上相比较,球面系统的均方根误差相差0.012λ,峰谷值相差0.051λ。     

Model calculations of atom-surface scattering

The elastic scattering of light mass, thermal-energy atoms from simple surfaces is investigated. The surface is represented by the model of a single planar square array of hard spheres. The effect of the surface potential well is treated semiclassically by simply shifting the energy of the incident atom ; furthermore a constant imaginary term is added to the energy to account for inelastic scattering and adsorption. As in the multiple scattering formalism of LEED the total scattering matrix of the lattice is expanded in terms of the individual gas atom-surface atom t-matrices. Propagation of the incident atom on the surface is described in terms of a one particle Green's function propagator with complex energy. The terms in the multiple scattering series are summed to all orders, by using standard matrix inversion techniques. The size of the matrix to be inverted limits to ten the total number of phase shifts that are included in the calculation. Thermal effects are included through angle dependent Debye-Waller factors.Model calculations have been performed to study the intensity of the specular and the diffracted beams as a function of the angles of incidence. The importance of surface temperature (introduced by the Debye-Waller factors), the incident energy and the depth of the potential well of the gas-surface interaction are discussed. The main feature of the results is the decrease of the intensity of the specular beam in going from glancing incidence to normal incidence and the presence of structure due to the appearance and disappearance of diffracted beams across the surface. The azimuthal behavior of the specular beam is in agreement with experimental observations.     

菌紫质同线偏振全息记录时再现光偏振方向对衍射效率的调制

当用相同偏振方向的物光和参考光在菌紫质薄膜上记录光栅时,再现光的偏振方向会影响其衍射效率.采用琼斯矩阵方法对此进行了理论分析,结果显示,再现光的偏振方向对衍射光的光强产生余弦调制;当再现光的偏振方向平行或垂直于记录光的偏振方向时,衍射光仍为线偏振光,其他情况下衍射光均变成椭圆偏振光.再现光偏振方向对衍射效率峰值的调制为正向余弦调制,对衍射效率稳定值的调制为反向余弦调制(与前者在相位上相差π).加入辅助紫光可抑制光栅的饱和,从而使得再现光偏振对衍射效率稳定值的调制由反向余弦调制变为正向余弦调制,并且提高了衍 关键词： 菌紫质 光致各向异性 衍射效率 琼斯矩阵     

Peculiarities of spontaneous grating generation in light-sensitive waveguide layers during holographic grating formation

The generation of spontaneous (noise) gratings during the simultaneous formation of a holographic grating in thin (on the order of the cutoff thickness of the TE₀ waveguide mode) AgCl-Ag films by two laser beams with λ = 532 nm and polarization vectors that make an angle of 45° with the plane of incidence have been studied. The electron microscopy images and diffraction patterns have revealed a significant difference of the spontaneous-grating structure from the structure obtained under irradiation by one laser beam. The spontaneous gratings have a significant spread in the directions of their wave vector, and the diffraction pattern (recorded using a probe beam with λ = 337 nm) has the form of a bundle of diverging arcs that intersect at one point. This difference is caused by self-diffraction from the holographic grating, which is responsible for the main diffraction peaks with odd orders, the growth of spontaneous gratings because of the interference of the beams diffracted by the holographic grating with the waveguide TE₀ modes scattered in the film, and silver transport to the interference minima. The diffraction patterns are quantitatively analyzed and the period of the new (formed under two-beam irradiation) spontaneous gratings is calculated. The calculation results are in good agreement with the experimental data.     

Phase singularities of nonparaxial cosh-Gaussian vortex beams diffracted by a rectangular aperture

Analytical expression for the propagation of nonparaxial cosh-Gaussian (ChG) beams diffracted by a rectangular aperture is derived based on the vector Rayleigh-Sommerfeld diffraction integrals and expansion of the aperture window function into a finite sum of complex Gaussian functions, and used to study the phase singularities of nonparaxial diffracted ChG vortex beams. The pair creation, annihilation, motion of phase singularities in the diffracted field and the dependence of position and number of phase singularities on the aperture and beam parameters, as well as on the beam nonparaxiality are illustrated by numerical examples.     

Diffraction of light by adjacent fundamental and second or fourth harmonic ultrasound beams: Comparison of exact and simplified formulae with experiment

Theoretical expressions and their approximate formulae for the intensities of light diffracted by two adjacent ultrasonic beams are discussed and compared with experimental data for the case when the second beam is an even harmonic of the first (fundamental). In the special case of the fundamental and its second or fourth harmonic, relatively simple formulae are found for the first and second diffraction orders describing the variation of light intensity with phase shift and intensity ratio.The approximate formulae describe the experiments satisfactorily only for small values of ζ₁ and α_n. For higher values the exact formulae give better agreement. Only the Raman-Nath region is considered.     

All-reflective Michelson, Sagnac, and Fabry-Perot interferometers based on grating beam splitters

All-reflective Michelson, Sagnac, and Fabry-Perot interferometers based on grating beam splitters are experimentally demonstrated at a wavelength of 1064 nm. A 1200-groove/mm grating diffracting 0 and -1 orders with an efficiency of 48.2% for each order was used as a near-50/50 beam splitter. The all-reflective Sagnac and Michelson interferometers were formed by reintroducing both of the diffracted beams back to the grating. The Fabry-Perot interferometer was formed in a Littrow configuration by using a 1700-groove/mm grating with a blazing efficiency of 91% as a cavity coupler. These interferometers encompass all the fundamental configurations of all-reflective laser interferometric gravitational-wave detectors, promising improved wave-front quality by avoiding volume thermal effects in transmissive optics under high-power laser illumination.     

The Forked Blazed Grating as a Quasioptical Element for Gyrotron Applications

In previous papers we have shown how beams of millimeter-wavelength electromagnetic radiation with phase singularities can be generated by diffraction from a specially-configured forked blazed grating. Here we consider how the hollow conical beam output of a gyrotron is diffracted by this kind of grating. Two applications are considered; using the grating (a) as a single-element quasioptical antenna to convert the output into a well-collimated gaussian-like beam and (b) as a device to enable the estimation of the fractions in oppositely-rotating modes in the gyrotron output.     

TEM image contrast from antiphase domains in GaAs: Ge(001) grown by MBE

Antiphase domains occur in thin GaAs epitaxial films grown on Ge(001) by molecular beam epitaxy. The domains have been imaged by transmission electron microscopy using 200-type reflections in dark field. The carefully chosen imaging conditions with convergent illumination ensure that doubly diffracted beams from a pair of first order Laue zone discs contribute to the singly diffracted 200-type beams. The three Bragg reflections may add in or out of phase to give domains in either light or dark contrast depending on their polarity.     

Two-dimensional transmission type volume holograms for incident plane waves of arbitrary amplitude distribution

Based on the differential equations of [1] a general solution in closed form is obtained for the amplitudes of the transmitted and diffracted beams for Bragg angle incidence in a lossless, transmission type volume hologram. Numerical solutions are plotted for Gaussian input beams. For the range of parameter values investigated it is shown that complete power transfer into the diffracted beam is not possible.     

Microscopy of non-birefringent transmissive phase samples using Sagnac laser interferometer

A cyclic interferometer, appropriately combined with a long working distance microscope objective, is adapted for quantitative phase microscopy. In such an arrangement, the sample information, in terms of the diffracted orders emerging from the sample, is carried by both the counter propagating beams within the cyclic interferometer. However, positioning the sample close to the input/output cube beam splitter and use of a suitably converging laser beam of light as the input to the interferometer ensure that only one of the counter propagating beams carries the object information to the objective while the other beam, which serves as the reference, allows only the undiffracted component to contribute to the process of image formation. Use of suitable polarization optics renders the interferometer its polarization phase shifting property. Using the proposed arrangement, the experimental results showing the quantitative 3D phase rendering of polystyrene microspheres and micro-wells etched in glass are presented.