Collinear diffraction of a divergent light beam by ultrasound in a paratellurite crystal

The collinear acousto-optical interaction of a divergent light beam with ultrasound along the approximate [110] direction in a TeO₂ paratellurite crystal is investigated theoretically and experimentally. The collinear diffraction is studied at an ultrasonic frequency f ≈ 149 MHz under exposure of the crystal to an uncollimated laser light beam at a wavelength λ = 633 nm and at an angle of divergence as large as 4°. It is shown that the collinear diffraction along the direction forbidden for acousto-optical interactions of plane waves occurs only under conditions where the light beam is uncollimated and the diffraction efficiency increases with an increase in the divergence of the light beam. It is proved that the attenuation of an acoustic wave brings about a decrease in the diffraction efficiency and an increase in the transmission bandwidth of the device used. A model of the collinear acousto-optical filter based on a paratellurite crystal with an interaction length l = 2.7 cm is analyzed. The collinear acousto-optical filter is characterized by a high resolving power (～3000), a high diffraction efficiency (I₁/I₀ ≈ 0.8), and a large angular aperture (Δ? ≈ 4°). This makes collinear diffraction promising for use in acousto-optical filters based on paratellurite crystals.     

Optimization of MO Bragg diffraction of guided optical waves by MSW in YIG films by using inclined magnetic bias field

We describe a new scheme of noncollinear interaction geometry for magneto-optical (MO) Bragg cells based on inelastic scattering of guided optical wave beams by magnetostatic waves in yttrium–iron–garnet (YIG) films. A great increase of the diffracted light intensity was obtained when using an inclined magnetization of the film, in the case when static in-plane magnetization component is directed along the light propagation direction. It is shown that the diffraction efficiency can be increased more than two times, at a specific value of the angle (≈35°) between the saturation magnetization vector and the normal to the film surface. The effect can be explained through a four-wave model of the diffraction process, which can take place in optical waveguides with MO gyrotropy. The results obtained by a simple analytical solution of the diffraction problem are found to be in good qualitative agreement with the experimental observations.     

Miniaturized bending-free solitons by restoring symmetry in periodically biased photorefractives

We consider optical propagation through a centrosymmetric photorefractive crystal with the externally applied bias voltage modulated along the optical propagation direction. We analytically prove that, if the modulation scale is smaller than the optical diffraction length, the resulting effective nonlinearity has an even parity in the transverse plane for an even-symmetric intensity profile and supports bending-free solitons down to few-micrometer beam widths. Numerical integration of the full photorefractive model for light-matter interaction allows us to confirm the feasibility of these miniaturized solitons and, for longer modulation periods, to investigate the excitation of self-trapped wiggling optical beams.     

The spatial structure of acousto-optic phase matching in biaxial crystal of alpha-iodic acid

Anisotropic acousto-optic diffraction in biaxial crystal of alpha-iodic acid has been studied in the case in which the wave vector of the ultrasound is almost orthogonal to one of the optical axes and the directions of incident and diffracted light beams are close to the optical axis. It is shown that, owing to the complex form of wave surfaces in the field of optical axes of a biaxial crystal, the considered variant of acousto-optic interaction is very sensitive to changes in the direction of the wave vector of the ultrasound that imposes special requirements to accuracy of manufacturing of acousto-optic devices.     

Acousto-optic interaction of diverging Gaussian beams in anisotropic media

A strong acousto-optic interaction of bounded light and sound beams of a Gaussian shape is considered for different geometries permitting long-term interaction. The anisotropic spreading of an acoustic beam in the course of its propagation is taken into account. The spectra of light beams are described by a Gaussian-polynomial expression, and a set of differential equations is derived which allows one to describe various geometries of acousto-optic diffraction. It is demonstrated that the transmission function of an acousto-optic cell essentially depends on the ratio between the dimensions of the light and sound beams and on the angle between the propagation direction of the diffracted beam and that of the incident beam. The degree of spreading of the acoustic beam noticeably affects the suppression of the transmission side lobes.     

三环非均匀混合偏振同轴矢量光束的聚焦特性

基于Richards-Wolf矢量衍射积分公式,数值分析了同轴三环非均匀混合偏振矢量光束经过高数值孔径透镜的聚焦特性。该矢量光束由同轴三环局域线偏振矢量光束通过一个相位延迟角为δ的液晶相位延迟器产生,光束偏振变为包含线偏振、圆偏振和椭圆偏振的混合态。同轴三环局域线偏振矢量光束的偏振分布是由径向向内偏振的外环光束、径向向外偏振的内环光束和线偏振方向与径向方向夹角为φ2的中环光束构成。数值模拟结果显示该混合偏振矢量光束的聚焦强度分布与参数φ2和相位延迟角δ密切相关,当选取适当的φ2和δ时,在焦平面附近产生沿光轴方向的三维多点光俘获结构——暗光链,这在光学微操纵领域具有潜在的应用价值。     

Propagation of a Gaussian beam in a gyrotropic medium

Propagation of a slightly diverging Gaussian beam in a gyrotropic medium [constitutive equation (1.1)] across the gyration vector g is considered. The polarization, phase, and geometrical features of the beams are elucidated. For a sufficiently small gyrotropy, the medium deflects the beams like a wedge while for a sufficiently large gyrotropy the medium focuses them like a cylindrical lens. For the field polarized along g, focusing automatically and completely eliminates the diffraction broadening of the beam along this direction.     

Effect of diffraction on stimulated Raman scattering of laser radiation in the middle atmosphere

The theoretical aspects of propagation of laser radiation along slanted paths in the atmosphere at high altitudes under conditions of stimulated Raman scattering (SRS) by molecular nitrogen are considered. The SRS power conversion coefficient, the transverse intensity distribution, and the effective size of laser beams with different initial spatial profiles are numerically simulated along the propagation path. The behavior of these parameters is studied for different ratios between the optical path length and the length of free diffraction of the initial laser beam. It is shown that, at a given level of the increment of the SRS amplification, the diffraction can both increase and decrease the efficiency of the Raman interaction of waves owing to the intensity redistribution in the transverse beam profile. This effect is the most pronounced for beams with non-Gaussian initial spatial intensity profiles.     

Optimal conditions of the acousto-optic interaction in crystals with gyrotropy

The conditions of the acousto-optic interaction in the crystals with gyrotropy are considered. The optimal length of the acousto-optic interaction and the diffraction efficiency in the gyrotropic direction are calculated. The diffraction efficiency is determined by the coupled wave method which allows calculation of the field interaction in the gyrotropic crystal [1]. It is theoretically shown and experimentally confirmed that the diffraction efficiency in the gyrotropic direction is independent of incident light polarization, when the polarization plane rotates by 45° along the interaction length.     

同轴双无衍射光的理论与实验

提出同轴双无衍射光的概念。如果两束汇聚角略有不同的同轴无衍射光同时存在，则它们相互之间叠加干涉后产生一种纵向呈周期变化的光场结构，这是一种新的光束空间分布，这种光束在横向仍是一种同心环光斑，可用于精密对准。而在不同纵向位置，这些同心环的强度分布是不同的，且是周期性变化的。同轴双无衍射光的轴向周期性可用于沿光束传播方向的定位。文中提出了双环缝法、分段圆锥透镜法、正弦相位环光栅法等实现同轴双无衍射光的理论与实验方法，分析了同轴双无衍射光的横向与纵向传播的衍射光斑特性，理论计算与实验测量的结果基本相符合。     

像散对轴棱锥衍射特性的影响与修正

光束斜入射到轴棱锥上引起的像散将导致其衍射光场发生畸变,由衍射理论出发推导了受像散影响的轴棱锥衍射光场表达式. 通过模拟不同像散的衍射光斑图和同一像散影响下随轴向距离变化的光强分布图,分析了轴外像散对轴棱锥衍射特性的影响. 提出修正像散的方法并通过实验验证利用可调精密旋转轴棱锥修正轴外像散导致的光束畸变,理论分析和实验结果相符合,研究结果使轴棱锥的应用更加广泛. 关键词： 像散 贝塞尔光 轴棱锥 光束畸变     

基于空域分解的非线性有限声束快速计算

研究非线性有限声束的一种快速数值计算算法.理论研究表明非线性有限声束存在多种耦合:谐波之间的全耦合,各场点沿轴向的递推耦合以及沿径向的局部耦合,因此可以通过声场的径向空间区域分割提高计算效率,采用多线程实现并行计算.对非线性高斯聚焦波的计算结果表明,当声场计算规模与分割线程数合理匹配时,算法能够显著提高计算速度同时保证计算精度,计算结果与理论分析相符.     

Angular splitting of the Bragg diffraction order in an acoustooptical modulator due to a frequency-modulated acoustic wave

Effects of angular splitting of the Bragg diffraction order arising in light acoustooptical diffraction by a frequency-modulated acoustic wave are considered. These effects occur when the size of the light spot in the acoustooptical interaction zone exceeds the characteristic spatial period of the modulating function. The Bragg diffraction order is found to be split into several beams. The directions of the additional beams, their number, and intensities are determined by the modulation parameters. In particular, there occurs a situation where the diffracted field consists of three beams of equal intensity spaced at a distance approximately equal to the diffraction divergence of the incident beam and the diffraction total efficiency is of the order of 100%. Therein lies the difference between this diffraction regime and the case where several independent acoustic waves are generated in the interaction domain and the diffraction total efficiency is limited to the intermodulation arisen. The effect is used in design of modulators for systems of image plotting with the help of high-power lasers.     

Interaction of pulsed laser beams in quadratic nonlinear media

A theory of three-wave cascade interaction of pulsed laser beams in quadratic nonlinear media is developed with regard to diffraction and dispersion. The space-time trajectories of signal motion in a medium with an inhomogeneity induced by high-power low-frequency pumping are analyzed. It is shown that total signal reflection from a moving localized inhomogeneity can be implemented. This reflection is accompanied by a change in the frequency, velocity, and propagation direction of the signal wave.     

采用衍射掩模产生白光横向平顶光束

白光横向平顶光束在定向背光式自由立体显示器中有重要应用.本文提出一种采用带蝶形小孔阵列的衍射掩模片获得白光横向平顶光束的方法.根据广义惠更斯-菲涅耳衍射积分和多波长叠加原理,推导出光强分布计算式.设计一套实验装置,数值模拟并实验验证出射光束在不同距离的横向光强分布以及小孔蝶形凹度(蝶形中心高度与边长的比值)对横向光强分布的影响.结果表明:当选择小孔蝶形凹度为0.50—0.66时,可以得到平顶因子F 0.89的白光横向平顶光束,横向平顶光束的宽度随着传输距离的增大而增大,而平顶因子基本不变.实验还发现柱面透镜的折射色散和衍射色散可以互相抵消,使白光横向平顶光束基本无色散.     

On-line beam diagnostics based on single-shot beam splitting phase retrieval

We propose a novel on-line beam diagnostic method based on single-shot beam splitting phase retrieval. The incident beam to be measured is diffracted into many replicas by a Dammann grating and then propagates through a weakly scattering phase plate with a known structure; the exiting beams propagate along their original direction and form an array of diffraction patterns on the detector plane. By applying the intensity of diffraction patterns into an iterative algorithm and calculating between the grating plane, weakly scattering plane, and detector plane, the complex field of the incident beam can be reconstructed rapidly; the feasibility of this method is verified experimentally with wavelengths of 1053 and 632.8 nm.     

拉盖尔-高斯截断级数展开法的应用

 用拉盖尔-高斯截断级数模拟了任意半径的圆孔硬边光阑窗口函数,并应用于研究高斯光束和零阶贝塞尔-高斯光束通过硬边光阑的衍射。对高斯光束和零阶贝塞尔-高斯光束的轴向和横向光强分布的计算结果表明：当积分面不是很靠近光阑时，用参数最佳化选取的拉盖尔-高斯截断级数法与用直接数值积分所得结果符合很好。     

激光光路追踪Wigner分布函数方法

提出了一种考虑衍射效应的激光几何光路追踪方法。引入由激光标量场定义的Wigner激光能量相空间分布函数,并给出该函数满足的刘维尔运动方程。Wigner分布函数用来描述经过空间任一点沿任一方向传输的激光光线上的能量分配。激光能量沿由波包色散关系定义的光线轨迹保持不变（真空中）或者衰减（等离子体中）。与传统几何光路追踪方法相比,该方法从理论上给出了激光光线初始携带能量份额的计算方法,并且将激光标量场的相位信息自然地包含在Wigner分布函数的定义里。算例表明,该方法与解析模型及广泛使用的菲涅耳衍射积分方法结果一致。     

Grazing incidence off-plane lamellar grating as a beam splitter for a 1-Å free electron laser

A beam splitter based on the diffraction grating working in the grazing incidence conical diffraction is proposed for x-ray free-electron laser (XFEL) experiments with coherent beams in plasma and atomic physics. Such a beam splitter can provide undistorted wavefronts, high-power radiation scattering, and split beams with equal intensities, which propagate with delay along different paths to the target chamber of the XFEL end station. Using the PCGrate software based on rigorous electromagnetic theory and developed for the short-wavelength range, it is shown that the plane grating with lamellar groove profile of a certain depth, operating in grazing conical incidence mount (grooves are parallel to the incident beam), separates three beams in the ?1, 0, and +1 orders with close diffraction efficiency. Numerical simulation predicts 23–27% absolute efficiency for 0.1-nm incident radiation in each separated order of a bulk or multilayer grating, taking into account the atomic level roughnesses and interdiffusion. When using a multilayer coating based on Ru/C or Ru/B₄C pairs, the optimum grazing angle providing approximately equal efficiencies is ～1.038° which is four times higher than for the Pt-coated grating. Such optimization of radiation geometry, groove profile shape, and multilayer coating parameters can be performed for various XFEL wavelengths. The proposed grating, in addition to diffraction, technological, and design advantages over the beam splitter based on a set of perfect crystals, can be fabricated and tested using currently available methods.     

Ab initio simulation of resonant forbidden reflections in Ge crystals

Forbidden reflections are observed in the case of diffraction of synchrotron radiation with wave-lengths close to the absorption edges in crystals. A new method for calculating the intensity of thermal-motion-induced (TMI) forbidden reflections is proposed in this paper. It includes two stages: simulation of instantaneous thermal atomic displacements using ab initio molecular dynamics and subsequent quantum-mechanical calculations of the resonance scattering amplitude for various configurations. This procedure is used to calculate the temperature dependence of the 600 reflection intensity for Ge. The proposed method for simulating forbidden TMI reflections is suitable for any crystal structures and can explain many results so far obtained using synchrotron.