Generation of thin and hollow beams by the axicon with a large open angle

We propose a method to produce diffraction-free thin and hollow beams. The method is based on Laguerre-Gaussian (LG) beams incident on a large open-angle axicon. We use the vector diffraction integrals and stationary phase method to deduce a simple and analytical formula of the propagating field of the linearly polarized LG beams through an axicon. The numerical results show that the hollow beams of whose diameter is in the order of the wavelength can be obtained by using the axicon with the refractive index n = 2 and the open angle α = 25°. These diffraction-free thin and hollow beams may be very useful to accurately trap and manipulate atoms. However, when the open angle is over large, the conversion efficiency from the LG beam to the diffraction-free hollow beam will decrease obviously.     

Extending the depth of focus with high NA lens axicon

Based on vectorial Debye theory, tight focusing of x-polarized beam with high NA lens axicon is studied. The high NA lens axicon utilizes spherical aberration to duplicate the performance of an axicon and to create an extended focal line. The intensity distribution in the focal region is illustrated by numerical calculations. We show that the high NA lens axicon system can generates a sub wavelength beam (0.826λ) with depth of focus around 10λ.     

Conversion of high-order Laguerre-Gaussian beams into Bessel beams of increased, reduced or zeroth order by use of a helical axicon

We propose a new method for transformation of a Laguerre-Gaussian beam of azimuthal index l and radial index n = 0 (LG_l,0) into a vortex, diverging or nondiverging Bessel beam, which can have increased or decreased phase singularity order, or into a zeroth order Bessel beam, by means of a helical axicon. The Bessel beam divergence or nondivergence depends upon the waist position of the input Laguerre-Gaussian beam, regarding the plane where the helical axicon is situated.The expressions for the amplitude and the intensity distribution of the diffracted wave field, in the process of Fresnel diffraction, are deduced using the stationary phase method. The theoretical analysis for the vortex radius and the maximum propagation distance of the Bessel beams obtained is presented.     

基于圆锥透镜生成双级无衍射光束的理论分析

为进一步完善多级无衍射光束的传输与转换理论,基于轴锥镜法和菲涅耳衍射理论对双级无衍射光束的光场分布做了详细理论分析,采用数值模拟软件对双级无衍射光束的空间光强分布与轴上光强分布进行仿真;基于锥镜加工工艺对锥镜顶点和一、二级锥镜临界点呈双曲线分布的双级轴棱锥透镜的光场分布进行研究,分析了双级无衍射光场的场强大小和影响光场振荡周期的因素。结果表明:理想双级轴棱锥透镜生成的无衍射光场由4个区域组成,在干涉重合区其光强为一、二级轴棱锥衍射场的耦合叠加,其余区域仍保持单级无衍射光场分布特性;锥镜顶点和一、二级锥镜临界点呈双曲线分布的双级轴棱锥透镜的光场分布受双曲线特征参数影响较大。其特殊的光场分布为多级无衍射光束拓展至大尺寸空间测量以及粒子微操作等提供了新的可能。     

Electric field controlled higher-order diffraction images of paraelectric potassium lithium tantalate niobate

We report some electric field controlled photorefractive higher-order diffraction phenomena of a paraelectric phase potassium lithium tantalate niobate crystal doped with iron. In experiments, a p-polarized semiconductor laser (532 nm) was used to record grating at a small incident angle. Higher-order diffraction images were observed when the signal beam was focused behind and in front of the crystal. Then the higher-order diffraction images were reconstructed by a p-polarized He–Ne laser (632.8 nm) in the direction perpendicular to the surface. The higher-order diffraction images could be controlled by the external electric field. A theory about the higher-order diffraction images of the K and 2K grating is developed. The results show that the even order diffraction images of the K grating and the odd order diffraction of the 2K grating overlap each other. The odd order diffraction images of the K grating are diffracted in unattached direction. The electric field controlled higher-order diffraction image provides a useful method for optical information processing.     

Anisotropic strain effects on light emission characteristics of CdZnO/ZnO quantum well structures

Anisotropic strain effects by strain relaxation on TE-polarized light emission characteristics of c-plane CdZnO/ZnO quantum well (QW) structures were theoretically investigated by using the multiband effective-mass theory. The CdZnO/ZnO QW structure with anisotropic strain has much larger emission intensity than conventional CdZnO/ZnO QW structure without the strain relaxation. In the case of the strain relaxation along x(or y)-direction, the x(or y)-polarized light emission is observed to be larger than the x(or y)-polarized light emission. In particular, in the case of the strain relaxation along both x- and y-directions, the increase in the spontaneous emission peak is significant. This can be explained by the fact that the internal field is reduced owing to the decrease in the piezoelectric field by the strain relaxation.     

Research of negative refractive direction of P-light in metal

This paper studies the light propagation in metal. Using the complex wave vector, we analyze the propagation direction of light energy in a metal, and find that P and S-polarized light propagate at a different refraction angle when a beam of light passes from the air to a metallic boundary at a certain angle. Especially, P-polarized light will be refracted at a negative angle, and the direction of P-polarized light is the same side of the incident light.     

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     

Electric-field-controlled two-dimensional Raman-Nath diffraction from paraelectric potassium lithium tantalate niobate

Electric-field-controlled two-dimensional Raman-Nath diffraction has been realized using a photorefractive diffraction grating. The grating was produced by two-wave coupling (at a wavelength of 632.8 nm) at small incidence angles using a potassium lithium tantalate niobate single crystal. Results for the Raman-Nath diffraction from the g₄₄ grating are presented, in which the externally applied field is perpendicular to both the grating vector and the wave vector of the incident beam. Two pairs of coherent beams were used to record the grating for two-dimensional Raman-Nath diffraction. The wave vector and the polarization of one pair lay in the (x, z) plane, and those of the other pair lay in the (y, z) plane. The influence of the applied electric field was studied, and the results show that the intensity of the Raman-Nath diffraction could be controlled by the direction and intensity of the applied field.     

圆锥透镜对倾斜球面波光束的衍射模式

由于球面波入射圆锥透镜所产生的出射光束具有焦深长和中心光斑直径较小的特点,适合激光通信以及长距离测量.在实际使用中,入射球面波很可能与圆锥透镜的光轴发生倾斜.研究了圆锥透镜对倾斜球面波光束的衍射特性,通过基尔霍夫衍射理论以及稳相法分析,分析了其径向衍射光场分布形式,并用计算机进行了仿真.使用了半径为15 mm、底角为1°的圆锥透镜进行实验,并对仿真结果进行了验证.仿真和实验证明,减小入射球面波曲率半径、出射光束传输距离和入射光束倾斜角都可以减弱入射光束倾斜对衍射图的影响.     

Light diffraction on acoustophotorefractive holographic gratings

The intermediate regime of light diffraction on acoustophotorefractive holographic gratings written in cubic photorefractive crystals according to the synchronous-detection mechanism is studied. It is shown that the diffraction efficiency in sillenite-type gyrotropic crystals only slightly depends on the incident light polarization and the external electric field. The highest diffraction efficiency in nongyrotropic crystals was achieved for p-polarized writing and reading light and at a considerable external electric field strength.     

THz near-field measurements of metal structures

We report on electro-optic measurements of THz electric fields in the near-field of metal structures lying on GaP electro-optic sampling crystals. With (110) oriented crystals, the x or y component of the THz electric field is measured, whereas with a (001) oriented crystal, the z-component is measured. With an estimated spatial resolution of 20 μm, the technique allows us to map the field on a scale, orders of magnitude smaller than the spatial dimensions of these structures. We illustrate the technique by showing results of measurements of the THz electric field in a plane underneath a metal sphere and a single square hole in a metal foil. The technique provides us with a wealth of information on the time-evolution of light fields near metal structures. To cite this article: A.J.L. Adam et al., C. R. Physique 9 (2008).     

Angular momentum conversion of elliptically polarized beams focused by high numerical-aperture phase Fresnel zone plates

Based on the vectorial Debye theory, we investigate the tight focusing of elliptically polarized light beams by high numerical-aperture (NA) phase Fresnel zone plates (FZP). The conversion of the spin angular momentum (SAM) and the orbital angular momentum (OAM) in the tight focusing of the elliptically polarized beams is investigated in great detail. It is shown that the direction and magnitude of the OAM can be directly modulated by the input polarization, providing effective evidence that the SAM carried by an elliptically polarized light beam is converted into OAM in the tight focusing process. The properties of phase retardation between x and y components of the focused field are also investigated. It is found that focused field of x and y components still keeps its original elliptical polarization state, indicating that the focused field composed of x and y components still carries SAM, whereas the focused field of z component is changed into carrying OAM. The influences of the total zone number and the phase difference of binary phase FZPs with high NA on the intensity distribution in the focal plane are also investigated.     

The effect of nonlinearity of the recording media response on the properties of thick phase holograms

The effect of nonlinearity of a photosensitive medium response on the diffraction properties of thick phase holograms is analyzed on the basis of coupled-wave equations. It is shown that, for a typical dependence of the refractive index on the exposure, the response nonlinearity lowers the diffraction efficiency of a hologram illuminated by an s-polarized light. For the p polarization of the reading beam, the response nonlinearity reduces the hologram efficiency when the angle between the beams diffracted into the zero and second orders (into the minus first and first orders) is smaller than 90°, increases the efficiency for angles larger than 90°, and hardly affects the diffraction efficiency when this angle is close to 90°. The results for p polarization are obtained, to the best of our knowledge, for the first time. The analysis of angular selectivity of the gratings has shown that the effect of nonlinearity becomes particularly important for light waves incident on the hologram at angles close to the Bragg one. It is also found that, for any thickness of the photosensitive medium, there exists an optimum value of the maximum change in the refractive index, for which the diffraction efficiency may be close to 100% in a wide range of exposures. In this case, the nonlinearity for s polarization stabilizes, to some extent, the dependence of the diffraction efficiency on the exposure.     

The nature of the vectorial photoelectric effect in the threshold energy region

Summary An immediate correlation has been proved to exist between the vectorial photoelectric effect and electronic surface structure modified due to adsorption. Experimental studies were performed for Cs overlayers on W(110) and Si(111) faces using visible exciting photons with energies below those of both bulk and surface plasmons. Considerable (more than 20 fold) growth of the effect was observed forp-polarized light in the vicinity of threshold as the light frequency approached the position of the maximum of local density in the surface-state band. A special case of the vectorial photoelectric effect forp-polarized light has been found in the absence of bulk photoemission excited bys-polarized light. Our results prove that the anomalous vectorial photoelectric effect is caused by the normal electric vector component of thep-polarized light under appropriate conditions for the particular photoemission enhancement on the surface. The effect can be related to optical absorption by the surface-state band and to subsequent electron emission into the vacuum, the normal electric vector component of thep-polarized light being essential for both processes.     

阶变折射率轴棱锥产生局域空心光束

提出利用折射率成阶跃性变化的轴棱锥产生局域空心光束(bottlebeam).讨论了折射率沿径向成阶跃式减小或增加两种模型,从几何光学角度分析了它们产生bottle beam的原理,利用衍射积分理论数值模拟两种轴棱锥光传输的光场分布和不同距离处的二维光斑图,研究结果表明折射率沿径向阶跃减小的轴棱锥产生单个bottle beam,而折射率沿径向阶跃增加的轴棱锥产生具有周期再现的bottle beams.bottle beam在原子引导和囚禁、光学俘获及光镊等方面有广泛的应用,因此本文的研究对bottlebeam的产生和实际应用具有指导意义.     

Effect of the parameters on diffraction efficiency after thermal fixing for reflection geometry hologram storage in LiNbO3:Fe

For reflection geometry hologram storage in LiNbO₃:Fe, we have shown that the diffraction efficiency increases with doping level and thickness of storage material monotonically. When the acute angle between reference and z-axis is large enough for getting a relative small Bragg angle that is needed for angle multiplexing, smaller angle does good to diffraction efficiency after thermal fixing. And for absorption coefficient, there is an appropriate value responding to optimal diffraction efficiency after thermal fixing and we develop a theoretical model that predicts achievable diffraction efficiency after thermal fixing as a function of crystal thickness, doping level, acute angle between reference and z-axis and absorption coefficient. We compare this model with experiment results and get a good agreement.     

Tight focusing of partially polarized vortex beams by binary phase Fresnel zone plates

Based on vectorial Debye theory, the focusing properties of partially polarized vortex beam by high numerical aperture Fresnel zone plate are investigated. The effects of the numerical apertures of and the phase difference of binary phase Fresnel zone plates, the topological charge of vortex beam and the degree of polarization of incident beam on the intensity distribution and degree of coherence in the focal plane are investigated in detail. It is shown that elliptical light spots and the flat top beam can be obtained by selecting certain parameters. Studies of degree of coherence reveal that the degree of coherence between x and y components of the electric field, which is zero in the source plane, is improved in the focal plane for vortex beam, but it is hardly changed for the nonvortex beam. It is also proved that any two of the three electric field components E_x, E_y and E_z are completely coherent everywhere in the focal region if the incident light beam is linearly polarized.     

Tight focusing of double ring shaped radially polarized beam with high NA lens axicon

A method is presented for generation of a sub wavelength (0.45λ) longitudinally polarized beam, which propagates without divergence over lengths of about 8λ in free space. This is achieved by tight focusing of double ring shaped radially polarized beam with a high NA lens axicon that utilizes spherical aberration to duplicate the performance of an axicon and to create an extended focal line. The intensity distributions were calculated based on the vector diffraction theory and it was observed that in the case of high numerical aperture (NA) lens axicon, the distribution of the total intensity near the focus had little effect on the degree of truncation of the incident beam by the pupil.     

非傍轴矢量拉盖尔-高斯光束的二阶矩表示

基于Porras提出的光传输的非傍轴矢量矩理论，推导出初始圆偏振的非傍轴矢量拉盖尔-高斯(LG)光束的特征参数，包括束宽、远场发散角和M²因子等的公式，并表示为级数求和形式.非傍轴矢量高斯光束公式作为特例给出.研究表明，基于二阶矩定义的束宽按双曲线规律传输，当w₀/λ→0(w₀为束宽，λ为波长)时，远场发散角θ趋于90°，大于非傍轴标量理论预示的值63.435°.非傍轴矢量LG光束的M²因子不仅与模指数p有关，而且还与w₀/λ有关.最后，对非傍轴矢量LG光束和非傍轴标量LG光束的传输作了比较，结果表明在w₀/λ较小时，矢量效应对远场发散角的影响十分显著.对θ→90°引起的问题和非傍轴矢量矩理论的适用范围，以及解决问题的可能途径作了分析和讨论. 关键词： 非傍轴矢量拉盖尔-高斯光束 圆偏振 非傍轴矢量矩理论 光束参数