Dynamics of topological multipoles: II. Creation, annihilation, and evolution of nonparaxial optical vortices

The behavior of nonparaxial combined beams transferring two or four optical vortices with opposite topological charges (topological dipole or quadrupole) is studied. The paraxial and nonparaxial approaches are compared. It is shown that the behavior of a topologically neutral wave system is well characterized by the position of a representative point on the parametric plane. It is found that there exists a large region on this plane for which spatial trajectories of the optical vortices, both for dipoles and quadrupoles, do not intersect the focal plane, i.e., the vortices cannot exist within the forbidden zone. At the edges of the forbidden zone, the vortices are either created or annihilated. In contrast, there exists a region on the parametric plane for which the optical vortices can exist only near the waist plane.     

阴极透镜象差的变分理论

本文运用变分原理研究了电磁复合聚焦阴极透镜的象差理论,导出了在任意象平面中象差系数的普遍公式。它们可以用Glaser导出的象差系数的线性组合来表示。这就表明了宽束与细束电子光学系统的象差都可以用统一的变分方法处理,并建立了两者之间的联系,本文采用矢量形式描写阴极透镜的近轴轨迹,并采用矩阵形式描写象差。本文所得的象差系数较之文献上已有结果形式更为简洁且适用于计算机计算。本文考虑了阴极面上磁场和横向电场不为零的情况,因而所得结果较为普遍。 关键词：     

Theory of paraxial lateral aberrations of electrostatic imaging electrostatic electron optics based on asymptotic solutions and its verification

In imaging electron optics, study of geometrical lateral aberrations of third order and paraxial lateral aberrations of second order has traditionally been paid more attention to, but the existence of paraxial chromatic aberrations of third order and paraxial chromatic aberrations of magnification of third order was almost ignored, and the general form of paraxial lateral aberration has not been studied theoretically.In the present paper, the paraxial lateral aberrations expressed in general form have been derived emphatically on the basis of asymptotic solutions of paraxial equation. The relationship between the coefficients of asymptotic solutions has been investigated, which proves that the coefficients of asymptotic solutions are related each other. Through a bi-electrode electrostatic spherical concentric system model, two special solutions expressed by asymptotic solutions and accurate solutions in a bi-electrode electrostatic spherical concentric system have been deduced, and the paraxial lateral aberrations have been verified and tested, in which the aberration coefficients are solved by asymptotic solutions of paraxial equation. Result completely proves that the approach based on asymptotic solutions to solve the paraxial lateral aberrations are practicable and accurate enough. The paraxial chromatic aberration of magnification of third order and the paraxial chromatic aberration of third order have been firstly derived, and the Recknagel-Artimovich formula of paraxial chromatic aberration of second order which possess an greatest part in the whole paraxial lateral aberrations has been deduced and confirmed. A simple and clear form for expressing paraxial lateral aberrations of imaging electron optics is suggested for practical use. Results of the present paper will have theoretical value for aberration theory of imaging electron optics and practical significance for the design of image tubes.     

Paraxial imaging electron optics and its spatial-temporal aberrations for a bi-electrode concentric spherical system with electrostatic focusing

The paraxial solutions play an important role in studying electron optical imaging system and its spatial-temporal aberrations, as was discussed in previous paper [1], but investigation of a bi-electrode concentric spherical system with electrostatic focusing directly from paraxial electron ray equation and paraxial electron motion equation has not been done before. In this paper, we shall use the paraxial equations to study the spatial-temporal trajectories and their aberrations for a bi-electrode concentric spherical system with electrostatic focusing.In the present paper, start from the paraxial ray equation and paraxial motion equation, the paraxial spatial-temporal trajectory of moving electron emitted from the photocathode has been solved for a bi-electrode concentric spherical system with electrostatic focusing. The paraxial static and dynamic electron optics, as well as the paraxial spatial-temporal aberrations in this system are then discussed, the general regularity of imaging in paraxial optical system has been explored. The paraxial spatial aberrations, as well as the paraxial temporal aberrations with different orders, have been defined and deduced, that are classified by the order of (?_z/?_ac)^1/2 and (?_T/?_ac)^1/2. Thus we get same conclusions about paraxial spatial and temporal aberrations as we have given in the previous paper and it completely shows that the paraxial spatial-temporal aberrations can be investigated directly from the paraxial ray equation and paraxial motion equation.     

体全息光栅透镜的设计和应用

设计了一种新型的体全息光栅透镜, 在一块光学平板（体全息记录材料）内可以将输入光束产生横向传输并聚焦, 或对输入光点产生横传的准直. 它由一束平面波和一束球面波正交入射到光学平板上干涉形成的. 研究了该体全息透镜的光栅间距变化情况, 为设计和制备体全息光栅透镜及相关器件提供了理论依据. 基于两光束耦合波理论, 得到了该光栅透镜的耦合波方程, 近似计算了该透镜的衍射效率及其达到高衍射效率时透镜的最佳尺寸. 最后, 讨论了该透镜在集成光学等领域中的应用.     

Lensless imaging of an arbitrary object

A new class of imaging systems that do not require the use of lenses or similar optical devices is introduced and theoretically investigated. In particular, it is demonstrated that, if an arbitrary plane object is illuminated by an appropriate spherical wave front (generated from a monochromatic point source), then a magnified image of the object intensity distribution can be observed in any transversal plane along the light-propagation direction within the far-field (Fraunhofer) diffraction region. The phenomenon is based on the fact that, under certain conditions, the spherical wave front can modify the energy's angular spectrum of the field distribution in the object plane such that this spectrum replicates the spatial intensity distribution of the object.     

Isotropic compensation of diffraction-driven angular dispersion

We report on an optical arrangement capable of compensating angular dispersion of paraxial wave fields developed by diffractive optical elements (DOEs). Schematically, the system is a beam expander in which two phase-only zone plates have been inserted, remaining afocal the coupled system. The DOE, which induces a continuous set of dispersive tilted plane waves, is placed at a specific position within the proposed setup providing an output spectrum with achromatic angular deviation. A directional matching between phase fronts and pulse fronts of output wave packets is demonstrated.     

光学系统实现热补偿的通用条件

运用光学系统的近轴成像公式，推导出微分形式的物面位于任意位置时热补偿的通用条件，包括薄单透镜、密接薄透镜组和分离薄透镜组等不同情况。推导过程中假设物面位置不随温度发生变化，并且忽略分离薄透镜组中各组分上光线入射高度随温度的变化。利用推导的条件建立了像距的归一化温度变化率与各透镜光热膨胀系数之间的关系，指出所得到的条件具有更加普遍的意义，能够指导机械和伺服控制系统的工程设计，并且在物面位于无穷远时与目前普遍采用的热补偿条件相吻合，即光学系统的光热膨胀系数等于壳体的热膨胀系数。     

A theoretical method based on Fourier spectrum analysis for the focusing performances of the X-ray compound refractive lenses

It is important to predict the intensity distribution in focusing plane for designing the X-ray compound refractive lenses. On the basis of analyzing the structure of X-ray compound lenses and comparing it with Fraunhofer diffraction system, it is concluded that the X-ray focusing system can be regarded as a kind of Fraunhofer diffraction system. Therefore, a method based on Fourier spectrum analysis is presented to predict the intensity distribution in the focusing plane for the X-ray lenses. A brief analysis on the relationship between the parameters of X-ray lenses and their focusing performance is also given in this paper.     

位相调制产生“热像”效应理论研究

通过理论分析和数值模拟方法，研究了高功率激光系统中的非线性“热像”效应. 利用菲涅耳-基尔霍夫衍射积分和非线性近轴波动方程，在远场近似及光学薄近似条件下，得出了位相调制产生“热像”出现的位置及强度满足的解析关系.结果表明，“热像”形成在非线性介质后与衍射物对称的位置，其强度可能比振幅调制产生“热像”的强度大几倍. 通过计算机模拟，并与理论预测结果进行比较，显示两者符合较好. 同时给“热像”的形成过程赋予了明确的物理意义，指出“热像”的形成类似于同轴位相夫琅禾费全息过程. 关键词： “热像”效应 全息成像 小尺度自聚焦 高功率激光     

不同2×2集束聚焦方式下高功率激光靶面光强分布特性

大口径高功率激光装置为提高激光靶面的光强强度, 通常采用2×2集束聚焦的模式进行打靶. 大口径楔形透镜是组成2×2集束聚焦系统的核心元件, 可分为二维离轴楔形透镜、一维离轴楔形透镜和非离轴楔形透镜3类. 为了获得理想靶面光强分布, 基于这3 类楔形透镜, 对比研究相应2×2集束聚焦系统下的靶面光强分布特性. 研究结果表明: 相比离轴楔形透镜, 采用基于非离轴楔形透镜的2×2集束聚焦系统时, 容易在激光靶面获得更窄的主瓣宽度、更强的峰值强度、更高的能量集中度. 研究结果对高功率激光靶场聚焦系统的配置选择有重要参考价值.     

Cc,Cs, and parasitic correction in quadrupole probe-forming lenses

Approximate expressions are derived for the second and third order aberrations of a quadrupole doublet, allowing for aberrations intrinsic to fields of perfect symmetry, for parasitic aberrations of imperfect symmetry, and for compensating multipole lenses. Five third-order coefficients are found, and expressed in terms of four octopole strengths and the first-order parameters of the doublet as determined by its dimensions. For compensation of third-order aberrations of achromatic quadrupole/octopole lenses, either skew octopole lenses are required externally, or lenses with more than 8 poles are required coincident with the quadrupoles. If an octopole lens is added between the quadrupoles of the achromatic doublet, the spherical aberration of a condenser lens may be compensated. Such a Cs and Cc compensated quadrupole doublet is suitable for use as a probe-forming lens in focused ion beam systems and ion microscopes.     

静电四极透镜中非线性传输的Lie代数分析

用Lie代数方法分析了带电粒子在静电四极透镜中的非线性传输,结果为三级近似.分析过程为:首先建立粒子在静电四极透镜中的运动的Hamilton函数,然后将Hamilton函数在平衡轨道附近展开成幂级数,最后计算粒子的非线性轨迹到三级近似.根据需要,还可以扩展到更高级近似解.     

X‐ray focusing by the system of refractive lens(es) placed inside asymmetric channel‐cut crystals

An X‐ray one‐dimensionally focusing system, a refracting–diffracting lens (RDL), composed of Bragg double‐asymmetric‐reflecting two‐crystal plane parallel plates and a double‐concave cylindrical parabolic lens placed in the gap between the plates is described. It is shown that the focal length of the RDL is equal to the focal distance of the separate lens multiplied by the square of the asymmetry factor. One can obtain RDLs with different focal lengths for certain applications. Using the point‐source function of dynamic diffraction, as well as the Green function in a vacuum with parabolic approximation, an expression for the double‐diffracted beam amplitude for an arbitrary incident wave is presented. Focusing of the plane incident wave and imaging of a point source are studied. The cases of non‐absorptive and absorptive lenses are discussed. The intensity distribution in the focusing plane and on the focusing line, and its dependence on wavelength, deviation from the Bragg angle and magnification is studied. Geometrical optical considerations are also given. RDLs can be applied to focus radiation from both laboratory and synchrotron X‐ray sources, for X‐ray imaging of objects, and for obtaining high‐intensity beams. RDLs can also be applied in X‐ray astronomy.     

基于双柱透镜慢轴准直激光二极管堆栈光束匀化系统

为实现高功率激光二极管堆栈光束的匀化与整形,提出基于双柱透镜慢轴准直的匀化系统。利用双柱透镜实现对高填充因子激光二极管慢轴方向光束发散角度的压缩,降低成像型多孔径光束积分器中微透镜的数值孔径,减小匀化系统体积。通过三个限定条件确定了双柱透镜参数取值范围,并通过像差分析对双柱透镜进行了优化,实现慢轴方向光束剩余发散角度1.74。结合成像型多孔径光束积分器,设计了激光二极管堆栈的匀化系统,并进行了实验测试。实验结果表明,在中心光斑尺寸约为6 mm6 mm范围内,光斑不均匀性为8.11%。     

簿透镜等效Woods透镜分析

本文利用等光程方法导出了薄透镜等效Woods透镜的折射率分布函数及两者结构参数之间的关系。并利用矩阵方法导出了Woods透镜的近轴成象公式。数值计算例子证明了所得结论的正确性。     

大尺度光学列阵的成像特性

本文由光线光学理论出发,分析了无单元像差的光学元件大尺度列阵的成像特性,得到了较傍轴近似更普适的成像特性变换矩阵,其结果包含了列阵的傍轴近似成像理论.并进一步证明了大尺度平面列阵的成像特性只具有近似的准相位共轭特性,且只有在傍轴近似下才是较完善的准相位共轭成像.该结论与以往理论相比更接近实际,且能更好地解释迄今为止所观察到的实验结果及本文的实验结果.     

一种静电像管优化设计方法的设想

从数值计算出发,以实例计算静电像管的均方根半径值,给出系统在最佳像面及其各附加像面处的均方根值,验证了理论分析的正确性,并从理论上提出了一种关于静电像管优化设计方法的设想。     

Virtual sources for a cosh-Gaussian beam

On the basis of superposition of beams, a group of virtual sources that generate a cosh-Gaussian wave is identified. A closed-form expression is derived for this cosh-Gaussian wave, which, in the appropriate limit, yields the paraxial approximation for the cosh-Gaussian beam. From this expression, the paraxial approximation and the nonparaxial corrections of all orders for the corresponding paraxial cosh-Gaussian beam are determined.