本文提出了一种基于Metasurface产生任意柱矢量光束的方法.采用的Metasurface是在熔融石英上刻蚀空间变化的非周期光栅构成.非周期光栅会形成空变的有效双折射,从而对光场的偏振态空间分布进行调制.通过琼斯矩阵的方法分析得出这样的Metasurface可以将入射线偏振光转换为柱矢量光束,并且只需要改变入射线偏振光的偏振方向即可获得高阶庞加莱球赤道上任意一点的柱矢量光束.最后,用Metasurface搭建了一套简单、高效的柱矢量光束产生系统,实验结果与理论分析一致.

A method of generating cylindrical vector beams based on metasurface is presented in this paper. The metasurface is a fused silica with a space-variant non-periodic grating which is written by laser. The non-periodic grating induces a space-variant effective birefringence that modulates the space distribution of polarization state. It is shown that an incident linearly polarized light can be converted to a cylindrical vector beam by the method of Jones matrix. We can obtain an arbitrary cylindrical vector beam on the equator of the higher-order Poincaré sphere. A simple and efficient experimental system is established with a metasurface. Experimental results are in agreement with the theoretical analysis.

为了求解柱坐标系下非傍轴矢量波动方程,得到光束的电场解析表达式,基于轴对称情况下沿角向偏振的电场,将非傍轴近似情况下的矢量波动方程进行了抛物线坐标的转化,利用分离变量法进行了相应求解,并给出了相应的数值计算。结果表明,非傍轴近似情况下,矢量波动方程的解能描述一种光束的电场,该场的解析表达式与合流超几何函数以及梅杰函数的解有关;光束的光强分布与第1类零阶贝塞尔模式光束类似;光束在近光轴处的光强表现为无限大并且沿边缘方向急剧衰减;在焦平面上沿着径向方向光强急剧减小。所得结果对于探究非傍轴近似情况下矢量光束的传输特性有一定的意义。

In order to solve the nonparaxial vector wave equation in the cylindrical coordinates and obtain electric field expression of the beams , based on the electric field along the azimuthal polarization under the axisymmetric circumstance , the vector wave equation under the nonparaxiality similar circumstances was transformed to the parabolic coordinates and was solved appropriately with the separation variables method .The corresponding numerical calculation was made .The results show that the new analytical solution of the nonparaxial vector wave equation is discussed to describe the propagation of a laser beam.The electric field of such a beam is found to be based on the solutions of the confluent hypergeometric function and the Meijer functions .The intensity distribution of beam is similar to the first-class zero-order Bessel beam mode.The intensity of the light beam near the optical axis is nearly infinite , and decays rapidly along the peripheral direction and decreases sharply alo

采用矢量角谱的方法分析了Airy-Gaussian光束的矢量结构,运用静态相位法得出了光束远场矢量结构的解析表达式.根据得到的TE项和TM项的解析表达式,分别研究了TE项和TM项及整个光束的能流分布.更好地阐明了Airy-Gaussian光束的物理图像,从而为操控光束提供潜在的新方法.

Based on the vector angular spectrum of the electromagnetic beam and the method of stationary phase, the analytical vectorial structure of the Airy-Gaussian beam in the far field has been presented. According to the analytical electromagnetic representations of the TE and TM terms, the energy flux distributions of the TE term, the TM term, and the whole beam in the far field are investigated respectively. The formulas obtained are applicable not only in the paraxial case, but also in the nonparaxial case. The physical pictures of Airy-Gaussian beams are well illustrated from the vectorial structure, which may provide a new approach to manipulate laser beams.

提出了一种组合非球面反射型太阳能聚光镜并给出了设计方法。聚光镜由38片非球面组成，每一片非球面都由一组特定系数C，a2，a4，a6，a8，a10的偶次非球面方程决定，是此特定非球面的一部分。根据非球面方程和光反射定律矢量形式，导出了非球面内壁上太阳反射光束的方向矢量与非球面系数C，a2，a4，a6，a8，a10的关系，适当地选择这些非球面系数，即适当地调整非球面面型，可以使太阳反射光束具有特定的方向矢量，使入射到非球面内壁上的太阳光束反射后全部聚焦在某一特定的区域内，形成小的光斑。每组特定系数都用粒子群优化算法求得，并经计算机模拟和实验证明其聚焦效果。聚光镜的光束压缩比为330∶1，其聚焦光斑可作为一种高温热源，而此聚光镜可以用在太阳能加热装置中。

In this paper , a build-up aspherical solar concentrating mirror and its design method are presented . It is composed of 38 pieces of revolution surfaces , and each piece of revolution surface is the part of the as-pheric surface defined by a set of specific coefficients C,a2 ,a4 ,a6 ,a8 ,a10 .According to the even aspherical e-quation and the law of reflection in vector form , the relationship between the direction vectors of rays of light reflected from the inner wall of aspheric surface and the coefficients of an aspherical equation , C,a2 ,a4 ,a6 , a8 ,a10 , has been derived .By appropriately choosing these aspherical coefficients , namely, appropriately ad-justing an aspherical surface type , the reflected light beam can have specific direction vectors , which can make the sunbeams incident on an aspherical inner wall focus on a particular area and form a small spot .Each group of specific coefficients is obtained by using particle swarm optimization algorithm .The focus

利用瑞利—索末菲矢量衍射公式导出偏振光波矩孔矢量夫琅禾费衍射的解析计算式,通过模拟实验研究了椭圆偏振光的一般孔和亚波长孔的矢量夫琅禾费衍射情形,可应用于偏振光波偏振度检测和偏振成像等方面,表明所得计算式的有效性和可靠性,可在微光学、近场光学、衍射成像、光束传输变换以及光信息处理等方面发挥作用。

The analytic calculation formula of the vector Fraunhofer diffraction of polarized light wave through-out rectangular aperture is derived with Rayleigh-Sommerfeld vector diffraction formula. Then Fraunhofer vector dif-fraction of elliptically polarized light throughout general aperture or sub-wavelength aperture cases are studied with simulation experiments, these can be used for the detection of the polarization degree of polarized light and polariza-tion imaging, etc. the vector diffraction and the diffraction situation of general aperture and sub-wavelength aperture is discussed. The simulations show that the calculation formula is valid and reliable, it can play a role in micro-op-tics, near-field optics, diffraction imaging, light beam transmission and transformation, and light information process-ing and so on.