﻿ 一种新型贝塞尔光束器件的设计方法
 光电工程  2020, Vol. 47 Issue (6): 190190      DOI: 10.12086/oee.2020.190190

1. 中国科学院光电技术研究所微细加工光学技术国家重点实验室，四川 成都 610209;
2. 中国科学院大学，北京 100049

A method of designing new Bessel beam generator
Dai Chengwei1,2, Yan Chao1,2, Zeng Qingyu1,2, Li Xiong1,2, Guo Yinghui1,2, Pu Mingbo1,2, Wang Changtao1,2, Luo Xiangang1,2
1. State Key Laboratory of Optical Technologies on Nano-Fabrication and Micro-Engineering, Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China;
2. University of Chinese Academy of Sciences, Beijing 100049, China
Abstract: Catenary nanostructures enable continuous phase control. However, the ordinary catenary nanostructure has narrow width at both ends and is not easy to be fabricated. On the other side, it was difficult to build complex model directly in simulation software CST, and the simulation process was complicated in the past. The equal-width catenary slit is proposed to replace the normal catenary slit. And the equal-width catenary-type metasurface has been designed to generate Bessel beam, which provides a new idea for the design of two-dimensional optical devices. In the process of modeling and simulation, CST is combined with Matlab for co-simulation, and all operations, such as modeling, simulations, and parameter modification, are completed directly in Matlab. This method can be used to design complex structures, and more ideal simulation results can be obtained combined with the numerical optimization ability of Matlab.
Keywords: metasurfaces    catenary    Bessel beam    CST    Matlab

1 引言

2 结构设计 2.1 等宽悬链线

 $y = \frac{\varLambda }{\pi }{\rm{ln}}\left( {\left| {{\rm{sec}}\left( {\frac{{\pi x}}{A}} \right)} \right|} \right),$ (1)

 图 1 悬链线狭缝结构示意图。(a)普通悬链线狭缝；(b)等宽悬链线狭缝 Fig. 1 Diagrams of catenary slits. (a) Ordinary catenary slit; (b) Equal-width catenary slit
 $\theta = {\rm{arctan}}\left( {\frac{{{y_{n + 1}} - {y_n}}}{{{x_{n + 1}} - {x_n}}}} \right){\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} ,$ (2)

 $\left\{ {\begin{array}{*{20}{l}} {x_n^\prime = {x_n} - w \cdot {\rm{cos}}\theta }\\ {y_n^\prime = {y_n} + w \cdot {\rm{sin}}\theta } \end{array}} \right.。$ (3)

2.2 基于等宽悬链线阵列的贝塞尔光束产生器

 $\begin{array}{*{20}{l}} {E(x, y, z, t) = \frac{1}{{2\pi }}{\rm{exp}}[{\rm{i}}({k_z}z - \omega t)]}\\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \cdot \int_0^{2\pi } {{\rm{exp}}} [{\rm{i}}{k_{\rm{r}}}(x{\kern 1pt} {\rm{cos}}{\kern 1pt} {\kern 1pt} \varphi + y{\kern 1pt} {\rm{sin}}{\kern 1pt} \varphi )]{\rm{d}}\varphi , } \end{array}$ (4)

 $E(r, \varphi ) = {{\rm{J}}_l}{\rm{exp}}({\rm{i}}{k_{\rm{r}}} + {\rm{i}}l\varphi + {k_z}z),$ (5)

 图 2 等宽悬链线阵列结构。(a)零阶贝塞尔光束相位分布图；(b)等宽悬链线零阶贝塞尔光束产生器件 Fig. 2 Equal-width catenary array structure. (a) Phase distribution of zero-order Bessel beam generator; (b) Zero-order Bessel beam generator constructed by equal-width catenary arrays
 $\varPhi = - 2\sigma {\kern 1pt} {\rm{arctan}}\left( {\frac{{{\rm{d}}y}}{{{\rm{d}}x}}} \right) = - 2\sigma \frac{\pi }{\varLambda }x,$ (6)

 $r = \frac{{(l - 2)\varphi + (2m + 1)\pi }}{{{k_{\rm{r}}}}},$ (7)

3 Matlab与CST联合仿真的具体方法

CST建模仿真有两种方式，一种是使用交互界面直接建模仿真，另一种是通过脚本语言Visual Basic for Applications (VBA)操作。使用交互界面进行的所有操作，均会在CST的历史命令里写入相应的VBA语句。所以，只要使用Matlab将VBA命令语句写入CST历史命令就可以实现建模仿真等一系列操作。Matlab调用CST建模仿真流程如图 3所示。首先用Matlab获得CST句柄，使得通过Matlab便可以控制CST软件。在得到CST句柄后，进行新建文件、保存文件、建模、设置参数以及进行仿真等操作。

 图 3 Matlab调用CST仿真流程图 Fig. 3 Flowchart of CST simulation called by Matlab

Matlab调用CST建模仿真的部分语句如表 1。使用Matlab内置actxserver函数可以返回CST对象。CST对象包含FileNew(创建新文件)，NewMWS(新建微波仿真)，Quit(退出CST)等方法。用Matlab中‘invoke’函数可以调用CST对象的上述方法。另外，‘invoke’函数还可以将VBA语句写入CST，从而完成建模仿真等步骤，如表 1最后一行语句所示。

 Function Code Calling CST cst=actxserver(‘CSTStuio.application’) Creating new MWS file mws=cst.invoke(‘NewMWS’); Saving MWS file mws.invoke(‘saveas’, ‘Bessl.cst’); Saving MWS file mws.invoke(‘AddToHistory’, VBA);
4 仿真过程及结果

 图 4 CST中的等宽悬链线阵列 Fig. 4 Equal-width catenary arrays in CST

 图 5 CST仿真得到的x-z平面Bessel光束光强分布 Fig. 5 Intensity distribution of Bessel beam on x-z plane obtained by CST

 图 6 x-y平面贝塞尔光束光强和相位分布。(a)~(d)距离结构一定距离处，x-y平面贝塞尔光束相位分布；(e)~(h)与相位对应的光强分布图；(i) ~ (l)图(e) ~ (h)虚线所示的光强截线图 Fig. 6 Intensity and phase distributions of Bessel beam on x-y plane. (a)~(d) Represent the phase distributions on x-y plane at certain distances from the structure; (e)~(h) Denote the intensity distributions corresponding to the phase distributions (a)~(d), respectively; (i)~(l) are the cross views of the intensity shown by the dashed lines in figures (e)~(h), respectively
5 结论

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