Evaluation of the Laguerre-Gaussian mode purity produced by 3D-printed microwave spiral phase plates

Computer-aided design software and additive manufacturing provide flexibility in the direct fabrication of multi-material devices. This design and fabrication versatility has been investigated for the manufacture of dielectric spiral phase plates (SPP) to generate electromagnetic waves with helical wave-fronts. Three types of SPPs designed to produce an orbital angular momentum (OAM) mode number l=|1| were additively manufactured using multi-material extrusion and multijet fabrication methods. The phase mode and mode characteristics of transformed helical microwaves as a function of the SPP geometrical features was investigated experimentally in the 12 to 18 GHz frequency range, providing high purity at characteristic frequencies. The SPPs were further combined with an additively manufactured dielectric lens that provided a marked improvement in OAM mode purity. Finally, multiplexing and de-multiplexing of two OAM modes were demonstrated successfully using the optimum SPP geometry and design.
Methods
Two oppositely directed horns were fed by commercial Ku-band SMA coax via waveguide adaptors (Flann Microwave) connected to a vector network analyzer (Rhode&Schwarz ZNB20) for excitation and response measurement in the frequency range 12 to 18 GHz. A computer-controlled X-Y gantry system was used to move the receiver horn in a pre-programmed pattern to map complex scattering parameters in the plane perpendicular to the beam direction, positioned at approximately 35 wavelengths from the stationary source horn.

The raw experimental data presents the table of the view (x, y, S21(12.0GHz), S21(12.5GHz), S21(13.0GHz), … S21(17.5GHz), S21(18.0GHz)  ) where x and y are the scans coordinate and S21(F) is the complex transmission parameter measured in this coordinate point at the frequency F (in the range 12–18 GHz with 0.5 GHz step).

The data has simple naming such TypeSPP.txt (for the type of the SPP please refer the manuscript).

The *.mat files contain the centre position of the S21 phase for corresponding SPP and need to be used in the SPP_Mode_Ratio.m script accordingly.

Files organised as follows:

// main code //

| - SPP_Mode_Ratio.m        

// Raw data //

| - GRINSPP.txt

| - GRINSPP_lens.txt

| - SmoothSPP.txt

| - SmoothSPP_lens.txt

| - StepSPP.txt

| - StepSPP_lens.txt

| - MPlex_Mode2.txt        // modulation l=2

| - DeMPlex_Mode0.txt    // demodulation l=0

// minimum amplitude table //

| - T_GRIN.mat

| - T_Smooth.mat

| - T_Step.mat

| - T_Mod.mat

| - T_DeMod.mat

The graphical representation of the data can be done using Matlab script.

计算机辅助设计（Computer-aided design, CAD）软件与增材制造（additive manufacturing）技术，可实现多材料器件的灵活直接制备。针对用于生成螺旋波前电磁波的介质螺旋相位板（spiral phase plates, SPP）的制造，研究者已对这种设计与制备的多功能性展开了相关探索。
本次研究制备了三类被设计用于产生轨道角动量（orbital angular momentum, OAM）模式数l=|1|的螺旋相位板，分别采用多材料挤出（multi-material extrusion）与多射流成型（multijet fabrication）两种增材制造工艺完成制备。在12至18 GHz的频率范围内，我们通过实验探究了变换后的螺旋微波的相位模式及模式特性随螺旋相位板几何特征的变化规律，在特征频率下实现了高模式纯度。
进一步将螺旋相位板与增材制造的介质透镜相结合，可显著提升轨道角动量模式的纯度。最后，借助优化后的螺旋相位板几何结构与设计方案，我们成功实现了两种轨道角动量模式的复用与解复用。

实验方法
两个相向放置的喇叭天线通过商用Ku波段SMA同轴电缆，经由波导适配器（Flann Microwave公司）连接至矢量网络分析仪（vector network analyzer, Rhode&Schwarz ZNB20），以在12至18 GHz的频率范围内完成激励与响应测量。我们采用计算机控制的X-Y龙门系统，以预设轨迹移动接收喇叭天线，在垂直于波束传播方向的平面内测绘复散射参数分布，接收平面与静止的发射喇叭天线间距约为35个波长。

原始实验数据以表格形式呈现，格式为(x, y, S21(12.0GHz), S21(12.5GHz), S21(13.0GHz), …, S21(17.5GHz), S21(18.0GHz))，其中x与y为扫描坐标，S21(F)为该坐标点在频率F下测得的复传输参数（频率覆盖范围12–18 GHz，步长0.5 GHz）。

数据集采用简洁命名规则，例如TypeSPP.txt（具体螺旋相位板类型请参阅研究手稿）。

*.mat格式文件存储了对应螺旋相位板的S21相位中心位置，可配合SPP_Mode_Ratio.m脚本进行后续分析。

文件组织形式如下：
// 主代码 //
| - SPP_Mode_Ratio.m

// 原始数据 //
| - GRINSPP.txt
| - GRINSPP_lens.txt
| - SmoothSPP.txt
| - SmoothSPP_lens.txt
| - StepSPP.txt
| - StepSPP_lens.txt
| - MPlex_Mode2.txt // 调制模式l=2
| - DeMPlex_Mode0.txt // 解调模式l=0

// 最小振幅表 //
| - T_GRIN.mat
| - T_Smooth.mat
| - T_Step.mat
| - T_Mod.mat
| - T_DeMod.mat

可通过Matlab脚本实现数据的可视化展示。