Source Code and Simulation Results: Chiral and directional optical emission from a dipole source coupled to a helical plasmonic antenna

Summary This publication supplements the article "Chiral and directional optical emission from a dipole source coupled to a helical plasmonic antenna" with tabulated data and Matlab code that allows the reproduction of the results. Within the article, the chiral behavior of single and double plasmonic nano antennas made from silver is numerically investigated with a focus on the coupling of a linear polarized dipole as an excitation source to the helix. Simulation Setup - FEM Simulations The script "run_wavlengthscan.m" allows to reproduce all simulations of the article. It can be chosen between the single and double helices, by specifying the keys parameter "keys.doppelhelix" where 0 gives a single and 1 a double helix. The number of turns can be specified by choosing "keys.case". The dipol is located within a 20nm thick hBN substrate layer, on glass (BK7). Results of the Purcell enhancement can be plotted using the scripts "display_results_single_helix.m" and "display_results_doublehelix.m" in the folder "results". The far-field plots can be reproduced using the scripts "display_farfiel_polarization_single_helix.m" and "display_farfiel_polarization_double_helix.m" of the folder "FunctionsAndScripts". The template for the mesh is contained in the folder "generate_grid_file", where the parameters of the helix (for example: radius, tube radius, and pitch height) can be modified. Within the folder "project3D" all required .jcm files are stored. Copy the "grid.jcm" file with the geometry of interest to this folder to perform simulations. All required keys parameters for the JCM template files (.jcmt, jcmpt) are set within the functions "set_numerical_parameter.m" and "set_physical_parameters.m", contained in the folder "FunctionsAndScripts". Therein, the function "set_sources.m" specifies the parameters for the dipole excitation, such as the position, and the strength (equivalent to the polarization). Semi-Analytical Model The Jupyter notebook "Semi_Analytical_Plasmonic_Helix.ipynb" contains the commented Python script for the semi-analytical design tool used to obtain far-field radiation patterns of the single helix. This semi-analytical design tool is based on an analytical model developed in [4]. The script can be divided into three parts. First, the single helix is defined, and a linear wavelength scaling law [5] is used to determine the illuminating wavelengths at which Fabry-Pérot resonances occur. Second, the overlap integral between the mode current on the helix and the incident electric field is evaluated for a given direction of incident light. Thirdly, the direction of incidence is varied to obtain the far-field radiation patterns. The script allows for the radiation patterns to be exported as a .csv file. Alternatively, the radiation patterns can be plotted directly using the provided single_plot functions. Material The material data has been taken from the refractiveindex.info database. For silver the data is taken from tabulated data from Johnson and Christy [1] . The dispersion relation for hBN comes from [2] and tabulated data for glass (BK7) from [3]. The MATLAB script "material_properties_plot.m" plots the material fits above the wavelengths of interest. The required tabulated data is given in the folder "material_data". With 'material_properties_plot.m' the fits to the material data can be reproduced and plotted. Usage The .zip folder Helix_FEM contains all data and scripts to reproduce the plots from the 3D FEM simulations. The Jupyter Notebook Semi_Analytical_Plasmonic_Helix reprouces the results from the semi-analytical model. Requirements JCMsuite (at least 5.4.0) MATLAB (tested with version R2023b) Python (tested with Version 3.10.9) Jupyter Notebook (tested with 6.5.2) To run the simulations with JCMsuite you must replace corresponding placeholders with a path to your installation of JCMsuite. Free trial licenses are available, please refer to the homepage of JCMwave. References [1] P. B. Johnson and R.-W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370 (1972). [2] S.-Y. Lee, T.-Y. Jeong, S. Jung, and K.-J. Yee, “Refractive index dispersion of hexagonal boron nitride in the visible and near-infrared,” Phys. Status Solidi B 256, 1800417 (2019). [3] “SCHOTT Zemax catalogue 2017-01-20b,” (2017). [4] K. Höflich et al., "Resonant behavior of a single plasmonic helix." Optica 6, 1098(2019). [5]L. Novotny, "Effective wavelength scaling for optical antennas", Phys. Rev. Lett. 98,266802 (2007).### 摘要 本数据集为论文《与螺旋等离激元天线耦合的偶极子源的手性与定向光发射》提供补充数据，包含可复现该论文研究结果的制表数据与MATLAB代码。论文针对银制单螺旋与双螺旋等离激元纳米天线的手性特性开展数值研究，重点探究了作为激发源的线偏振偶极子与螺旋结构的耦合过程。 ### 仿真设置——有限元法(Finite Element Method, FEM)仿真 脚本"run_wavlengthscan.m"可复现论文中的全部仿真内容。通过指定参数"keys.doppelhelix"可选择单螺旋或双螺旋结构：参数值为0时对应单螺旋，值为1则对应双螺旋。可通过"keys.case"参数设置螺旋的匝数。偶极子位于玻璃（BK7）基底上一层厚度为20 nm的六方氮化硼（hBN）衬底中。珀塞尔增强(Purcell enhancement)的结果可通过"results"文件夹下的"display_results_single_helix.m"与"display_results_doublehelix.m"脚本进行绘图。远场辐射方向图可通过"FunctionsAndScripts"文件夹下的"display_farfiel_polarization_single_helix.m"与"display_farfiel_polarization_double_helix.m"脚本复现。 网格模板存储于"generate_grid_file"文件夹中，可在此修改螺旋结构的相关参数，例如半径、管半径与螺距高度。 "project3D"文件夹中存储了所有必需的.jcm文件。将包含目标几何结构的"grid.jcm"文件复制至该文件夹即可开展仿真。 JCM模板文件（.jcmt、.jcmpt）所需的全部参数均在"FunctionsAndScripts"文件夹下的"set_numerical_parameter.m"与"set_physical_parameters.m"函数中配置。其中，"set_sources.m"函数用于指定偶极子激发的相关参数，包括位置与强度（等价于偏振态）。 ### 半解析模型 Jupyter Notebook "Semi_Analytical_Plasmonic_Helix.ipynb"包含了用于获取单螺旋远场辐射方向图的半解析设计工具的带注释Python脚本。该半解析设计工具基于文献[4]提出的解析模型。脚本可分为三个部分：首先，定义单螺旋结构，并利用线性波长缩放定律[5]确定法布里-珀罗(Fabry-Pérot)共振对应的激发波长；其次，针对给定的入射光方向，计算螺旋上的模式电流与入射电场之间的重叠积分；最后，改变入射方向以获得完整的远场辐射方向图。该脚本支持将辐射方向图导出为.csv文件，也可通过提供的单绘图函数直接绘制辐射方向图。 ### 材料参数 材料数据取自refractiveindex.info数据库。其中银的材料数据来自Johnson与Christy的制表数据[1]，六方氮化硼（hBN）的色散关系来自文献[2]，玻璃（BK7）的制表数据来自文献[3]。MATLAB脚本"material_properties_plot.m"可绘制目标波长范围内的材料拟合曲线。所需的原始制表数据存储于"material_data"文件夹中。通过运行"material_properties_plot.m"即可复现并绘制材料数据的拟合结果。 ### 使用方法 压缩文件夹"Helix_FEM"包含了复现3D有限元法仿真绘图所需的全部数据与脚本。 Jupyter Notebook "Semi_Analytical_Plasmonic_Helix"可复现半解析模型的计算结果。 ### 运行需求 需安装以下软件环境： - JCMsuite（版本至少为5.4.0） - MATLAB（经R2023b版本测试） - Python（经3.10.9版本测试） - Jupyter Notebook（经6.5.2版本测试） 若需使用JCMsuite运行仿真，需将对应占位符替换为JCMsuite的本地安装路径。免费试用许可证可申请，请参阅JCMwave官方主页。 ### 参考文献 [1] P. B. Johnson 与 R.-W. Christy, "Optical constants of the noble metals," *Phys. Rev. B* 6, 4370 (1972). [2] S.-Y. Lee, T.-Y. Jeong, S. Jung 与 K.-J. Yee, "Refractive index dispersion of hexagonal boron nitride in the visible and near-infrared," *Phys. Status Solidi B* 256, 1800417 (2019). [3] "SCHOTT Zemax catalogue 2017-01-20b," (2017). [4] K. Höflich et al., "Resonant behavior of a single plasmonic helix." *Optica* 6, 1098(2019). [5] L. Novotny, "Effective wavelength scaling for optical antennas", *Phys. Rev. Lett.* 98,266802 (2007).