DOI: 10.5281/zenodo.14194107
title: Data and code for "Ultrathin 3R-MoS2 metasurfaces with atomically precise edges for efficient nonlinear nanophotonics."

description: # Data and code for "Ultrathin 3R-MoS2 metasurfaces with atomically precise edges for efficient nonlinear nanophotonics."

 

 

1) The linear spectra and SHG of a bare MoS2 flake on top of a glass substrate were calculated using Matlab 2017a. The script to run the calculation is 'shg_from_MoS2_flake.m'. SHG is calculated using Lorentz reciprocity. Input data are the MoS2 permittivity and chi2 tensor taken from elsewhere. Important parameters to set are:

 

N - number of layers

l - wavelength range defined from photon energies

 

The layers are defined in the loop over flake thickness begining lin line 71. The relevant variables are:

 

e - permittivity of the layers vs wavelength

z - positions of interfaces

SHG_num - define layer for SHG calculation.

 

2) Linear reflection calculations were performed using the RCWA code fmmax under python. The following python packages were used in the calculations. Installation is possible via pip.

Package             Version    

------------------- -----------

contourpy           1.1.1      

cycler              0.12.1     

fmmax               0.4.1      

fonttools           4.49.0     

importlib-metadata  7.0.2      

importlib-resources 6.1.3      

jax                 0.4.13     

jaxlib              0.4.13     

joblib              1.3.2      

kiwisolver          1.4.5      

matplotlib          3.7.5      

ml-dtypes           0.2.0      

numpy               1.24.4     

opt-einsum          3.3.0      

packaging           23.2       

pillow              10.2.0     

pip                 20.0.2     

pkg-resources       0.0.0      

pyparsing           3.1.2      

python-dateutil     2.9.0.post0

scipy               1.10.1     

setuptools          44.0.0     

six                 1.16.0     

zipp                3.17.0  

 

The 'grating-asym-tri-v9.py' script calculates the linear spectra for an MoS2 grating. The parameters that can ba adjusted are:

asymmetry: 0...1 with 0 being a circle, 1 a pointed triangle, and intermadiate values a triangle with rounded corners.

lattices: period

fractions: fraction of the grating taken by the hole

thicknesses: layer thickness

azim_angle_values: azimuthal direction of incidence

polar_angle: angle of incidence

 

The 'plot-a_result-v9-compare.py' script plots the saved data calculated using the above script. It presently requires two datasets to be available with the same parameters differing only by the asymmetry.

 

 

3) Comsol-linear-and-nonlinear folder contains 6 files - 3 Comsol Multiphysics 6.2 models (earlier version would not open the files), and 3 txt files. GZ thanks Dr. Olga Sergaeva for the Comsol SHG master model of the periodic arrays. [https://doi.org/10.1039/D2NR00641C]

 

3 txt files are:

- nxx 3R-MoS2 refractive index dispersion in xx and yy in-plane direction. First column is a wavelength in nm. The second, and the third columns are values of n, and k at a given wavelength in nm. [https://doi.org/10.1021/acsphotonics.2c00433]

- nzz 3R-MoS2 refractive index dispersion in zz out-of-plane direction. First column is a wavelength in nm. The second column is a value of n at a given wavelength in nm. [https://doi.org/10.1021/acsphotonics.2c00433]

- Chi2xxy_Tomasz - chi2 tensor components values (yyy = -yxx = -xxy = -xyx) at a given pump wavelength. The dispersion is obtained by means of DFT calculation. [https://doi.org/10.1038/s41566-024-01444-9]

 

3 Comsol Multiphysics models containing information and postprocessed values of SHG spectra, and SHG polarization plots for a triangular hole metasurface, circular hole metasurface, and the bare 3R-MoS2 flake. All the geometrical properties are as described in the main text.

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NB!:To correctly run a simulation please check the location of the browsed files in the interpolation of the nxx, nzz.

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- SHG film is a model consisting of rectangular geometry with 2 periodic boundary planes - xz, and yz (walls), representing periodiciy in x and y direction. Cell is quadratic, even though the model calculates the SHG response of the bare 3R-MoS2. This is made to correctly compare the SHG intensity with the metasurface cases.

  The model has two ports - plane wave excitation (upper one) and collection (bottom). The first electromegnetic waves physics (ewfd) calculates the Electromagnetic field distribution in the computational domain, specifically in the 3R-MoS2 material.

  The second physics operates at the doubled frequency (\lambda/2) by using the induced nonlinearity which roughly can be described as P(2\omega) ~ chi2*E^2(\omega). The induced nonlinearity and SHG emission is governed by chi2 tensor and the E-field distribution at the fundamental wavelength.

  The nonlinearity is described through nonlinear current components in the second physics in the 3R-MoS2 material.

  To run a simulation select a parametric sweep over parameters of interest. The Poynting vector analysis for polarization purposes (with a given Jones matrix). The SHG intensity and efficiency are extracted from the Derived values section (global evaluation and/or integrations). Please check the variables section to determine the values of interest.

The SHG tri and SHG circ models are similar to the master model, but they have triangular and circular holes, respectively, in the 3R-MoS2 layer, serving as unit cells for the periodic array.