Title: Simulation data for "Examining and explaining the “Generalized Laws of Reflection and Refraction” at metasurface gratings"
Authors: Schake, Markus, Physikalisch-Technische Bundesanstalt (PTB), Fachbereich 4.2, Bild- und Wellenoptik, ORCID: 0000-0002-9883-3494
Contributors: HostingInstitution: Physikalisch-Technische Bundesanstalt (PTB), ISNI: 0000 0001 2186 1887
Language:en
DOI:10.7795/710.20220601
Resource Type: Dataset / Simulation Data
Publisher: Physikalisch-Technische Bundesanstalt (PTB)
Rights: https://creativecommons.org/licenses/by/4.0/
CC-BY 4.0 International
Dates: Available: 2022-06-02
Created: 2022-06-01
Classifications: OCIS 260.1960 Diffraction theory ; OCIS 160.3918 Metamaterials ; OCIS 070.2580 Paraxial wave optics ; OCIS 260.3160 Interference ; OCIS 350.2770 Gratings
File: Download File (application/zip) 1.28 MB (1347314 Bytes)
MD5 Checksum: 4859118beef7129b36bceb72e2bfab95
SHA256 Checksum: 8e37edb0052c5251294a25fe25e681bc9fec0189076eecdbe4b7e023fed5db32
Keywords: light interference ; light diffraction ; metasurfaces ; geometrical optics ; physical optics (wave optics) ; light propagation ; light transmission ; diffraction gratings
Abstract: The provided simulation software enables the immediate replication of the results presented in "Examining and explaining the “Generalized Laws of Reflection and Refraction” at metasurface gratings" and its supplemental materials.

The simulation data are structured with respect to the figures presented in the contribution. Each subfolder contains all necessary simulation data to receive the figure from the contribution by running a MATLAB file. Therefore, it is possible to compare the results with full context to those presented in the contribution.

The simulations demonstrate the far field intensity distribution obtained by diffraction theory for metasurface gratings with varying design parameters.
Other: Recommended software to open the data:recommended software to open the data: MATLAB R2016b, Python (https://docs.scipy.org/doc/scipy/reference/generated/scipy.io.loadmat.html)
- The files with extension *.m contain the simulation code and require MATLAB to be executed. However, they may be opened in a text editor to view the code.
- The files with extension *.mat contain the simulation results and may be opened with MATLAB, but may also be imported into Python and transfered into alternative data formats like *.h5.

Description of the individual files:
Each subfolder refers to a figure in the contribution and contains
- a "*.m" file to be executed in MATLAB, which will generate the associated figure and contains the commented implementation of the simulation,
- as well as a "*.mat" file, which contains the parameter values and simulation results of the dataset which is plotted in the article.

Each "*.mat" file contains the following parameters:
-Theta_m -> Angle of the incident wave [degrees]
-n_1 -> Refractive index of the first medium
-n_2 -> Refrective index of the second medium (air)
-lambda -> Wavelength in vacuum [µm]
-P -> Number of periodes in x_1 direction
-Gamma_array -> Grating period of the phase shift pattern [µm]
-Q -> Number of resonators per periode
-p_B -> Design parameter for the phase gradient
-ratio -> Parameter determining the ratio of the total interface covered by the antenna resonators

Details of the single subfolders/figures:

Fig_1_b_Normalized_interference_function_farfield_distribution: Contains the analytical and numerical simulation for the far field diffraction pattern of the metasurface described in the article.
The '*.mat' file contains:
-xi_analytic_transmission -> This is the spatial frequency evolution in the observation plane
-nif_transmission -> The far field distribution of the normalized interference function for transmission
-ifs_transmission -> The far field distribution of the normalized intensity function of a single grating period/slit/motif for transmission

Fig_S1_a_Gratingperiod_variation_diffraction_angle: Contains a simulation for consideration of the changes in the gratings far field distribution when manipulating the grating period.
The '*.mat' file contains:
-xangle -> Angular position vector for the far field distribution of numerical results
-I_x_2_T_R_array -> Far field intensity distribution determined with numerical method for transmission
-xangle_analytic -> Angular position vector for the far field distribution of analytical results
-I_x2_analytic_transmission -> Far field intensity distribution determined with analytical method for transmission
-blazed_grating_angle_transmission -> Refraction angles predicted by "Generalized Snell's law" for transmisson

Fig_S1_b_Incidenceangle_variation_diffraction_angle: Contains a simulation for consideration of the changes in the gratings far field distribution when manipulating the angle of incidence of the incoming wave.
The '*.mat' file contains:
-refraction_angle_rig -> Refraction angles calculated from the numerical model
-refraction_angle_ana -> Refraction angles calculated with the analytical model
-blazed_grating_angle_transmission -> Refraction angles predicted by "Generalized Snell's law" for transmisson

Fig_S2_a_Noninteger_phase_gradient_side_lobes_visibility: Contains a simulation for consideration of the changes in the gratings far field distribution when changing the linear phase gradient on the grating periods to a non integer multiple of 2Pi.
The '*.mat' file contains:
-xangle -> Angular position vector for the far field distribution of numerical results
-I_x_2_T_R_array -> Far field intensity distribution determined with numerical method for transmission
-xangle_analytic -> Angular position vector for the far field distribution of analytical results
-I_x2_analytic_transmission -> Far field intensity distribution determined with analytical method for transmission
-blazed_grating_angle_transmission -> Refraction angles predicted by "Generalized Snell's law" for transmisson

Fig_S2_b_Nonlinear_phase_gradient_side_lobes_visibility: Contains a simulation for consideration of the changes in the gratings far field distribution when having a nonlinear phase gradient caused by a not equidistant resonator spacing along the grating interface.
The '*.mat' file contains:
-xangle -> Angular position vector for the far field distribution of numerical results
-I_x_2_T_R_array -> Far field intensity distribution determined with numerical method for transmission