
DOI: 10.7795/710.20220601		
title:	Simulation data for "Examining and explaining the “Generalized Laws of Reflection and Refraction” at metasurface gratings"

summary: 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.

creators: Markus Schake https://orcid.org/0000-0002-9883-3494 (1)
1) Physikalisch-Technische Bundesanstalt,
Bundesallee 100,
38116 Braunschweig
OE 4.22

license:	CC-BY 4.0 International

keywords:    light interference ; light diffraction ; metasurfaces ; geometrical optics ; physical optics (wave optics) ; light propagation ; light transmission ; diffraction gratings

classification:  OCIS 260.1960 Diffraction theory; OCIS 160.3918 Metamaterials; OCIS 070.2580 Paraxial wave optics; OCIS 260.3160 Interference; OCIS 350.2770 Gratings

funder:	There is no funding for this research

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