Simulation Results Problem about Electric Field Perpendicular to Grating Wire

[QifengHu]

Hi guys,

After investigating electric field parallel to grating wires with normal incidence, I simply change the direction of the electric field (Ez) into (Ey) to study the performance of the field perpendicular to grating wires. However, the results are unexpected in these 2D simulations, as followed,

To our knowledge, wire grid polarizers transmit radiation with an electric field vector perpendicular to the wire and reflect radiation with the electric field vector parallel to the wire.
The results are not in an agreement with the statement.

I attached our code at the bottom, Could you help us check if there is anything required to be adjusted? Or, is there any knowledge that could explain the results.

Thank you,
Qifeng

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
import meep as mp
import math
import numpy as np
import matplotlib.pyplot as plt
from meep.materials import SiO2, Ag
# valid wavelength range: (0.25, 1.77)
import pandas as pd

# Setup parameters are unchanged
resolution = 200
dpml = 1.0
dSiO2 = 10
gh = 0.03
gp = 0.5
dpad = 10

gdc = 0.5
s_height = 8
r_height = 6
t_depth = 8

sx = 2 * dpml + dSiO2 + gh + dpad
sy = gp

sio2_idx = 1.55
silica = mp.Medium(index=sio2_idx)
dt     = 50

cell_size = mp.Vector3(sx, sy, 0)
pml_layers = [mp.PML(thickness=dpml, direction=mp.X)]

wvl_min = 0.8
wvl_max = 5.0
fmin = 1 / wvl_max
fmax = 1 / wvl_min

fcen = 0.5 * (fmax + fmin)
df = fmax - fmin
nfreq = 100

source_height = -sx / 2 + dpml + dSiO2 + 1 * gh + s_height
sources = [
    mp.Source(mp.GaussianSource(fcen, fwidth=df),
              component=mp.Ey,
              center=mp.Vector3(x=source_height),
              size=mp.Vector3(y=sy))
]

k_point = mp.Vector3(0, 0, 0)
symmetries = [mp.Mirror(mp.Y)]

# Initialize the simulation
sim = mp.Simulation(cell_size=cell_size,
                    boundary_layers=pml_layers,
                    sources=sources,
                    k_point=k_point,
                    symmetries=symmetries,
                    resolution=resolution)

# Add flux monitor for reflectance

#Creation of a FluxRegion centered at 
ref_height = -sx / 2 + dpml + dSiO2 + 1 * gh + r_height
refl_fr =  mp.FluxRegion(center=mp.Vector3(x=ref_height), size=mp.Vector3(y=sy))
refl_mon = sim.add_flux(fcen, df, nfreq, refl_fr)

trans_height =  -sx / 2 + dpml + dSiO2 + gh - t_depth
trans_fr = mp.FluxRegion(center=mp.Vector3(x=trans_height), size=mp.Vector3(y=sy))
trans_mon = sim.add_flux(fcen, df, nfreq, trans_fr)

#f=plt.figure(dpi=120)
#sim.plot2D(ax=f.gca())
#plt.show()

# Run the simulation
sim.run(until_after_sources=mp.stop_when_fields_decayed(dt, mp.Ey, mp.Vector3(x=trans_height), 1e-8))

# Calculate reflected flux
empty_flux = mp.get_fluxes(refl_mon)
empty_data = sim.get_flux_data(refl_mon) # store the Flux Data from the EMPTY RUN into "empty_data"

#empty_trans_flux = mp.get_fluxes(trans_mon)
#empty_trans_data = sim.get_flux_data(trans_mon)

sim.reset_meep()


# Redefine the geometry including any layers, blocks, etc.
geometry = [
    mp.Block(
        mp.Vector3(dpml + dSiO2, mp.inf, mp.inf),
        center=mp.Vector3(-sx / 2 + 0.5* dpml + 0.5 * dSiO2),
        material=silica#SiO2
    ),
    mp.Block(
        mp.Vector3(gh, gdc * gp, mp.inf),
        center=mp.Vector3(-sx / 2 + dpml + dSiO2 + 0.5 * gh),
        material=Ag
    )
]

# Reinitialize the simulation with the same parameters but updated geometry
sim = mp.Simulation(
    resolution=resolution,
    cell_size=cell_size,
    boundary_layers=pml_layers,
    geometry=geometry,
    k_point=k_point,
    sources=sources,
    symmetries=symmetries
)

#sim.plot2D(fields=mp.Ey,
#           field_parameters={'alpha':0.8, 'cmap':'RdBu', 'interpolation':'none'},
#           boundary_parameters={'hatch':'o', 'linewidth':1.5, 'facecolor':'y', 'edgecolor':'b', 'alpha':0.3})
#plt.show()
#adding the FluxRegion "refl_fr" to the simulation
refl = sim.add_flux(fcen, df, nfreq, refl_fr)
trans = sim.add_flux(fcen, df, nfreq, trans_fr)

#f = plt.figure(dpi=120)
#ax=f.gca()
#sim.plot2D(ax=ax)
#ax.set_aspect(10)
#plt.show()


#Load the EMPTY RUN Flux Data using .load_minus_flux_data to SUBTRACT the fluxes from the next run.
# (Basically removing the empty run fluxes to leave only the reflectance)
sim.load_minus_flux_data(refl, empty_data)
# sim.load_minus_flux_data(trans, empty_trans_data)


# Run the simulation
sim.run(#mp.at_beginning(mp.output_epsilon), 
        until_after_sources=mp.stop_when_fields_decayed(dt, mp.Ey, mp.Vector3(x=trans_height), 1e-8))


refl_flux = mp.get_fluxes(refl) # store the flux data of the Second run in "refl_flux"
R_meep = -1*np.divide(refl_flux,empty_flux) #calculate the reflectance from MEEP simulation runs

trans_flux = mp.get_fluxes(trans)
T_meep = np.divide(trans_flux, empty_flux)
# Reset the simulation to reuse the structure and source definition
sim.reset_meep()







freqs = mp.get_flux_freqs(refl)
wvls = np.divide(1,freqs)

# post_process
if mp.am_really_master() == True:
    legend_text = [
        f"SiO2 refractive index: {sio2_idx}",
        f"Thickness of SiO2: {dSiO2}μm",
        f"Thickness of Ag: {gh}μm",
        f"Grating Period: {gp}μm",
        "Metal:Dielectric width ratio: {}".format(gdc),
        "Resolution: {} pixels/μm;".format(resolution),
        "Source Height: {} μm".format(s_height),
        "Flux Region Height of Reflectance: {} μm".format(r_height),
        "Flux Region Depth of Transmittance: {} μm".format(t_depth),
        f'Wavelength range: [{wvl_min}, {wvl_max}]',
        f'Number of frequency: {nfreq}',
    ]

    # Combine into a single string with newline characters
    legend_label = '\n'.join(legend_text)

    df = pd.DataFrame({"Wavelength": wvls, "Reflectance": R_meep, "Transimittance": T_meep})
    df.to_csv(f"data/silica{sio2_idx}_wvls{wvl_min}_{wvl_max}_n{nfreq}_R_T_ratio{gdc}_dSiO2{dSiO2}_SourceH{s_height}_FluxRegionH_R{r_height}_T{t_depth}_{resolution}px_converge{dt}.csv")

    # Create the figure and the first axis
    fig, ax = plt.subplots()
    ax.plot(wvls,R_meep,'bo-', label = 'Reflectance')
    ax.plot(wvls, T_meep, 'ro-', label = "Transmittance")
    ax.plot(wvls, R_meep+T_meep, 'k--', label='R+T')
    ax.set_xlabel("Wavelength (μm)")
    ax.set_ylabel("Power Percentage")
    ax.legend(frameon=False)
    ax.set_ylim([0.,1.])
    ax.set_xlim([0.2,5.1])    
    fig.set_size_inches(9,4)
    plt.figtext(0.7, 0.2, legend_label, wrap=True, horizontalalignment='left', fontsize=12)
    plt.subplots_adjust(right=0.65)
    
        # Show the plot
    plt.title(f"SiO2 refractive index: {sio2_idx}")
    plt.savefig(f"pic/silica_effect_of_refraidx{sio2_idx}_EPerp2Line_spaceratio{gdc}_SourceH{s_height}_ReflFluxH{r_height}_TranFluxH{t_depth}_{resolution}px.png")
    plt.show()

[mochen4]

When you use Ey polarization, you also need to change the symmetry to symmetries = [mp.Mirror(mp.Y, phase=-1)].

[YIF27]

Thanks very much! I really appreciate your time and support, Mo! The result looks more reasonable now.