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import math
import matplotlib.pyplot as plt
import numpy as np
import meep as mp
# True: plot the scattered fields in the extended air region adjacent to the grating
# False: plot the diffraction spectra based on a 1d cross section of the scattered fields
field_profile = True
resolution = 50 # pixels/μm
dpml = 1.0 # PML thickness
dsub = 2.0 # substrate thickness
dpad = 1.0 # flat-surface padding
gp = 1.0 # grating periodicity
gh = 0.5 # grating height
gdc = 0.5 # grating duty cycle
num_cells = 5 # number of grating unit cells
# air region thickness adjacent to grating
dair = 10 if field_profile else dpad
wvl = 0.5 # center wavelength
fcen = 1 / wvl # center frequency
k_point = mp.Vector3()
glass = mp.Medium(index=1.5)
pml_layers = [mp.PML(thickness=dpml)]
symmetries = [mp.Mirror(mp.Y)]
sx = dpml + dsub + gh + dair + dpml
sy = dpml + dpad + num_cells * gp + dpad + dpml
cell_size = mp.Vector3(sx, sy)
src_pt = mp.Vector3(-0.5 * sx + dpml + 0.5 * dsub)
sources = [
mp.Source(
mp.GaussianSource(fcen, fwidth=0.2 * fcen, is_integrated=True),
component=mp.Ez,
center=src_pt,
size=mp.Vector3(y=sy),
)
]
geometry = [
mp.Block(
material=glass,
size=mp.Vector3(dpml + dsub, mp.inf, mp.inf),
center=mp.Vector3(-0.5 * sx + 0.5 * (dpml + dsub)),
)
]
sim = mp.Simulation(
resolution=resolution,
cell_size=cell_size,
boundary_layers=pml_layers,
geometry=geometry,
k_point=k_point,
sources=sources,
symmetries=symmetries,
)
mon_pt = mp.Vector3(0.5 * sx - dpml - 0.5 * dair)
near_fields = sim.add_dft_fields(
[mp.Ez],
fcen,
0,
1,
center=mon_pt,
size=mp.Vector3(dair if field_profile else 0, sy - 2 * dpml),
)
sim.run(until_after_sources=100)
flat_dft = sim.get_dft_array(near_fields, mp.Ez, 0)
sim.reset_meep()
geometry.extend(
mp.Block(
material=glass,
size=mp.Vector3(gh, gdc * gp, mp.inf),
center=mp.Vector3(
-0.5 * sx + dpml + dsub + 0.5 * gh, -0.5 * sy + dpml + dpad + (j + 0.5) * gp
),
)
for j in range(num_cells)
)
sim = mp.Simulation(
resolution=resolution,
cell_size=cell_size,
boundary_layers=pml_layers,
geometry=geometry,
k_point=k_point,
sources=sources,
symmetries=symmetries,
)
near_fields = sim.add_dft_fields(
[mp.Ez],
fcen,
0,
1,
center=mon_pt,
size=mp.Vector3(dair if field_profile else 0, sy - 2 * dpml),
)
sim.run(until_after_sources=100)
grating_dft = sim.get_dft_array(near_fields, mp.Ez, 0)
scattered_field = grating_dft - flat_dft
scattered_amplitude = np.abs(scattered_field) ** 2
[x, y, z, w] = sim.get_array_metadata(dft_cell=near_fields)
if field_profile:
if mp.am_master():
plt.figure(dpi=150)
plt.pcolormesh(
x,
y,
np.rot90(scattered_amplitude),
cmap="inferno",
shading="gouraud",
vmin=0,
vmax=scattered_amplitude.max(),
)
plt.gca().set_aspect("equal")
plt.xlabel("x (μm)")
plt.ylabel("y (μm)")
# ensure that the height of the colobar matches that of the plot
from mpl_toolkits.axes_grid1 import make_axes_locatable
divider = make_axes_locatable(plt.gca())
cax = divider.append_axes("right", size="5%", pad=0.05)
plt.colorbar(cax=cax)
plt.tight_layout()
plt.show()
else:
ky = np.fft.fftshift(np.fft.fftfreq(len(scattered_field), 1 / resolution))
FT_scattered_field = np.fft.fftshift(np.fft.fft(scattered_field))
if mp.am_master():
plt.figure(dpi=150)
plt.subplots_adjust(hspace=0.3)
plt.subplot(2, 1, 1)
plt.plot(y, scattered_amplitude, "bo-")
plt.xlabel("y (μm)")
plt.ylabel("field amplitude")
plt.subplot(2, 1, 2)
plt.plot(ky, np.abs(FT_scattered_field) ** 2, "ro-")
plt.gca().ticklabel_format(axis="y", style="sci", scilimits=(0, 0))
plt.xlabel(r"wavevector k$_y$, 2π (μm)$^{-1}$")
plt.ylabel("Fourier transform")
plt.gca().set_xlim([-3, 3])
plt.tight_layout(pad=1.0)
plt.show()
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