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import math
import matplotlib.pyplot as plt
import numpy as np
from numpy import linalg as LA
import meep as mp
resolution = 25 # pixels/μm
dpml = 1.0 # PML thickness
dsub = 3.0 # substrate thickness
dpad = 3.0 # padding between grating and PML
gp = 10.0 # grating period
gh = 0.5 # grating height
gdc = 0.5 # grating duty cycle
nperiods = 10 # number of unit cells in finite periodic grating
ff_distance = 1e8 # far-field distance from near-field monitor
ff_angle = 20 # far-field cone angle
ff_npts = 500 # number of far-field points
ff_length = ff_distance * math.tan(math.radians(ff_angle))
ff_res = ff_npts / ff_length
sx = dpml + dsub + gh + dpad + dpml
cell_size = mp.Vector3(sx)
pml_layers = [mp.PML(thickness=dpml, direction=mp.X)]
symmetries = [mp.Mirror(mp.Y)]
wvl_min = 0.4 # min wavelength
wvl_max = 0.6 # max wavelength
fmin = 1 / wvl_max # min frequency
fmax = 1 / wvl_min # max frequency
fcen = 0.5 * (fmin + fmax) # center frequency
df = fmax - fmin # frequency width
src_pt = mp.Vector3(-0.5 * sx + dpml + 0.5 * dsub)
sources = [
mp.Source(mp.GaussianSource(fcen, fwidth=df), component=mp.Ez, center=src_pt)
]
k_point = mp.Vector3()
glass = mp.Medium(index=1.5)
sim = mp.Simulation(
resolution=resolution,
cell_size=cell_size,
boundary_layers=pml_layers,
k_point=k_point,
default_material=glass,
sources=sources,
)
nfreq = 21
n2f_pt = mp.Vector3(0.5 * sx - dpml - 0.5 * dpad)
n2f_obj = sim.add_near2far(fcen, df, nfreq, mp.Near2FarRegion(center=n2f_pt))
sim.run(until_after_sources=mp.stop_when_fields_decayed(50, mp.Ez, n2f_pt, 1e-9))
ff_source = sim.get_farfields(
n2f_obj,
ff_res,
center=mp.Vector3(ff_distance, 0.5 * ff_length),
size=mp.Vector3(y=ff_length),
)
sim.reset_meep()
### unit cell with periodic boundaries
sy = gp
cell_size = mp.Vector3(sx, sy)
sources = [
mp.Source(
mp.GaussianSource(fcen, fwidth=df, 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)),
),
mp.Block(
material=glass,
size=mp.Vector3(gh, gdc * gp, mp.inf),
center=mp.Vector3(-0.5 * sx + dpml + dsub + 0.5 * gh),
),
]
sim = mp.Simulation(
resolution=resolution,
split_chunks_evenly=True,
cell_size=cell_size,
boundary_layers=pml_layers,
geometry=geometry,
k_point=k_point,
sources=sources,
symmetries=symmetries,
)
n2f_obj = sim.add_near2far(
fcen,
df,
nfreq,
mp.Near2FarRegion(center=n2f_pt, size=mp.Vector3(y=sy)),
nperiods=nperiods,
)
sim.run(until_after_sources=mp.stop_when_fields_decayed(50, mp.Ez, n2f_pt, 1e-9))
ff_unitcell = sim.get_farfields(
n2f_obj,
ff_res,
center=mp.Vector3(ff_distance, 0.5 * ff_length),
size=mp.Vector3(y=ff_length),
)
sim.reset_meep()
### finite periodic grating with flat surface termination extending into PML
num_cells = 2 * nperiods + 1
sy = dpml + num_cells * gp + dpml
cell_size = mp.Vector3(sx, sy)
pml_layers = [mp.PML(thickness=dpml)]
sources = [
mp.Source(
mp.GaussianSource(fcen, fwidth=df, 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)),
)
]
for j in range(num_cells):
geometry.append(
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 + (j + 0.5) * gp
),
)
)
sim = mp.Simulation(
resolution=resolution,
split_chunks_evenly=True,
cell_size=cell_size,
boundary_layers=pml_layers,
geometry=geometry,
k_point=k_point,
sources=sources,
symmetries=symmetries,
)
n2f_obj = sim.add_near2far(
fcen, df, nfreq, mp.Near2FarRegion(center=n2f_pt, size=mp.Vector3(y=sy - 2 * dpml))
)
sim.run(until_after_sources=mp.stop_when_fields_decayed(50, mp.Ez, n2f_pt, 1e-9))
ff_supercell = sim.get_farfields(
n2f_obj,
ff_res,
center=mp.Vector3(ff_distance, 0.5 * ff_length),
size=mp.Vector3(y=ff_length),
)
norm_err = LA.norm(ff_unitcell["Ez"] - ff_supercell["Ez"]) / nperiods
print(f"error:, {nperiods}, {norm_err}")
freqs = mp.get_near2far_freqs(n2f_obj)
wvl = np.divide(1, freqs)
ff_lengths = np.linspace(0, ff_length, ff_npts)
angles = [math.degrees(math.atan(f)) for f in ff_lengths / ff_distance]
wvl_slice = 0.5
idx_slice = np.where(np.asarray(freqs) == 1 / wvl_slice)[0][0]
rel_enh = np.absolute(ff_unitcell["Ez"]) ** 2 / np.absolute(ff_source["Ez"]) ** 2
plt.figure(dpi=150)
plt.subplot(1, 2, 1)
plt.pcolormesh(wvl, angles, rel_enh, cmap="Blues", shading="flat")
plt.axis([wvl_min, wvl_max, 0, ff_angle])
plt.xlabel("wavelength (μm)")
plt.ylabel("angle (degrees)")
plt.grid(linewidth=0.5, linestyle="--")
plt.xticks([t for t in np.arange(wvl_min, wvl_max + 0.1, 0.1)])
plt.yticks([t for t in range(0, ff_angle + 1, 10)])
plt.title("far-field spectra")
plt.subplot(1, 2, 2)
plt.plot(angles, rel_enh[:, idx_slice], "bo-")
plt.xlim(0, ff_angle)
plt.ylim(0)
plt.xticks([t for t in range(0, ff_angle + 1, 10)])
plt.xlabel("angle (degrees)")
plt.ylabel("relative enhancement")
plt.grid(axis="x", linewidth=0.5, linestyle="--")
plt.title(f"f.-f. spectra @ λ = {wvl_slice:.1} μm")
plt.tight_layout(pad=0.5)
plt.show()
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