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"""A demonstration of computing the flux emitted in a single direction from a
collection of dipole emitters in an LED-like structure using reciprocity.
"""
from typing import List
import numpy as np
import matplotlib.pyplot as plt
import meep as mp
from meep.materials import Ag
resolution = 200 # pixels/μm
nfreq = 100 # number of frequencies
ndipole = 10 # number of point dipoles in forward simulation
fcen = 1.0 # center frequency of Gaussian source/monitors
df = 0.2 # frequency bandwidth of source/monitors
dpml = 1.0 # PML thickness
dair = 2.0 # air padding thickness
hrod = 0.7 # grating height
wrod = 0.5 # graing width
dsub = 5.0 # substrate thickness
dAg = 0.5 # Ag back reflecter thickness
sx = 1.1
sy = dpml + dair + hrod + dsub + dAg
cell_size = mp.Vector3(sx, sy)
pml_layers = [mp.PML(direction=mp.Y, thickness=dpml, side=mp.High)]
def substrate_geometry(is_textured: bool):
"""Returns the geometry of the LED-like structure.
Args:
is_textured: whether the substrate is textured or not.
"""
geometry = [
mp.Block(
material=mp.Medium(index=3.45),
center=mp.Vector3(0, 0.5 * sy - dpml - dair - hrod - 0.5 * dsub),
size=mp.Vector3(mp.inf, dsub, mp.inf),
),
mp.Block(
material=Ag,
center=mp.Vector3(0, -0.5 * sy + 0.5 * dAg),
size=mp.Vector3(mp.inf, dAg, mp.inf),
),
]
if is_textured:
geometry.append(
mp.Block(
material=mp.Medium(index=3.45),
center=mp.Vector3(0, 0.5 * sy - dpml - dair - 0.5 * hrod),
size=mp.Vector3(wrod, hrod, mp.inf),
)
)
return geometry
def forward(n: int, rt: int, is_textured: bool) -> [List, np.ndarray]:
"""Computes the Poynting flux in the +y direction in air
given a point dipole source positioned somewhere along a
line in the middle of the high-index substrate.
Args:
n: n'th position along a line of equally spaced dipoles.
rt: runtime of simulation after the source has turned off
in units of nfreq/df.
is_textured: whether the substrate is textured or not.
Returns:
The frequency and Poynting flux spectra.
"""
sources = [
mp.Source(
mp.GaussianSource(fcen, fwidth=df),
component=mp.Ez,
center=mp.Vector3(
sx * (-0.5 + n / ndipole),
-0.5 * sy + dAg + 0.5 * dsub,
),
)
]
geometry = substrate_geometry(is_textured)
sim = mp.Simulation(
cell_size=cell_size,
resolution=resolution,
k_point=mp.Vector3(),
boundary_layers=pml_layers,
geometry=geometry,
sources=sources,
)
flux_mon = sim.add_flux(
fcen,
df,
nfreq,
mp.FluxRegion(center=mp.Vector3(0, 0.5 * sy - dpml), size=mp.Vector3(sx)),
)
run_time = rt * nfreq / df
sim.run(until_after_sources=run_time)
res = sim.get_eigenmode_coefficients(flux_mon, [1], eig_parity=mp.ODD_Z)
flux = np.abs(res.alpha[0, :, 0]) ** 2
freqs = mp.get_flux_freqs(flux_mon)
return freqs, flux
def backward(rt: int, is_textured: bool) -> [List, np.ndarray]:
"""Computes the Poynting flux spectrum of the dipole emission using
an overlap integral of the DFT fields from a line monitor in the
high-index substrate given a planewave source in air propagating
in the -y direction.
Args:
rt: runtime of simulation after the source has turned off
in units of nfreq/df.
is_textured: whether the substrate is textured or not.
Returns:
The frequency and Poynting flux spectra.
"""
sources = [
mp.Source(
mp.GaussianSource(fcen, fwidth=df),
component=mp.Ez,
center=mp.Vector3(0, 0.5 * sy - dpml),
size=mp.Vector3(sx, 0),
)
]
geometry = substrate_geometry(is_textured)
sim = mp.Simulation(
cell_size=cell_size,
resolution=resolution,
k_point=mp.Vector3(),
boundary_layers=pml_layers,
geometry=geometry,
sources=sources,
)
dft_mon = sim.add_dft_fields(
[mp.Ez],
fcen,
df,
nfreq,
center=mp.Vector3(0, -0.5 * sy + dAg + 0.5 * dsub),
size=mp.Vector3(sx),
)
run_time = rt * nfreq / df
sim.run(until_after_sources=run_time)
freqs = mp.get_flux_freqs(dft_mon)
abs_flux = np.zeros(nfreq)
for nf in range(nfreq):
dft_ez = sim.get_dft_array(dft_mon, mp.Ez, nf)
abs_flux[nf] = np.sum(np.abs(dft_ez) ** 2)
return freqs, abs_flux
if __name__ == "__main__":
fwd_flat_flux = np.zeros((nfreq, ndipole))
fwd_text_flux = np.zeros((nfreq, ndipole))
for d in range(ndipole):
fwd_freqs, fwd_flat_flux[:, d] = forward(d, 2, False)
_, fwd_text_flux[:, d] = forward(d, 4, True)
fwd_norm_flux = np.mean(fwd_text_flux, axis=1) / np.mean(fwd_flat_flux, axis=1)
bwd_freqs, bwd_flat_flux = backward(2, False)
_, bwd_text_flux = backward(4, True)
bwd_norm_flux = bwd_text_flux / bwd_flat_flux
plt.figure()
plt.semilogy(fwd_freqs, fwd_norm_flux, "b-", label="forward")
plt.semilogy(bwd_freqs, bwd_norm_flux, "r-", label="backward")
plt.xlabel("frequency")
plt.ylabel("normalized flux")
plt.legend()
if mp.am_master():
plt.savefig(
"forward_vs_backward_flux_spectrum.png",
bbox_inches="tight",
dpi=150,
)
|
