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import math
import matplotlib
matplotlib.use("agg")
import matplotlib.pyplot as plt
import numpy as np
import meep as mp
resolution = 50 # pixels/um
sxy = 4
dpml = 1
cell = mp.Vector3(sxy + 2 * dpml, sxy + 2 * dpml)
pml_layers = [mp.PML(dpml)]
fcen = 1.0
df = 0.4
src_cmpt = mp.Ex
sources = [
mp.Source(
src=mp.GaussianSource(fcen, fwidth=df), center=mp.Vector3(), component=src_cmpt
)
]
if src_cmpt == mp.Ex:
symmetries = [mp.Mirror(mp.X, phase=-1), mp.Mirror(mp.Y, phase=+1)]
elif src_cmpt == mp.Ey:
symmetries = [mp.Mirror(mp.X, phase=+1), mp.Mirror(mp.Y, phase=-1)]
elif src_cmpt == mp.Ez:
symmetries = [mp.Mirror(mp.X, phase=+1), mp.Mirror(mp.Y, phase=+1)]
else:
symmetries = []
sim = mp.Simulation(
cell_size=cell,
resolution=resolution,
sources=sources,
symmetries=symmetries,
boundary_layers=pml_layers,
)
nearfield_box = sim.add_near2far(
fcen,
0,
1,
mp.Near2FarRegion(center=mp.Vector3(0, +0.5 * sxy), size=mp.Vector3(sxy, 0)),
mp.Near2FarRegion(
center=mp.Vector3(0, -0.5 * sxy), size=mp.Vector3(sxy, 0), weight=-1
),
mp.Near2FarRegion(center=mp.Vector3(+0.5 * sxy, 0), size=mp.Vector3(0, sxy)),
mp.Near2FarRegion(
center=mp.Vector3(-0.5 * sxy, 0), size=mp.Vector3(0, sxy), weight=-1
),
)
flux_box = sim.add_flux(
fcen,
0,
1,
mp.FluxRegion(center=mp.Vector3(0, +0.5 * sxy), size=mp.Vector3(sxy, 0)),
mp.FluxRegion(center=mp.Vector3(0, -0.5 * sxy), size=mp.Vector3(sxy, 0), weight=-1),
mp.FluxRegion(center=mp.Vector3(+0.5 * sxy, 0), size=mp.Vector3(0, sxy)),
mp.FluxRegion(center=mp.Vector3(-0.5 * sxy, 0), size=mp.Vector3(0, sxy), weight=-1),
)
sim.run(until_after_sources=mp.stop_when_dft_decayed())
near_flux = mp.get_fluxes(flux_box)[0]
# half side length of far-field square box OR radius of far-field circle
r = 1000 / fcen
# resolution of far fields (points/μm)
res_ff = 1
far_flux_box = (
nearfield_box.flux(
mp.Y, mp.Volume(center=mp.Vector3(y=r), size=mp.Vector3(2 * r)), res_ff
)[0]
- nearfield_box.flux(
mp.Y, mp.Volume(center=mp.Vector3(y=-r), size=mp.Vector3(2 * r)), res_ff
)[0]
+ nearfield_box.flux(
mp.X, mp.Volume(center=mp.Vector3(r), size=mp.Vector3(y=2 * r)), res_ff
)[0]
- nearfield_box.flux(
mp.X, mp.Volume(center=mp.Vector3(-r), size=mp.Vector3(y=2 * r)), res_ff
)[0]
)
npts = 100 # number of points in [0,2*pi) range of angles
angles = 2 * math.pi / npts * np.arange(npts)
E = np.zeros((npts, 3), dtype=np.complex128)
H = np.zeros((npts, 3), dtype=np.complex128)
for n in range(npts):
ff = sim.get_farfield(
nearfield_box, mp.Vector3(r * math.cos(angles[n]), r * math.sin(angles[n]))
)
E[n, :] = [ff[j] for j in range(3)]
H[n, :] = [ff[j + 3] for j in range(3)]
Px = np.real(np.conj(E[:, 1]) * H[:, 2] - np.conj(E[:, 2]) * H[:, 1])
Py = np.real(np.conj(E[:, 2]) * H[:, 0] - np.conj(E[:, 0]) * H[:, 2])
Pr = np.sqrt(np.square(Px) + np.square(Py))
# integrate the radial flux over the circle circumference
far_flux_circle = np.sum(Pr) * 2 * np.pi * r / len(Pr)
print(f"flux:, {near_flux:.6f}, {far_flux_box:.6f}, {far_flux_circle:.6f}")
# Analytic formulas for the radiation pattern as the Poynting vector
# of an electric dipole in vacuum. From Section 4.2 "Infinitesimal Dipole"
# of Antenna Theory: Analysis and Design, 4th Edition (2016) by C. Balanis.
if src_cmpt == mp.Ex:
flux_theory = np.sin(angles) ** 2
elif src_cmpt == mp.Ey:
flux_theory = np.cos(angles) ** 2
elif src_cmpt == mp.Ez:
flux_theory = np.ones((npts,))
fig, ax = plt.subplots(subplot_kw={"projection": "polar"}, figsize=(6, 6))
ax.plot(angles, Pr / max(Pr), "b-", label="Meep")
ax.plot(angles, flux_theory, "r--", label="theory")
ax.set_rmax(1)
ax.set_rticks([0, 0.5, 1])
ax.grid(True)
ax.set_rlabel_position(22)
ax.legend()
if mp.am_master():
fig.savefig(
f"radiation_pattern_{mp.component_name(src_cmpt)}.png",
dpi=150,
bbox_inches="tight",
)
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