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import matplotlib.pyplot as plt
import numpy as np
import PyMieScatt as ps
import meep as mp
r = 1.0 # radius of sphere
frq_cen = 1.0
resolution = 20 # pixels/um
dpml = 0.5
dair = 1.5 # at least 0.5/frq_cen padding between source and near-field monitor
pml_layers = [mp.PML(thickness=dpml)]
s = 2 * (dpml + dair + r)
cell_size = mp.Vector3(s, s, s)
# circularly-polarized source with propagation axis along x
# is_integrated=True necessary for any planewave source extending into PML
sources = [
mp.Source(
mp.GaussianSource(frq_cen, fwidth=0.2 * frq_cen, is_integrated=True),
center=mp.Vector3(-0.5 * s + dpml),
size=mp.Vector3(0, s, s),
component=mp.Ez,
),
mp.Source(
mp.GaussianSource(frq_cen, fwidth=0.2 * frq_cen, is_integrated=True),
center=mp.Vector3(-0.5 * s + dpml),
size=mp.Vector3(0, s, s),
component=mp.Ey,
amplitude=1j,
),
]
sim = mp.Simulation(
resolution=resolution,
cell_size=cell_size,
boundary_layers=pml_layers,
sources=sources,
k_point=mp.Vector3(),
)
box_flux = sim.add_flux(
frq_cen,
0,
1,
mp.FluxRegion(center=mp.Vector3(x=-2 * r), size=mp.Vector3(0, 4 * r, 4 * r)),
)
nearfield_box = sim.add_near2far(
frq_cen,
0,
1,
mp.Near2FarRegion(
center=mp.Vector3(x=-2 * r), size=mp.Vector3(0, 4 * r, 4 * r), weight=+1
),
mp.Near2FarRegion(
center=mp.Vector3(x=+2 * r), size=mp.Vector3(0, 4 * r, 4 * r), weight=-1
),
mp.Near2FarRegion(
center=mp.Vector3(y=-2 * r), size=mp.Vector3(4 * r, 0, 4 * r), weight=+1
),
mp.Near2FarRegion(
center=mp.Vector3(y=+2 * r), size=mp.Vector3(4 * r, 0, 4 * r), weight=-1
),
mp.Near2FarRegion(
center=mp.Vector3(z=-2 * r), size=mp.Vector3(4 * r, 4 * r, 0), weight=+1
),
mp.Near2FarRegion(
center=mp.Vector3(z=+2 * r), size=mp.Vector3(4 * r, 4 * r, 0), weight=-1
),
)
sim.run(until_after_sources=10)
input_flux = mp.get_fluxes(box_flux)[0]
nearfield_box_data = sim.get_near2far_data(nearfield_box)
sim.reset_meep()
n_sphere = 2.0
geometry = [
mp.Sphere(material=mp.Medium(index=n_sphere), center=mp.Vector3(), radius=r)
]
sim = mp.Simulation(
resolution=resolution,
cell_size=cell_size,
boundary_layers=pml_layers,
sources=sources,
k_point=mp.Vector3(),
geometry=geometry,
)
nearfield_box = sim.add_near2far(
frq_cen,
0,
1,
mp.Near2FarRegion(
center=mp.Vector3(x=-2 * r), size=mp.Vector3(0, 4 * r, 4 * r), weight=+1
),
mp.Near2FarRegion(
center=mp.Vector3(x=+2 * r), size=mp.Vector3(0, 4 * r, 4 * r), weight=-1
),
mp.Near2FarRegion(
center=mp.Vector3(y=-2 * r), size=mp.Vector3(4 * r, 0, 4 * r), weight=+1
),
mp.Near2FarRegion(
center=mp.Vector3(y=+2 * r), size=mp.Vector3(4 * r, 0, 4 * r), weight=-1
),
mp.Near2FarRegion(
center=mp.Vector3(z=-2 * r), size=mp.Vector3(4 * r, 4 * r, 0), weight=+1
),
mp.Near2FarRegion(
center=mp.Vector3(z=+2 * r), size=mp.Vector3(4 * r, 4 * r, 0), weight=-1
),
)
sim.load_minus_near2far_data(nearfield_box, nearfield_box_data)
sim.run(until_after_sources=100)
npts = 100 # number of points in [0,pi) range of polar angles to sample far fields along semi-circle
angles = np.pi / npts * np.arange(npts)
ff_r = 10000 * r # radius of far-field semi-circle
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, ff_r * mp.Vector3(np.cos(angles[n]), 0, np.sin(angles[n]))
)
E[n, :] = [np.conj(ff[j]) for j in range(3)]
H[n, :] = [ff[j + 3] for j in range(3)]
Px = np.real(np.multiply(E[:, 1], H[:, 2]) - np.multiply(E[:, 2], H[:, 1]))
Py = np.real(np.multiply(E[:, 2], H[:, 0]) - np.multiply(E[:, 0], H[:, 2]))
Pz = np.real(np.multiply(E[:, 0], H[:, 1]) - np.multiply(E[:, 1], H[:, 0]))
Pr = np.sqrt(np.square(Px) + np.square(Py) + np.square(Pz))
intensity = input_flux / (4 * r) ** 2
diff_cross_section = ff_r**2 * Pr / intensity
scatt_cross_section_meep = (
2 * np.pi * np.sum(np.multiply(diff_cross_section, np.sin(angles))) * np.pi / npts
)
scatt_cross_section_theory = (
ps.MieQ(n_sphere, 1000 / frq_cen, 2 * r * 1000, asDict=True, asCrossSection=True)[
"Csca"
]
* 1e-6
) # units of um^2
print(
"scatt:, {:.16f} (meep), {:.16f} (theory)".format(
scatt_cross_section_meep, scatt_cross_section_theory
)
)
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