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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
wvl_min = 2 * np.pi * r / 10
wvl_max = 2 * np.pi * r / 2
frq_min = 1 / wvl_max
frq_max = 1 / wvl_min
frq_cen = 0.5 * (frq_min + frq_max)
dfrq = frq_max - frq_min
nfrq = 100
## at least 8 pixels per smallest wavelength, i.e. np.floor(8/wvl_min)
resolution = 25
dpml = 0.5 * wvl_max
dair = 0.5 * wvl_max
pml_layers = [mp.PML(thickness=dpml)]
symmetries = [mp.Mirror(mp.Y), mp.Mirror(mp.Z, phase=-1)]
s = 2 * (dpml + dair + r)
cell_size = mp.Vector3(s, s, s)
# is_integrated=True necessary for any planewave source extending into PML
sources = [
mp.Source(
mp.GaussianSource(frq_cen, fwidth=dfrq, is_integrated=True),
center=mp.Vector3(-0.5 * s + dpml),
size=mp.Vector3(0, s, s),
component=mp.Ez,
)
]
sim = mp.Simulation(
resolution=resolution,
cell_size=cell_size,
boundary_layers=pml_layers,
sources=sources,
k_point=mp.Vector3(),
symmetries=symmetries,
)
box_x1 = sim.add_flux(
frq_cen,
dfrq,
nfrq,
mp.FluxRegion(center=mp.Vector3(x=-r), size=mp.Vector3(0, 2 * r, 2 * r)),
)
box_x2 = sim.add_flux(
frq_cen,
dfrq,
nfrq,
mp.FluxRegion(center=mp.Vector3(x=+r), size=mp.Vector3(0, 2 * r, 2 * r)),
)
box_y1 = sim.add_flux(
frq_cen,
dfrq,
nfrq,
mp.FluxRegion(center=mp.Vector3(y=-r), size=mp.Vector3(2 * r, 0, 2 * r)),
)
box_y2 = sim.add_flux(
frq_cen,
dfrq,
nfrq,
mp.FluxRegion(center=mp.Vector3(y=+r), size=mp.Vector3(2 * r, 0, 2 * r)),
)
box_z1 = sim.add_flux(
frq_cen,
dfrq,
nfrq,
mp.FluxRegion(center=mp.Vector3(z=-r), size=mp.Vector3(2 * r, 2 * r, 0)),
)
box_z2 = sim.add_flux(
frq_cen,
dfrq,
nfrq,
mp.FluxRegion(center=mp.Vector3(z=+r), size=mp.Vector3(2 * r, 2 * r, 0)),
)
sim.run(until_after_sources=10)
freqs = mp.get_flux_freqs(box_x1)
box_x1_data = sim.get_flux_data(box_x1)
box_x2_data = sim.get_flux_data(box_x2)
box_y1_data = sim.get_flux_data(box_y1)
box_y2_data = sim.get_flux_data(box_y2)
box_z1_data = sim.get_flux_data(box_z1)
box_z2_data = sim.get_flux_data(box_z2)
box_x1_flux0 = mp.get_fluxes(box_x1)
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(),
symmetries=symmetries,
geometry=geometry,
)
box_x1 = sim.add_flux(
frq_cen,
dfrq,
nfrq,
mp.FluxRegion(center=mp.Vector3(x=-r), size=mp.Vector3(0, 2 * r, 2 * r)),
)
box_x2 = sim.add_flux(
frq_cen,
dfrq,
nfrq,
mp.FluxRegion(center=mp.Vector3(x=+r), size=mp.Vector3(0, 2 * r, 2 * r)),
)
box_y1 = sim.add_flux(
frq_cen,
dfrq,
nfrq,
mp.FluxRegion(center=mp.Vector3(y=-r), size=mp.Vector3(2 * r, 0, 2 * r)),
)
box_y2 = sim.add_flux(
frq_cen,
dfrq,
nfrq,
mp.FluxRegion(center=mp.Vector3(y=+r), size=mp.Vector3(2 * r, 0, 2 * r)),
)
box_z1 = sim.add_flux(
frq_cen,
dfrq,
nfrq,
mp.FluxRegion(center=mp.Vector3(z=-r), size=mp.Vector3(2 * r, 2 * r, 0)),
)
box_z2 = sim.add_flux(
frq_cen,
dfrq,
nfrq,
mp.FluxRegion(center=mp.Vector3(z=+r), size=mp.Vector3(2 * r, 2 * r, 0)),
)
sim.load_minus_flux_data(box_x1, box_x1_data)
sim.load_minus_flux_data(box_x2, box_x2_data)
sim.load_minus_flux_data(box_y1, box_y1_data)
sim.load_minus_flux_data(box_y2, box_y2_data)
sim.load_minus_flux_data(box_z1, box_z1_data)
sim.load_minus_flux_data(box_z2, box_z2_data)
sim.run(until_after_sources=100)
box_x1_flux = mp.get_fluxes(box_x1)
box_x2_flux = mp.get_fluxes(box_x2)
box_y1_flux = mp.get_fluxes(box_y1)
box_y2_flux = mp.get_fluxes(box_y2)
box_z1_flux = mp.get_fluxes(box_z1)
box_z2_flux = mp.get_fluxes(box_z2)
scatt_flux = (
np.asarray(box_x1_flux)
- np.asarray(box_x2_flux)
+ np.asarray(box_y1_flux)
- np.asarray(box_y2_flux)
+ np.asarray(box_z1_flux)
- np.asarray(box_z2_flux)
)
intensity = np.asarray(box_x1_flux0) / (2 * r) ** 2
scatt_cross_section = np.divide(scatt_flux, intensity)
scatt_eff_meep = scatt_cross_section * -1 / (np.pi * r**2)
scatt_eff_theory = [
ps.MieQ(n_sphere, 1000 / f, 2 * r * 1000, asDict=True)["Qsca"] for f in freqs
]
if mp.am_master():
plt.figure(dpi=150)
plt.loglog(2 * np.pi * r * np.asarray(freqs), scatt_eff_meep, "bo-", label="Meep")
plt.loglog(
2 * np.pi * r * np.asarray(freqs), scatt_eff_theory, "ro-", label="theory"
)
plt.grid(True, which="both", ls="-")
plt.xlabel("(sphere circumference)/wavelength, 2πr/λ")
plt.ylabel("scattering efficiency, σ/πr$^{2}$")
plt.legend(loc="upper right")
plt.title("Mie Scattering of a Lossless Dielectric Sphere")
plt.tight_layout()
plt.savefig("mie_scattering.png")
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