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import meep as mp
import numpy as np
import matplotlib.pyplot as plt
import PyMieScatt as ps
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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