1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
|
import meep as mp
import numpy as np
import matplotlib.pyplot as plt
r = 0.7 # radius of cylinder
h = 2.3 # height of cylinder
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 = 1.0*wvl_max
pml_layers = [mp.PML(thickness=dpml)]
sr = r+dair+dpml
sz = dpml+dair+h+dair+dpml
cell_size = mp.Vector3(sr,0,sz)
sources = [mp.Source(mp.GaussianSource(frq_cen,fwidth=dfrq,is_integrated=True),
component=mp.Er,
center=mp.Vector3(0.5*sr,0,-0.5*sz+dpml),
size=mp.Vector3(sr)),
mp.Source(mp.GaussianSource(frq_cen,fwidth=dfrq,is_integrated=True),
component=mp.Ep,
center=mp.Vector3(0.5*sr,0,-0.5*sz+dpml),
size=mp.Vector3(sr),
amplitude=-1j)]
sim = mp.Simulation(cell_size=cell_size,
boundary_layers=pml_layers,
resolution=resolution,
sources=sources,
dimensions=mp.CYLINDRICAL,
m=-1)
box_z1 = sim.add_flux(frq_cen, dfrq, nfrq, mp.FluxRegion(center=mp.Vector3(0.5*r,0,-0.5*h),size=mp.Vector3(r)))
box_z2 = sim.add_flux(frq_cen, dfrq, nfrq, mp.FluxRegion(center=mp.Vector3(0.5*r,0,+0.5*h),size=mp.Vector3(r)))
box_r = sim.add_flux(frq_cen, dfrq, nfrq, mp.FluxRegion(center=mp.Vector3(r),size=mp.Vector3(z=h)))
sim.run(until_after_sources=10)
freqs = mp.get_flux_freqs(box_z1)
box_z1_data = sim.get_flux_data(box_z1)
box_z2_data = sim.get_flux_data(box_z2)
box_r_data = sim.get_flux_data(box_r)
box_z1_flux0 = mp.get_fluxes(box_z1)
sim.reset_meep()
n_cyl = 2.0
geometry = [mp.Block(material=mp.Medium(index=n_cyl),
center=mp.Vector3(0.5*r),
size=mp.Vector3(r,0,h))]
sim = mp.Simulation(cell_size=cell_size,
geometry=geometry,
boundary_layers=pml_layers,
resolution=resolution,
sources=sources,
dimensions=mp.CYLINDRICAL,
m=-1)
box_z1 = sim.add_flux(frq_cen, dfrq, nfrq, mp.FluxRegion(center=mp.Vector3(0.5*r,0,-0.5*h),size=mp.Vector3(r)))
box_z2 = sim.add_flux(frq_cen, dfrq, nfrq, mp.FluxRegion(center=mp.Vector3(0.5*r,0,+0.5*h),size=mp.Vector3(r)))
box_r = sim.add_flux(frq_cen, dfrq, nfrq, mp.FluxRegion(center=mp.Vector3(r),size=mp.Vector3(z=h)))
sim.load_minus_flux_data(box_z1, box_z1_data)
sim.load_minus_flux_data(box_z2, box_z2_data)
sim.load_minus_flux_data(box_r, box_r_data)
sim.run(until_after_sources=100)
box_z1_flux = mp.get_fluxes(box_z1)
box_z2_flux = mp.get_fluxes(box_z2)
box_r_flux = mp.get_fluxes(box_r)
scatt_flux = np.asarray(box_z1_flux)-np.asarray(box_z2_flux)-np.asarray(box_r_flux)
intensity = np.asarray(box_z1_flux0)/(np.pi*r**2)
scatt_cross_section = np.divide(-scatt_flux,intensity)
if mp.am_master():
plt.figure(dpi=150)
plt.loglog(2*np.pi*r*np.asarray(freqs),scatt_cross_section,'bo-')
plt.grid(True,which="both",ls="-")
plt.xlabel('(cylinder circumference)/wavelength, 2πr/λ')
plt.ylabel('scattering cross section, σ')
plt.title('Scattering Cross Section of a Lossless Dielectric Cylinder')
plt.tight_layout()
plt.savefig("cylinder_cross_section.png")
|
