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
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
|
import math
import unittest
import numpy as np
import parameterized
from utils import ApproxComparisonTestCase
import meep as mp
class TestReflAngular(ApproxComparisonTestCase):
@classmethod
def setUpClass(cls):
cls.resolution = 400 # pixels/μm
cls.n1 = 1.4 # refractive index of medium 1
cls.n2 = 3.5 # refractive index of medium 2
cls.dpml = 1.0
cls.dz = 7.0
cls.sz = cls.dz + 2 * cls.dpml
cls.wvl_min = 0.4
cls.wvl_max = 0.8
cls.fmin = 1 / cls.wvl_max
cls.fmax = 1 / cls.wvl_min
cls.fcen = 0.5 * (cls.fmin + cls.fmax)
cls.df = cls.fmax - cls.fmin
cls.nfreq = 11
def refl_angular(self, theta):
theta_r = math.radians(theta)
# wavevector (in source medium); plane of incidence is XZ
k = (
mp.Vector3(0, 0, 1)
.rotate(mp.Vector3(0, 1, 0), theta_r)
.scale(self.n1 * self.fmin)
)
dimensions = 1 if theta == 0 else 3
cell_size = mp.Vector3(z=self.sz)
pml_layers = [mp.PML(self.dpml)]
sources = [
mp.Source(
mp.GaussianSource(self.fcen, fwidth=self.df),
component=mp.Ex, # P polarization
center=mp.Vector3(z=-0.5 * self.sz + self.dpml),
)
]
sim = mp.Simulation(
resolution=self.resolution,
cell_size=cell_size,
dimensions=dimensions,
default_material=mp.Medium(index=self.n1),
sources=sources,
boundary_layers=pml_layers,
k_point=k,
)
mon_pt = -0.5 * self.sz + self.dpml + 0.25 * self.dz
refl_fr = mp.FluxRegion(center=mp.Vector3(z=mon_pt))
refl = sim.add_flux(self.fcen, self.df, self.nfreq, refl_fr)
termination_cond = mp.stop_when_fields_decayed(
50, mp.Ex, mp.Vector3(z=mon_pt), 1e-9
)
sim.run(until_after_sources=termination_cond)
empty_data = sim.get_flux_data(refl)
empty_flux = mp.get_fluxes(refl)
sim.reset_meep()
geometry = [
mp.Block(
size=mp.Vector3(mp.inf, mp.inf, 0.5 * self.sz),
center=mp.Vector3(z=0.25 * self.sz),
material=mp.Medium(index=self.n2),
)
]
sim = mp.Simulation(
resolution=self.resolution,
cell_size=cell_size,
dimensions=dimensions,
default_material=mp.Medium(index=self.n1),
sources=sources,
boundary_layers=pml_layers,
k_point=k,
geometry=geometry,
)
refl = sim.add_flux(self.fcen, self.df, self.nfreq, refl_fr)
sim.load_minus_flux_data(refl, empty_data)
sim.run(until_after_sources=termination_cond)
refl_flux = mp.get_fluxes(refl)
freqs = mp.get_flux_freqs(refl)
Rs = -np.array(refl_flux) / np.array(empty_flux)
thetas = [math.asin(k.x / (self.n1 * freqs[i])) for i in range(self.nfreq)]
return freqs, thetas, Rs
@parameterized.parameterized.expand([(0,), (20.6,)])
def test_refl_angular(self, theta):
fmeep, tmeep, Rmeep = self.refl_angular(theta)
# angle of refracted planewave in medium n2 for an
# incident planewave in medium n1 at angle theta_in
theta_out = lambda theta_in: math.asin(self.n1 * math.sin(theta_in) / self.n2)
# Fresnel reflectance for P polarization in medium n2 for
# an incident planewave in medium n1 at angle theta_in
Rfresnel = lambda theta_in: (
math.fabs(
(self.n1 * math.cos(theta_out(theta_in)) - self.n2 * math.cos(theta_in))
/ (
self.n1 * math.cos(theta_out(theta_in))
+ self.n2 * math.cos(theta_in)
)
)
** 2
)
Ranalytic = np.empty((self.nfreq,))
print(
"refl:, wavelength (μm), incident angle (°), reflectance (Meep), reflectance (analytic), error"
)
for i in range(self.nfreq):
Ranalytic[i] = Rfresnel(tmeep[i])
err = abs(Rmeep[i] - Ranalytic[i]) / Ranalytic[i]
print(
"refl:, {:4.2f}, {:4.2f}, {:8.6f}, {:8.6f}, {:6.4f}".format(
1 / fmeep[i], math.degrees(tmeep[i]), Rmeep[i], Ranalytic[i], err
)
)
tol = 0.005 if mp.is_single_precision() else 0.004
self.assertClose(Rmeep, Ranalytic, epsilon=tol)
if __name__ == "__main__":
unittest.main()
|
