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
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
|
### compute the transmitted diffraction orders of a binary grating using mode decomposition
### based on two different methods: (1) MPB eigensolver and (2) DiffractedPlanewave object.
### Also, verify that the total power in all the orders is equivalent to the Poynting flux.
### for normal incidence, compute only positive diff. orders (total transmittance <= 0.50)
### for oblique incidence, compute ALL diff. orders (total transmittance <= 1.00)
import cmath
import math
import numpy as np
import meep as mp
def binary_grating_diffraction(gp, gh, gdc, theta):
resolution = 50 # pixels/μm
dpml = 1.0 # PML thickness
dsub = 3.0 # substrate thickness
dpad = 3.0 # length of padding between grating and PML
sx = dpml + dsub + gh + dpad + dpml
sy = gp
cell_size = mp.Vector3(sx, sy, 0)
pml_layers = [mp.PML(thickness=dpml, direction=mp.X)]
wvl = 0.5 # center wavelength
fcen = 1 / wvl # center frequency
df = 0.05 * fcen # frequency width
ng = 1.5
glass = mp.Medium(index=ng)
# rotation angle of incident planewave; counter clockwise (CCW) about Z axis, 0 degrees along +X axis
theta_in = math.radians(theta)
eig_parity = mp.EVEN_Z
# k (in source medium) with correct length (plane of incidence: XY)
k = mp.Vector3(fcen * ng).rotate(mp.Vector3(z=1), theta_in)
symmetries = []
if theta_in == 0:
k = mp.Vector3()
eig_parity += mp.ODD_Y
symmetries = [mp.Mirror(direction=mp.Y, phase=-1)]
def pw_amp(k, x0):
def _pw_amp(x):
return cmath.exp(1j * 2 * math.pi * k.dot(x + x0))
return _pw_amp
src_pt = mp.Vector3(-0.5 * sx + dpml, 0, 0)
sources = [
mp.Source(
mp.GaussianSource(fcen, fwidth=df),
component=mp.Hz,
center=src_pt,
size=mp.Vector3(0, sy, 0),
amp_func=pw_amp(k, src_pt),
)
]
sim = mp.Simulation(
resolution=resolution,
cell_size=cell_size,
boundary_layers=pml_layers,
k_point=k,
default_material=glass,
sources=sources,
symmetries=symmetries,
)
tran_pt = mp.Vector3(0.5 * sx - dpml, 0, 0)
tran_mon = sim.add_flux(
fcen, 0, 1, mp.FluxRegion(center=tran_pt, size=mp.Vector3(0, sy, 0))
)
sim.run(until_after_sources=50)
input_flux = mp.get_fluxes(tran_mon)
sim.reset_meep()
geometry = [
mp.Block(
material=glass,
size=mp.Vector3(dpml + dsub, mp.inf, mp.inf),
center=mp.Vector3(-0.5 * sx + 0.5 * (dpml + dsub), 0, 0),
),
mp.Block(
material=glass,
size=mp.Vector3(gh, gdc * gp, mp.inf),
center=mp.Vector3(-0.5 * sx + dpml + dsub + 0.5 * gh, 0, 0),
),
]
sim = mp.Simulation(
resolution=resolution,
cell_size=cell_size,
boundary_layers=pml_layers,
geometry=geometry,
k_point=k,
sources=sources,
symmetries=symmetries,
)
tran_mon = sim.add_mode_monitor(
fcen, 0, 1, mp.FluxRegion(center=tran_pt, size=mp.Vector3(0, sy, 0))
)
sim.run(until_after_sources=100)
# number of (non-evanescent) transmitted orders
nm_t = np.floor((fcen - k.y) * gp) - np.ceil((-fcen - k.y) * gp)
if theta_in == 0:
nm_t = nm_t / 2
nm_t = int(nm_t) + 1
bands = range(1, nm_t + 1)
if theta_in == 0:
orders = range(0, nm_t)
else:
orders = range(
int(np.ceil((-fcen - k.y) * gp)), int(np.floor((fcen - k.y) * gp)) + 1
)
eig_sum = 0
dp_sum = 0
for band, order in zip(bands, orders):
res = sim.get_eigenmode_coefficients(tran_mon, [band], eig_parity=eig_parity)
if res is not None:
tran_eig = abs(res.alpha[0, 0, 0]) ** 2 / input_flux[0]
if theta_in == 0:
tran_eig = 0.5 * tran_eig
else:
tran_eig = 0
eig_sum += tran_eig
res = sim.get_eigenmode_coefficients(
tran_mon, mp.DiffractedPlanewave((0, order, 0), mp.Vector3(0, 1, 0), 0, 1)
)
if res is not None:
tran_dp = abs(res.alpha[0, 0, 0]) ** 2 / input_flux[0]
if (theta_in == 0) and (order == 0):
tran_dp = 0.5 * tran_dp
else:
tran_dp = 0
dp_sum += tran_dp
if theta_in == 0:
err = abs(tran_eig - tran_dp) / tran_eig
print(
"tran:, {:2d}, {:.8f}, {:2d}, {:.8f}, {:.8f}".format(
band, tran_eig, order, tran_dp, err
)
)
else:
print(
"tran:, {:2d}, {:.8f}, {:2d}, {:.8f}".format(
band, tran_eig, order, tran_dp
)
)
flux = mp.get_fluxes(tran_mon)
t_flux = flux[0] / input_flux[0]
if theta_in == 0:
t_flux = 0.5 * t_flux
err = abs(dp_sum - t_flux) / t_flux
print(f"flux:, {eig_sum:.8f}, {dp_sum:.8f}, {t_flux:.8f}, {err:.8f}")
if __name__ == "__main__":
binary_grating_diffraction(2.6, 0.4, 0.3, 0)
binary_grating_diffraction(3.7, 0.6, 0.4, 13.5)
|
