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import cmath
import math
import unittest
import numpy as np
import parameterized
import meep as mp
class TestEigCoeffs(unittest.TestCase):
@classmethod
def setUpClass(cls):
cls.resolution = 30 # pixels/μm
cls.dpml = 1.0 # PML thickness
cls.dsub = 1.0 # substrate thickness
cls.dpad = 1.0 # padding thickness between grating and PML
cls.gp = 6.0 # grating period
cls.gh = 0.5 # grating height
cls.gdc = 0.5 # grating duty cycle
cls.sx = cls.dpml + cls.dsub + cls.gh + cls.dpad + cls.dpml
cls.sy = cls.gp
cls.cell_size = mp.Vector3(cls.sx, cls.sy, 0)
# replace anisotropic PML with isotropic Absorber to
# attenuate parallel-directed fields of oblique source
cls.abs_layers = [mp.Absorber(thickness=cls.dpml, direction=mp.X)]
wvl = 0.5 # center wavelength
cls.fcen = 1 / wvl # center frequency
cls.df = 0.05 * cls.fcen # frequency width
cls.ng = 1.5
cls.glass = mp.Medium(index=cls.ng)
cls.geometry = [
mp.Block(
material=cls.glass,
size=mp.Vector3(cls.dpml + cls.dsub, mp.inf, mp.inf),
center=mp.Vector3(-0.5 * cls.sx + 0.5 * (cls.dpml + cls.dsub), 0, 0),
),
mp.Block(
material=cls.glass,
size=mp.Vector3(cls.gh, cls.gdc * cls.gp, mp.inf),
center=mp.Vector3(
-0.5 * cls.sx + cls.dpml + cls.dsub + 0.5 * cls.gh, 0, 0
),
),
]
@parameterized.parameterized.expand([(0,), (10.7,)])
def test_binary_grating_oblique(self, theta):
# rotation angle of incident planewave
# counterclockwise (CCW) about Z axis, 0 degrees along +X axis
theta_in = math.radians(theta)
# k (in source medium) with correct length (plane of incidence: XY)
k = mp.Vector3(self.fcen * self.ng).rotate(mp.Vector3(0, 0, 1), theta_in)
symmetries = []
eig_parity = mp.ODD_Z
if theta_in == 0:
symmetries = [mp.Mirror(mp.Y)]
eig_parity += mp.EVEN_Y
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 * self.sx + self.dpml, 0, 0)
sources = [
mp.Source(
mp.GaussianSource(self.fcen, fwidth=self.df),
component=mp.Ez, # S polarization
center=src_pt,
size=mp.Vector3(0, self.sy, 0),
amp_func=pw_amp(k, src_pt),
)
]
sim = mp.Simulation(
resolution=self.resolution,
cell_size=self.cell_size,
boundary_layers=self.abs_layers,
k_point=k,
default_material=self.glass,
sources=sources,
symmetries=symmetries,
)
refl_pt = mp.Vector3(-0.5 * self.sx + self.dpml + 0.5 * self.dsub, 0, 0)
refl_flux = sim.add_flux(
self.fcen,
0,
1,
mp.FluxRegion(center=refl_pt, size=mp.Vector3(0, self.sy, 0)),
)
sim.run(until_after_sources=mp.stop_when_dft_decayed())
input_flux = mp.get_fluxes(refl_flux)
input_flux_data = sim.get_flux_data(refl_flux)
sim.reset_meep()
sim = mp.Simulation(
resolution=self.resolution,
cell_size=self.cell_size,
boundary_layers=self.abs_layers,
geometry=self.geometry,
k_point=k,
sources=sources,
symmetries=symmetries,
)
refl_flux = sim.add_flux(
self.fcen,
0,
1,
mp.FluxRegion(center=refl_pt, size=mp.Vector3(0, self.sy, 0)),
)
sim.load_minus_flux_data(refl_flux, input_flux_data)
tran_pt = mp.Vector3(0.5 * self.sx - self.dpml - 0.5 * self.dpad, 0, 0)
tran_flux = sim.add_flux(
self.fcen,
0,
1,
mp.FluxRegion(center=tran_pt, size=mp.Vector3(0, self.sy, 0)),
)
sim.run(until_after_sources=mp.stop_when_dft_decayed())
# number of reflected orders
nm_r = np.floor((self.fcen * self.ng - k.y) * self.gp) - np.ceil(
(-self.fcen * self.ng - k.y) * self.gp
)
if theta_in == 0:
nm_r = nm_r / 2 # since eig_parity removes degeneracy in y-direction
nm_r = int(nm_r)
res = sim.get_eigenmode_coefficients(
refl_flux, range(1, nm_r + 1), eig_parity=eig_parity
)
r_coeffs = res.alpha
Rsum = 0
for nm in range(nm_r):
Rsum += abs(r_coeffs[nm, 0, 1]) ** 2 / input_flux[0]
# number of transmitted orders
nm_t = np.floor((self.fcen - k.y) * self.gp) - np.ceil(
(-self.fcen - k.y) * self.gp
)
if theta_in == 0:
nm_t = nm_t / 2 # since eig_parity removes degeneracy in y-direction
nm_t = int(nm_t)
res = sim.get_eigenmode_coefficients(
tran_flux, range(1, nm_t + 1), eig_parity=eig_parity
)
t_coeffs = res.alpha
Tsum = 0
for nm in range(nm_t):
Tsum += abs(t_coeffs[nm, 0, 0]) ** 2 / input_flux[0]
r_flux = mp.get_fluxes(refl_flux)
t_flux = mp.get_fluxes(tran_flux)
Rflux = -r_flux[0] / input_flux[0]
Tflux = t_flux[0] / input_flux[0]
print(f"refl:, {Rsum}, {Rflux}")
print(f"tran:, {Tsum}, {Tflux}")
print(f"sum:, {Rsum + Tsum}, {Rflux + Tflux}")
self.assertAlmostEqual(Rsum, Rflux, places=2)
self.assertAlmostEqual(Tsum, Tflux, places=2)
self.assertAlmostEqual(Rsum + Tsum, 1.00, places=2)
@parameterized.parameterized.expand(
[(13.2, "real/imag"), (17.7, "complex"), (21.2, "3d")]
)
def test_binary_grating_special_kz(self, theta, kz_2d):
# rotation angle of incident planewave
# counterclockwise (CCW) about Y axis, 0 degrees along +X axis
theta_in = math.radians(theta)
# k (in source medium) with correct length (plane of incidence: XZ)
k = mp.Vector3(self.fcen * self.ng).rotate(mp.Vector3(0, 1, 0), theta_in)
symmetries = [mp.Mirror(mp.Y)]
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 * self.sx + self.dpml, 0, 0)
sources = [
mp.Source(
mp.GaussianSource(self.fcen, fwidth=self.df),
component=mp.Ez,
center=src_pt,
size=mp.Vector3(0, self.sy, 0),
amp_func=pw_amp(k, src_pt),
)
]
sim = mp.Simulation(
resolution=self.resolution,
cell_size=self.cell_size,
boundary_layers=self.abs_layers,
k_point=k,
default_material=self.glass,
sources=sources,
symmetries=symmetries,
kz_2d=kz_2d,
)
refl_pt = mp.Vector3(-0.5 * self.sx + self.dpml + 0.5 * self.dsub, 0, 0)
refl_flux = sim.add_mode_monitor(
self.fcen,
0,
1,
mp.FluxRegion(center=refl_pt, size=mp.Vector3(0, self.sy, 0)),
)
sim.run(until_after_sources=mp.stop_when_dft_decayed())
input_flux = mp.get_fluxes(refl_flux)
input_flux_data = sim.get_flux_data(refl_flux)
sim.reset_meep()
sim = mp.Simulation(
resolution=self.resolution,
cell_size=self.cell_size,
boundary_layers=self.abs_layers,
geometry=self.geometry,
k_point=k,
sources=sources,
symmetries=symmetries,
kz_2d=kz_2d,
)
refl_flux = sim.add_mode_monitor(
self.fcen,
0,
1,
mp.FluxRegion(center=refl_pt, size=mp.Vector3(0, self.sy, 0)),
)
sim.load_minus_flux_data(refl_flux, input_flux_data)
tran_pt = mp.Vector3(0.5 * self.sx - self.dpml - 0.5 * self.dpad, 0, 0)
tran_flux = sim.add_mode_monitor(
self.fcen,
0,
1,
mp.FluxRegion(center=tran_pt, size=mp.Vector3(0, self.sy, 0)),
)
sim.run(until_after_sources=mp.stop_when_dft_decayed())
# number of reflected orders
nm_r = np.ceil(
(np.sqrt((self.fcen * self.ng) ** 2 - k.z**2) - k.y) * self.gp
) - np.floor((-np.sqrt((self.fcen * self.ng) ** 2 - k.z**2) - k.y) * self.gp)
nm_r = int(nm_r / 2)
Rsum = 0
for nm in range(nm_r):
for S_pol in [False, True]:
res = sim.get_eigenmode_coefficients(
refl_flux,
mp.DiffractedPlanewave(
[0, nm, 0],
mp.Vector3(1, 0, 0),
1 if S_pol else 0,
0 if S_pol else 1,
),
)
r_coeffs = res.alpha
Rmode = abs(r_coeffs[0, 0, 1]) ** 2 / input_flux[0]
print(
"refl-order:, {}, {}, {}".format("s" if S_pol else "p", nm, Rmode)
)
Rsum += Rmode if nm == 0 else 2 * Rmode
# number of transmitted orders
nm_t = np.ceil((np.sqrt(self.fcen**2 - k.z**2) - k.y) * self.gp) - np.floor(
(-np.sqrt(self.fcen**2 - k.z**2) - k.y) * self.gp
)
nm_t = int(nm_t / 2)
Tsum = 0
for nm in range(nm_t):
for S_pol in [False, True]:
res = sim.get_eigenmode_coefficients(
tran_flux,
mp.DiffractedPlanewave(
[0, nm, 0],
mp.Vector3(1, 0, 0),
1 if S_pol else 0,
0 if S_pol else 1,
),
)
t_coeffs = res.alpha
Tmode = abs(t_coeffs[0, 0, 0]) ** 2 / input_flux[0]
print(
"tran-order:, {}, {}, {}".format("s" if S_pol else "p", nm, Tmode)
)
Tsum += Tmode if nm == 0 else 2 * Tmode
r_flux = mp.get_fluxes(refl_flux)
t_flux = mp.get_fluxes(tran_flux)
Rflux = -r_flux[0] / input_flux[0]
Tflux = t_flux[0] / input_flux[0]
print(f"refl:, {Rsum}, {Rflux}")
print(f"tran:, {Tsum}, {Tflux}")
print(f"sum:, {Rsum + Tsum}, {Rflux + Tflux}")
self.assertAlmostEqual(Rsum, Rflux, places=2)
self.assertAlmostEqual(Tsum, Tflux, places=2)
self.assertAlmostEqual(Rsum + Tsum, 1.00, places=2)
if __name__ == "__main__":
unittest.main()
|
