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import cmath
import math
import unittest
from time import time
import parameterized
import meep as mp
class TestSpecialKz(unittest.TestCase):
def refl_planar(self, theta, kz_2d):
resolution = 100 # pixels/um
dpml = 1.0
sx = 3.0 + 2 * dpml
sy = 1 / resolution
cell_size = mp.Vector3(sx, sy)
pml_layers = [mp.PML(dpml, direction=mp.X)]
fcen = 1.0
# plane of incidence is XZ
k_point = mp.Vector3(1, 0, 0).rotate(mp.Vector3(0, 1, 0), theta).scale(fcen)
sources = [
mp.Source(
mp.GaussianSource(fcen, fwidth=0.2 * fcen),
component=mp.Ez, # P-polarization
center=mp.Vector3(-0.5 * sx + dpml),
size=mp.Vector3(y=sy),
)
]
sim = mp.Simulation(
cell_size=cell_size,
boundary_layers=pml_layers,
sources=sources,
k_point=k_point,
kz_2d=kz_2d,
resolution=resolution,
)
refl_fr = mp.FluxRegion(center=mp.Vector3(-0.25 * sx), size=mp.Vector3(y=sy))
refl = sim.add_flux(fcen, 0, 1, refl_fr)
sim.run(
until_after_sources=mp.stop_when_fields_decayed(
50, mp.Ez, mp.Vector3(), 1e-9
)
)
empty_flux = mp.get_fluxes(refl)
empty_data = sim.get_flux_data(refl)
sim.reset_meep()
geometry = [
mp.Block(
material=mp.Medium(index=3.5),
size=mp.Vector3(0.5 * sx, mp.inf, mp.inf),
center=mp.Vector3(0.25 * sx),
)
]
sim = mp.Simulation(
cell_size=cell_size,
boundary_layers=pml_layers,
geometry=geometry,
sources=sources,
k_point=k_point,
kz_2d=kz_2d,
resolution=resolution,
)
refl = sim.add_flux(fcen, 0, 1, refl_fr)
sim.load_minus_flux_data(refl, empty_data)
sim.run(
until_after_sources=mp.stop_when_fields_decayed(
50, mp.Ez, mp.Vector3(), 1e-9
)
)
refl_flux = mp.get_fluxes(refl)
return -refl_flux[0] / empty_flux[0]
def test_special_kz(self):
n1 = 1
n2 = 3.5
# compute angle of refracted planewave in medium n2
# for incident planewave in medium n1 at angle theta_in
theta_out = lambda theta_in: math.asin(n1 * math.sin(theta_in) / n2)
# compute Fresnel reflectance for P-polarization in medium n2
# for incident planewave in medium n1 at angle theta_in
Rfresnel = (
lambda theta_in: math.fabs(
(n1 * math.cos(theta_out(theta_in)) - n2 * math.cos(theta_in))
/ (n1 * math.cos(theta_out(theta_in)) + n2 * math.cos(theta_in))
)
** 2
)
# angle of incident planewave; clockwise (CW) about Y axis, 0 degrees along +X axis
theta = math.radians(23)
start = time()
Rmeep_complex = self.refl_planar(theta, "complex")
t_complex = time() - start
start = time()
Rmeep_real_imag = self.refl_planar(theta, "real/imag")
t_real_imag = time() - start
Rfres = Rfresnel(theta)
self.assertAlmostEqual(Rmeep_complex, Rfres, places=2)
self.assertAlmostEqual(Rmeep_real_imag, Rfres, places=2)
# the real/imag algorithm should be faster, but on CI machines performance is too variable
# for this to reliably hold
# self.assertLess(t_real_imag,t_complex)
@parameterized.parameterized.expand([("complex",), ("real/imag",)])
def test_eigsrc_kz(self, kz_2d):
resolution = 30 # pixels/um
cell_size = mp.Vector3(14, 14)
pml_layers = [mp.PML(thickness=2)]
geometry = [
mp.Block(
center=mp.Vector3(),
size=mp.Vector3(mp.inf, 1, mp.inf),
material=mp.Medium(epsilon=12),
)
]
fsrc = 0.3 # frequency of eigenmode or constant-amplitude source
bnum = 1 # band number of eigenmode
kz = 0.2 # fixed out-of-plane wavevector component
sources = [
mp.EigenModeSource(
src=mp.GaussianSource(fsrc, fwidth=0.2 * fsrc),
center=mp.Vector3(),
size=mp.Vector3(y=14),
eig_band=bnum,
eig_parity=mp.EVEN_Y,
eig_match_freq=True,
)
]
sim = mp.Simulation(
cell_size=cell_size,
resolution=resolution,
boundary_layers=pml_layers,
sources=sources,
geometry=geometry,
symmetries=[mp.Mirror(mp.Y)],
k_point=mp.Vector3(z=kz),
kz_2d=kz_2d,
)
tran = sim.add_flux(
fsrc, 0, 1, mp.FluxRegion(center=mp.Vector3(x=5), size=mp.Vector3(y=14))
)
sim.run(until_after_sources=50)
res = sim.get_eigenmode_coefficients(tran, [1, 2], eig_parity=mp.EVEN_Y)
total_flux = mp.get_fluxes(tran)[0]
mode1_flux = abs(res.alpha[0, 0, 0]) ** 2
mode2_flux = abs(res.alpha[1, 0, 0]) ** 2
mode1_frac = 0.99
self.assertGreater(mode1_flux / total_flux, mode1_frac)
self.assertLess(mode2_flux / total_flux, 1 - mode1_frac)
d = 3.5
ez1 = sim.get_field_point(mp.Ez, mp.Vector3(2.3, -5.7, 4.8))
ez2 = sim.get_field_point(mp.Ez, mp.Vector3(2.3, -5.7, 4.8 + d))
ratio_ez = ez2 / ez1
phase_diff = cmath.exp(1j * 2 * cmath.pi * kz * d)
self.assertAlmostEqual(ratio_ez.real, phase_diff.real, places=10)
self.assertAlmostEqual(ratio_ez.imag, phase_diff.imag, places=10)
if __name__ == "__main__":
unittest.main()
|
