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|
import unittest
import numpy as np
import meep as mp
class TestModeCoeffs(unittest.TestCase):
def run_mode_coeffs(self, mode_num, kpoint_func, nf=1, resolution=15):
w = 1 # width of waveguide
L = 10 # length of waveguide
Si = mp.Medium(epsilon=12.0)
dair = 3.0
dpml = 3.0
sx = dpml + L + dpml
sy = dpml + dair + w + dair + dpml
cell_size = mp.Vector3(sx, sy, 0)
prism_x = sx + 1
prism_y = w / 2
vertices = [
mp.Vector3(-prism_x, prism_y),
mp.Vector3(prism_x, prism_y),
mp.Vector3(prism_x, -prism_y),
mp.Vector3(-prism_x, -prism_y),
]
geometry = [mp.Prism(vertices, height=mp.inf, material=Si)]
boundary_layers = [mp.PML(dpml)]
# mode frequency
fcen = 0.20 # > 0.5/sqrt(11) to have at least 2 modes
df = 0.5 * fcen
source = mp.EigenModeSource(
src=mp.GaussianSource(fcen, fwidth=df),
eig_band=mode_num,
size=mp.Vector3(0, sy - 2 * dpml, 0),
center=mp.Vector3(-0.5 * sx + dpml, 0, 0),
)
symmetries = [mp.Mirror(mp.Y, phase=1 if mode_num % 2 == 1 else -1)]
sim = mp.Simulation(
resolution=resolution,
cell_size=cell_size,
boundary_layers=boundary_layers,
geometry=geometry,
sources=[source],
symmetries=symmetries,
)
xm = 0.5 * sx - dpml # x-coordinate of monitor
mflux = sim.add_mode_monitor(
fcen,
df,
nf,
mp.ModeRegion(center=mp.Vector3(xm, 0), size=mp.Vector3(0, sy - 2 * dpml)),
)
mode_flux = sim.add_flux(
fcen,
df,
nf,
mp.FluxRegion(center=mp.Vector3(xm, 0), size=mp.Vector3(0, sy - 2 * dpml)),
)
# sim.run(until_after_sources=mp.stop_when_fields_decayed(50, mp.Ez, mp.Vector3(-0.5*sx+dpml,0), 1e-10))
sim.run(until_after_sources=100)
##################################################
# If the number of analysis frequencies is >1, we
# are testing the unit-power normalization
# of the eigenmode source: we observe the total
# power flux through the mode_flux monitor (which
# equals the total power emitted by the source as
# there is no scattering in this ideal waveguide)
# and check that it agrees with the prediction
# of the eig_power() class method in EigenmodeSource.
##################################################
if nf > 1:
power_observed = mp.get_fluxes(mode_flux)
freqs = mp.get_flux_freqs(mode_flux)
power_expected = [source.eig_power(f) for f in freqs]
return freqs, power_expected, power_observed
modes_to_check = [
1,
2,
] # indices of modes for which to compute expansion coefficients
res = sim.get_eigenmode_coefficients(
mflux, modes_to_check, kpoint_func=kpoint_func
)
self.assertTrue(res.kpoints[0].close(mp.Vector3(0.604301, 0, 0)))
self.assertTrue(res.kpoints[1].close(mp.Vector3(0.494353, 0, 0), tol=1e-2))
self.assertTrue(res.kdom[0].close(mp.Vector3(0.604301, 0, 0)))
self.assertTrue(res.kdom[1].close(mp.Vector3(0.494353, 0, 0), tol=1e-2))
self.assertAlmostEqual(res.cscale[0], 0.50000977, places=5)
self.assertAlmostEqual(res.cscale[1], 0.50096888, places=5)
mode_power = mp.get_fluxes(mode_flux)[0]
TestPassed = True
TOLERANCE = 5.0e-3
c0 = res.alpha[
mode_num - 1, 0, 0
] # coefficient of forward-traveling wave for mode #mode_num
for nm in range(1, len(modes_to_check) + 1):
if nm != mode_num:
cfrel = np.abs(res.alpha[nm - 1, 0, 0]) / np.abs(c0)
cbrel = np.abs(res.alpha[nm - 1, 0, 1]) / np.abs(c0)
if cfrel > TOLERANCE or cbrel > TOLERANCE:
TestPassed = False
self.sim = sim
# test 1: coefficient of excited mode >> coeffs of all other modes
self.assertTrue(TestPassed, msg=f"cfrel: {cfrel}, cbrel: {cbrel}")
# test 2: |mode coeff|^2 = power
self.assertAlmostEqual(mode_power / abs(c0**2), 1.0, places=1)
return res
def test_modes(self):
self.run_mode_coeffs(1, None)
res = self.run_mode_coeffs(2, None)
# Test mp.get_eigenmode and EigenmodeData
vol = mp.Volume(center=mp.Vector3(5), size=mp.Vector3(y=7))
emdata = self.sim.get_eigenmode(0.2, mp.X, vol, 2, mp.Vector3())
self.assertEqual(emdata.freq, 0.2)
self.assertEqual(emdata.band_num, 2)
self.assertTrue(emdata.kdom.close(res.kdom[1]))
eval_point = mp.Vector3(0.7, -0.2, 0.3)
ex_at_eval_point = emdata.amplitude(eval_point, mp.Ex)
hz_at_eval_point = emdata.amplitude(eval_point, mp.Hz)
places = 5 if mp.is_single_precision() else 7
self.assertAlmostEqual(
ex_at_eval_point, 0.4887779638178009 + 0.484240145324284j, places=places
)
self.assertAlmostEqual(
hz_at_eval_point, 3.4249236584603495 - 3.455974863884166j, places=places
)
def test_kpoint_func(self):
def kpoint_func(freq, mode):
return mp.Vector3()
self.run_mode_coeffs(1, kpoint_func)
def test_eigensource_normalization(self):
f, p_exp, p_obs = self.run_mode_coeffs(1, None, nf=51, resolution=15)
# self.assertAlmostEqual(max(p_exp),max(p_obs),places=1)
max_exp, max_obs = max(p_exp), max(p_obs)
self.assertLess(abs(max_exp - max_obs), 0.5 * max(abs(max_exp), abs(max_obs)))
def test_reciprocity_kpoint(self):
resolution = 40
sx = 7.0
sy = 5.0
cell_size = mp.Vector3(sx, sy)
dpml = 1.0
pml_layers = [mp.PML(thickness=dpml)]
w = 1.0
geometry = [
mp.Block(
center=mp.Vector3(),
size=mp.Vector3(mp.inf, w, mp.inf),
material=mp.Medium(epsilon=12),
)
]
fsrc = 0.15
sources = [
mp.EigenModeSource(
src=mp.GaussianSource(fsrc, fwidth=0.2 * fsrc),
center=mp.Vector3(x=-0.5 * sx + dpml),
size=mp.Vector3(y=sy),
eig_parity=mp.EVEN_Y + mp.ODD_Z,
)
]
symmetries = [mp.Mirror(mp.Y)]
sim = mp.Simulation(
cell_size=cell_size,
resolution=resolution,
boundary_layers=pml_layers,
sources=sources,
geometry=geometry,
symmetries=symmetries,
)
tran = sim.add_mode_monitor(
fsrc,
0,
1,
mp.ModeRegion(center=mp.Vector3(x=0.5 * sx - dpml), size=mp.Vector3(y=sy)),
yee_grid=False,
)
sim.run(until_after_sources=50)
res_fwd = sim.get_eigenmode_coefficients(
tran,
[1],
eig_parity=mp.EVEN_Y + mp.ODD_Z,
direction=mp.NO_DIRECTION,
kpoint_func=lambda f, n: mp.Vector3(+1, 0, 0),
)
res_bwd = sim.get_eigenmode_coefficients(
tran,
[1],
eig_parity=mp.EVEN_Y + mp.ODD_Z,
direction=mp.NO_DIRECTION,
kpoint_func=lambda f, n: mp.Vector3(-1, 0, 0),
)
print(f"S11:, {res_fwd.alpha[0,0,1]}, {res_bwd.alpha[0,0,0]}")
print(f"S21:, {res_fwd.alpha[0,0,0]}, {res_bwd.alpha[0,0,1]}")
# |S11|^2
self.assertAlmostEqual(
abs(res_fwd.alpha[0, 0, 1]) ** 2, abs(res_bwd.alpha[0, 0, 0]) ** 2, places=4
)
# |S21|^2
self.assertAlmostEqual(
abs(res_fwd.alpha[0, 0, 0]) ** 2 / abs(res_bwd.alpha[0, 0, 1]) ** 2,
1.00,
places=2,
)
def test_reciprocity_monitor(self):
resolution = 25
sx = 7.0
sy = 5.0
cell_size = mp.Vector3(sx, sy)
dpml = 1.0
pml_layers = [mp.PML(thickness=dpml)]
w = 1.0
geometry = [
mp.Block(
center=mp.Vector3(),
size=mp.Vector3(mp.inf, w, mp.inf),
material=mp.Medium(epsilon=12),
)
]
fsrc = 0.15
# source is at the left edge of the waveguide
sources = [
mp.EigenModeSource(
src=mp.GaussianSource(fsrc, fwidth=0.2 * fsrc),
center=mp.Vector3(x=-0.5 * sx + dpml),
size=mp.Vector3(y=sy),
eig_parity=mp.EVEN_Y + mp.ODD_Z,
)
]
symmetries = [mp.Mirror(mp.Y)]
sim = mp.Simulation(
cell_size=cell_size,
resolution=resolution,
boundary_layers=pml_layers,
sources=sources,
geometry=geometry,
symmetries=symmetries,
)
# monitor is at the right edge of the waveguide
tran = sim.add_mode_monitor(
fsrc,
0,
1,
mp.ModeRegion(center=mp.Vector3(x=0.5 * sx - dpml), size=mp.Vector3(y=sy)),
yee_grid=False,
)
sim.run(until_after_sources=50)
res_fwd = sim.get_eigenmode_coefficients(
tran, [1], eig_parity=mp.EVEN_Y + mp.ODD_Z
)
print(f"S11:, {res_fwd.alpha[0,0,1]}")
print(f"S21:, {res_fwd.alpha[0,0,0]}")
sim.reset_meep()
# source is at the right edge of the waveguide
sources = [
mp.EigenModeSource(
src=mp.GaussianSource(fsrc, fwidth=0.2 * fsrc),
center=mp.Vector3(x=0.5 * sx - dpml),
size=mp.Vector3(y=sy),
direction=mp.NO_DIRECTION,
eig_kpoint=mp.Vector3(-1, 0, 0),
eig_parity=mp.EVEN_Y + mp.ODD_Z,
)
]
sim = mp.Simulation(
cell_size=cell_size,
resolution=resolution,
boundary_layers=pml_layers,
sources=sources,
geometry=geometry,
symmetries=symmetries,
)
# monitor is at the left edge of the waveguide
tran = sim.add_mode_monitor(
fsrc,
0,
1,
mp.ModeRegion(center=mp.Vector3(x=-0.5 * sx + dpml), size=mp.Vector3(y=sy)),
yee_grid=False,
)
sim.run(until_after_sources=50)
res_bwd = sim.get_eigenmode_coefficients(
tran, [1], eig_parity=mp.EVEN_Y + mp.ODD_Z
)
print(f"S12:, {res_bwd.alpha[0,0,1]}")
print(f"S22:, {res_bwd.alpha[0,0,0]}")
# |S21|^2 = |S12|^2
self.assertAlmostEqual(
abs(res_fwd.alpha[0, 0, 0]) ** 2 / abs(res_bwd.alpha[0, 0, 1]) ** 2,
1.00,
places=2,
)
# |S11|^2 = |S22|^2
self.assertAlmostEqual(
abs(res_fwd.alpha[0, 0, 1]) ** 2, abs(res_bwd.alpha[0, 0, 0]) ** 2, places=2
)
if __name__ == "__main__":
unittest.main()
|
