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import math
import unittest
import numpy as np
from utils import ApproxComparisonTestCase
import meep as mp
class TestAntennaRadiation(ApproxComparisonTestCase):
@classmethod
def setUp(cls):
cls.resolution = 100 # pixels/μm
cls.h = 1.125 # height of point source above ground plane
cls.n = 1.2 # refractive index of surrounding medium
cls.src_cmpt = mp.Ez
cls.wvl = 0.65
cls.npts = 50 # number of points in [0,pi/2) range of angles
cls.angles = 0.5 * math.pi / cls.npts * np.arange(cls.npts)
cls.r = 1000 * cls.wvl # radius of far-field hemicircle
def radial_flux(self, sim, nearfield_box, r):
E = np.zeros((self.npts, 3), dtype=np.complex128)
H = np.zeros((self.npts, 3), dtype=np.complex128)
for n in range(self.npts):
ff = sim.get_farfield(
nearfield_box,
mp.Vector3(r * math.sin(self.angles[n]), r * math.cos(self.angles[n])),
)
E[n, :] = [np.conj(ff[j]) for j in range(3)]
H[n, :] = [ff[j + 3] for j in range(3)]
Px = np.real(E[:, 1] * H[:, 2] - E[:, 2] * H[:, 1]) # Ey*Hz-Ez*Hy
Py = np.real(E[:, 2] * H[:, 0] - E[:, 0] * H[:, 2]) # Ez*Hx-Ex*Hz
return np.sqrt(np.square(Px) + np.square(Py))
def free_space_radiation(self):
sxy = 4
dpml = 1
cell_size = mp.Vector3(sxy + 2 * dpml, sxy + 2 * dpml)
pml_layers = [mp.PML(dpml)]
fcen = 1 / self.wvl
sources = [
mp.Source(
src=mp.GaussianSource(fcen, fwidth=0.2 * fcen),
center=mp.Vector3(),
component=self.src_cmpt,
)
]
if self.src_cmpt == mp.Hz:
symmetries = [mp.Mirror(mp.X, phase=-1), mp.Mirror(mp.Y, phase=-1)]
elif self.src_cmpt == mp.Ez:
symmetries = [mp.Mirror(mp.X, phase=+1), mp.Mirror(mp.Y, phase=+1)]
else:
symmetries = []
sim = mp.Simulation(
cell_size=cell_size,
resolution=self.resolution,
sources=sources,
symmetries=symmetries,
boundary_layers=pml_layers,
default_material=mp.Medium(index=self.n),
)
nearfield_box = sim.add_near2far(
fcen,
0,
1,
mp.Near2FarRegion(
center=mp.Vector3(0, +0.5 * sxy), size=mp.Vector3(sxy, 0)
),
mp.Near2FarRegion(
center=mp.Vector3(0, -0.5 * sxy), size=mp.Vector3(sxy, 0), weight=-1
),
mp.Near2FarRegion(
center=mp.Vector3(+0.5 * sxy, 0), size=mp.Vector3(0, sxy)
),
mp.Near2FarRegion(
center=mp.Vector3(-0.5 * sxy, 0), size=mp.Vector3(0, sxy), weight=-1
),
)
sim.run(until_after_sources=mp.stop_when_dft_decayed())
return self.radial_flux(sim, nearfield_box, self.r)
def pec_ground_plane_radiation(self):
L = 8.0 # length of non-PML region
dpml = 1.0 # thickness of PML
sxy = dpml + L + dpml
cell_size = mp.Vector3(sxy, sxy, 0)
boundary_layers = [mp.PML(dpml)]
fcen = 1 / self.wvl
# The near-to-far field transformation feature only supports
# homogeneous media which means it cannot explicitly take into
# account the ground plane. As a workaround, we use two antennas
# of _opposite_ sign surrounded by a single near2far box which
# encloses both antennas. We then use an odd mirror symmetry to
# cut the computational cell in half which is effectively
# equivalent to a PEC boundary condition on one side.
# Note: This setup means that the radiation pattern can only
# be measured in the top half above the dipole.
sources = [
mp.Source(
src=mp.GaussianSource(fcen, fwidth=0.2 * fcen),
component=self.src_cmpt,
center=mp.Vector3(0, +self.h),
),
mp.Source(
src=mp.GaussianSource(fcen, fwidth=0.2 * fcen),
component=self.src_cmpt,
center=mp.Vector3(0, -self.h),
amplitude=-1 if self.src_cmpt == mp.Ez else +1,
),
]
symmetries = [
mp.Mirror(direction=mp.X, phase=+1 if self.src_cmpt == mp.Ez else -1),
mp.Mirror(direction=mp.Y, phase=-1 if self.src_cmpt == mp.Ez else +1),
]
sim = mp.Simulation(
resolution=self.resolution,
cell_size=cell_size,
boundary_layers=boundary_layers,
sources=sources,
symmetries=symmetries,
default_material=mp.Medium(index=self.n),
)
nearfield_box = sim.add_near2far(
fcen,
0,
1,
mp.Near2FarRegion(
center=mp.Vector3(0, 2 * self.h), size=mp.Vector3(2 * self.h, 0)
),
mp.Near2FarRegion(
center=mp.Vector3(0, -2 * self.h),
size=mp.Vector3(2 * self.h, 0),
weight=-1,
),
mp.Near2FarRegion(
center=mp.Vector3(self.h, 0), size=mp.Vector3(0, 4 * self.h)
),
mp.Near2FarRegion(
center=mp.Vector3(-self.h, 0), size=mp.Vector3(0, 4 * self.h), weight=-1
),
)
sim.run(until_after_sources=mp.stop_when_dft_decayed())
return self.radial_flux(sim, nearfield_box, self.r)
def test_pec_ground_plane(self):
"""Unit test for near-to-far field transformation and symmetries.
Verifies that the radiation pattern for a point dipole source a
given height above a perfect-electric conductor (PEC) ground plane
agrees with the theoretical result.
The radiation pattern of a two-element antenna array is equivalent
to the radiation pattern of a single antenna multiplied by its array
factor as derived in Section 6.2 "Two-Element Array" of Antenna Theory:
Analysis and Design, Fourth Edition (2016) by C.A. Balanis.
"""
Pr_fsp = self.free_space_radiation()
Pr_pec = self.pec_ground_plane_radiation()
k = 2 * np.pi / (self.wvl / self.n) # wavevector in medium
Pr_theory = np.zeros(
self.npts,
)
for i, ang in enumerate(self.angles):
Pr_theory[i] = Pr_fsp[i] * 2 * np.sin(k * self.h * np.cos(ang))
Pr_pec_norm = Pr_pec / np.max(Pr_pec)
Pr_theory_norm = (Pr_theory / max(Pr_theory)) ** 2
tol = 0.02
self.assertClose(Pr_pec_norm, Pr_theory_norm, epsilon=tol)
def test_poynting_theorem(self):
"""Unit test for near-to-far field transformation in 2d.
Verifies that the Poynting flux of an Ez-polarized point
dipole source in vacuum is independent of the shape of the
enclosing measurement box due to Poynting's theorem by
considering three arrangements:
(1) bounding box of thenear fields,
(2) bounding circle of the far fields, and
(3) bounding box of the far fields.
"""
resolution = 50
sxy = 4
dpml = 1
cell = mp.Vector3(sxy + 2 * dpml, sxy + 2 * dpml)
pml_layers = mp.PML(dpml)
fcen = 1.0
df = 0.4
sources = [
mp.Source(
src=mp.GaussianSource(fcen, fwidth=df),
center=mp.Vector3(),
component=mp.Ez,
)
]
symmetries = [mp.Mirror(mp.X), mp.Mirror(mp.Y)]
sim = mp.Simulation(
cell_size=cell,
resolution=resolution,
sources=sources,
symmetries=symmetries,
boundary_layers=[pml_layers],
)
nearfield_box = sim.add_near2far(
fcen,
0,
1,
mp.Near2FarRegion(mp.Vector3(y=0.5 * sxy), size=mp.Vector3(sxy)),
mp.Near2FarRegion(
mp.Vector3(y=-0.5 * sxy), size=mp.Vector3(sxy), weight=-1
),
mp.Near2FarRegion(mp.Vector3(0.5 * sxy), size=mp.Vector3(y=sxy)),
mp.Near2FarRegion(
mp.Vector3(-0.5 * sxy), size=mp.Vector3(y=sxy), weight=-1
),
)
flux_box = sim.add_flux(
fcen,
0,
1,
mp.FluxRegion(mp.Vector3(y=0.5 * sxy), size=mp.Vector3(sxy)),
mp.FluxRegion(mp.Vector3(y=-0.5 * sxy), size=mp.Vector3(sxy), weight=-1),
mp.FluxRegion(mp.Vector3(0.5 * sxy), size=mp.Vector3(y=sxy)),
mp.FluxRegion(mp.Vector3(-0.5 * sxy), size=mp.Vector3(y=sxy), weight=-1),
)
sim.run(
until_after_sources=mp.stop_when_fields_decayed(
50, mp.Ez, mp.Vector3(), 1e-8
)
)
near_flux = mp.get_fluxes(flux_box)[0]
r = 1000 / fcen # radius of far field circle
Pr = self.radial_flux(sim, nearfield_box, r)
far_flux_circle = 4 * np.sum(Pr) * 0.5 * np.pi * r / len(Pr)
rr = 20 / fcen # length of far-field square box
res_far = 20 # resolution of far-field square box
far_flux_square = (
nearfield_box.flux(
mp.Y,
mp.Volume(center=mp.Vector3(y=0.5 * rr), size=mp.Vector3(rr)),
res_far,
)[0]
- nearfield_box.flux(
mp.Y,
mp.Volume(center=mp.Vector3(y=-0.5 * rr), size=mp.Vector3(rr)),
res_far,
)[0]
+ nearfield_box.flux(
mp.X,
mp.Volume(center=mp.Vector3(0.5 * rr), size=mp.Vector3(y=rr)),
res_far,
)[0]
- nearfield_box.flux(
mp.X,
mp.Volume(center=mp.Vector3(-0.5 * rr), size=mp.Vector3(y=rr)),
res_far,
)[0]
)
print(
"flux:, {:.6f}, {:.6f}, {:.6f}".format(
near_flux, far_flux_circle, far_flux_square
)
)
self.assertAlmostEqual(near_flux, far_flux_circle, places=2)
self.assertAlmostEqual(far_flux_circle, far_flux_square, places=2)
self.assertAlmostEqual(far_flux_square, near_flux, places=2)
if __name__ == "__main__":
unittest.main()
|
