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import unittest
import numpy as np
import meep as mp
class TestLDOS(unittest.TestCase):
@classmethod
def setUp(cls):
cls.resolution = 25 # pixels/μm
cls.dpml = 0.5 # thickness of PML
cls.dair = 1.0 # thickness of air padding
cls.L = 6.0 # length of non-PML region
cls.n = 2.4 # refractive index of surrounding medium
cls.wvl = 1.0 # wavelength (in vacuum)
cls.fcen = 1 / cls.wvl
# source properties (cylindrical)
cls.df = 0.05 * cls.fcen
cls.cutoff = 10.0
cls.src = mp.GaussianSource(cls.fcen, fwidth=cls.df, cutoff=cls.cutoff)
# termination criteria
cls.tol = 1e-8
def bulk_ldos_cyl(self):
"""Computes the LDOS of a point dipole in a homogeneous dielectric
medium in cylindrical coordinates.
"""
sr = self.L + self.dpml
sz = self.L + 2 * self.dpml
cell_size = mp.Vector3(sr, 0, sz)
pml_layers = [mp.PML(self.dpml)]
sources = [
mp.Source(
src=self.src,
component=mp.Er,
center=mp.Vector3(),
)
]
sim = mp.Simulation(
resolution=self.resolution,
cell_size=cell_size,
boundary_layers=pml_layers,
sources=sources,
dimensions=mp.CYLINDRICAL,
m=-1,
default_material=mp.Medium(index=self.n),
)
sim.run(
mp.dft_ldos(self.fcen, 0, 1),
until_after_sources=mp.stop_when_fields_decayed(
20, mp.Er, mp.Vector3(), self.tol
),
)
return sim.ldos_data[0]
def cavity_ldos_cyl(self, sz):
"""Computes the LDOS of a point dipole in a planar cavity with
lossless metallic walls in cylindrical coordinates.
Args:
sz: thickness of cavity.
"""
sr = self.L + self.dpml
cell_size = mp.Vector3(sr, 0, sz)
pml_layers = [mp.PML(self.dpml, direction=mp.R)]
sources = [
mp.Source(
src=self.src,
component=mp.Er,
center=mp.Vector3(),
)
]
sim = mp.Simulation(
resolution=self.resolution,
cell_size=cell_size,
boundary_layers=pml_layers,
sources=sources,
dimensions=mp.CYLINDRICAL,
m=-1,
default_material=mp.Medium(index=self.n),
)
sim.run(
mp.dft_ldos(self.fcen, 0, 1),
until_after_sources=mp.stop_when_fields_decayed(
20, mp.Er, mp.Vector3(), self.tol
),
)
return sim.ldos_data[0]
def bulk_ldos_3D(self):
"""Computes the LDOS of a point dipole in a homogeneous dielectric
medium in 3D Cartesian coordinates.
"""
s = self.L + 2 * self.dpml
cell_size = mp.Vector3(s, s, s)
pml_layers = [mp.PML(self.dpml)]
sources = [
mp.Source(
src=mp.GaussianSource(self.fcen, fwidth=0.2 * self.fcen),
component=mp.Ex,
center=mp.Vector3(),
)
]
symmetries = [
mp.Mirror(direction=mp.X, phase=-1),
mp.Mirror(direction=mp.Y),
mp.Mirror(direction=mp.Z),
]
sim = mp.Simulation(
resolution=self.resolution,
cell_size=cell_size,
boundary_layers=pml_layers,
sources=sources,
symmetries=symmetries,
default_material=mp.Medium(index=self.n),
)
sim.run(
mp.dft_ldos(self.fcen, 0, 1),
until_after_sources=mp.stop_when_fields_decayed(
20, mp.Ex, mp.Vector3(), self.tol
),
)
return sim.ldos_data[0]
def cavity_ldos_3D(self, sz):
"""Computes the LDOS of a point dipole in a planar cavity with
lossless metallic walls in 3D Cartesian coordinates.
Args:
sz: thickness of cavity.
"""
sxy = self.L + 2 * self.dpml
cell_size = mp.Vector3(sxy, sxy, sz)
boundary_layers = [
mp.PML(self.dpml, direction=mp.X),
mp.PML(self.dpml, direction=mp.Y),
]
sources = [
mp.Source(
src=mp.GaussianSource(self.fcen, fwidth=0.2 * self.fcen),
component=mp.Ex,
center=mp.Vector3(),
)
]
symmetries = [
mp.Mirror(direction=mp.X, phase=-1),
mp.Mirror(direction=mp.Y),
mp.Mirror(direction=mp.Z),
]
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),
)
sim.run(
mp.dft_ldos(ldos=mp.Ldos(self.fcen, 0, 1)),
until_after_sources=mp.stop_when_fields_decayed(
20, mp.Ex, mp.Vector3(), self.tol
),
)
return sim.ldos_data[0]
def purcell_enh_theory(self, c):
"""Computes the Purcell enhancement factor of a point dipole in a planar
dielectric cavity with lossless metallic walls using equation 7 of:
I. Abram et al., IEEE J. Quantum Electronics, Vol. 34, pp. 71-76 (1998).
Args:
c: cavity thickness in units of wavelength in the cavity medium.
"""
return 3 * np.fix(c + 0.5) / (4 * c) + (
4 * np.power(np.fix(c + 0.5), 3) - np.fix(c + 0.5)
) / (16 * np.power(c, 3))
def ext_eff_cyl(self, dmat, h):
"""Computes the extraction efficiency of a point dipole embedded
within a dielectric layer above a lossless ground plane in
cylindrical coordinates.
Args:
dmat: thickness of dielectric layer.
h: height of dipole above ground plane as fraction of dmat.
"""
sr = self.L + self.dpml
sz = dmat + self.dair + self.dpml
cell_size = mp.Vector3(sr, 0, sz)
boundary_layers = [
mp.PML(self.dpml, direction=mp.R),
mp.PML(self.dpml, direction=mp.Z, side=mp.High),
]
src_cmpt = mp.Er
src_pt = mp.Vector3(0, 0, -0.5 * sz + h * dmat)
sources = [mp.Source(src=self.src, component=src_cmpt, center=src_pt)]
geometry = [
mp.Block(
material=mp.Medium(index=self.n),
center=mp.Vector3(0, 0, -0.5 * sz + 0.5 * dmat),
size=mp.Vector3(mp.inf, mp.inf, dmat),
)
]
sim = mp.Simulation(
resolution=self.resolution,
cell_size=cell_size,
dimensions=mp.CYLINDRICAL,
m=-1,
boundary_layers=boundary_layers,
sources=sources,
geometry=geometry,
)
flux_air = sim.add_flux(
self.fcen,
0,
1,
mp.FluxRegion(
center=mp.Vector3(0.5 * self.L, 0, 0.5 * sz - self.dpml),
size=mp.Vector3(self.L, 0, 0),
),
mp.FluxRegion(
center=mp.Vector3(self.L, 0, 0.5 * sz - self.dpml - 0.5 * self.dair),
size=mp.Vector3(0, 0, self.dair),
),
)
sim.run(
mp.dft_ldos(self.fcen, 0, 1),
until_after_sources=mp.stop_when_fields_decayed(
20, src_cmpt, src_pt, self.tol
),
)
out_flux = mp.get_fluxes(flux_air)[0]
dV = np.pi / (self.resolution**3)
total_flux = -np.real(sim.ldos_Fdata[0] * np.conj(sim.ldos_Jdata[0])) * dV
ext_eff = out_flux / total_flux
print(f"extraction efficiency (cyl):, " f"{dmat:.4f}, {h:.4f}, {ext_eff:.6f}")
return ext_eff
def ext_eff_3D(self, dmat, h):
"""Computes the extraction efficiency of a point dipole embedded
within a dielectric layer above a lossless ground plane in
3D Cartesian coordinates.
Args:
dmat: thickness of dielectric layer.
h: height of dipole above ground plane as fraction of dmat.
"""
sxy = self.L + 2 * self.dpml
sz = dmat + self.dair + self.dpml
cell_size = mp.Vector3(sxy, sxy, sz)
symmetries = [mp.Mirror(direction=mp.X, phase=-1), mp.Mirror(direction=mp.Y)]
boundary_layers = [
mp.PML(self.dpml, direction=mp.X),
mp.PML(self.dpml, direction=mp.Y),
mp.PML(self.dpml, direction=mp.Z, side=mp.High),
]
src_cmpt = mp.Ex
src_pt = mp.Vector3(0, 0, -0.5 * sz + h * dmat)
sources = [
mp.Source(
src=mp.GaussianSource(self.fcen, fwidth=0.1 * self.fcen),
component=src_cmpt,
center=src_pt,
)
]
geometry = [
mp.Block(
material=mp.Medium(index=self.n),
center=mp.Vector3(0, 0, -0.5 * sz + 0.5 * dmat),
size=mp.Vector3(mp.inf, mp.inf, dmat),
)
]
sim = mp.Simulation(
resolution=self.resolution,
cell_size=cell_size,
boundary_layers=boundary_layers,
sources=sources,
geometry=geometry,
symmetries=symmetries,
)
flux_air = sim.add_flux(
self.fcen,
0,
1,
mp.FluxRegion(
center=mp.Vector3(0, 0, 0.5 * sz - self.dpml),
size=mp.Vector3(self.L, self.L, 0),
),
mp.FluxRegion(
center=mp.Vector3(
0.5 * self.L, 0, 0.5 * sz - self.dpml - 0.5 * self.dair
),
size=mp.Vector3(0, self.L, self.dair),
),
mp.FluxRegion(
center=mp.Vector3(
-0.5 * self.L, 0, 0.5 * sz - self.dpml - 0.5 * self.dair
),
size=mp.Vector3(0, self.L, self.dair),
weight=-1.0,
),
mp.FluxRegion(
center=mp.Vector3(
0, 0.5 * self.L, 0.5 * sz - self.dpml - 0.5 * self.dair
),
size=mp.Vector3(self.L, 0, self.dair),
),
mp.FluxRegion(
center=mp.Vector3(
0, -0.5 * self.L, 0.5 * sz - self.dpml - 0.5 * self.dair
),
size=mp.Vector3(self.L, 0, self.dair),
weight=-1.0,
),
)
sim.run(
mp.dft_ldos(self.fcen, 0, 1),
until_after_sources=mp.stop_when_fields_decayed(
20, src_cmpt, src_pt, self.tol
),
)
out_flux = mp.get_fluxes(flux_air)[0]
dV = 1 / (self.resolution**3)
total_flux = -np.real(sim.ldos_Fdata[0] * np.conj(sim.ldos_Jdata[0])) * dV
ext_eff = out_flux / total_flux
print(f"extraction efficiency (3D):, " f"{dmat:.4f}, {h:.4f}, {ext_eff:.6f}")
return ext_eff
def test_ldos_cyl(self):
"""Verifies that the Purcell enhancement factor of a parallel dipole
in a planar dielectric cavity with lossless metallic walls computed in
cylindrical coordinates agrees with the analytic result.
"""
ldos_bulk = self.bulk_ldos_cyl()
# not a Van Hove singularity
cavity_thickness = 1.63
gap = cavity_thickness * self.wvl / self.n
ldos_cavity = self.cavity_ldos_cyl(gap)
# Purcell enhancement factor (relative to bulk medium)
pe_meep = ldos_cavity / ldos_bulk
pe_theory = self.purcell_enh_theory(cavity_thickness)
rel_err = abs(pe_meep - pe_theory) / pe_theory
print(
"ldos-cyl:, {:.6f} (Meep), {:.6f} (theory), "
"{:.6f} (error)".format(pe_meep, pe_theory, rel_err)
)
self.assertAlmostEqual(pe_meep, pe_theory, delta=0.1)
def test_ldos_3D(self):
"""Verifies that the Purcell enhancement factor of a parallel dipole
in a planar dielectric cavity with lossless metallic walls computed in
3D Cartesian coordinates agrees with the analytic result.
"""
ldos_bulk = self.bulk_ldos_3D()
# not a Van Hove singularity
cavity_thickness = 0.75
gap = cavity_thickness * self.wvl / self.n
ldos_cavity = self.cavity_ldos_3D(gap)
# Purcell enhancement factor (relative to bulk medium)
pe_meep = ldos_cavity / ldos_bulk
pe_theory = self.purcell_enh_theory(cavity_thickness)
rel_err = abs(pe_meep - pe_theory) / pe_theory
print(
"ldos-3D:, {:.6f} (Meep), {:.6f} (theory), "
"{:.6f} (error)".format(pe_meep, pe_theory, rel_err)
)
self.assertAlmostEqual(pe_meep, pe_theory, delta=0.1)
def test_ldos_ext_eff(self):
"""Verifies that the extraction efficiency of a point dipole in a
dielectric layer above a lossless ground plane computed in cylindrical
and 3D Cartesian coordinates agree.
"""
layer_thickness = 0.5 * self.wvl / self.n
dipole_height = 0.5
ext_eff_cyl = self.ext_eff_cyl(layer_thickness, dipole_height)
ext_eff_3D = self.ext_eff_3D(layer_thickness, dipole_height)
self.assertAlmostEqual(ext_eff_cyl, ext_eff_3D, places=2)
if __name__ == "__main__":
unittest.main()
|
