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import argparse
import numpy as np
import meep as mp
def main(args):
if args.perpendicular:
src_cmpt = mp.Hz
fcen = 0.21 # pulse center frequency
else:
src_cmpt = mp.Ez
fcen = 0.17 # pulse center frequency
n = 3.4 # index of waveguide
w = 1 # ring width
r = 1 # inner radius of ring
pad = 4 # padding between waveguide and edge of PML
dpml = 2 # thickness of PML
pml_layers = [mp.PML(dpml)]
sxy = 2 * (r + w + pad + dpml)
cell_size = mp.Vector3(sxy, sxy)
symmetries = [
mp.Mirror(mp.X, phase=+1 if args.perpendicular else -1),
mp.Mirror(mp.Y, phase=-1 if args.perpendicular else +1),
]
geometry = [
mp.Cylinder(
material=mp.Medium(index=n),
radius=r + w,
height=mp.inf,
center=mp.Vector3(),
),
mp.Cylinder(material=mp.vacuum, radius=r, height=mp.inf, center=mp.Vector3()),
]
# find resonant frequency of unperturbed geometry using broadband source
df = 0.2 * fcen # pulse width (in frequency)
sources = [
mp.Source(
mp.GaussianSource(fcen, fwidth=df),
component=src_cmpt,
center=mp.Vector3(r + 0.1),
),
mp.Source(
mp.GaussianSource(fcen, fwidth=df),
component=src_cmpt,
center=mp.Vector3(-(r + 0.1)),
amplitude=-1,
),
]
sim = mp.Simulation(
cell_size=cell_size,
geometry=geometry,
boundary_layers=pml_layers,
resolution=args.res,
sources=sources,
symmetries=symmetries,
)
h = mp.Harminv(src_cmpt, mp.Vector3(r + 0.1), fcen, df)
sim.run(mp.after_sources(h), until_after_sources=100)
frq_unperturbed = h.modes[0].freq
sim.reset_meep()
# unperturbed geometry with narrowband source centered at resonant frequency
fcen = frq_unperturbed
df = 0.05 * fcen
sources = [
mp.Source(
mp.GaussianSource(fcen, fwidth=df),
component=src_cmpt,
center=mp.Vector3(r + 0.1),
),
mp.Source(
mp.GaussianSource(fcen, fwidth=df),
component=src_cmpt,
center=mp.Vector3(-(r + 0.1)),
amplitude=-1,
),
]
sim = mp.Simulation(
cell_size=cell_size,
geometry=geometry,
boundary_layers=pml_layers,
resolution=args.res,
sources=sources,
symmetries=symmetries,
)
sim.run(until_after_sources=100)
deps = 1 - n**2
deps_inv = 1 - 1 / n**2
if args.perpendicular:
para_integral = (
deps
* 2
* np.pi
* (
r * abs(sim.get_field_point(mp.Ey, mp.Vector3(r))) ** 2
- (r + w) * abs(sim.get_field_point(mp.Ey, mp.Vector3(r + w))) ** 2
)
)
perp_integral = (
deps_inv
* 2
* np.pi
* (
-r * abs(sim.get_field_point(mp.Dy, mp.Vector3(y=r))) ** 2
+ (r + w) * abs(sim.get_field_point(mp.Dy, mp.Vector3(y=r + w))) ** 2
)
)
numerator_integral = para_integral + perp_integral
else:
numerator_integral = (
deps
* 2
* np.pi
* (
r * abs(sim.get_field_point(mp.Ez, mp.Vector3(r))) ** 2
- (r + w) * abs(sim.get_field_point(mp.Ez, mp.Vector3(r + w))) ** 2
)
)
denominator_integral = sim.electric_energy_in_box(
center=mp.Vector3(), size=mp.Vector3(sxy - 2 * dpml, sxy - 2 * dpml)
)
perturb_theory_dw_dR = (
-frq_unperturbed * numerator_integral / (8 * denominator_integral)
)
# perturbed geometry with narrowband source
dr = 0.04
sim.reset_meep()
sources = [
mp.Source(
mp.GaussianSource(fcen, fwidth=df),
component=src_cmpt,
center=mp.Vector3(r + dr + 0.1),
),
mp.Source(
mp.GaussianSource(fcen, fwidth=df),
component=src_cmpt,
center=mp.Vector3(-(r + dr + 0.1)),
amplitude=-1,
),
]
geometry = [
mp.Cylinder(
material=mp.Medium(index=n),
radius=r + dr + w,
height=mp.inf,
center=mp.Vector3(),
),
mp.Cylinder(
material=mp.vacuum, radius=r + dr, height=mp.inf, center=mp.Vector3()
),
]
sim = mp.Simulation(
cell_size=cell_size,
geometry=geometry,
boundary_layers=pml_layers,
resolution=args.res,
sources=sources,
symmetries=symmetries,
)
h = mp.Harminv(src_cmpt, mp.Vector3(r + dr + 0.1), fcen, df)
sim.run(mp.after_sources(h), until_after_sources=100)
frq_perturbed = h.modes[0].freq
finite_diff_dw_dR = (frq_perturbed - frq_unperturbed) / dr
print(
f"dwdR:, {perturb_theory_dw_dR} (pert. theory), {finite_diff_dw_dR} (finite diff.)"
)
if __name__ == "__main__":
parser = argparse.ArgumentParser()
parser.add_argument(
"-perpendicular",
action="store_true",
help="use perpendicular field source (default: parallel field source)",
)
parser.add_argument(
"-res", type=int, default=30, help="resolution (default: 30 pixels/um)"
)
args = parser.parse_args()
main(args)
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