1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187
|
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
m = 5 # angular dependence
pml_layers = [mp.PML(dpml)]
sr = r + w + pad + dpml # radial size (cell is from 0 to sr)
dimensions = mp.CYLINDRICAL # coordinate system is (r,phi,z) instead of (x,y,z)
cell = mp.Vector3(sr)
geometry = [
mp.Block(
center=mp.Vector3(r + (w / 2)),
size=mp.Vector3(w, mp.inf, mp.inf),
material=mp.Medium(index=n),
)
]
# 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),
)
]
sim = mp.Simulation(
cell_size=cell,
geometry=geometry,
boundary_layers=pml_layers,
resolution=args.res,
sources=sources,
dimensions=dimensions,
m=m,
)
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),
)
]
sim = mp.Simulation(
cell_size=cell,
geometry=geometry,
boundary_layers=pml_layers,
resolution=args.res,
sources=sources,
dimensions=dimensions,
m=m,
)
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.Ep, mp.Vector3(r))) ** 2
- (r + w) * abs(sim.get_field_point(mp.Ep, mp.Vector3(r + w))) ** 2
)
)
perp_integral = (
deps_inv
* 2
* np.pi
* (
-r * abs(sim.get_field_point(mp.Dr, mp.Vector3(r))) ** 2
+ (r + w) * abs(sim.get_field_point(mp.Dr, mp.Vector3(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(0.5 * sr), size=mp.Vector3(sr)
)
perturb_theory_dw_dR = (
-frq_unperturbed * numerator_integral / (4 * denominator_integral)
)
sim.reset_meep()
# perturbed geometry with narrowband source
dr = 0.01
sources = [
mp.Source(
mp.GaussianSource(fcen, fwidth=df),
component=src_cmpt,
center=mp.Vector3(r + dr + 0.1),
)
]
geometry = [
mp.Block(
center=mp.Vector3(r + dr + (w / 2)),
size=mp.Vector3(w, mp.inf, mp.inf),
material=mp.Medium(index=n),
)
]
sim = mp.Simulation(
cell_size=cell,
geometry=geometry,
boundary_layers=pml_layers,
resolution=args.res,
sources=sources,
dimensions=dimensions,
m=m,
)
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=100, help="resolution (default: 100 pixels/um)"
)
args = parser.parse_args()
main(args)
|