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import meep as mp
import numpy as np
import argparse
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("dwdR:, {} (pert. theory), {} (finite diff.)".format(perturb_theory_dw_dR,finite_diff_dw_dR))
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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