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import math
import matplotlib.pyplot as plt
import numpy as np
from meep.materials import fused_quartz
import meep as mp
resolution = 200 # pixels/μm
dpml = 1.0
sz = 10 + 2 * dpml
cell_size = mp.Vector3(z=sz)
pml_layers = [mp.PML(dpml)]
wvl_min = 0.4
wvl_max = 0.8
fmin = 1 / wvl_max
fmax = 1 / wvl_min
fcen = 0.5 * (fmax + fmin)
df = fmax - fmin
nfreq = 50
sources = [
mp.Source(
mp.GaussianSource(fcen, fwidth=df),
component=mp.Ex,
center=mp.Vector3(z=-0.5 * sz + dpml),
)
]
sim = mp.Simulation(
cell_size=cell_size,
boundary_layers=pml_layers,
sources=sources,
dimensions=1,
resolution=resolution,
)
refl_fr = mp.FluxRegion(center=mp.Vector3(z=-0.25 * sz))
refl = sim.add_flux(fcen, df, nfreq, refl_fr)
sim.run(until_after_sources=mp.stop_when_fields_decayed(50, mp.Ex, mp.Vector3(), 1e-9))
empty_flux = mp.get_fluxes(refl)
empty_data = sim.get_flux_data(refl)
sim.reset_meep()
geometry = [
mp.Block(
mp.Vector3(mp.inf, mp.inf, 0.5 * sz),
center=mp.Vector3(z=0.25 * sz),
material=fused_quartz,
)
]
sim = mp.Simulation(
cell_size=cell_size,
boundary_layers=pml_layers,
geometry=geometry,
sources=sources,
dimensions=1,
resolution=resolution,
)
refl = sim.add_flux(fcen, df, nfreq, refl_fr)
sim.load_minus_flux_data(refl, empty_data)
sim.run(until_after_sources=mp.stop_when_fields_decayed(50, mp.Ex, mp.Vector3(), 1e-9))
refl_flux = mp.get_fluxes(refl)
R_meep = -1 * np.divide(refl_flux, empty_flux)
freqs = mp.get_flux_freqs(refl)
wvls = np.divide(1, freqs)
eps_quartz = (
lambda l: 1
+ 0.6961663 * math.pow(l, 2) / (pow(l, 2) - pow(0.0684043, 2))
+ 0.4079426 * pow(l, 2) / (pow(l, 2) - pow(0.1162414, 2))
+ 0.8974794 * pow(l, 2) / (pow(l, 2) - pow(9.896161, 2))
)
R_fresnel = lambda l: math.pow(
math.fabs(1 - math.sqrt(eps_quartz(l))) / (1 + math.sqrt(eps_quartz(l))), 2
)
R_analytic = [R_fresnel(i) for i in wvls]
plt.figure()
plt.plot(wvls, R_meep, "bo-", label="meep")
plt.plot(wvls, R_analytic, "rs-", label="analytic")
plt.xlabel("wavelength (μm)")
plt.ylabel("reflectance")
plt.axis([0.4, 0.8, 0.0340, 0.0365])
plt.xticks(list(np.arange(0.4, 0.9, 0.1)))
plt.legend(loc="upper right")
plt.show()
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