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import math
import matplotlib.pyplot as plt
import numpy as np
import meep as mp
resolution = 60 # pixels/μm
dpml = 1.0 # PML thickness
dsub = 3.0 # substrate thickness
dpad = 3.0 # padding between grating and PML
gp = 10.0 # grating period
gh = 0.5 # grating height
gdc = 0.5 # grating duty cycle
sx = dpml + dsub + gh + dpad + dpml
sy = gp
cell_size = mp.Vector3(sx, sy, 0)
pml_layers = [mp.PML(thickness=dpml, direction=mp.X)]
wvl_min = 0.4 # min wavelength
wvl_max = 0.6 # max wavelength
fmin = 1 / wvl_max # min frequency
fmax = 1 / wvl_min # max frequency
fcen = 0.5 * (fmin + fmax) # center frequency
df = fmax - fmin # frequency width
src_pt = mp.Vector3(-0.5 * sx + dpml + 0.5 * dsub, 0, 0)
sources = [
mp.Source(
mp.GaussianSource(fcen, fwidth=df),
component=mp.Ez,
center=src_pt,
size=mp.Vector3(0, sy, 0),
)
]
k_point = mp.Vector3(0, 0, 0)
glass = mp.Medium(index=1.5)
symmetries = [mp.Mirror(mp.Y)]
sim = mp.Simulation(
resolution=resolution,
cell_size=cell_size,
boundary_layers=pml_layers,
k_point=k_point,
default_material=glass,
sources=sources,
symmetries=symmetries,
)
nfreq = 21
mon_pt = mp.Vector3(0.5 * sx - dpml - 0.5 * dpad, 0, 0)
flux_mon = sim.add_flux(
fcen, df, nfreq, mp.FluxRegion(center=mon_pt, size=mp.Vector3(0, sy, 0))
)
sim.run(until_after_sources=mp.stop_when_fields_decayed(50, mp.Ez, mon_pt, 1e-9))
input_flux = mp.get_fluxes(flux_mon)
sim.reset_meep()
geometry = [
mp.Block(
material=glass,
size=mp.Vector3(dpml + dsub, mp.inf, mp.inf),
center=mp.Vector3(-0.5 * sx + 0.5 * (dpml + dsub), 0, 0),
),
mp.Block(
material=glass,
size=mp.Vector3(gh, gdc * gp, mp.inf),
center=mp.Vector3(-0.5 * sx + dpml + dsub + 0.5 * gh, 0, 0),
),
]
sim = mp.Simulation(
resolution=resolution,
cell_size=cell_size,
boundary_layers=pml_layers,
geometry=geometry,
k_point=k_point,
sources=sources,
symmetries=symmetries,
)
mode_mon = sim.add_flux(
fcen, df, nfreq, mp.FluxRegion(center=mon_pt, size=mp.Vector3(0, sy, 0))
)
sim.run(until_after_sources=mp.stop_when_fields_decayed(50, mp.Ez, mon_pt, 1e-9))
freqs = mp.get_eigenmode_freqs(mode_mon)
nmode = 10
res = sim.get_eigenmode_coefficients(
mode_mon, range(1, nmode + 1), eig_parity=mp.ODD_Z + mp.EVEN_Y
)
coeffs = res.alpha
kdom = res.kdom
mode_wvl = []
mode_angle = []
mode_tran = []
for nm in range(nmode):
for nf in range(nfreq):
mode_wvl.append(1 / freqs[nf])
mode_angle.append(math.degrees(math.acos(kdom[nm * nfreq + nf].x / freqs[nf])))
tran = abs(coeffs[nm, nf, 0]) ** 2 / input_flux[nf]
mode_tran.append(0.5 * tran if nm != 0 else tran)
print(
"grating{}:, {:.5f}, {:.2f}, {:.8f}".format(
nm, mode_wvl[-1], mode_angle[-1], mode_tran[-1]
)
)
tran_max = round(max(mode_tran), 1)
plt.figure()
plt.pcolormesh(
np.reshape(mode_wvl, (nmode, nfreq)),
np.reshape(mode_angle, (nmode, nfreq)),
np.reshape(mode_tran, (nmode, nfreq)),
cmap="Blues",
shading="nearest",
vmin=0,
vmax=tran_max,
)
plt.axis([min(mode_wvl), max(mode_wvl), min(mode_angle), max(mode_angle)])
plt.xlabel("wavelength (μm)")
plt.ylabel("diffraction angle (degrees)")
plt.xticks(list(np.arange(0.4, 0.7, 0.1)))
plt.yticks(list(range(0, 35, 5)))
plt.title("transmittance of diffraction orders")
cbar = plt.colorbar()
cbar.set_ticks(list(np.arange(0, tran_max + 0.1, 0.1)))
cbar.set_ticklabels([f"{t:.1f}" for t in np.arange(0, tran_max + 0.1, 0.1)])
plt.show()
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