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import matplotlib.pyplot as plt
import meep as mp
resolution = 25 # pixels/μm
w1 = 1.0 # width of waveguide 1
w2 = 2.0 # width of waveguide 2
Lw = 10.0 # length of waveguides 1 and 2
# lengths of waveguide taper
Lts = [2**m for m in range(4)]
dair = 3.0 # length of air region
dpml_x = 6.0 # length of PML in x direction
dpml_y = 2.0 # length of PML in y direction
sy = dpml_y + dair + w2 + dair + dpml_y
Si = mp.Medium(epsilon=12.0)
boundary_layers = [mp.PML(dpml_x, direction=mp.X), mp.PML(dpml_y, direction=mp.Y)]
lcen = 6.67 # mode wavelength
fcen = 1 / lcen # mode frequency
symmetries = [mp.Mirror(mp.Y)]
R_coeffs = []
R_flux = []
for Lt in Lts:
sx = dpml_x + Lw + Lt + Lw + dpml_x
cell_size = mp.Vector3(sx, sy, 0)
src_pt = mp.Vector3(-0.5 * sx + dpml_x + 0.2 * Lw)
sources = [
mp.EigenModeSource(
src=mp.GaussianSource(fcen, fwidth=0.2 * fcen),
center=src_pt,
size=mp.Vector3(y=sy - 2 * dpml_y),
eig_match_freq=True,
eig_parity=mp.ODD_Z + mp.EVEN_Y,
)
]
# straight waveguide
vertices = [
mp.Vector3(-0.5 * sx - 1, 0.5 * w1),
mp.Vector3(0.5 * sx + 1, 0.5 * w1),
mp.Vector3(0.5 * sx + 1, -0.5 * w1),
mp.Vector3(-0.5 * sx - 1, -0.5 * w1),
]
sim = mp.Simulation(
resolution=resolution,
cell_size=cell_size,
boundary_layers=boundary_layers,
geometry=[mp.Prism(vertices, height=mp.inf, material=Si)],
sources=sources,
symmetries=symmetries,
)
mon_pt = mp.Vector3(-0.5 * sx + dpml_x + 0.7 * Lw)
flux = sim.add_flux(
fcen, 0, 1, mp.FluxRegion(center=mon_pt, size=mp.Vector3(y=sy - 2 * dpml_y))
)
sim.run(until_after_sources=mp.stop_when_fields_decayed(50, mp.Ez, mon_pt, 1e-9))
res = sim.get_eigenmode_coefficients(flux, [1], eig_parity=mp.ODD_Z + mp.EVEN_Y)
incident_coeffs = res.alpha
incident_flux = mp.get_fluxes(flux)
incident_flux_data = sim.get_flux_data(flux)
sim.reset_meep()
# linear taper
vertices = [
mp.Vector3(-0.5 * sx - 1, 0.5 * w1),
mp.Vector3(-0.5 * Lt, 0.5 * w1),
mp.Vector3(0.5 * Lt, 0.5 * w2),
mp.Vector3(0.5 * sx + 1, 0.5 * w2),
mp.Vector3(0.5 * sx + 1, -0.5 * w2),
mp.Vector3(0.5 * Lt, -0.5 * w2),
mp.Vector3(-0.5 * Lt, -0.5 * w1),
mp.Vector3(-0.5 * sx - 1, -0.5 * w1),
]
sim = mp.Simulation(
resolution=resolution,
cell_size=cell_size,
boundary_layers=boundary_layers,
geometry=[mp.Prism(vertices, height=mp.inf, material=Si)],
sources=sources,
symmetries=symmetries,
)
flux = sim.add_flux(
fcen, 0, 1, mp.FluxRegion(center=mon_pt, size=mp.Vector3(y=sy - 2 * dpml_y))
)
sim.load_minus_flux_data(flux, incident_flux_data)
sim.run(until_after_sources=mp.stop_when_fields_decayed(50, mp.Ez, mon_pt, 1e-9))
res2 = sim.get_eigenmode_coefficients(flux, [1], eig_parity=mp.ODD_Z + mp.EVEN_Y)
taper_coeffs = res2.alpha
taper_flux = mp.get_fluxes(flux)
R_coeffs.append(
abs(taper_coeffs[0, 0, 1]) ** 2 / abs(incident_coeffs[0, 0, 0]) ** 2
)
R_flux.append(-taper_flux[0] / incident_flux[0])
print(f"refl:, {Lt}, {R_coeffs[-1]:.8f}, {R_flux[-1]:.8f}")
if mp.am_master():
plt.figure()
plt.loglog(Lts, R_coeffs, "bo-", label="mode decomposition")
plt.loglog(Lts, R_flux, "ro-", label="Poynting flux")
plt.loglog(
Lts,
[0.005 / Lt**2 for Lt in Lts],
"k-",
label=r"quadratic reference (1/Lt$^2$)",
)
plt.legend(loc="upper right")
plt.xlabel("taper length Lt (μm)")
plt.ylabel("reflectance")
plt.show()
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