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import math
import matplotlib.pyplot as plt
import numpy as np
import meep as mp
resolution = 25 # pixels/μm
dpml = 1.0 # PML thickness
dsub = 2.0 # substrate thickness
dpad = 2.0 # padding betweeen zone plate and PML
zh = 0.5 # zone-plate height
zN = 25 # number of zones (odd zones: π phase shift, even zones: none)
focal_length = 200 # focal length of zone plate
spot_length = 100 # far-field line length
ff_res = 10 # far-field resolution
pml_layers = [mp.PML(thickness=dpml)]
wvl_cen = 0.5
frq_cen = 1 / wvl_cen
dfrq = 0.2 * frq_cen
## radii of zones
## ref: eq. 7 of http://zoneplate.lbl.gov/theory
r = [
math.sqrt(n * wvl_cen * (focal_length + n * wvl_cen / 4)) for n in range(1, zN + 1)
]
sr = r[-1] + dpad + dpml
sz = dpml + dsub + zh + dpad + dpml
cell_size = mp.Vector3(sr, 0, sz)
sources = [
mp.Source(
mp.GaussianSource(frq_cen, fwidth=dfrq, is_integrated=True),
component=mp.Er,
center=mp.Vector3(0.5 * sr, 0, -0.5 * sz + dpml),
size=mp.Vector3(sr),
),
mp.Source(
mp.GaussianSource(frq_cen, fwidth=dfrq, is_integrated=True),
component=mp.Ep,
center=mp.Vector3(0.5 * sr, 0, -0.5 * sz + dpml),
size=mp.Vector3(sr),
amplitude=-1j,
),
]
glass = mp.Medium(index=1.5)
geometry = [
mp.Block(
material=glass,
size=mp.Vector3(sr, 0, dpml + dsub),
center=mp.Vector3(0.5 * sr, 0, -0.5 * sz + 0.5 * (dpml + dsub)),
)
]
geometry.extend(
mp.Block(
material=glass if n % 2 == 0 else mp.vacuum,
size=mp.Vector3(r[n], 0, zh),
center=mp.Vector3(0.5 * r[n], 0, -0.5 * sz + dpml + dsub + 0.5 * zh),
)
for n in range(zN - 1, -1, -1)
)
sim = mp.Simulation(
cell_size=cell_size,
boundary_layers=pml_layers,
resolution=resolution,
sources=sources,
geometry=geometry,
dimensions=mp.CYLINDRICAL,
m=-1,
)
## near-field monitor
n2f_obj = sim.add_near2far(
frq_cen,
0,
1,
mp.Near2FarRegion(
center=mp.Vector3(0.5 * (sr - dpml), 0, 0.5 * sz - dpml),
size=mp.Vector3(sr - dpml),
),
mp.Near2FarRegion(
center=mp.Vector3(sr - dpml, 0, 0.5 * sz - dpml - 0.5 * (dsub + zh + dpad)),
size=mp.Vector3(z=dsub + zh + dpad),
),
)
sim.plot2D()
if mp.am_master():
plt.savefig("zone_plate_epsilon.png", bbox_inches="tight", dpi=150)
sim.run(until_after_sources=100)
ff_r = sim.get_farfields(
n2f_obj,
ff_res,
center=mp.Vector3(
0.5 * (sr - dpml), 0, -0.5 * sz + dpml + dsub + zh + focal_length
),
size=mp.Vector3(sr - dpml),
)
ff_z = sim.get_farfields(
n2f_obj,
ff_res,
center=mp.Vector3(z=-0.5 * sz + dpml + dsub + zh + focal_length),
size=mp.Vector3(z=spot_length),
)
E2_r = (
np.absolute(ff_r["Ex"]) ** 2
+ np.absolute(ff_r["Ey"]) ** 2
+ np.absolute(ff_r["Ez"]) ** 2
)
E2_z = (
np.absolute(ff_z["Ex"]) ** 2
+ np.absolute(ff_z["Ey"]) ** 2
+ np.absolute(ff_z["Ez"]) ** 2
)
if mp.am_master():
plt.figure(dpi=200)
plt.subplot(1, 2, 1)
plt.semilogy(np.linspace(0, sr - dpml, len(E2_r)), E2_r, "bo-")
plt.xlim(-2, 20)
plt.xticks(list(np.arange(0, 25, 5)))
plt.grid(True, axis="y", which="both", ls="-")
plt.xlabel(r"$r$ coordinate (μm)")
plt.ylabel(r"energy density of far fields, |E|$^2$")
plt.subplot(1, 2, 2)
plt.semilogy(
np.linspace(
focal_length - 0.5 * spot_length,
focal_length + 0.5 * spot_length,
len(E2_z),
),
E2_z,
"bo-",
)
plt.grid(True, axis="y", which="both", ls="-")
plt.xlabel(r"$z$ coordinate (μm)")
plt.ylabel(r"energy density of far fields, |E|$^2$")
plt.suptitle(f"binary-phase zone plate with focal length $z$ = {focal_length} μm")
plt.tight_layout()
plt.savefig("zone_plate_farfields.png")
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