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# -*- coding: utf-8 -*-
import meep as mp
import numpy as np
import matplotlib.pyplot as plt
resolution = 50 # pixels/μm
dpml = 1.0 # PML thickness
dsub = 2.0 # substrate thickness
dpad = 2.0 # padding between grating and PML
lcen = 0.5 # center wavelength
fcen = 1/lcen # center frequency
df = 0.2*fcen # frequency width
focal_length = 200 # focal length of metalens
spot_length = 100 # far field line length
ff_res = 10 # far field resolution (points/μm)
k_point = mp.Vector3(0,0,0)
glass = mp.Medium(index=1.5)
pml_layers = [mp.PML(thickness=dpml,direction=mp.X)]
symmetries=[mp.Mirror(mp.Y)]
def grating(gp,gh,gdc_list):
sx = dpml+dsub+gh+dpad+dpml
src_pt = mp.Vector3(-0.5*sx+dpml+0.5*dsub)
mon_pt = mp.Vector3(0.5*sx-dpml-0.5*dpad)
geometry = [mp.Block(material=glass,
size=mp.Vector3(dpml+dsub,mp.inf,mp.inf),
center=mp.Vector3(-0.5*sx+0.5*(dpml+dsub)))]
num_cells = len(gdc_list)
if num_cells == 1:
sy = gp
cell_size = mp.Vector3(sx,sy,0)
sources = [mp.Source(mp.GaussianSource(fcen, fwidth=df),
component=mp.Ez,
center=src_pt,
size=mp.Vector3(y=sy))]
sim = mp.Simulation(resolution=resolution,
cell_size=cell_size,
boundary_layers=pml_layers,
k_point=k_point,
default_material=glass,
sources=sources,
symmetries=symmetries)
flux_obj = sim.add_flux(fcen, 0, 1, mp.FluxRegion(center=mon_pt, size=mp.Vector3(y=sy)))
sim.run(until_after_sources=50)
input_flux = mp.get_fluxes(flux_obj)
sim.reset_meep()
geometry.append(mp.Block(material=glass, size=mp.Vector3(gh,gdc_list[0]*gp,mp.inf), center=mp.Vector3(-0.5*sx+dpml+dsub+0.5*gh)))
sim = mp.Simulation(resolution=resolution,
cell_size=cell_size,
boundary_layers=pml_layers,
geometry=geometry,
k_point=k_point,
sources=sources,
symmetries=symmetries)
flux_obj = sim.add_flux(fcen, 0, 1, mp.FluxRegion(center=mon_pt, size=mp.Vector3(y=sy)))
sim.run(until_after_sources=200)
freqs = mp.get_eigenmode_freqs(flux_obj)
res = sim.get_eigenmode_coefficients(flux_obj, [1], eig_parity=mp.ODD_Z+mp.EVEN_Y)
coeffs = res.alpha
mode_tran = abs(coeffs[0,0,0])**2/input_flux[0]
mode_phase = np.angle(coeffs[0,0,0])
if mode_phase > 0:
mode_phase -= 2*np.pi
return mode_tran, mode_phase
else:
sy = num_cells*gp
cell_size = mp.Vector3(sx,sy,0)
sources = [mp.Source(mp.GaussianSource(fcen, fwidth=df),
component=mp.Ez,
center=src_pt,
size=mp.Vector3(y=sy))]
for j in range(num_cells):
geometry.append(mp.Block(material=glass,
size=mp.Vector3(gh,gdc_list[j]*gp,mp.inf),
center=mp.Vector3(-0.5*sx+dpml+dsub+0.5*gh,-0.5*sy+(j+0.5)*gp)))
sim = mp.Simulation(resolution=resolution,
cell_size=cell_size,
boundary_layers=pml_layers,
geometry=geometry,
k_point=k_point,
sources=sources,
symmetries=symmetries)
n2f_obj = sim.add_near2far(fcen, 0, 1, mp.Near2FarRegion(center=mon_pt, size=mp.Vector3(y=sy)))
sim.run(until_after_sources=500)
return abs(sim.get_farfields(n2f_obj, ff_res, center=mp.Vector3(-0.5*sx+dpml+dsub+gh+focal_length), size=mp.Vector3(spot_length))['Ez'])**2
gp = 0.3 # grating periodicity
gh = 1.8 # grating height
gdc = np.linspace(0.1,0.9,30) # grating duty cycle
mode_tran = np.empty((gdc.size))
mode_phase = np.empty((gdc.size))
for n in range(gdc.size):
mode_tran[n], mode_phase[n] = grating(gp,gh,[gdc[n]])
plt.figure(dpi=200)
plt.subplot(1,2,1)
plt.plot(gdc, mode_tran, 'bo-')
plt.xlim(gdc[0],gdc[-1])
plt.xticks([t for t in np.linspace(0.1,0.9,5)])
plt.xlabel("grating duty cycle")
plt.ylim(0.96,1.00)
plt.yticks([t for t in np.linspace(0.96,1.00,5)])
plt.title("transmittance")
plt.subplot(1,2,2)
plt.plot(gdc, mode_phase, 'rs-')
plt.grid(True)
plt.xlim(gdc[0],gdc[-1])
plt.xticks([t for t in np.linspace(0.1,0.9,5)])
plt.xlabel("grating duty cycle")
plt.ylim(-2*np.pi,0)
plt.yticks([t for t in np.linspace(-6,0,7)])
plt.title("phase (radians)")
plt.tight_layout(pad=0.5)
plt.show()
gdc_new = np.linspace(0.16,0.65,500)
mode_phase_interp = np.interp(gdc_new, gdc, mode_phase)
print("phase-range:, {:.6f}".format(mode_phase_interp.max()-mode_phase_interp.min()))
phase_tol = 1e-2
num_cells = [100,200,400]
ff_nc = np.empty((spot_length*ff_res,len(num_cells)))
for k in range(len(num_cells)):
gdc_list = []
for j in range(-num_cells[k],num_cells[k]+1):
phase_local = 2*np.pi/lcen * (focal_length-((j*gp)**2 + focal_length**2)**0.5) # local phase at the center of the j'th unit cell
phase_mod = phase_local % (-2*np.pi) # restrict phase to [-2*pi,0]
if phase_mod > mode_phase_interp.max():
phase_mod = mode_phase_interp.max()
if phase_mod < mode_phase_interp.min():
phase_mod = mode_phase_interp.min()
idx = np.transpose(np.nonzero(np.logical_and(mode_phase_interp > phase_mod-phase_tol, mode_phase_interp < phase_mod+phase_tol)))
gdc_list.append(gdc_new[idx[0][0]])
ff_nc[:,k] = grating(gp,gh,gdc_list)
x = np.linspace(focal_length-0.5*spot_length,focal_length+0.5*spot_length,ff_res*spot_length)
plt.figure(dpi=200)
plt.semilogy(x,abs(ff_nc[:,0])**2,'bo-',label='num_cells = {}'.format(2*num_cells[0]+1))
plt.semilogy(x,abs(ff_nc[:,1])**2,'ro-',label='num_cells = {}'.format(2*num_cells[1]+1))
plt.semilogy(x,abs(ff_nc[:,2])**2,'go-',label='num_cells = {}'.format(2*num_cells[2]+1))
plt.xlabel('x coordinate (μm)')
plt.ylabel(r'energy density of far-field electric fields, |E$_z$|$^2$')
plt.title('focusing properties of a binary-grating metasurface lens')
plt.legend(loc='upper right')
plt.tight_layout()
plt.show()
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