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# -*- coding: utf-8 -*-
import meep as mp
import math
import numpy as np
from numpy import linalg as LA
import matplotlib.pyplot as plt
resolution = 25 # 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
nperiods = 10 # number of unit cells in finite periodic grating
ff_distance = 1e8 # far-field distance from near-field monitor
ff_angle = 20 # far-field cone angle
ff_npts = 500 # number of far-field points
ff_length = ff_distance*math.tan(math.radians(ff_angle))
ff_res = ff_npts/ff_length
sx = dpml+dsub+gh+dpad+dpml
cell_size = mp.Vector3(sx)
pml_layers = [mp.PML(thickness=dpml,direction=mp.X)]
symmetries = [mp.Mirror(mp.Y)]
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)
sources = [mp.Source(mp.GaussianSource(fcen, fwidth=df), component=mp.Ez, center=src_pt)]
k_point = mp.Vector3()
glass = mp.Medium(index=1.5)
sim = mp.Simulation(resolution=resolution,
cell_size=cell_size,
boundary_layers=pml_layers,
k_point=k_point,
default_material=glass,
sources=sources)
nfreq = 21
n2f_pt = mp.Vector3(0.5*sx-dpml-0.5*dpad)
n2f_obj = sim.add_near2far(fcen, df, nfreq, mp.Near2FarRegion(center=n2f_pt))
sim.run(until_after_sources=mp.stop_when_fields_decayed(50, mp.Ez, n2f_pt, 1e-9))
ff_source = sim.get_farfields(n2f_obj, ff_res, center=mp.Vector3(ff_distance,0.5*ff_length), size=mp.Vector3(y=ff_length))
sim.reset_meep()
### unit cell with periodic boundaries
sy = gp
cell_size = mp.Vector3(sx,sy)
sources = [mp.Source(mp.GaussianSource(fcen, fwidth=df, is_integrated=True),
component=mp.Ez,
center=src_pt,
size=mp.Vector3(y=sy))]
geometry = [mp.Block(material=glass, size=mp.Vector3(dpml+dsub,mp.inf,mp.inf), center=mp.Vector3(-0.5*sx+0.5*(dpml+dsub))),
mp.Block(material=glass, size=mp.Vector3(gh,gdc*gp,mp.inf), center=mp.Vector3(-0.5*sx+dpml+dsub+0.5*gh))]
sim = mp.Simulation(resolution=resolution,
split_chunks_evenly=True,
cell_size=cell_size,
boundary_layers=pml_layers,
geometry=geometry,
k_point=k_point,
sources=sources,
symmetries=symmetries)
n2f_obj = sim.add_near2far(fcen, df, nfreq, mp.Near2FarRegion(center=n2f_pt, size=mp.Vector3(y=sy)), nperiods=nperiods)
sim.run(until_after_sources=mp.stop_when_fields_decayed(50, mp.Ez, n2f_pt, 1e-9))
ff_unitcell = sim.get_farfields(n2f_obj, ff_res, center=mp.Vector3(ff_distance,0.5*ff_length), size=mp.Vector3(y=ff_length))
sim.reset_meep()
### finite periodic grating with flat surface termination extending into PML
num_cells = 2*nperiods+1
sy = dpml+num_cells*gp+dpml
cell_size = mp.Vector3(sx,sy)
pml_layers = [mp.PML(thickness=dpml)]
sources = [mp.Source(mp.GaussianSource(fcen, fwidth=df, is_integrated=True),
component=mp.Ez,
center=src_pt,
size=mp.Vector3(y=sy))]
geometry = [mp.Block(material=glass, size=mp.Vector3(dpml+dsub,mp.inf,mp.inf), center=mp.Vector3(-0.5*sx+0.5*(dpml+dsub)))]
for j in range(num_cells):
geometry.append(mp.Block(material=glass,
size=mp.Vector3(gh,gdc*gp,mp.inf),
center=mp.Vector3(-0.5*sx+dpml+dsub+0.5*gh,-0.5*sy+dpml+(j+0.5)*gp)))
sim = mp.Simulation(resolution=resolution,
split_chunks_evenly=True,
cell_size=cell_size,
boundary_layers=pml_layers,
geometry=geometry,
k_point=k_point,
sources=sources,
symmetries=symmetries)
n2f_obj = sim.add_near2far(fcen, df, nfreq, mp.Near2FarRegion(center=n2f_pt, size=mp.Vector3(y=sy-2*dpml)))
sim.run(until_after_sources=mp.stop_when_fields_decayed(50, mp.Ez, n2f_pt, 1e-9))
ff_supercell = sim.get_farfields(n2f_obj, ff_res, center=mp.Vector3(ff_distance,0.5*ff_length), size=mp.Vector3(y=ff_length))
norm_err = LA.norm(ff_unitcell['Ez']-ff_supercell['Ez'])/nperiods
print("error:, {}, {}".format(nperiods,norm_err))
freqs = mp.get_near2far_freqs(n2f_obj)
wvl = np.divide(1,freqs)
ff_lengths = np.linspace(0,ff_length,ff_npts)
angles = [math.degrees(math.atan(f)) for f in ff_lengths/ff_distance]
wvl_slice = 0.5
idx_slice = np.where(np.asarray(freqs) == 1/wvl_slice)[0][0]
rel_enh = np.absolute(ff_unitcell['Ez'])**2/np.absolute(ff_source['Ez'])**2
plt.figure(dpi=150)
plt.subplot(1,2,1)
plt.pcolormesh(wvl,angles,rel_enh,cmap='Blues',shading='flat')
plt.axis([wvl_min,wvl_max,0,ff_angle])
plt.xlabel("wavelength (μm)")
plt.ylabel("angle (degrees)")
plt.grid(linewidth=0.5,linestyle='--')
plt.xticks([t for t in np.arange(wvl_min,wvl_max+0.1,0.1)])
plt.yticks([t for t in range(0,ff_angle+1,10)])
plt.title("far-field spectra")
plt.subplot(1,2,2)
plt.plot(angles,rel_enh[:,idx_slice],'bo-')
plt.xlim(0,ff_angle)
plt.ylim(0)
plt.xticks([t for t in range(0,ff_angle+1,10)])
plt.xlabel("angle (degrees)")
plt.ylabel("relative enhancement")
plt.grid(axis='x',linewidth=0.5,linestyle='--')
plt.title("f.-f. spectra @ λ = {:.1} μm".format(wvl_slice))
plt.tight_layout(pad=0.5)
plt.show()
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