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diffracted_planewave.py
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diffracted_planewave.py
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### compute the transmitted diffraction orders of a binary grating using mode decomposition
### based on two different methods: (1) MPB eigensolver and (2) DiffractedPlanewave object.
### Also, verify that the total power in all the orders is equivalent to the Poynting flux.
### for normal incidence, compute only positive diff. orders (total transmittance <= 0.50)
### for oblique incidence, compute ALL diff. orders (total transmittance <= 1.00)
import meep as mp
import math
import cmath
import numpy as np
def binary_grating_diffraction(gp, gh, gdc, theta):
resolution = 50 # pixels/μm
dpml = 1.0 # PML thickness
dsub = 3.0 # substrate thickness
dpad = 3.0 # length of padding between grating and PML
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 = 0.5 # center wavelength
fcen = 1/wvl # center frequency
df = 0.05*fcen # frequency width
ng = 1.5
glass = mp.Medium(index=ng)
# rotation angle of incident planewave; counter clockwise (CCW) about Z axis, 0 degrees along +X axis
theta_in = math.radians(theta)
eig_parity = mp.EVEN_Z
# k (in source medium) with correct length (plane of incidence: XY)
k = mp.Vector3(fcen*ng).rotate(mp.Vector3(z=1), theta_in)
symmetries = []
if theta_in == 0:
k = mp.Vector3()
eig_parity += mp.ODD_Y
symmetries = [mp.Mirror(direction=mp.Y,phase=-1)]
def pw_amp(k,x0):
def _pw_amp(x):
return cmath.exp(1j*2*math.pi*k.dot(x+x0))
return _pw_amp
src_pt = mp.Vector3(-0.5*sx+dpml,0,0)
sources = [mp.Source(mp.GaussianSource(fcen,fwidth=df),
component=mp.Hz,
center=src_pt,
size=mp.Vector3(0,sy,0),
amp_func=pw_amp(k,src_pt))]
sim = mp.Simulation(resolution=resolution,
cell_size=cell_size,
boundary_layers=pml_layers,
k_point=k,
default_material=glass,
sources=sources,
symmetries=symmetries)
tran_pt = mp.Vector3(0.5*sx-dpml,0,0)
tran_mon = sim.add_flux(fcen, 0, 1,
mp.FluxRegion(center=tran_pt, size=mp.Vector3(0,sy,0)))
sim.run(until_after_sources=50)
input_flux = mp.get_fluxes(tran_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,
sources=sources,
symmetries=symmetries)
tran_mon = sim.add_mode_monitor(fcen, 0, 1,
mp.FluxRegion(center=tran_pt, size=mp.Vector3(0,sy,0)))
sim.run(until_after_sources=100)
# number of (non-evanescent) transmitted orders
nm_t = np.floor((fcen-k.y)*gp)-np.ceil((-fcen-k.y)*gp)
if theta_in == 0:
nm_t = nm_t/2
nm_t = int(nm_t)+1
bands = range(1,nm_t+1)
if theta_in == 0:
orders = range(0,nm_t)
else:
orders = range(int(np.ceil((-fcen-k.y)*gp)),int(np.floor((fcen-k.y)*gp))+1)
eig_sum = 0
dp_sum = 0
for band,order in zip(bands,orders):
res = sim.get_eigenmode_coefficients(tran_mon, [band], eig_parity=eig_parity)
if res is not None:
tran_eig = abs(res.alpha[0,0,0])**2/input_flux[0]
if theta_in == 0:
tran_eig = 0.5*tran_eig
else:
tran_eig = 0
eig_sum += tran_eig
res = sim.get_eigenmode_coefficients(tran_mon, mp.DiffractedPlanewave((0,order,0),mp.Vector3(0,1,0),0,1))
if res is not None:
tran_dp = abs(res.alpha[0,0,0])**2/input_flux[0]
if (theta_in == 0) and (order == 0):
tran_dp = 0.5*tran_dp
else:
tran_dp = 0
dp_sum += tran_dp
if theta_in == 0:
err = abs(tran_eig-tran_dp)/tran_eig
print("tran:, {:2d}, {:.8f}, {:2d}, {:.8f}, {:.8f}".format(band,tran_eig,order,tran_dp,err))
else:
print("tran:, {:2d}, {:.8f}, {:2d}, {:.8f}".format(band,tran_eig,order,tran_dp))
flux = mp.get_fluxes(tran_mon)
t_flux = flux[0]/input_flux[0]
if (theta_in == 0):
t_flux = 0.5*t_flux
err = abs(dp_sum-t_flux)/t_flux
print("flux:, {:.8f}, {:.8f}, {:.8f}, {:.8f}".format(eig_sum,
dp_sum,
t_flux,
err))
if __name__ == '__main__':
binary_grating_diffraction(2.6,0.4,0.3,0)
binary_grating_diffraction(3.7,0.6,0.4,13.5)