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from __future__ import division
import unittest
import meep as mp
import math
import cmath
import numpy as np
class TestEigCoeffs(unittest.TestCase):
def run_binary_grating_oblique(self, theta):
resolution = 30 # pixels/um
dpml = 1.0 # PML thickness
dsub = 1.0 # substrate thickness
dpad = 1.0 # length of padding between grating and pml
gp = 6.0 # grating period
gh = 0.5 # grating height
gdc = 0.5 # grating duty cycle
sx = dpml+dsub+gh+dpad+dpml
sy = gp
cell_size = mp.Vector3(sx,sy,0)
# replace anisotropic PML with isotropic Absorber to attenuate parallel-directed fields of oblique source
abs_layers = [mp.Absorber(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; CCW about Y axis, 0 degrees along +X axis
theta_in = math.radians(theta)
# k (in source medium) with correct length (plane of incidence: XY)
k = mp.Vector3(math.cos(theta_in),math.sin(theta_in),0).scale(fcen*ng)
symmetries = []
eig_parity = mp.ODD_Z
if theta_in == 0:
k = mp.Vector3(0,0,0)
symmetries = [mp.Mirror(mp.Y)]
eig_parity += mp.EVEN_Y
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+0.3*dsub,0,0)
sources = [mp.Source(mp.GaussianSource(fcen,fwidth=df),
component=mp.Ez,
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=abs_layers,
k_point=k,
default_material=glass,
sources=sources,
symmetries=symmetries)
refl_pt = mp.Vector3(-0.5*sx+dpml+0.5*dsub,0,0)
refl_flux = sim.add_flux(fcen, 0, 1, mp.FluxRegion(center=refl_pt, size=mp.Vector3(0,sy,0)))
sim.run(until_after_sources=100)
input_flux = mp.get_fluxes(refl_flux)
input_flux_data = sim.get_flux_data(refl_flux)
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=abs_layers,
geometry=geometry,
k_point=k,
sources=sources,
symmetries=symmetries)
refl_flux = sim.add_flux(fcen, 0, 1, mp.FluxRegion(center=refl_pt, size=mp.Vector3(0,sy,0)))
sim.load_minus_flux_data(refl_flux,input_flux_data)
tran_pt = mp.Vector3(0.5*sx-dpml-0.5*dpad,0,0)
tran_flux = sim.add_flux(fcen, 0, 1, mp.FluxRegion(center=tran_pt, size=mp.Vector3(0,sy,0)))
sim.run(until_after_sources=100)
nm_r = np.floor((fcen*ng-k.y)*gp)-np.ceil((-fcen*ng-k.y)*gp) # number of reflected orders
if theta_in == 0:
nm_r = nm_r/2 # since eig_parity removes degeneracy in y-direction
nm_r = int(nm_r)
res = sim.get_eigenmode_coefficients(refl_flux, range(1,nm_r+1), eig_parity=eig_parity)
r_coeffs = res.alpha
Rsum = 0
for nm in range(nm_r):
Rsum += abs(r_coeffs[nm,0,1])**2/input_flux[0]
nm_t = np.floor((fcen-k.y)*gp)-np.ceil((-fcen-k.y)*gp) # number of transmitted orders
if theta_in == 0:
nm_t = nm_t/2 # since eig_parity removes degeneracy in y-direction
nm_t = int(nm_t)
res = sim.get_eigenmode_coefficients(tran_flux, range(1,nm_t+1), eig_parity=eig_parity)
t_coeffs = res.alpha
Tsum = 0
for nm in range(nm_t):
Tsum += abs(t_coeffs[nm,0,0])**2/input_flux[0]
r_flux = mp.get_fluxes(refl_flux)
t_flux = mp.get_fluxes(tran_flux)
Rflux = -r_flux[0]/input_flux[0]
Tflux = t_flux[0]/input_flux[0]
self.assertAlmostEqual(Rsum,Rflux,places=2)
self.assertAlmostEqual(Tsum,Tflux,places=2)
def test_binary_grating(self):
self.run_binary_grating_oblique(0)
self.run_binary_grating_oblique(10.7)
if __name__ == '__main__':
unittest.main()
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