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import cmath
import math
import unittest
import numpy as np
import meep as mp
# Computes the mode coefficient of the transmitted orders of
# a binary grating given an incident planewave and verifies
# that the results are the same when using either a band number
# or `DiffractedPlanewave` object in `get_eigenmode_coefficients`.
class TestDiffractedPlanewave(unittest.TestCase):
@classmethod
def setUp(cls):
cls.resolution = 50 # pixels/um
cls.dpml = 1.0 # PML thickness
cls.dsub = 3.0 # substrate thickness
cls.dpad = 3.0 # length of padding between grating and PML
cls.wvl = 0.5 # center wavelength
cls.fcen = 1 / cls.wvl # center frequency
cls.ng = 1.5
cls.glass = mp.Medium(index=cls.ng)
cls.pml_layers = [mp.PML(thickness=cls.dpml, direction=mp.X)]
def run_binary_grating_diffraction(self, gp, gh, gdc, theta):
sx = self.dpml + self.dsub + gh + self.dpad + self.dpml
sy = gp
cell_size = mp.Vector3(sx, sy, 0)
# rotation angle of incident planewave
# counter clockwise (CCW) about Z 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(self.fcen * self.ng).rotate(mp.Vector3(z=1), theta_in)
eig_parity = mp.ODD_Z
if theta == 0:
k = mp.Vector3()
eig_parity += mp.EVEN_Y
symmetries = [mp.Mirror(direction=mp.Y)]
else:
symmetries = []
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 + self.dpml, 0, 0)
sources = [
mp.Source(
mp.GaussianSource(self.fcen, fwidth=0.1 * self.fcen),
component=mp.Ez,
center=src_pt,
size=mp.Vector3(0, sy, 0),
amp_func=pw_amp(k, src_pt),
)
]
geometry = [
mp.Block(
material=self.glass,
size=mp.Vector3(self.dpml + self.dsub, mp.inf, mp.inf),
center=mp.Vector3(-0.5 * sx + 0.5 * (self.dpml + self.dsub), 0, 0),
),
mp.Block(
material=self.glass,
size=mp.Vector3(gh, gdc * gp, mp.inf),
center=mp.Vector3(-0.5 * sx + self.dpml + self.dsub + 0.5 * gh, 0, 0),
),
]
sim = mp.Simulation(
resolution=self.resolution,
cell_size=cell_size,
boundary_layers=self.pml_layers,
geometry=geometry,
k_point=k,
sources=sources,
symmetries=symmetries,
)
tran_pt = mp.Vector3(0.5 * sx - self.dpml, 0, 0)
tran_flux = sim.add_mode_monitor(
self.fcen, 0, 1, mp.FluxRegion(center=tran_pt, size=mp.Vector3(0, sy, 0))
)
sim.run(
until_after_sources=mp.stop_when_fields_decayed(20, mp.Ez, src_pt, 1e-6)
)
m_plus = int(np.floor((self.fcen - k.y) * gp))
m_minus = int(np.ceil((-self.fcen - k.y) * gp))
if theta == 0:
orders = range(m_plus)
else:
# ordering of the modes computed by MPB is according to *decreasing*
# values of kx (i.e., closest to propagation direction of 0° or +x)
ms = range(m_minus, m_plus + 1)
kx = lambda m: np.power(self.fcen, 2) - np.power(k.y + m / gp, 2)
kxs = [kx(m) for m in ms]
ids = np.flip(np.argsort(kxs))
orders = [ms[d] for d in ids]
for band, order in enumerate(orders):
res = sim.get_eigenmode_coefficients(
tran_flux, [band + 1], eig_parity=eig_parity
)
tran_ref = abs(res.alpha[0, 0, 0]) ** 2
if theta == 0:
tran_ref = 0.5 * tran_ref
vg_ref = res.vgrp[0]
kdom_ref = res.kdom[0]
res = sim.get_eigenmode_coefficients(
tran_flux,
mp.DiffractedPlanewave((0, order, 0), mp.Vector3(0, 1, 0), 1, 0),
)
tran_dp = abs(res.alpha[0, 0, 0]) ** 2
if (theta == 0) and (order == 0):
tran_dp = 0.5 * tran_dp
vg_dp = res.vgrp[0]
kdom_dp = res.kdom[0]
err = abs(tran_ref - tran_dp) / tran_ref
print(
"tran:, {:2d} (band), {:2d} (order), "
"{:10.8f} (band num.), {:10.8f} (diff. pw.), "
"{:10.8f} (error)".format(band, order, tran_ref, tran_dp, err)
)
self.assertAlmostEqual(vg_ref, vg_dp, places=4)
self.assertAlmostEqual(tran_ref, tran_dp, places=4)
if theta == 0:
self.assertAlmostEqual(abs(kdom_ref.x), kdom_dp.x, places=5)
self.assertAlmostEqual(abs(kdom_ref.y), kdom_dp.y, places=5)
self.assertAlmostEqual(abs(kdom_ref.z), kdom_dp.z, places=5)
else:
self.assertAlmostEqual(kdom_ref.x, kdom_dp.x, places=5)
self.assertAlmostEqual(kdom_ref.y, kdom_dp.y, places=5)
self.assertAlmostEqual(kdom_ref.z, kdom_dp.z, places=5)
print("PASSED.")
def test_diffracted_planewave(self):
self.run_binary_grating_diffraction(2.6, 0.4, 0.6, 0)
self.run_binary_grating_diffraction(2.6, 0.4, 0.6, 13.4)
# self.run_binary_grating_diffraction(10.0,0.5,0.5,0)
# self.run_binary_grating_diffraction(10.0,0.5,0.5,10.7)
if __name__ == "__main__":
unittest.main()
|
