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import math
from typing import List, Tuple
import unittest
import numpy as np
import parameterized
from utils import ApproxComparisonTestCase
import meep as mp
class TestReflectanceAngular(ApproxComparisonTestCase):
@classmethod
def setUpClass(cls):
cls.resolution = 200 # pixels/μm
cls.n1 = 1.4 # refractive index of medium 1
cls.n2 = 3.5 # refractive index of medium 2
cls.t_pml = 1.0
cls.length_z = 7.0
cls.size_z = cls.length_z + 2 * cls.t_pml
cls.wavelength_min = 0.4
cls.wavelength_max = 0.8
cls.frequency_min = 1 / cls.wavelength_max
cls.frequency_max = 1 / cls.wavelength_min
cls.frequency_center = 0.5 * (cls.frequency_min + cls.frequency_max)
cls.frequency_width = cls.frequency_max - cls.frequency_min
cls.num_freq = 11
def reflectance_angular(
self, theta_deg: float, use_bfast: bool
) -> Tuple[List, List, np.ndarray]:
"""Computes properties of the incident and reflected planewave.
Args:
theta_deg: angle of incident planewave.
use_bfast: whether to use the same angle for the incident planewave
for all frequencies. If False, the incident angle is frequency
dependent.
Returns:
A 3-tuple comprising the frequencies of the incident planewave,
angles of the incident planewave, and the reflectance.
"""
theta_rad = math.radians(theta_deg)
if use_bfast:
bfast_scaled_k = (self.n1 * np.sin(theta_rad), 0, 0)
Courant = (1 - bfast_scaled_k[0]) / 3**0.5
k = mp.Vector3()
else:
bfast_scaled_k = (0, 0, 0)
Courant = 0.5
# Wavevector in source medium with refractive index n1.
# Plane of incidence is XZ. Rotation is counter clockwise about
# Y axis. A rotation angle of zero is the +Z axis.
k = (
mp.Vector3(0, 0, 1)
.rotate(mp.Vector3(0, 1, 0), theta_rad)
.scale(self.n1 * self.frequency_min)
)
dimensions = 1 if theta_deg == 0 else 3
cell_size = mp.Vector3(z=self.size_z)
pml_layers = [mp.PML(self.t_pml)]
# P polarization.
source_component = mp.Ex
sources = [
mp.Source(
mp.GaussianSource(self.frequency_center, fwidth=self.frequency_width),
component=source_component,
center=mp.Vector3(z=-0.5 * self.size_z + self.t_pml),
)
]
sim = mp.Simulation(
resolution=self.resolution,
cell_size=cell_size,
dimensions=dimensions,
default_material=mp.Medium(index=self.n1),
sources=sources,
boundary_layers=pml_layers,
k_point=k,
bfast_scaled_k=bfast_scaled_k,
Courant=Courant,
)
monitor_point = -0.5 * self.size_z + self.t_pml + 0.25 * self.length_z
monitor_region = mp.FluxRegion(center=mp.Vector3(z=monitor_point))
flux_monitor = sim.add_flux(
self.frequency_center, self.frequency_width, self.num_freq, monitor_region
)
termination_criteria = mp.stop_when_fields_decayed(
50, source_component, mp.Vector3(z=monitor_point), 1e-6
)
sim.run(until_after_sources=termination_criteria)
empty_data = sim.get_flux_data(flux_monitor)
empty_flux = mp.get_fluxes(flux_monitor)
sim.reset_meep()
geometry = [
mp.Block(
size=mp.Vector3(mp.inf, mp.inf, 0.5 * self.size_z),
center=mp.Vector3(z=0.25 * self.size_z),
material=mp.Medium(index=self.n2),
)
]
sim = mp.Simulation(
resolution=self.resolution,
cell_size=cell_size,
dimensions=dimensions,
default_material=mp.Medium(index=self.n1),
sources=sources,
boundary_layers=pml_layers,
k_point=k,
bfast_scaled_k=bfast_scaled_k,
Courant=Courant,
geometry=geometry,
)
flux_monitor = sim.add_flux(
self.frequency_center, self.frequency_width, self.num_freq, monitor_region
)
sim.load_minus_flux_data(flux_monitor, empty_data)
sim.run(until_after_sources=termination_criteria)
flux_monitor_flux = mp.get_fluxes(flux_monitor)
freqs = mp.get_flux_freqs(flux_monitor)
reflectance = -np.array(flux_monitor_flux) / np.array(empty_flux)
if use_bfast:
theta_in_rad = [theta_rad] * self.num_freq
else:
# Returns the angle of the incident planewave in medium n1 based
# on its frequency given a fixed wavevector component in X.
theta_in_rad = [
math.asin(k.x / (self.n1 * freqs[i])) for i in range(self.num_freq)
]
return freqs, theta_in_rad, reflectance
@parameterized.parameterized.expand([(0, False), (20.6, False), (35.7, True)])
def test_reflectance_angular(self, theta_deg: float, use_bfast: bool):
(
frequency_meep,
theta_in_rad_meep,
reflectance_meep,
) = self.reflectance_angular(theta_deg, use_bfast)
# Returns angle of refracted planewave in medium n2 given
# an incident planewave in medium n1 at angle theta_in_rad.
theta_out = lambda theta_in_rad: math.asin(
self.n1 * math.sin(theta_in_rad) / self.n2
)
# Returns Fresnel reflectance for P polarization in medium n2
# for an incident planewave in medium n1 at angle theta_in_rad.
reflectance_fresnel = lambda theta_in_rad: (
math.fabs(
(
self.n1 * math.cos(theta_out(theta_in_rad))
- self.n2 * math.cos(theta_in_rad)
)
/ (
self.n1 * math.cos(theta_out(theta_in_rad))
+ self.n2 * math.cos(theta_in_rad)
)
)
** 2
)
reflectance_analytic = np.empty((self.num_freq,))
print(
"refl:, wavelength (μm), incident angle (°), reflectance (Meep), "
"reflectance (analytic), error"
)
for i in range(self.num_freq):
reflectance_analytic[i] = reflectance_fresnel(theta_in_rad_meep[i])
err = (
abs(reflectance_meep[i] - reflectance_analytic[i])
/ reflectance_analytic[i]
)
print(
"refl:, {:4.2f}, {:4.2f}, {:8.6f}, {:8.6f}, {:6.4f}".format(
1 / frequency_meep[i],
math.degrees(theta_in_rad_meep[i]),
reflectance_meep[i],
reflectance_analytic[i],
err,
)
)
tol = 0.03
self.assertClose(reflectance_meep, reflectance_analytic, epsilon=tol)
if __name__ == "__main__":
unittest.main()
|
