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test_slant.py
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import tensorflow as tf
from RCWA.Domain import Domain
from RCWA.Modes import Modes
from RCWA.EigenMode import EigenMode
from RCWA.ScatterMat import ScatterMatBuilder
from RCWA.Device import SlantGrating
from RCWA import Utils
import numpy as np
import matplotlib.pyplot as plt
# Reference:
# [1] M. A. Golub and A. A. Friesem,
# “Effective grating theory for resonance domain surface-relief diffraction gratings,”
# J. Opt. Soc. Am. A, vol. 22, no. 6, p. 1115, Jun. 2005, doi: 10.1364/JOSAA.22.001115.
period = 0.583
n1 = 1
n2 = 1.46
er1 = n1**2
er2 = n2**2
ur1 = 1
ur2 = 1
domain = Domain()
domain.set_period_centered(period, period)
modes = Modes(domain)
modes.set_harmonics(10, 0)
def run(AOI, slant_angle, depth):
modes.set_incidence_AOI_POI(
AOI=np.deg2rad(AOI),
POI=np.deg2rad(0))
modes.set_wavelength(0.530)
# Default Matrix
sbuilder = ScatterMatBuilder(modes)
ref_mode = EigenMode(modes)
trn_mode = EigenMode(modes)
ref_mode.from_homogeneous(er1, ur1)
trn_mode.from_homogeneous(er2, ur2)
Sref = sbuilder.BuildScatterRef(ref_mode)
Strn = sbuilder.BuildScatterTrn(trn_mode)
Sglobal = Sref
# Create Device
S = SlantGrating(modes, sbuilder, n1=n1, n2=n2,
ff=0.5,
slant_angle=np.deg2rad(slant_angle),
depth=depth,
dff=-1,
dz=0.02)
Sglobal = Sglobal @ S
Sglobal = Sglobal @ Strn
# Incidence
delta = (modes.mx == 0)*(modes.my == 0)
# Set amplitudes for s and p polarizations
pol_angle = np.deg2rad(90)
amp_s = tf.sin(pol_angle) # 90 degree
amp_p = tf.cos(pol_angle) # 0 degree
# Calculate the polarization vector based on s and p amplitudes
pol = modes.pol_vec_p * amp_p + modes.pol_vec_s * amp_s
# Calculate the incident electric field components
Einc = tf.cast(
tf.concat([delta*pol[0], delta*pol[1]], 0), tf.dtypes.complex128)
Einc_z = delta*pol[2]
# Calculate the incident intensity
Iinc = tf.reduce_sum(np.abs(Einc)**2)+tf.reduce_sum(np.abs(Einc_z)**2)
# Calculate the longitudinal wave vector components
kz_r = tf.sqrt((n1**2-modes.kx**2-modes.ky**2).astype('complex'))
kz_t = tf.sqrt((n2**2-modes.kx**2-modes.ky**2).astype('complex'))
def incidence(S):
# Calculate the electric field components using the scattering matrix
Eref = tf.reshape((S.value[0]@Einc[:, None]), [2, -1])
Etrn = tf.reshape((S.value[2]@Einc[:, None]), [2, -1])
# Calculate the longitudinal electric field components
Eref_z = -(Eref[0]*modes.kx+Eref[1]*modes.ky)/kz_r
Etrn_z = -(Etrn[0]*modes.kx+Etrn[1]*modes.ky)/kz_t
# Calculate the reflected and transmitted intensities
Iref = tf.reduce_sum(tf.abs(Eref)**2, 0)+tf.abs(Eref_z)**2
Itrn = tf.reduce_sum(tf.abs(Etrn)**2, 0)+tf.abs(Etrn_z)**2
# Calculate the reflection and transmission coefficients
R = Iref*tf.math.real(kz_r)/modes.k0z/Iinc
T = Itrn*tf.math.real(kz_t)/modes.k0z/Iinc
return Eref, Etrn, R, T
Eref, Etrn, R, T = incidence(Sglobal)
# Reshape the reflection and transmission coefficients into 2D arrays
R_2d = tf.reshape(R, [modes.num_modes_y, modes.num_modes_x])
T_2d = tf.reshape(T, [modes.num_modes_y, modes.num_modes_x])
# Plot the reflection and transmission coefficients
# plt.subplot(2, 1, 1)
# plt.title("Reflection")
# plt.imshow(R_2d, cmap='jet', vmin=0)
# plt.colorbar()
# plt.subplot(2, 1, 2)
# plt.title("Transmission")
# plt.imshow(T_2d, cmap='jet', vmin=0)
# plt.colorbar()
# plt.tight_layout()
# plt.show()
# Calculate the sum of reflection and transmission coefficients
print(np.sum(R+T))
print("Error:", 1-np.sum(R+T))
return R, T
plt.figure(figsize=(6, 4), dpi=150)
for case in range(3):
slant_angle = [23.289, 12.55, 0][case]
depth = [1.219, 1.309, 1.346][case]
label = ['Case a', 'Case b', 'Case c'][case]
ts = []
AOIs = np.linspace(-20, 50, 36)
for AOI in AOIs:
R, T = run(AOI, slant_angle, depth)
ts.append(np.sum(T * (modes.mx == -1) * (modes.my == 0)))
plt.plot(AOIs, ts, label=label)
np.save(f'./save/slant_{label}',ts)
plt.grid()
plt.ylabel('Diffraction Efficiency, 1st order')
plt.xlabel('Incidence Angle')
plt.legend()
plt.tight_layout()
plt.show()