L = Berreman4x4.RepeatedLayers([L_TiO2, L_SiO2], 8, 0, 1)
# To reduce the number of printed characters in the numbers:
# numpy.set_printoptions(suppress=True, precision=3)
Kx = 0.0
# Structure
s = Berreman4x4.Structure(front, [L], back)
# Calculation
(lbda1, lbda2) = (1.1e-6, 2.5e-6)
lbda_list = numpy.linspace(lbda1, lbda2, 200)
data = numpy.array([s.getJones(Kx, 2*pi/lbda) for lbda in lbda_list])
r = Berreman4x4.extractCoefficient(data, 'r_ss')
R = abs(r)**2
t = Berreman4x4.extractCoefficient(data, 't_ss')
T = s.getPowerTransmissionCorrection(Kx) * abs(t)**2
# Plotting
fig = pyplot.figure()
ax = fig.add_subplot("111")
ax.plot(lbda_list, R, label="$R$")
ax.plot(lbda_list, T, label="$T$")
ax.legend(loc='center right')
ax.set_xlabel(r"Wavelength $\lambda$ (m)")
ax.set_ylabel(r"Power reflection $R$ or transmission $T$")
ax.set_title(r"Bragg mirror: Air/{TiO$_2$/SiO$_2$}x8/TiO$_2$/Glass")
def plotTransmission(label):
"""Plots power transmission vs. wavenumber."""
data = numpy.array([s.getJones(Kx,k0) for k0 in k0_list])
t_pp = Berreman4x4.extractCoefficient(data, 't_pp')
T = abs(t_pp)**2 # valid if back and front media are identical
ax.plot(k0_list, T, 'x', label=label)
"'Spectroscopic Ellipsometry',\nby H. Fujiwara.\n")
print("*** Air / anisotropic sample ***")
print("We reproduce figure 6.16, p. 238...")
# Orientations of the anisotropic substrate
Φ_E = pi/2 # 1st Euler angle
θ_E_list = [0, pi/4, pi/2] # 2nd Eulet angle
# Incidence angles
Φ_i_list = numpy.linspace(0, 0.999*pi/2, 300) # array of Φ_i values
Φ_i_deg = Φ_i_list*180/pi
Kx_list = front.get_Kx_from_Phi(Φ_i_list) # array of Kx values
data = Berreman4x4.DataList()
for θ_E in θ_E_list:
R = Berreman4x4.rotation_Euler((Φ_E, θ_E, 0))
back.setMaterial(uniaxialMaterialRef.rotated(R))
data.append([s.evaluate(Kx) for Kx in Kx_list])
Psi = data.get('Ψ')
fig = pyplot.figure()
ax = fig.add_subplot(111)
ax.plot(Φ_i_deg, Psi.T)
ax.set_xlabel(r"$\theta_i$")
ax.set_ylabel(r"$\Psi_{pp}$")
pyplot.tight_layout()
##############################################################################
# We reproduce figure 6.17
from Berreman4x4 import c, pi, e_y, C, D, invC, invD import matplotlib.pyplot as pyplot ############################################################################ # Structure # Materials glass = Berreman4x4.IsotropicNonDispersiveMaterial(1.6) front = back = Berreman4x4.IsotropicHalfSpace(glass) # Liquid crystal oriented along the x direction (no, ne) = (1.5, 1.7) Dn = ne-no n_med = (ne + no)/2 LC = Berreman4x4.UniaxialNonDispersiveMaterial(no, ne) # ne along z R = Berreman4x4.rotation_v_theta(e_y, pi/2) # rotation round y LC = LC.rotated(R) # apply rotation from z to x # Cholesteric pitch: p = 0.65e-6 # One half turn of a right-handed helix: TN = Berreman4x4.TwistedMaterial(LC, p/2, angle=+pi, div=25) # Inhomogeneous layer, repeated layer, and structure IL = Berreman4x4.InhomogeneousLayer(TN) N = 5 # number half pitch repetitions h = N * p/2 L = Berreman4x4.RepeatedLayers([IL], N) s = Berreman4x4.Structure(front, [L], back) # Normal incidence: Kx = 0.0
#!/usr/bin/python
# encoding: utf-8
# Berreman4x4 example
# Author: O. Castany
# Simple example: reflection on an air/glass interface, at normal indicence.
print("*** Air / glass interface ***\n")
import numpy, Berreman4x4
from Berreman4x4 import c, pi
# Materials:
air = Berreman4x4.IsotropicNonDispersiveMaterial(1.0)
glass = Berreman4x4.IsotropicNonDispersiveMaterial(1.5)
# Half-spaces:
front = Berreman4x4.IsotropicHalfSpace(air)
back = Berreman4x4.IsotropicHalfSpace(glass)
# Structure:
s = Berreman4x4.Structure(front, [], back)
# Incidence angle (Kx = n sin(Φ):
Kx = 0.0
print("When the basis is the linear polarizations ('p','s')...")
J = s.getJones(Kx, k0=1e6)
(Jr, Jt) = J
print("Jones matrix for reflection (Jr):")
"'Spectroscopic Ellipsometry',\nby H. Fujiwara.\n")
print("*** Air / anisotropic sample ***")
print("We reproduce figure 6.16, p. 238...")
# Orientations of the anisotropic substrate
Phi_E = pi/2 # 1st Euler angle
Theta_E_list = [0, pi/4, pi/2] # 2nd Eulet angle
# Incidence angles
Phi_i_list = numpy.linspace(0, 0.999*pi/2, 37) # array of Phi_i values
Phi_i_deg = Phi_i_list*180/pi
Kx_list = front.get_Kx_from_Phi(Phi_i_list) # array of Kx values
data = []
for Theta_E in Theta_E_list:
R = Berreman4x4.rotation_Euler((Phi_E, Theta_E, 0))
back.setMaterial(uniaxialMaterialRef.rotated(R))
l = []
for Kx in Kx_list:
Jr = s.getJones(Kx)[0]
l.append(Berreman4x4.extractEllipsoParam(Jr))
data.append(l)
data = numpy.array(data)
fig = pyplot.figure()
ax = fig.add_subplot(111)
ax.plot(Phi_i_deg, data[:,:,0,0].T)
ax.set_xlabel(r"$\theta_i$")
ax.set_ylabel(r"$\Psi_{pp}$")
pyplot.tight_layout()
We consider a birefringence Δn = 0.10 and a thickness d = 4.33 µm. The first minimum should be at λ = 500 nm, or k0 = 1.257e7 m⁻¹. Note: Gooch-Tarry law does not take into account interferences between the two glass substrates. A glass with n = 1.55 minimizes the interferences. """ # Materials glass = Berreman4x4.IsotropicNonDispersiveMaterial(1.55) front = back = Berreman4x4.IsotropicHalfSpace(glass) # Liquid crystal oriented along the x direction (no, ne) = (1.5, 1.6) Dn = ne-no LC = Berreman4x4.UniaxialNonDispersiveMaterial(no, ne) R = Berreman4x4.rotation_v_theta(e_y, pi/2) LC = LC.rotated(R) d = 4.33e-6 TN = Berreman4x4.TwistedMaterial(LC, d) # Inhomogeneous layer IL = Berreman4x4.InhomogeneousLayer(TN) # Structure s = Berreman4x4.Structure(front, [IL], back) # Normal incidence: Kx = 0.0 # Calculation parameters (lbda_min, lbda_max) = (200e-9, 1) # (m)
We consider a birefringence Δn = 0.10 and a thickness d = 4.33 µm. The first
minimum should be at λ = 500 nm, or k0 = 1.257e7 m⁻¹.
Note: Gooch-Tarry law does not take into account interferences between the two
glass substrates. A glass with n = 1.55 minimizes the interferences.
"""
# Materials
glass = Berreman4x4.IsotropicNonDispersiveMaterial(1.55)
front = back = Berreman4x4.IsotropicHalfSpace(glass)
# Liquid crystal oriented along the x direction
(no, ne) = (1.5, 1.6)
Dn = ne-no
LC = Berreman4x4.UniaxialNonDispersiveMaterial(no, ne)
R = Berreman4x4.rotation_v_theta([0,1,0], pi/2)
LC = LC.rotated(R)
d = 4.33e-6
TN = Berreman4x4.TwistedMaterial(LC, d)
# Inhomogeneous layer
IL = Berreman4x4.InhomogeneousLayer(TN)
# IL.setMethod("symplectic","Padé",3)
# Structure
s = Berreman4x4.Structure(front, [IL], back)
# Normal incidence:
Kx = 0.0
# Calculation
import numpy, Berreman4x4
from Berreman4x4 import c, pi
from numpy import exp, cos, arcsin, real, sqrt
import matplotlib.pyplot as pyplot
print("\n*** Glass / Air ***\n")
############################################################################
# Structure definition
# Refractive indices
n_f = 1.5
n_b = 1.0
# Materials:
glass = Berreman4x4.IsotropicNonDispersiveMaterial(n_f)
air = Berreman4x4.IsotropicNonDispersiveMaterial(n_b)
# Layer and half-spaces:
front = Berreman4x4.IsotropicHalfSpace(glass)
back = Berreman4x4.IsotropicHalfSpace(air)
# Structure:
s = Berreman4x4.Structure(front, [], back)
# Wavelength and wavenumber:
lbda = 1e-6
k0 = 2 * pi / lbda
# Variation of incidence angle
Phi_list = numpy.linspace(0, pi / 2 * 0.999)
- liquid crystal aligned along x at z=0.
- input and output polarizers aligned parallel to x
Gooch-Tarry law gives: T_pp = sin²(pi/2·√(1+u²)) / (1+u²),
with u = 2dΔn/λ.
The transmission minima are given by u = ((2m)²-1)^{-1/2} = √(3),√(15),√(35),…
We consider a birefringence Δn = 0.10 and a thickness d = 4.33 µm. The first
minimum should be at λ = 500 nm, or k0 = 1.257e7 m⁻¹.
Note: Gooch-Tarry law does not take into account interferences between the two
glass substrates. A glass with n = 1.55 minimizes the interferences.
"""
# Materials
glass = Berreman4x4.IsotropicNonDispersiveMaterial(1.55)
front = back = Berreman4x4.IsotropicHalfSpace(glass)
# Liquid crystal oriented along the x direction
(no, ne) = (1.5, 1.6)
Dn = ne - no
LC = Berreman4x4.UniaxialNonDispersiveMaterial(no, ne)
R = Berreman4x4.rotation_v_theta(e_y, pi / 2)
LC = LC.rotated(R)
d = 4.33e-6
TN = Berreman4x4.TwistedMaterial(LC, d)
# Inhomogeneous layer
IL = Berreman4x4.InhomogeneousLayer(TN)
# Structure
def plotTransmission(label):
"""Plots power transmission vs. wavenumber."""
data = Berreman4x4.DataList([s.evaluate(Kx, k0) for k0 in k0_list])
T = data.get('T_pp')
ax.plot(k0_list, T, 'x', label=label)
#!/usr/bin/python
# encoding: utf-8
# Berreman4x4 example
# Author: O. Castany
# The simplest example: a homogeneous glass layer in air
import numpy, Berreman4x4
from Berreman4x4 import c, pi
import matplotlib.pyplot as pyplot
print("\n*** Air / glass / air ***\n")
# Materials:
air = Berreman4x4.IsotropicNonDispersiveMaterial(1.0)
glass = Berreman4x4.IsotropicNonDispersiveMaterial(1.5)
# Layer and half-spaces:
layer = Berreman4x4.HomogeneousIsotropicLayer(glass)
front = back = Berreman4x4.IsotropicHalfSpace(air)
# Structure:
s = Berreman4x4.Structure(front, [layer], back)
# Wavelength and wavenumber:
lbda = 1e-6
k0 = 2*pi/lbda
# Incidence angle (Kx = n sin(Φ):
Kx = 0.5
numpy.set_printoptions(suppress=True, precision=4)
n_i = 1.0 # incident medium is air
n_o = 2.0 # ordinary index of thin layer
n_e = 2.5 # extraordinary index of thin layer
w = 3.04e15 # pulsation (rad/s)
Phi_i = 70*pi/180 # 70° indicence angle (rad)
d = 0.1e-6 # thin layer thickness (m)
# Orientation of the anisotropy of the thin layer
Phi_E = pi/4 # 1st Euler angle
Theta_E = pi/4 # 2nd Eulet angle
print("\n*** Air / anisotropic film / silicon substrate ***")
filmMaterialRef = Berreman4x4.UniaxialNonDispersiveMaterial(n_o,n_e)
R = Berreman4x4.rotation_Euler((Phi_E, Theta_E, 0))
filmMaterial = filmMaterialRef.rotated(R)
print("\nPermittivity tensor of the anisotropic film (eq 6.63, p. 241):")
print(filmMaterial.getTensor())
"""
matrix([[ 4.5625, -0.5625, 0.7955],
[-0.5625, 4.5625, -0.7955],
[ 0.7955, -0.7955, 5.125 ]])
"""
air = Berreman4x4.IsotropicNonDispersiveMaterial(n_i)
front = Berreman4x4.IsotropicHalfSpace(air) # Front half-space
Kx = front.get_Kx_from_Phi(Phi_i)
print("\nValue of Kx: {:.4f}".format(Kx))
"""
Kx = 0.9397
# Berreman4x4 example # Author: O. Castany, C. Molinaro # Example of a cholesteric liquid crystal import numpy, Berreman4x4 from numpy import sin, sqrt, abs, exp from Berreman4x4 import c, pi, e_y import matplotlib.pyplot as pyplot ############################################################################ # Structure # Materials glass = Berreman4x4.IsotropicNonDispersiveMaterial(1.6) front = back = Berreman4x4.IsotropicHalfSpace(glass) # Liquid crystal oriented along the x direction (no, ne) = (1.5, 1.7) Dn = ne-no n_med = (ne + no)/2 LC = Berreman4x4.UniaxialNonDispersiveMaterial(no, ne) # ne along z R = Berreman4x4.rotation_v_theta(e_y, pi/2) # rotation round y LC = LC.rotated(R) # apply rotation from z to x # Cholesteric pitch: p = 0.65e-6 # One half turn of a right-handed helix: TN = Berreman4x4.TwistedMaterial(LC, p/2, angle=+pi, div=25) # Inhomogeneous layer, repeated layer, and structure
Kx = 0.0
print("When the basis is the linear polarizations ('p','s')...")
J = s.getJones(Kx, k0=1e6)
(Jr, Jt) = J
print("Jones matrix for reflection (Jr):")
print(Jr)
print("Jones matrix for transmission (Jt):")
print(Jt)
"""
(matrix([[-0.2, 0. ], matrix([[ 0.8, 0. ],
[ 0. , -0.2]]), [ 0. , 0.8]]))
"""
print("\nWhen the basis is the circular polarizations ('L','R')...")
Jc = Berreman4x4.circularJones(J)
(Jcr,Jct) = Jc
print("Jones matrix for reflection (Jcr):")
print(Jcr)
print("Jones matrix for transmission (Jct):")
print(Jct)
"""
array([[ 0.0+0.j, -0.2+0.j], array([[ 0.8+0.j, 0.0+0.j],
[-0.2+0.j, 0.0+0.j]]) [ 0.0+0.j, 0.8+0.j]])
"""
print(
"""
In a reflexion, the handedness of an elliptic polarization is reversed,
so the matrix 'Jcr' is anti-diagonal.
""")
import numpy, Berreman4x4 from numpy import sin, sqrt, abs from Berreman4x4 import c, pi, e_y import matplotlib.pyplot as pyplot # Materials glass = Berreman4x4.IsotropicNonDispersiveMaterial(1.55) front = back = Berreman4x4.IsotropicHalfSpace(glass) # Liquid crystal oriented along the x direction (no, ne) = (1.5, 1.7) Dn = ne-no n_med = (ne + no)/2 LC = Berreman4x4.UniaxialNonDispersiveMaterial(no, ne) # ne along z R = Berreman4x4.rotation_v_theta(e_y, pi/2) # rotation of pi/2 along y LC = LC.rotated(R) # apply rotation from z to x # Cholesteric pitch (m): p = 0.65e-6 # One half turn of a right-handed helix: TN = Berreman4x4.TwistedMaterial(LC, p/2, angle=+pi, div=35) # Inhomogeneous layer, repeated layer, and structure IL = Berreman4x4.InhomogeneousLayer(TN) N = 15 # number half pitch repetitions h = N * p/2 L = Berreman4x4.RepeatedLayers([IL], N) s = Berreman4x4.Structure(front, [L], back) # Normal incidence: Kx = 0.0
# Verification of the code against results presented in Fujiwara's book
# p. 237 (section 6.4.1). We reproduce figures 6.16 and 6.17.
import numpy, Berreman4x4
from Berreman4x4 import c, pi
import matplotlib.pyplot as pyplot
n_i = 1.0 # incident medium is air
n_o = 2.0 # ordinary index of thin layer
n_e = 2.5 # extraordinary index of thin layer
##############################################################################
# Setting up the structure
# Front half-space (air)
air = Berreman4x4.IsotropicNonDispersiveMaterial(n_i)
front = Berreman4x4.IsotropicHalfSpace(air)
# Anisotropic substrate
uniaxialMaterialRef = Berreman4x4.UniaxialNonDispersiveMaterial(n_o, n_e)
back = Berreman4x4.HalfSpace()
s = Berreman4x4.Structure(front, [], back)
##############################################################################
# We reproduce figure 6.16
print("\nWe reproduce results from section 6.4.1 in " +
"'Spectroscopic Ellipsometry',\nby H. Fujiwara.\n")
print("*** Air / anisotropic sample ***")
print("We reproduce figure 6.16, p. 238...")
if len(sys.argv) > 1 and (sys.argv[1] == '-h' or sys.argv[1] == '--help'):
print("Usage: interface-reflection.py [-h, --help] n1 n2\n")
sys.exit()
if len(sys.argv) > 2:
(n1, n2) = map(float, sys.argv[1:3])
else:
(n1, n2) = (1.0, 1.5) # default values
print("\n*** Interface n1 = {:} / n2 = {:} ***\n".format(n1, n2))
############################################################################
# Structure definition
# Materials
medium1 = Berreman4x4.IsotropicNonDispersiveMaterial(n1)
medium2 = Berreman4x4.IsotropicNonDispersiveMaterial(n2)
# Half-spaces
front = Berreman4x4.IsotropicHalfSpace(medium1)
back = Berreman4x4.IsotropicHalfSpace(medium2)
# Structure
s = Berreman4x4.Structure(front, [], back)
# Parameters for the calculation
lbda = 1e-6
k0 = 2 * pi / lbda
Phi_i = numpy.linspace(0, pi / 2 * 0.9999) # range for the incidence angles
############################################################################
t2_th_p= (abs((t_bs_p*t_sf_p*exp(1j*kz_s*d)) \
/(1+r_bs_p*r_sf_p*exp(2j*kz_s*d))))**2
correction = real(n_b*cos(Phi_b)/(n_f*cos(Phi_list.astype(complex))))
# This is a correction term used in R +T*correction = 1
T_th_s = t2_th_s*correction
T_th_p = t2_th_p*correction
############################################################################
# Calculation with Berreman4x4
data = numpy.array([s.getJones(kx,k0) for kx in Kx])
data = abs(data)**2
R_p = Berreman4x4.extractCoefficient(data, 'r_pp')
R_s = Berreman4x4.extractCoefficient(data, 'r_ss')
t2_p = Berreman4x4.extractCoefficient(data, 't_pp')
t2_s = Berreman4x4.extractCoefficient(data, 't_ss')
T_s = t2_s*correction
T_p = t2_p*correction
############################################################################
# Plotting
fig = pyplot.figure(figsize=(12., 6.))
pyplot.rcParams['axes.color_cycle'] = ['b','g','r','c','b','g']
ax = fig.add_axes([0.1, 0.1, 0.7, 0.8])
y = numpy.vstack((R_s,R_p,t2_s,t2_p,T_s,T_p)).T
legend1 = ("R_s","R_p","t2_s","t2_p","T_s","T_p")
lines1 = ax.plot(Kx, y)
import numpy, Berreman4x4 from numpy import sin, sqrt, abs from Berreman4x4 import c, pi import matplotlib.pyplot as pyplot # Materials glass = Berreman4x4.IsotropicNonDispersiveMaterial(1.55) front = back = Berreman4x4.IsotropicHalfSpace(glass) # Liquid crystal oriented along the x direction (no, ne) = (1.5, 1.7) Dn = ne-no n_med = (ne + no)/2 LC = Berreman4x4.UniaxialNonDispersiveMaterial(no, ne) # ne along z R = Berreman4x4.rotation_v_theta([0,1,0], pi/2) # rotation of pi/2 along y LC = LC.rotated(R) # apply rotation from z to x # Cholesteric pitch: p = 0.65e-6 # One half turn of a right-handed helix: TN = Berreman4x4.TwistedMaterial(LC, p/2, angle=+pi, div=35) # Inhomogeneous layer, repeated layer, and structure IL = Berreman4x4.InhomogeneousLayer(TN) N = 15 # number half pitch repetitions h = N * p/2 L = Berreman4x4.RepeatedLayers([IL], N) s = Berreman4x4.Structure(front, [L], back) # Normal incidence: Kx = 0.0
/ (1 + r_ab[p-1] * U(p)*exp(2j*kz[p]*d[p]))
return res
return U(0)
# Power reflexion coefficient for different incidence angles and polarisations
R_th_ss_0 = (abs(ReflectionCoeff(0, 's')))**2 # Phi_i = 0
R_th_ss = (abs(ReflectionCoeff(pi/4, 's')))**2 # Phi_i = pi/4
R_th_pp = (abs(ReflectionCoeff(pi/4, 'p')))**2
############################################################################
# Calculation with Berreman4x4
# Incidence angle Phi_i = 0, 's' polarization
Kx = front.get_Kx_from_Phi(0)
data = numpy.array([s.getJones(Kx, 2*pi/lbda) for lbda in lbda_list])
r_ss = Berreman4x4.extractCoefficient(data, 'r_ss')
R_ss_0 = abs(r_ss)**2
# Incidence angle Phi_i = pi/4, 's' and 'p' polarizations
Kx = front.get_Kx_from_Phi(pi/4)
data = numpy.array([s.getJones(Kx, 2*pi/lbda) for lbda in lbda_list])
r_ss = Berreman4x4.extractCoefficient(data, 'r_ss')
r_pp = Berreman4x4.extractCoefficient(data, 'r_pp')
R_ss = abs(r_ss)**2
R_pp = abs(r_pp)**2
############################################################################
# Plotting
fig = pyplot.figure(figsize=(12., 6.))
pyplot.rcParams['axes.color_cycle'] = ['b','g','r']
ax = fig.add_axes([0.1, 0.1, 0.7, 0.8])
from Berreman4x4 import c, pi
from numpy import exp, cos, arcsin, real, sqrt
import matplotlib.pyplot as pyplot
print("\n*** Glass1 / Air / Glass2 ***\n")
############################################################################
# Structure definition
# Refractive indices
n_f = 1.5
n_s = 1.0
n_b = 1.7
# Materials:
glass1 = Berreman4x4.IsotropicNonDispersiveMaterial(n_f)
air = Berreman4x4.IsotropicNonDispersiveMaterial(n_s)
glass2 = Berreman4x4.IsotropicNonDispersiveMaterial(n_b)
# Layer and half-spaces:
front = Berreman4x4.IsotropicHalfSpace(glass1)
layer = Berreman4x4.HomogeneousIsotropicLayer(air)
back = Berreman4x4.IsotropicHalfSpace(glass2)
# Structure:
s = Berreman4x4.Structure(front, [layer], back)
# Wavelength and wavenumber:
lbda = 1e-6
k0 = 2 * pi / lbda
Phi_i = pi / 2 * 0.6 # Incidence angle (higher than the limit angle)
import numpy, Berreman4x4
import scipy.linalg
import matplotlib.pyplot as pyplot
from Berreman4x4 import c, pi
from numpy import newaxis, exp, sin
print("\n*** TiO2/SiO2 Bragg mirror ***\n")
############################################################################
# Structure definition
# Front and back materials
n_a = 1.0
n_g = 1.5
air = Berreman4x4.IsotropicNonDispersiveMaterial(n_a)
glass = Berreman4x4.IsotropicNonDispersiveMaterial(n_g)
front = Berreman4x4.IsotropicHalfSpace(air)
back = Berreman4x4.IsotropicHalfSpace(glass)
# Materials for a SiO2/TiO2 Bragg mirror
lbda0 = 1.550e-6
k0 = 2 * pi / lbda0
nr_SiO2 = 1.47
nr_TiO2 = 2.23
alpha_SiO2 = 0e2 # (m⁻¹)
alpha_TiO2 = 42e2 # (m⁻¹)
ni_SiO2 = alpha_SiO2 * lbda0 / (4 * pi)
ni_TiO2 = alpha_TiO2 * lbda0 / (4 * pi)
n_SiO2 = nr_SiO2 + 1j * ni_SiO2
# reduces the number of printed figures in numbers:
numpy.set_printoptions(suppress=True, precision=4)
n_i = 1.0 # incident medium is air
n_o = 2.0 # ordinary index of thin layer
n_e = 2.5 # extraordinary index of thin layer
w = 3.04e15 # pulsation (rad/s)
Phi_i = 70 * pi / 180 # 70° indicence angle (rad)
d = 0.1e-6 # thin layer thickness (m)
# Orientation of the anisotropy of the thin layer
Phi_E = pi / 4 # 1st Euler angle
Theta_E = pi / 4 # 2nd Eulet angle
print("\n*** Air / anisotropic film / silicon substrate ***")
filmMaterialRef = Berreman4x4.UniaxialNonDispersiveMaterial(n_o, n_e)
R = Berreman4x4.rotation_Euler((Phi_E, Theta_E, 0))
filmMaterial = filmMaterialRef.rotated(R)
print("\nPermittivity tensor of the anisotropic film (eq 6.63, p. 241):")
print(filmMaterial.getTensor())
"""
matrix([[ 4.5625, -0.5625, 0.7955],
[-0.5625, 4.5625, -0.7955],
[ 0.7955, -0.7955, 5.125 ]])
"""
air = Berreman4x4.IsotropicNonDispersiveMaterial(n_i)
front = Berreman4x4.IsotropicHalfSpace(air) # Front half-space
Kx = front.get_Kx_from_Phi(Phi_i)
print("\nValue of Kx: {:.4f}".format(Kx))
"""