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
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
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)
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: 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
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
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)
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 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
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
