"""
Cholesteric Liquid Crystal Simulation
=====================================
"""

# %%
# Example of a cholesteric liquid crystal
# ---------------------------------------
# Authors: O. Castany, C. Molinaro, M. Müller
#
# This notebook demonstrates how to model and simulate the optical properties of a cholesteric liquid crystal using pyElli.
# We will build a helical structure and observe its characteristic selective reflection of circularly polarized light.

# %%
import elli
import elli.plot as elliplot
import matplotlib.pyplot as plt
import numpy as np
from scipy.constants import c, pi

# %%
# Setup materials
# ---------------
# We start by defining the materials for our model.
# The liquid crystal will be sandwiched between two layers of isotropic glass with a constant refractive index of 1.55.
#
# The liquid crystal (LC) itself is uniaxial and will be rotated to have the extraordinary axis orientated in x-direction.

glass = elli.IsotropicMaterial(elli.ConstantRefractiveIndex(1.55))
front = back = glass

# Define the ordinary (no) and extraordinary (ne) refractive indices for the LC
(no, ne) = (1.5, 1.7)
Dn = ne - no
n_med = (ne + no) / 2

# Create a uniaxial material with ne oriented along the z-axis by default
LC = elli.UniaxialMaterial(
    elli.ConstantRefractiveIndex(no), elli.ConstantRefractiveIndex(ne)
)

# Rotate the material so the extraordinary axis is along x instead of z
R = elli.rotation_v_theta(elli.E_Y, 90)  # rotation of pi/2 along y
LC.set_rotation(R)  # apply rotation from z to x

# %%
# Building the Helical Structure
# ------------------------------
#
# The defining feature of a cholesteric liquid crystal is its helical structure.
# The distance over which the director rotates by 360° is known as the cholesteric pitch (p).
#
# We model this by first creating a single TwistedLayer that represents one half-turn of the helix (180° rotation over a distance of p/2).
# We then stack this layer multiple times using RepeatedLayers to build the full thickness (7.5p) of the liquid crystal cell.

# Cholesteric pitch (nm):
p = 650

# One half turn of a right-handed helix:
TN = elli.TwistedLayer(LC, p / 2, angle=180, div=35)

# Repetition the helix layer
N = 15  # number half pitch repetitions
h = N * p / 2
L = elli.RepeatedLayers([TN], N)
s = elli.Structure(front, [L], back)

# %%
# Setting Calculation Parameters
# ------------------------------
#
# Finally, we define the wavelength range for our simulation around the central wavelength of the reflection band,
# which is determined by the average refractive index and the pitch.

# Define wavelength range in nm for the calculation
lbda_min, lbda_max = 800, 1200
lbda_B = p * n_med  # Expected center of the reflection band
lbda_list = np.linspace(lbda_min, lbda_max, 100)

# %%
# Analytical calculation for the maximal reflection
# -------------------------------------------------
# For a cholesteric liquid crystal, we can analytically calculate the approximate edges of the reflection band and the maximum reflectance.
# This serves as a good check for our full simulation.

# Theoretical maximum reflectance
R_th = np.tanh(Dn / n_med * pi * h / p) ** 2

# Theoretical wavelength edges of the reflection band
lbda_B1, lbda_B2 = p * no, p * ne

# %%
# Calculation with pyElli
# -----------------------
# Now we run the simulation using the s.evaluate() method. This calculates the Jones matrix elements for transmission and reflection.
# They are extracted for linear (s and p), as well as circular polarized light (R and L)

# Run the full optical simulation for the defined structure and wavelength list
data = s.evaluate(lbda_list, 0)

# Extract transmission coefficients for linear polarization
T_pp = data.T_pp
T_ps = data.T_ps
T_ss = data.T_ss
T_sp = data.T_sp

# Calculate transmission for unpolarized incident light
T_nn = 0.5 * (T_pp + T_ps + T_sp + T_ss)

# Transmission coefficients for 's' and 'p' polarized light, with
# unpolarized measurement.
T_ns = T_ps + T_ss
T_np = T_pp + T_sp

# Right-circular wave is reflected in the stop-band.
# A right-handed helix reflects right-circular (RR) light.
R_RR = data.Rc_RR
R_LR = data.Rc_LR
T_RR = data.Tc_RR
T_LR = data.Tc_LR

# Left-circular wave is transmitted in the full spectrum.
# T_RL, R_RL, R_LL close to zero, T_LL close to 1.
T_LL = data.Tc_LL
R_LL = data.Rc_LL

# %%
# Plotting
# --------
# Finally, we plot the results. The plot will show the transmission and reflection spectra for various polarizations.
#
# We also draw a shaded rectangle representing the analytically calculated photonic stop-band.
# Inside this band, we expect to see strong reflection for a specific circular polarization.
# As our model is a right-handed helix, it should strongly reflect right-circularly polarized light (R_RR).

fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)

# Draw rectangle for λ ∈ [p·no, p·ne], and T ∈ [0, R_th]
rectangle = plt.Rectangle((lbda_B1, 0), lbda_B2 - lbda_B1, R_th, color="cyan")
ax.add_patch(rectangle)

ax.plot(lbda_list, R_RR, "--", label="R_RR")
ax.plot(lbda_list, T_RR, label="T_RR")
ax.plot(lbda_list, T_nn, label="T_nn")
ax.plot(lbda_list, T_ns, label="T_ns")
ax.plot(lbda_list, T_np, label="T_np")

ax.legend(loc="center right", bbox_to_anchor=(1.00, 0.50))

ax.set_title(
    "Right-handed Cholesteric Liquid Crystal, aligned along \n"
    + "the $x$ direction, with {:.1f} helix pitches.".format(N / 2.0)
)
ax.set_xlabel(r"Wavelength $\lambda_0$ (nm)")
ax.set_ylabel(r"Power transmission $T$ and reflexion $R$")
plt.show()

# %%
# Additionally we can visualize the refractive index n x direction of the structure in dependance of z position.
elliplot.draw_structure(s)