.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/plot_cholesteric_lq.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_plot_cholesteric_lq.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_plot_cholesteric_lq.py:


Cholesteric Liquid Crystal
==========================

.. GENERATED FROM PYTHON SOURCE LINES 7-10

Example of a cholesteric liquid crystal
---------------------------------------
Authors: O. Castany, C. Molinaro, M. Müller

.. GENERATED FROM PYTHON SOURCE LINES 12-18

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 19-21

Setup materials and structure
-----------------------------

.. GENERATED FROM PYTHON SOURCE LINES 21-51

.. code-block:: Python

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

    # Liquid crystal oriented along the x direction
    (no, ne) = (1.5, 1.7)
    Dn = ne - no
    n_med = (ne + no) / 2
    LC = elli.UniaxialMaterial(
        elli.ConstantRefractiveIndex(no), elli.ConstantRefractiveIndex(ne)
    )  # ne is along 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

    # 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)

    # Calculation parameters
    lbda_min, lbda_max = 800, 1200  # (nm)
    lbda_B = p * n_med
    lbda_list = np.linspace(lbda_min, lbda_max, 100)








.. GENERATED FROM PYTHON SOURCE LINES 52-54

Analytical calculation for the maximal reflection
-------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 54-57

.. code-block:: Python

    R_th = np.tanh(Dn / n_med * pi * h / p) ** 2
    lbda_B1, lbda_B2 = p * no, p * ne








.. GENERATED FROM PYTHON SOURCE LINES 58-60

Calculation with pyElli
-----------------------

.. GENERATED FROM PYTHON SOURCE LINES 60-89

.. code-block:: Python

    data = s.evaluate(lbda_list, 0)

    T_pp = data.T_pp
    T_ps = data.T_ps
    T_ss = data.T_ss
    T_sp = data.T_sp

    # Transmission coefficients for incident unpolarized light:
    T_pn = 0.5 * (T_pp + T_ps)
    T_sn = 0.5 * (T_sp + T_ss)
    T_nn = T_sn + T_pn

    # 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.
    # R_LR, T_LR close to zero.
    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








.. GENERATED FROM PYTHON SOURCE LINES 90-92

Plotting
--------

.. GENERATED FROM PYTHON SOURCE LINES 92-116

.. code-block:: Python

    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()

    elliplot.draw_structure(s)



.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /auto_examples/images/sphx_glr_plot_cholesteric_lq_001.png
         :alt: Right-handed Cholesteric Liquid Crystal, aligned along  the $x$ direction, with 7.5 helix pitches.
         :srcset: /auto_examples/images/sphx_glr_plot_cholesteric_lq_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/images/sphx_glr_plot_cholesteric_lq_002.png
         :alt: plot cholesteric lq
         :srcset: /auto_examples/images/sphx_glr_plot_cholesteric_lq_002.png
         :class: sphx-glr-multi-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    <Axes: xlabel='z (nm)', ylabel="n'">




.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.370 seconds)


.. _sphx_glr_download_auto_examples_plot_cholesteric_lq.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_cholesteric_lq.ipynb <plot_cholesteric_lq.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_cholesteric_lq.py <plot_cholesteric_lq.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_cholesteric_lq.zip <plot_cholesteric_lq.zip>`