.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/plot_interface_reflection.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_interface_reflection.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_plot_interface_reflection.py:


Interface reflection
=====================

.. GENERATED FROM PYTHON SOURCE LINES 7-13

Interface between two materials
-------------------------------
Authors: O. Castany, C. Molinaro, M. Müller

Interface between two materials n1/n2.
Calculations of the transmission and reflexion coefficients with varying incidence angle.

.. GENERATED FROM PYTHON SOURCE LINES 13-18

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 19-21

Structure definition
------------------------

.. GENERATED FROM PYTHON SOURCE LINES 21-34

.. code-block:: Python

    n1 = 1
    n2 = 1.5
    front = elli.IsotropicMaterial(elli.ConstantRefractiveIndex(n1))
    back = elli.IsotropicMaterial(elli.ConstantRefractiveIndex(n2))

    # Structure
    s = elli.Structure(front, [], back)

    # Parameters for the calculation
    lbda = 1000
    k0 = 2 * pi / lbda
    Phi_list = np.linspace(0, 89, 90)  #  range for the incidence angles








.. GENERATED FROM PYTHON SOURCE LINES 35-37

Analytical calculation
------------------------

.. GENERATED FROM PYTHON SOURCE LINES 37-58

.. code-block:: Python

    Phi_i = np.deg2rad(Phi_list)

    Phi_t = np.arcsin((n1 * np.sin(Phi_i) / n2).astype(complex))
    kz1 = n1 * k0 * np.cos(Phi_i)
    kz2 = n2 * k0 * np.cos(Phi_t)
    r_s = (kz1 - kz2) / (kz1 + kz2)
    t_s = 1 + r_s
    r_p = (kz1 * n2**2 - kz2 * n1**2) / (kz1 * n2**2 + kz2 * n1**2)
    t_p = np.cos(Phi_i) * (1 - r_p) / np.cos(Phi_t)

    # Reflection and transmission coefficients, polarisation s and p
    R_th_ss = abs(r_s) ** 2
    R_th_pp = abs(r_p) ** 2
    t2_th_ss = abs(t_s) ** 2
    t2_th_pp = abs(t_p) ** 2
    # The power transmission coefficient is T = Re(kz2/kz1) × |t|^2
    correction = np.real(kz2 / kz1)
    T_th_ss = correction * t2_th_ss
    T_th_pp = correction * t2_th_pp









.. GENERATED FROM PYTHON SOURCE LINES 59-61

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

.. GENERATED FROM PYTHON SOURCE LINES 61-72

.. code-block:: Python

    data = elli.ResultList([s.evaluate(lbda, Phi_i) for Phi_i in Phi_list])

    R_pp = data.R_pp
    R_ss = data.R_ss

    T_pp = data.T_pp
    T_ss = data.T_ss

    t2_pp = np.abs(data.t_pp) ** 2
    t2_ss = np.abs(data.t_ss) ** 2








.. GENERATED FROM PYTHON SOURCE LINES 73-75

Plotting
----------

.. GENERATED FROM PYTHON SOURCE LINES 75-101

.. code-block:: Python

    fig = plt.figure(figsize=(12.0, 6.0))
    plt.rcParams["axes.prop_cycle"] = plt.cycler("color", "bgrcmk")
    ax = fig.add_axes([0.1, 0.1, 0.7, 0.8])

    d = np.vstack((R_ss, R_pp, t2_ss, t2_pp, T_ss, T_pp)).T
    lines1 = ax.plot(Phi_list, d)
    legend1 = ("R_ss", "R_pp", "t2_ss", "t2_pp", "T_ss", "T_pp")

    d = np.vstack((R_th_ss, R_th_pp, t2_th_ss, t2_th_pp, T_th_ss, T_th_pp)).T
    lines2 = ax.plot(Phi_list, d, ".")
    legend2 = ("R_th_ss", "R_th_pp", "t2_th_ss", "t2_th_pp", "T_th_ss", "T_th_pp")

    ax.legend(
        lines1 + lines2,
        legend1 + legend2,
        loc="upper left",
        bbox_to_anchor=(1.05, 1),
        borderaxespad=0.0,
    )

    ax.set_title("Interface n$_1$={:} / n$_2$={:}".format(n1, n2))
    ax.set_xlabel(r"Incidence angle $\Phi_i$ ")
    ax.set_ylabel(r"Reflexion and transmission coefficients $R$, $T$, $|t|^2$")

    plt.show()




.. image-sg:: /auto_examples/images/sphx_glr_plot_interface_reflection_001.png
   :alt: Interface n$_1$=1 / n$_2$=1.5
   :srcset: /auto_examples/images/sphx_glr_plot_interface_reflection_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.112 seconds)


.. _sphx_glr_download_auto_examples_plot_interface_reflection.py:

.. only:: html

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

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

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

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

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

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

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