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

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

.. _sphx_glr_auto_examples_plot_bragg_mirror.py:


TiO2/SiO2 Bragg mirror
======================

.. GENERATED FROM PYTHON SOURCE LINES 7-14

TiO2/SiO2 Bragg mirror simulation
---------------------------------

Authors: O. Castany, M.Müller

This notebook simulates a Bragg mirror composed of alternating layers of TiO₂ and SiO₂, each a quarter-wavelength thick at a central wavelength of 1550 nm.
The mirror contains 8.5 periods, with air as the incident medium and glass as the substrate.

.. GENERATED FROM PYTHON SOURCE LINES 16-23

.. code-block:: Python

    import elli
    import elli.plot as elliplot
    import matplotlib.pyplot as plt
    import numpy as np

    np.set_printoptions(suppress=True, precision=3)








.. GENERATED FROM PYTHON SOURCE LINES 24-28

Material definition
-------------------
We define all required materials with constant (non-dispersive) refractive indicies.
Air as incidence material and glass as exit material. The Bragg mirror materials are SiO2 and TiO2.

.. GENERATED FROM PYTHON SOURCE LINES 28-34

.. code-block:: Python


    air = elli.AIR
    glass = elli.ConstantRefractiveIndex(1.5).get_mat()
    SiO2 = elli.ConstantRefractiveIndex(1.47).get_mat()
    TiO2 = elli.ConstantRefractiveIndex(2.23 + 1j * 5.2e-4).get_mat()








.. GENERATED FROM PYTHON SOURCE LINES 35-39

Create layers and structure
---------------------------
The SiO2 and TiO2 layers are set to the thickness of an
quarterwaveplate of the respective material at 1550 nm.

.. GENERATED FROM PYTHON SOURCE LINES 39-52

.. code-block:: Python


    lbda0 = 1550

    d_SiO2 = elli.get_qwp_thickness(SiO2, lbda0)
    d_TiO2 = elli.get_qwp_thickness(TiO2, lbda0)

    print("Thickness of the SiO2 QWP: {} nm".format(d_SiO2))
    print("Thickness of the TiO2 QWP: {} nm".format(d_TiO2))

    L_SiO2 = elli.Layer(SiO2, d_SiO2)
    L_TiO2 = elli.Layer(TiO2, d_TiO2)






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

 .. code-block:: none

    Thickness of the SiO2 QWP: 263.6054421768708 nm
    Thickness of the TiO2 QWP: 173.76681614349775 nm




.. GENERATED FROM PYTHON SOURCE LINES 53-59

Create layers and structure
---------------------------
We now build the multilayer stack:
Alternating layers of TiO2 / SiO2:
- 8 full periods + 1 TiO2 layer at the end → "8.5 periods"
- Placed between air (front) and glass (back)

.. GENERATED FROM PYTHON SOURCE LINES 59-67

.. code-block:: Python


    # Define periodic stack
    # Repeated layers: 8.5 periods: Parameters (Substructure, repetitions, number of layers before, number of layers after the stack)
    layerstack = elli.RepeatedLayers([L_TiO2, L_SiO2], 8, 0, 1)

    # Build full structure
    s = elli.Structure(air, [layerstack], glass)








.. GENERATED FROM PYTHON SOURCE LINES 68-70

Structure Graph: Visualization of the refractive index profile in z-direction.
------------------------------------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 70-72

.. code-block:: Python

    elliplot.draw_structure(s)




.. image-sg:: /auto_examples/images/sphx_glr_plot_bragg_mirror_001.png
   :alt: plot bragg mirror
   :srcset: /auto_examples/images/sphx_glr_plot_bragg_mirror_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


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



.. GENERATED FROM PYTHON SOURCE LINES 73-76

Optical calculation
-------------------
Calculation of the reflection and transmission of the structure at normal incidence (0°).

.. GENERATED FROM PYTHON SOURCE LINES 76-84

.. code-block:: Python

    (lbda1, lbda2) = (1100, 2500)
    lbda_list = np.linspace(lbda1, lbda2, 200)

    data = s.evaluate(lbda_list, 0)

    R = data.R
    T = data.T








.. GENERATED FROM PYTHON SOURCE LINES 85-88

Reflection and Transmission data
--------------------------------
The plot shows the high reflection in the stopband region around the design wavelength and the interference patterns around it.

.. GENERATED FROM PYTHON SOURCE LINES 88-97

.. code-block:: Python

    fig = plt.figure()
    ax = fig.add_subplot(1, 1, 1)
    ax.plot(lbda_list, T, label="$T$")
    ax.plot(lbda_list, R, label="$R$")
    ax.legend(loc="center right")
    ax.set_xlabel(r"Wavelength $\lambda$ (nm)")
    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")
    plt.show()



.. image-sg:: /auto_examples/images/sphx_glr_plot_bragg_mirror_002.png
   :alt: Bragg mirror: Air/{TiO$_2$/SiO$_2$}x8/TiO$_2$/Glass
   :srcset: /auto_examples/images/sphx_glr_plot_bragg_mirror_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.240 seconds)


.. _sphx_glr_download_auto_examples_plot_bragg_mirror.py:

.. only:: html

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

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

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

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

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

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

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