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

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_plot_phc.py>`
        to download the full example code or to run this example in your browser via Binder

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

.. _sphx_glr_examples_plot_phc.py:


Band diagram of 2D photonic crystal
===================================

Calculation of the band diagram of a two-dimensional photonic crystal.

.. GENERATED FROM PYTHON SOURCE LINES 15-24

.. code-block:: Python



    import matplotlib.pyplot as plt
    import numpy as np

    import protis as pt

    pi = np.pi








.. GENERATED FROM PYTHON SOURCE LINES 25-32

Reference results are taken from  :cite:p:`Joannopoulos2008` (Chapter 5 Fig. 2).

The structure is a square lattice of dielectric
columns, with radius r and dielectric constant :math:`\varepsilon`.
The material is invariant along the z direction  and periodic along
:math:`x` and :math:`y` with lattice constant :math:`a`.
We will define the lattie using the class :class:`~protis.Lattice`

.. GENERATED FROM PYTHON SOURCE LINES 32-37

.. code-block:: Python


    a = 1
    lattice = pt.Lattice([[a, 0], [0, a]], discretization=2**9)









.. GENERATED FROM PYTHON SOURCE LINES 38-39

Define the permittivity

.. GENERATED FROM PYTHON SOURCE LINES 39-43

.. code-block:: Python

    epsilon = lattice.ones() * 1
    rod = lattice.circle(center=(0.5, 0.5), radius=0.2)
    epsilon[rod] = 8.9








.. GENERATED FROM PYTHON SOURCE LINES 44-45

We define here the wavevector path:

.. GENERATED FROM PYTHON SOURCE LINES 45-53

.. code-block:: Python

    Gamma = (0, 0)
    X = (pi / a, 0)
    M = (pi / a, pi / a)
    sym_points = [Gamma, X, M, Gamma]

    Nb = 21
    kpath = pt.init_bands(sym_points, Nb)








.. GENERATED FROM PYTHON SOURCE LINES 54-55

Calculate the band diagram:

.. GENERATED FROM PYTHON SOURCE LINES 55-71

.. code-block:: Python


    sim = pt.Simulation(lattice, epsilon=epsilon, nh=100)

    BD = {}
    for polarization in ["TE", "TM"]:
        ev_band = []
        for kx, ky in kpath:
            sim.k = kx, ky
            sim.solve(polarization, vectors=False)
            ev_norma = sim.eigenvalues * a / (2 * pi)
            ev_band.append(ev_norma)
        BD[polarization] = ev_band
    BD["TM"] = pt.backend.stack(BD["TM"]).real
    BD["TE"] = pt.backend.stack(BD["TE"]).real









.. GENERATED FROM PYTHON SOURCE LINES 72-73

Plot the bands:

.. GENERATED FROM PYTHON SOURCE LINES 73-86

.. code-block:: Python


    labels = ["$\Gamma$", "$X$", "$M$", "$\Gamma$"]


    plt.figure()
    plotTM = pt.plot_bands(sym_points, Nb, BD["TM"], color="#4199b0")
    plotTE = pt.plot_bands(sym_points, Nb, BD["TE"], xtickslabels=labels, color="#cf5268")

    plt.annotate("TM modes", (1, 0.05), c="#4199b0")
    plt.annotate("TE modes", (0.33, 0.33), c="#cf5268")
    plt.ylim(0, 0.8)
    plt.ylabel(r"Frequency $\omega a/2\pi c$")
    plt.tight_layout()



.. image-sg:: /examples/images/sphx_glr_plot_phc_001.png
   :alt: plot phc
   :srcset: /examples/images/sphx_glr_plot_phc_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 1.143 seconds)

**Estimated memory usage:**  27 MB


.. _sphx_glr_download_examples_plot_phc.py:

.. only:: html

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

    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/protis/protis.gitlab.io/doc?filepath=notebooks/examples/plot_phc.ipynb
        :alt: Launch binder
        :width: 150 px

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

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

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

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


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_