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

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_tutorials_plot_permittivity_fft.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_tutorials_plot_permittivity_fft.py:


Permittivity approximation
==========================

Get the Fourier representation of the permittivity as a function of number of harmonics.

.. GENERATED FROM PYTHON SOURCE LINES 15-33

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    import nannos as nn

    lattice = nn.Lattice([[1.5, 0], [0.4, 1]], discretization=(2**10, 2**10))
    sup = lattice.Layer("Superstrate", epsilon=1)
    sub = lattice.Layer("Substrate", epsilon=1)
    hole = lattice.ellipse(center=(1.1, 0.6), radii=(0.2, 0.4), rotate=60)
    incl = lattice.rectangle(center=(0.5, 0.3), widths=(0.2, 0.4), rotate=-45)
    epsilon = lattice.ones() * 4
    epsilon[hole] = 1
    epsilon[incl] = 6
    ms = lattice.Layer("Metasurface", thickness=0.5, epsilon=epsilon)
    pw = nn.PlaneWave(wavelength=1.5, angles=(0, 0, 0))









.. GENERATED FROM PYTHON SOURCE LINES 34-35

Lets first plot the permmitivity we want to approximate

.. GENERATED FROM PYTHON SOURCE LINES 35-44

.. code-block:: Python


    plt.figure()
    ims = ms.plot(cmap="viridis")
    plt.xlabel("$x$")
    plt.ylabel("$y$")
    plt.colorbar(ims[0], orientation="horizontal")
    plt.tight_layout()





.. image-sg:: /tutorials/images/sphx_glr_plot_permittivity_fft_001.png
   :alt: plot permittivity fft
   :srcset: /tutorials/images/sphx_glr_plot_permittivity_fft_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 45-46

Loop through number of harmonics

.. GENERATED FROM PYTHON SOURCE LINES 46-58

.. code-block:: Python


    for n in [3, 5, 7, 11, 21, 41]:
        sim = nn.Simulation([sup, ms, sub], pw, nh=n**2)
        eps = sim.get_epsilon(ms)
        plt.figure(figsize=(2, 2))
        approx = plt.pcolormesh(*lattice.grid, eps.real)
        ims = ms.plot(alpha=0.1, cmap="Greys")
        plt.xlabel("$x$")
        plt.ylabel("$y$")
        plt.colorbar(approx, orientation="horizontal")
        plt.title(rf"$n_h = {sim.nh}$")
        plt.tight_layout()



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


    *

      .. image-sg:: /tutorials/images/sphx_glr_plot_permittivity_fft_002.png
         :alt: $n_h = 7$
         :srcset: /tutorials/images/sphx_glr_plot_permittivity_fft_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /tutorials/images/sphx_glr_plot_permittivity_fft_003.png
         :alt: $n_h = 23$
         :srcset: /tutorials/images/sphx_glr_plot_permittivity_fft_003.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /tutorials/images/sphx_glr_plot_permittivity_fft_004.png
         :alt: $n_h = 47$
         :srcset: /tutorials/images/sphx_glr_plot_permittivity_fft_004.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /tutorials/images/sphx_glr_plot_permittivity_fft_005.png
         :alt: $n_h = 117$
         :srcset: /tutorials/images/sphx_glr_plot_permittivity_fft_005.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /tutorials/images/sphx_glr_plot_permittivity_fft_006.png
         :alt: $n_h = 433$
         :srcset: /tutorials/images/sphx_glr_plot_permittivity_fft_006.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /tutorials/images/sphx_glr_plot_permittivity_fft_007.png
         :alt: $n_h = 1679$
         :srcset: /tutorials/images/sphx_glr_plot_permittivity_fft_007.png
         :class: sphx-glr-multi-img






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

   **Total running time of the script:** (0 minutes 15.720 seconds)

**Estimated memory usage:**  1099 MB


.. _sphx_glr_download_tutorials_plot_permittivity_fft.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/nannos/nannos.gitlab.io/doc?filepath=notebooks/tutorials/plot_permittivity_fft.ipynb
        :alt: Launch binder
        :width: 150 px

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

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

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

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

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

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


.. only:: html

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

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