.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/basic/plot_1d_grating.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_basic_plot_1d_grating.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_basic_plot_1d_grating.py:


One dimensional grating
=========================

Convergence.

.. GENERATED FROM PYTHON SOURCE LINES 15-22

.. code-block:: Python



    import matplotlib.pyplot as plt
    import numpy as np

    import nannos as nn








.. GENERATED FROM PYTHON SOURCE LINES 24-25

We will study the 1D metallic grating as in :cite:p:`Li1993`.

.. GENERATED FROM PYTHON SOURCE LINES 25-80

.. code-block:: Python



    def convergence_study(form, psi, Nh):
        ts0 = []
        tsm1 = []
        ns = []
        for nh in Nh:
            lattice = nn.Lattice(1, 2**9)
            eps_metal = (0.22 + 6.71j) ** 2
            epsgrid = lattice.ones() * 1
            hole = lattice.stripe(0.5, 0.5)
            epsgrid[hole] = eps_metal
            sup = lattice.Layer("Superstrate")
            sub = lattice.Layer("Substrate", epsilon=eps_metal)
            grating = lattice.Layer("Grating", thickness=1)
            grating.epsilon = epsgrid
            stack = [sup, grating, sub]
            pw = nn.PlaneWave(wavelength=1, angles=(30, 0, psi))
            sim = nn.Simulation(stack, pw, nh, formulation=form)
            R, T = sim.diffraction_efficiencies()
            Ri, Ti = sim.diffraction_efficiencies(orders=True)
            R0 = sim.get_order(Ri, 0)
            Rm1 = sim.get_order(Ri, -1)
            ts0.append(R0)
            tsm1.append(Rm1)
            ns.append(sim.nh)
        return np.array(ns), 100 * np.array(ts0), 100 * np.array(tsm1)


    def run(psi):
        Nh = range(5, 125, 2)
        fig, ax = plt.subplots(2, 1, figsize=(2.0, 3.0))
        title = "TM" if psi == 0 else "TE"
        ns, ts0, tsm1 = convergence_study("original", psi, Nh)
        ax[0].plot(ns, ts0, "-o", label="original", c="#dd803d", ms=1)
        ax[1].plot(ns, tsm1, "-o", label="original", c="#dd803d", ms=1)
        ns_tan, ts0_tan, tsm1_tan = convergence_study("tangent", psi, Nh)
        ax[0].plot(
            ns_tan, ts0_tan, "--s", label="tangent", c="#4a4082", ms=2, mew=0.4, mfc="None"
        )
        ax[1].plot(
            ns_tan, tsm1_tan, "--s", label="tangent", c="#4a4082", ms=2, mew=0.4, mfc="None"
        )
        ax[0].set_title("order 0")
        ax[1].set_title("order -1")
        ax[0].legend()
        ax[1].legend()
        ax[0].set_xlabel("number of harmonics")
        ax[0].set_ylabel("diffraction efficiency (%)")
        ax[1].set_ylabel("diffraction efficiency (%)")
        plt.suptitle(title, weight="bold", size=8)
        plt.tight_layout()
        plt.pause(0.1)









.. GENERATED FROM PYTHON SOURCE LINES 81-82

For TE polarization the two formulations are equivalent:

.. GENERATED FROM PYTHON SOURCE LINES 82-86

.. code-block:: Python


    run(psi=90)





.. image-sg:: /examples/basic/images/sphx_glr_plot_1d_grating_001.png
   :alt: TE, order 0, order -1
   :srcset: /examples/basic/images/sphx_glr_plot_1d_grating_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 87-90

We can see that in TM polarization, the convergence is greatly
improved by using proper Fourier factorization rules implemented by the
``tangent`` formulation.

.. GENERATED FROM PYTHON SOURCE LINES 90-93

.. code-block:: Python



    run(psi=0)



.. image-sg:: /examples/basic/images/sphx_glr_plot_1d_grating_002.png
   :alt: TM, order 0, order -1
   :srcset: /examples/basic/images/sphx_glr_plot_1d_grating_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 22.449 seconds)

**Estimated memory usage:**  715 MB


.. _sphx_glr_download_examples_basic_plot_1d_grating.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/examples/basic/plot_1d_grating.ipynb
        :alt: Launch binder
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_1d_grating.ipynb <plot_1d_grating.ipynb>`

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

      :download:`Download Python source code: plot_1d_grating.py <plot_1d_grating.py>`

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

      :download:`Download zipped: plot_1d_grating.zip <plot_1d_grating.zip>`


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

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