.. _sphx_glr_api_gallery_optics_interference:

Interference in layered media
-----------------------------

Multiple-beam interference computed with the characteristic-matrix method:
the Fabry-Pérot interferometer, thin-film antireflection coatings, and the
band gap of a 1D photonic crystal.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

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    <div class="sphx-glr-thumbcontainer" tooltip="Two parallel mirrors of reflectance R a distance L apart send light back and forth many times, and the transmitted beams add with a round-trip phase \delta = 4\pi nL\cos\theta/\lambda. Summing the geometric series gives the Airy function (Fabry and Pérot, 1899)">

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  .. image:: /api/gallery/optics/interference/images/thumb/sphx_glr_plot_fabry_perot_interferometer_thumb.png
    :alt:

  :doc:`/api/gallery/optics/interference/plot_fabry_perot_interferometer`

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      <div class="sphx-glr-thumbnail-title">The Fabry-Pérot interferometer: multiple-beam interference and finesse</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="A periodic stack of two dielectrics is to light what a crystal lattice is to electrons. Writing one period&#x27;s characteristic matrix M_{\text{period}}, Bloch&#x27;s theorem gives the modes of the infinite stack,">

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  .. image:: /api/gallery/optics/interference/images/thumb/sphx_glr_plot_photonic_crystal_band_gap_thumb.png
    :alt:

  :doc:`/api/gallery/optics/interference/plot_photonic_crystal_band_gap`

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      <div class="sphx-glr-thumbnail-title">Photonic band gaps in a 1D photonic crystal</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Light reflected from the top and bottom of a thin film interferes, which is why soap bubbles and oil slicks show colours. Around 1935 Alexander Smakula at Zeiss turned this into the antireflection coating. A film of index n_1 and optical thickness \lambda_0/4 on glass of index n_s sends back two reflections half a wave apart, and their amplitudes cancel when n_1 = \sqrt{n_0 n_s}:">

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  .. image:: /api/gallery/optics/interference/images/thumb/sphx_glr_plot_thin_film_antireflection_thumb.png
    :alt:

  :doc:`/api/gallery/optics/interference/plot_thin_film_antireflection`

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      <div class="sphx-glr-thumbnail-title">Thin-film interference: the antireflection coating</div>
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    </div>


.. toctree::
   :hidden:

   /api/gallery/optics/interference/plot_fabry_perot_interferometer
   /api/gallery/optics/interference/plot_photonic_crystal_band_gap
   /api/gallery/optics/interference/plot_thin_film_antireflection