.. _sphx_glr_auto_examples_optical:

Optical
-------

Fibre propagation and its compensation, nonlinear interference, Raman amplification,
optical modulators; optical wireless links (visible light indoors, free-space optics).


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    <div class="sphx-glr-thumbcontainer" tooltip="Standard single-mode fibre spreads a 32 GBd signal over many symbols: D = 17 ps/(nm·km) accumulate 1360 ps/nm over 80 km, and the received 16-QAM constellation collapses into a cloud. Dispersion is an all-pass filter, e^{j \beta_2 \omega^2 L / 2}, so the receiver undoes it exactly in the frequency domain (comnum.cdc), or with an FIR whose length grows with the accumulated dispersion (comnum.cd_fir_taps).">

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  .. image:: /auto_examples/optical/images/thumb/sphx_glr_plot_01_chromatic_dispersion_thumb.png
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  :doc:`/auto_examples/optical/plot_01_chromatic_dispersion`

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      <div class="sphx-glr-thumbnail-title">Chromatic dispersion and its compensation</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="The classical launch-power sweep of a long-haul optical link: 16-QAM at 32 GBd over 10 spans of 80 km of standard single-mode fibre with an EDFA (noise figure 4.5 dB) after every span, simulated by the split-step Fourier method (1 km steps). At low power the amplified spontaneous emission limits the SNR, which grows by 1 dB per dB of launch power; at high power the Kerr nonlinearity (\gamma = 1.3 /(W·km)) takes over and the SNR falls. The optimum is the maximum of this &quot;bell&quot;.">

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  .. image:: /auto_examples/optical/images/thumb/sphx_glr_plot_02_launch_power_dbp_thumb.png
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  :doc:`/auto_examples/optical/plot_02_launch_power_dbp`

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      <div class="sphx-glr-thumbnail-title">Nonlinear fibre propagation and digital back-propagation</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Fig. 5 of C. Häger and H. D. Pfister, &quot;Physics-based deep learning for fiber-optic communication systems&quot;, IEEE J. Sel. Areas Commun. 39(1), 2021 (arXiv:2010.14258), gives the effective SNR against the launch power of a single channel over 25 spans of 80 km of standard fibre at 10.7 GBd with Gaussian symbols, for linear equalisation (dispersion compensation alone) and digital back-propagation (DBP) with one step per span. The link is that of the paper: \beta_2 = -21.683 ps²/km at 194.6 THz, \gamma = 1.3 /W/km, 0.2 dB/km, a noise figure of 5 dB, root-raised-cosine pulses of roll-off 0.1, propagation at 6 samples per symbol and receivers at 2.">

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  .. image:: /auto_examples/optical/images/thumb/sphx_glr_plot_03_hager2021_fig5_thumb.png
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  :doc:`/auto_examples/optical/plot_03_hager2021_fig5`

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      <div class="sphx-glr-thumbnail-title">Häger & Pfister 2021, Fig. 5: linear equalisation and back-propagation</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Dual-polarisation channels at 32 GBd propagated together by the Manakov equation (comnum.ManakovSsfm, the split step with the phase at the middle of the step), with EDFAs of noise figure 4.5 dB after every span of 80 km of standard fibre.">

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  .. image:: /auto_examples/optical/images/thumb/sphx_glr_plot_04_wdm_nonlinearity_thumb.png
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  :doc:`/auto_examples/optical/plot_04_wdm_nonlinearity`

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      <div class="sphx-glr-thumbnail-title">WDM nonlinearity: the GN model and digital back-propagation</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="The pumps of a distributed Raman amplifier transfer their power to the signals about 13 THz below them, all along the span. comnum.raman_profile solves the coupled power equations of stimulated Raman scattering (Bromage 2004) for the signals and any number of co- and counter-propagating pumps, with the measured gain spectrum of standard single-mode fibre.">

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  .. image:: /auto_examples/optical/images/thumb/sphx_glr_plot_05_raman_amplification_thumb.png
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  :doc:`/auto_examples/optical/plot_05_raman_amplification`

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      <div class="sphx-glr-thumbnail-title">Raman amplification: pumps, gain flattening and the hybrid link</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="A Mach–Zehnder modulator (MZM) splits the optical field into two arms, shifts their phases with the driving voltage and recombines them. Driven in push-pull, the two arms move in opposite directions and the output field is real (no chirp):">

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  .. image:: /auto_examples/optical/images/thumb/sphx_glr_plot_06_mach_zehnder_thumb.png
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  :doc:`/auto_examples/optical/plot_06_mach_zehnder`

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      <div class="sphx-glr-thumbnail-title">Mach–Zehnder and IQ modulators</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Light as the medium outside the fibre, in three panels to open next to the figures of the papers they reproduce.">

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  .. image:: /auto_examples/optical/images/thumb/sphx_glr_plot_07_optical_wireless_thumb.png
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  :doc:`/auto_examples/optical/plot_07_optical_wireless`

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      <div class="sphx-glr-thumbnail-title">Optical wireless: an LED-lit room and a turbulent free-space link</div>
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.. toctree::
   :hidden:

   /auto_examples/optical/plot_01_chromatic_dispersion
   /auto_examples/optical/plot_02_launch_power_dbp
   /auto_examples/optical/plot_03_hager2021_fig5
   /auto_examples/optical/plot_04_wdm_nonlinearity
   /auto_examples/optical/plot_05_raman_amplification
   /auto_examples/optical/plot_06_mach_zehnder
   /auto_examples/optical/plot_07_optical_wireless