.. _sphx_glr_api_gallery_optics_ray_optics:

Ray optics
----------

Paraxial ray-transfer (ABCD) matrix optics: Gauss's composition rule for a
compound optical system as a product of elementary matrices, the
two-mirror resonator stability criterion behind Maiman's ruby laser
cavity, and the sinusoidal ray confinement of Kao's graded-index (GRIN)
optical fiber.


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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="Carl Friedrich Gauss showed that any centered optical system, however many lenses and refracting surfaces it contains, can be fully characterized in the paraxial approximation by linear algebra rather than surface-by-surface trigonometry: every elementary optical element is a linear map on the ray state (y, \theta) -- height above the axis and angle to it --">

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  .. image:: /api/gallery/optics/ray_optics/images/thumb/sphx_glr_plot_abcd_system_matrix_thumb.png
    :alt:

  :doc:`/api/gallery/optics/ray_optics/plot_abcd_system_matrix`

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      <div class="sphx-glr-thumbnail-title">Gauss's ABCD formalism: a composite system as a matrix product</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Charles Kao and George Hockham&#x27;s insight that glass fiber could in principle be purified to carry light over kilometers launched the fiber-optic communications industry. The graded-index (GRIN) fiber profile that followed guides light by continuously bending rays back toward the core axis, rather than by a single sharp core-cladding interface: for the standard quadratic radial index profile n(r) = n_0(1 - n_2 r^2/2), paraxial rays oscillate sinusoidally about the axis instead of walking off it. grin_medium builds the ABCD matrix of exactly this profile; chaining it through OpticalSystem and calling trace_ray reproduces the self-confining ray trajectory below, contrasted against the same ray walking away from the axis in a homogeneous medium.">

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  .. image:: /api/gallery/optics/ray_optics/images/thumb/sphx_glr_plot_grin_fiber_guiding_thumb.png
    :alt:

  :doc:`/api/gallery/optics/ray_optics/plot_grin_fiber_guiding`

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      <div class="sphx-glr-thumbnail-title">Graded-index fiber guiding (Kao's low-loss optical fiber)</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Theodore Maiman&#x27;s 1960 ruby laser used a resonator formed by two mirrors bounding an amplifying medium -- precisely the kind of optical cavity that ray-transfer matrix theory was soon developed to analyze. This package does not model laser gain media, but spherical_mirror and cavity_round_trip_matrix build the ABCD round-trip matrix of a two-mirror resonator like Maiman&#x27;s, and cavity_stability tests whether such a cavity traps light indefinitely (a stable resonator, |A+D| \le 2) or walks rays out of the cavity on successive round trips.">

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  .. image:: /api/gallery/optics/ray_optics/images/thumb/sphx_glr_plot_laser_cavity_stability_thumb.png
    :alt:

  :doc:`/api/gallery/optics/ray_optics/plot_laser_cavity_stability`

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      <div class="sphx-glr-thumbnail-title">Two-mirror resonator stability (Maiman's ruby laser cavity)</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /api/gallery/optics/ray_optics/plot_abcd_system_matrix
   /api/gallery/optics/ray_optics/plot_grin_fiber_guiding
   /api/gallery/optics/ray_optics/plot_laser_cavity_stability