.. _sphx_glr_api_gallery_optics_lasers:

Laser dynamics
--------------

What happens inside the gain medium: the rate equations behind the
lasing threshold, gain clamping and relaxation oscillations, and the
Maxwell-Bloch equations whose bad-cavity instability makes a single-mode
laser chaotic.


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    <div class="sphx-glr-thumbcontainer" tooltip="Schawlow and Townes (1958) showed that an optical cavity containing an inverted medium oscillates once the gain from stimulated emission beats the cavity loss. In the rate equations for the inversion N and the photon number q (~physicskit.optics.lasers.LaserRateEquations) this happens at the threshold inversion N_{\rm th} = 1/(B\tau_c). Above threshold the inversion is clamped there and the output grows linearly with the pump. When the laser is switched on, it overshoots in a train of spikes that settle through damped relaxation oscillations.">

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  :doc:`/api/gallery/optics/lasers/plot_laser_threshold_rate_equations`

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      <div class="sphx-glr-thumbnail-title">Schawlow and Townes: the lasing threshold from the laser rate equations</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Rate equations ignore the atomic polarization. Keeping it, the semiclassical single-mode laser obeys the Maxwell-Bloch equations for the field E, polarization P and inversion D (~physicskit.optics.lasers.MaxwellBloch). Haken (1975) noticed these are the Lorenz equations. The laser switches on at r = 1, and in a &quot;bad cavity&quot; (:math:`\kappa &gt; \gamma_\perp + \gamma_\parallel`) the steady lasing state becomes unstable at a second threshold r_H, after which the output intensity is chaotic.">

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  .. image:: /api/gallery/optics/lasers/images/thumb/sphx_glr_plot_maxwell_bloch_laser_chaos_thumb.png
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  :doc:`/api/gallery/optics/lasers/plot_maxwell_bloch_laser_chaos`

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      <div class="sphx-glr-thumbnail-title">Haken's laser-Lorenz analogy: Maxwell-Bloch dynamics and laser chaos</div>
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.. toctree::
   :hidden:

   /api/gallery/optics/lasers/plot_laser_threshold_rate_equations
   /api/gallery/optics/lasers/plot_maxwell_bloch_laser_chaos