Editing Kerr-lens modelocking (section)

{{Short description|Laser mode-locking method}}
{{Multiple issues|
{{Refimprove|date=November 2016}}
{{More footnotes|date=October 2019}}
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{{Use American English|date = March 2019}}
'''Kerr-lens mode-locking''' ('''KLM''') is a method of [[mode-locking]] [[laser]]s via the [[nonlinear optics|nonlinear optical]] [[Kerr effect]]. This method allows the generation of pulses of light with a duration as short as a few [[femtosecond]]s.

The optical [[Kerr effect]] is a process which results from the nonlinear response of an optical medium to the [[electric field]] of an [[electromagnetic wave]]. The [[refractive index]] of the medium is dependent on the field strength.<ref>{{cite journal|last1=Vaziri|first1=M R R|title=Comment on "Nonlinear refraction measurements of materials using the moiré deflectometry"|journal=Optics Communications|volume=357|pages=200–201|doi=10.1016/j.optcom.2014.09.017|bibcode=2015OptCo.357..200R|date=2015-12-15}}</ref>
[[Image:Kerr-lens Modelocking.png|thumb|400px|Hard aperture Kerr-lens modelocking principle]]
[[Image:Kerr-lens_modelocking.svg|thumb|400px|Soft aperture Kerr-lens modelocking. Within crystal from inside to outside: Green=pump, blue=pulsed light, red=continuous waves]]
Because of the non-uniform power density distribution in a [[Gaussian beam]] (as found in laser resonators) the refractive index changes across the beam profile; the refractive index experienced by the beam is greater in the center of the beam than at the edge. Thus a rod of an active Kerr medium functions as a lens for high intensity light. This is called [[nonlinear optics|self-focusing]] and in extreme cases leads to material destruction. In the laser cavity short bursts of light will then be focused differently from continuous waves.

To favor the pulsed mode over continuous-wave, the cavity could be made unstable for [[Continuous wave#Laser physics|continuous-wave operation]], but more often a low stability is a by-product of a cavity design putting emphasis on aperture effects. Older designs used a hard aperture, that simply cuts off, while modern designs use a soft aperture, that means the overlap between the pumped region of the gain medium and the pulse. While the effect of a lens on a free laser beam is quite obvious, inside a cavity the whole beam tries to adapt to this change. The standard cavity with flat mirrors and a thermal lens in the laser crystal has the smallest beam width on the end-mirrors. With the additional Kerr lens the width on the end-mirror gets even smaller. Therefore, small end-mirrors (hard aperture) favor pulses. In Ti:Sapphire oscillators telescopes are inserted around the crystal to increase the intensity.

For a soft aperture consider an infinite laser crystal with a thermal lens. A laser beam is guided like in a glass fiber. With an additional Kerr lens the beam width gets smaller. In a real laser the crystal is finite. The cavity on both sides features a concave mirror and then a relative long path to a flat mirror. The continuous-wave light exits the crystal end face with a larger beam width and slight divergence. It illuminates a smaller area on the concave mirror, leading to a small beam-width on the way to the flat mirror. Thus [[diffraction]] is stronger. Because of the divergence the light is effectively coming from a point farther apart and leads to more convergence after the concave mirror. This convergence is balanced with diffraction. The pulsed light exits the end face with a smaller beam width and no divergence. Thus it illuminates a larger area on the concave mirror and is less convergent afterwards. So both continuous waves and pulsed light fronts are mirrored back onto themselves. A cavity close to a confocal one means to be close to instability, which means the beam diameter is sensitive to cavity changes.  This emphasizes the modulation.  With a slightly asymmetric cavity prolonging the cavity emphasizes diffraction and even makes it unstable for [[Continuous wave#Laser physics|continuous-wave operation]], while staying stable for [[Pulsed laser|pulsed operation]].
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 but for a soft aperture laser the cavity mirrors are designed to act as a 1:1 [[telescope]] imaging the light, which exits an end-face, back onto the same end-face. So for the beam, the crystal looks infinite. -->

The length of the medium used for KLM is limited by [[group velocity]] dispersion.  KLM is used in [[Carrier envelope offset control]].