Kerr lens

The formation of a Kerr lens (according to John Kerr ) is an effect of non-linear optics and is based on the Kerr effect .

Explanation

If the refractive index in a non-linear medium depends linearly on the intensity of the light, then the following applies (Kerr effect): ${\displaystyle n}$ ${\displaystyle I}$

${\displaystyle n(I)=n_{0}+n_{2}\cdot I}$

With

• ${\displaystyle n_{0}}$: Refractive index in the absence of light
• ${\displaystyle n_{2}}$: Kerr coefficient.

If a high-intensity laser beam, the beam profile of which is strongest in the middle, falls on the medium, the phase change is highest at this point according to the refractive index, while it is smaller in the edge areas. For positive this will lead to self-focusing , for negative to Selbstdefokussierung . ${\displaystyle n_{2}}$ ${\displaystyle n_{2}}$

Example: Gaussian beam

If the beam profile is Gaussian , a focal length can be specified for the medium : ${\displaystyle f}$

${\displaystyle f={\frac {\pi }{4}}\cdot {\frac {w^{4}}{n_{2}\cdot d\cdot P}}}$

With

• ${\displaystyle w}$: Beam radius
• ${\displaystyle d}$: Thickness of the medium
• ${\displaystyle P}$: Power of the laser.

application

The Kerr lens in the titanium-sapphire laser ensures stable ultra-short pulse operation. Lenses are used to widen the light in the resonator in such a way that only the ultra-short pulses focused by the Kerr lens are reflected with high intensity from end mirror to end mirror without loss. The cw components, on the other hand, are expanded and experience higher losses, which is why the pulses prevail in the resonator.

Web links

• Kerr Lens in the Encyclopedia of Laser Physics and Technology (Engl.)