When a short optical pulse propagates through a nonlinear medium, the Kerr effect leads to a phase delay which is largest on the beam axis (where the optical intensity is highest) and smaller outside the axis. This is similar to the action of a lens: the wavefronts are deformed, so that the pulse is focused (assuming a positive nonlinear index n2). This effect is called self-focusing and has important implications for passive mode locking of lasers (→ Kerr lens mode locking) and for optical damage of media (catastrophic self-focusing). For negative n2, the nonlinearity is self-defocusing.
When a Gaussian beam with optical power P and beam radius w propagates through a thin piece (thickness d) of a nonlinear medium with nonlinear index n2, the dioptric power (inverse focal length) of the Kerr lens is
when considering only the phase changes near the beam axis in a parabolic approximation. This equation can be derived by calculating the radially dependent nonlinear phase change and comparing it with that of a lens.
The equation shows that for a given optical power Kerr lensing becomes more important for stronger beam focusing: this increases the optical intensities and even more so the intensity gradients.
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