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.
|||P. A. Belanger and C. Pare, “Self-focusing of Gaussian beams: an alternate derivation”, Appl. Opt. 22 (9), 1293 (1983)|
|||F. Salin et al., “Modelocking of Ti:sapphire lasers and self-focusing: a Gaussian approximation”, Opt. Lett. 16 (21), 1674 (1991)|
|||V. Magni et al., “Astigmatism in Gaussian-beam self-focusing and in resonators for Kerr-lens mode locking”, J. Opt. Soc. Am. B 12 (3), 476 (1995)|
|||J. H. Marburger, “Self-focusing: theory”, in Progress in Quantum Electronics, J. H. Sanders and S. Stenholm, eds. (Pergamon, Oxford, 1977), Vol. 4, pp. 35-110 (1977)|
|||Y. R. Shen, “Self-focusing: experimental”, in Progress in Quantum Electronics, J. H. Sanders and S. Stenholm, eds. (Pergamon, Oxford, 1977), Vol. 4, pp. 1-34 (1977)|
See also: dioptric power, focal length, Kerr effect, lenses, self-focusing, laser-induced damage, Kerr lens mode locking, self-phase modulation
and other articles in the categories nonlinear optics, physical foundations