Self-focussing: This intensity-dependent phase-delay can be very similar to that imposed deliberately on weak light by the use of a lens -- the thicker central portion of a (positive) lens has a greater optical path length and retards the phase of light passing there, relative to light passing through the lens-edge, and by this brings light to a focus. Focussing like this therefore occurs even in flat plates of glass, as the intensity distribution of the intense light causes lateral differences in the index of refraction, and therefore similar differences in the optical path length. In a high-power solid-state laser system this can cause the whole beam, or parts of it, to collapse to a focus even within the laser rod itself, with catastrophic results.
Filamentation: Instead of the whole beam collapsing, it is possible that a beam which is not perfectly smooth in its intensity profile will break up into beamlets and each of those may self-focus. Between whole-beam self-focussing and filamentation, the difference is only the relative growth rates of different spatial-frequency components of the beam, and the initial amplitude of those components.
Self-phase modulation: Equally, in time there can be similar phase distortions. By virtue of the changing intensity of a pulse of light, it becomes possible for the phase-fronts in the weaker leading edge of the pulse to 'run away' from phase fronts in the more intense part of the pulse. Because of intensity-dependent differences in the index of refraction, it therefore becomes possible to add to the period between phase fronts, thereby reducing the frequency of the lightwave. Similarly, on the trailing edge of the pulse, phase fronts of weaker light may tend to 'catch up' to the intense parts of the pulse, with the effect of decreasing the optical period and increasing the frequency.
In this, new frequencies of light are created in the pulse, and the pulse acquires a component of changing frequency -- it becomes optically chirped.
This optical sleight-of-hand is accomplished using matched pairs of diffraction
gratings. A laser pulse comprises many frequencies, according to its Fourier
transform. In striking a diffraction grating, the pulse spreads out in angle,
each frequncy component leaving at a slightly different dispersed angle.
In travelling between two such gratings, different frequencies take different
paths, and the total distances of the different paths through this diffraction-grating
system are not the same. Thus it is that at the output of a grating expander
the frequency components arrive at staggered times, ordered by their frequencies.
The result is a temporally stretched-out pulse of steadily rising frequency
-- a positively chirped pulse.
In proportion to the time-dilation of the pulse, the peak intensity of the pulse drops. Made more tractable in this way, the pulse can be amplified to substantial energies without encountering intensity-related problems. When amplification is complete, a complementary arrangement of diffraction gratings can almost exactly compensate, recompressing the pulse to its original prototype duration, but with now with orders of magnitude greater peak power than would have been possible without the CPA technique.