A peculiar effect happens in air when laser pulses reach crazy-high intensities. The pulses start to get focused inward by the effect of the light on the air itself. The laser pulses are saved from catastrophic over-focusing by starting to make a plasma out of the air when their intensity gets too high, which acts to de-focus the beam. So we have a stable system with feedback - not intense enough? Then there’s not enough plasma to compensate for the self-focusing and the beam converges. Too intense? then there’s an excess of plasma and the beam spreads out a bit. This self-focusing lets the beam overcome the diffraction limit. You end up with an inner core of sparsely ionized plasma surrounded by a sheath of high intensity light. 
These self-focused laser pulses, called laser filaments, have some really out there properties. Filaments tend to converge on a size of around 0.1 mm diameter and a power of 10 GW. If a filament gets more power than that, it will split into more filaments to keep the power down. If it has less power and there are other nearby filaments, it will merge with those filaments to bring its power back up.   Adjacent filaments tend to attract each other and propagate together as tight bundles.
Filaments cause ionization, so they lose energy to the air the farther they go. Their range depends on the energy in the pulse - the power per filament may be fixed, but longer duration pulses can have more energy. Roughly, a filament will lose about 2 μJ / m. But there’s an upper limit to the energy of a filament, too. If the duration is longer than about a picosecond, the electrons the laser pulse creates will have time to accelerate in the pulse’s electric field and crash into other atoms, freeing more electrons which will in turn make even more electrons - a runaway process called cascade ionization. If this happens, the plasma will absorb all of the pulse’s energy. If you send another pulse through before the old plasma has had time to recombine, that pulse could be blocked as well. It takes about 10 ns for the plasma to recombine enough to send another pulse after it.
So with 10 GW of power and 1 ps maximum duration, individual filaments won’t have more than 0.01 J or so, and thus they won’t get much farther than 5 km. High powered pulses that split into multiple filaments can go further by having the depleted filaments combine into full power filaments again.
Laser filaments are visible as bright streaks. This lets you see where you are shooting, but also lets your enemies see where you are shooting from. Wouldn’t it be nice if there was some way to have your beam not form filaments until you wanted it to? Turns out, there is. Different frequencies of light go through the air at slightly different speeds. So if you emit a pulse below the threshold for filamentation but with slow frequencies in front and fast frequencies behind, the light piles up as it goes and the intensity rises. Adjust this pulse just right, and you get filaments forming right where you want them. This method of separating out the timing of the light by frequency is called chirping. If you can pull this off, you could overcome the problems inherent in the limited depth of focus of laser beams, because once the filaments start they won’t spread out again.
Author: Luke Campbell
- S. L. Chin, “Some Fundamental Concepts of Femtosecond Laser Filamentation”, Journal of the Korean Physical Society, Vol. 49, No. 1, July 2006, pp. 281-285.
- Alexander L. Gaeta, “Collapsing Light Really Shines”, Science Vol. 301 pp. 54-55, 4 July 2003