It isn’t easy to deliver the concentrated power of a laser beam through air to a distant target—whether to disarm some military threat, say, or to remotely detect hazardous materials. The light diffracts, can be scattered and absorbed, and may experience phase-distorting turbulence and temperature fluctuations that blur its focus. Worse, a high-powered beam can suffer what’s known as thermal blooming, in which the beam heats the air it passes through and spreads much faster than it normally would by diffraction.

If a beam is intense enough, though, it focuses itself—no lens required—thanks to the slight dependence of the index of refraction on light intensity. Brighter in the center than on its edges, a femtosecond pulse with peak power of a few gigawatts generates its own refractive-index gradient that causes the wavefront to collapse about the center and form a tighter focus. Positive feedback drives the self-focusing until the energy...

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