The everyday concept of optics is of transparent elements, such as glass lenses, that bend beams of light in useful ways. The small lenses in our smartphones are now almost as ubiquitous as the lenses in our eyes. In both cases, the lenses redirect the rays of light scattered from, say, a tree and project them to form an image of the tree on the camera’s photosensitive chip or on our retinas.

Suppose you directed a laser beam into your smartphone lens. (Don’t even think about doing the same with your eye.) The lens redirects the beam to a near-point-like focal spot on the chip. The milliwatts of power delivered by common laser pointers is more than enough to damage your smartphone. But what if you dialed up the beam’s power enough that the beam damaged the lens before arriving at the focus? For a high-average-power continuous-wave beam, the small...

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