How does bright light ionize air?

A long time ago in a galaxy far, far away, I went to grad school, where my friends and I had the privilege of working with some fairly powerful lasers. These were pulsed lasers, not continuous output, so their time-averaged power output wasn’t very high - but each pulse was very brief, and contained sufficient energy such that their instantaneous power was on the order of megawatts.

During that time I saw it demonstrated that if the beam was focused by a suitable lens, the intensity of light at the focal point was such that the air there ionized. This was indicated by a loud cracking sound and a bright flash of light at the focal point, even though the beam itself wasn’t visible, and even though that focal point was in mid-air, with no solid material anywhere nearby.

What was happening? Why/how does very bright light cause air to ionize?

Ordinarily, you’re right: It’s not the intensity of light (the number of photons) that causes ionization, but its frequency (the energy of each individual photon). Depending on what you’re trying to ionize, this usually requires something in the UV range, or maybe X rays, neither of which you’re likely to get from a laser.

But if you get enough intensity, that can change, in a couple of ways. First, if you have enough photons, you can sometimes get two close enough together that, even though neither is enough to ionize by itself, the pair of them can. Second, you can get heating of the material, possibly up to a temperature sufficient for ionization.

I believe the effect Chronos mentioned is typically called multi-photon ionization

Here is a video demonstrating this with longer pulse lasers, which tend to produce the popping effect you described.

But the newer demonstrations by lasers that can switch on and off in the pico second range is even more impressive.

The light is produced by called Bremsstrahlung radiation. I am fairly sure that the actual mechanism hasn’t been fully described yet, but here is a link to a paper that may help.