These are pictures of various transverse electromagnetic modes for the laser we’re working with.
Laser beams aren’t constrained to being nice little smooth dots, though that’s one of the possible modes (TEM00). Since TEM00 has the most tightly focused beam, and the fewest irregularities, it’s the one many laser manufacturers force their device to operate at. There are other possible solutions, with varying patterns. The subscripts here indicate the number of divisions in the beam—I’m guessing on some of the higher ones. There’s also a strange pattern which looks like it has radial, not rectilinear, divisions; I’m not sure what that is, exactly.
These pictures are taken by projecting the beam through an enlarging lens onto a whiteboard. Kind of a hack, but it works surprisingly well. Images are enhanced to show contrast; in reality, they’re just red.