Are there two different lasers that can be invisible when not overlapping, but visible when overlapping? I desire to build a hologram-ish thing, but with lasers. The system would use many lasers that intersect each other at points to build an image in midair. Is this possible?
It's depend what you call "visible" and "invisible" and "air". :-) In air with a little bit of mist, one laser could just be dim, while the crossing superimposition of several could make the added value more visible in the intersecting region: this is a question of contrast rather than on-off.
Also, there exist a technology where this principle is used to "crack" (ionize) air at the aimed position. It works (3D points in air), but what you see is not the laser per se.
PS: I would avoid calling "hologram" what you really mean to be 3D: real hologram produce a 3D impression from a non-3D plate, since the image change with the view angle (and this is often done with lasers, which thus adds to the confusion).