[gliese1337]

Get the beam powerful enough and it will have meaurable gravitational field. All beams of any intensity technically do contribute some, albeit infinitesimal, component to the gravitational field.

It's a fun exercise to calculate just how strong a laser beam you'd need to have to make a black hole entirely out of photons.

[stcredzero]

A black hole can actually cause an additional singularity due to the blueshifting of infalling light. IIRC, one researcher studied this phenomenon and called it a "blue sheet."