The Space Elevator Blog has a detailed interview with laser supplier Trumpf. They're in the business of (among other things of course) helping the Space Elevator Games laser teams. The post goes into some ideas on how a laser source could be designed to work at the distances and with the focus needed at altitudes relevant to a Space Elevator.
The discussion suggests a third Space Elevator Games challenge - cooling the beam power receiver in the vacuum of space.
The details of what Trumpf is offering to the teams are also discussed.
The blog also has a post on a video of E-T-C, one of the beam power teams. It looks like they must have stopped off at in New Mexico at the space museum along the way?