My grandfather worked on high-energy laser weapons back in the 70s. The laser would, indeed, melt their own mirrors. They had to develop a whole technology of self-deforming mirrors in order to avoid hot spots on the mirrors.

From the descriptions that gramps used to give me, I'm not sure how what's described here is an advance over what he did back in the late 70s. I guess one thing is that back then, they were nowhere near being able to put the whole assembly into a pod that could be mounted on a fighter jet's wing.

(gramps also worked on the Hubble Telescope, and spy satellites)