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)
[1] Am I getting old or is it weird realizing that 1970 was almost 50 years ago?
Aircraft these days have much better electrical power systems (since all control surfaces and a lot more engine operation is electrically powered), and new aircraft carriers and surface combatants are being designed with about 50-100% margin on electrical power to make them compatible with these systems in the future.
High quality mirror material with > 99.8% reflectivity near infrared region would do the job. Multi layer metal substrate, usually copper based or fused silica to withstand thermal expansion and dielectric coating. High macroscopic surface quality is not needed. It's enough that it reflects.
Even the mirrors used in laser erode. Laser weapon uses larger mirror area to focus tighter beam to the target. But unlike laser mirror missile surface don't have to withstand erosion long time and you can rotate the missile to divide the thermal power to larger area.
There are practical reasons why the best practical option is not mirror but material with high thermal resistance. Hypersonic missiles already use those materials and they are protected against current generation of military lasers (50 to few 100s of kilowatts). You need megawatt lasers if you try shooting down HGV.