An extended family member worked on using lasers to launch payloads to orbits. [0]

Here's a quick video demonstrating the technology, using lasers to lift a small prototype several meters, back in, what I believe is the 90s: https://www.youtube.com/watch?v=i81f3LifpWY

[0] https://en.wikipedia.org/wiki/Leik_Myrabo

Another great resource for hypothetical space stuffs (with math!) is Atomic Rockets / Project Rho, here's some of their articles on laser propulsion: https://www.projectrho.com/public_html/rocket/enginelist.php

Electric propulsion using high power laser beaming makes way more sense outside the atmosphere for non-launch use cases, where thrust requirements to achieve desired delta-V usually aren't measured in kN and the mission longevity implied by higher Isp matters so much more and there isn't a pesky atmosphere in the way of power beaming or any concern about accidentally ablating airliners.

Numerous startups are tackling the power beaming issue with relatively short timelines and in some cases a lot of funding, but the scale of what's actually been publicly demonstrated with lasers is unimpressive...

I think they’ll have a hard time pushing that much energy through the atmosphere without striking a plasma. Indeed, at least one of the concepts relies on striking a plasma in atmospheric gas by reflecting and focusing the incident radiation.

Laser retro-propulsion seems interesting for landing space-mined materials on earth. The obvious (to me) way to do that is to wrap the mined material in a vague lifting-body shape of metal or maybe just slag, thick enough that after it ablates away there's still enough to be economical (to be clear there's at least a couple major options: high value payload wrapped in low-value vehicle, or big aerodynamic blob of low-mid value material, with more options in between). But if you have a big laser you can shine at it to slow it down, maybe you could get away with a lot less sacrificial material.