I've come across a Korian Viridian Laser. They seem like a good option for a laser-focused loadout due to their shield penetration, but I can't seem to find any more. I haven't found any stores that sell them, and random encounters that drop them seem to be so rare as to be nonexistent. Beyond just running around looking for encounters and hoping I get lucky, how can I get more of these weapons?
The Korian Outsiders faction has a chance to drop these, but they're pretty rare, unfortunately. There's no way to buy them that I've ever found.
You can try hanging out around Korian stations, or take missions where you'll be up against Korian Outsiders (ie, ones where you'll lose faction rep with them) to encounter more ships. Scanning their cargo holds before you open fire has proven useful to some.
Probably the highest percentage chance is from Korian Pirate Lords, who have a 66% chance of dropping them with the rank of the laser chosen with the rank of the Pirate Lord as a factor.