The idea is a direct optically pumped 445nm->222nm conversion.
Zinc Oxide doped with fluoride has been pumped with 1064nm and it shows there is a possible pumping path for what I want to do because they used it for making UVC leds. I am hoping to convert this LED action to laser action. It also looks like this material should be tunable by imposing an electric field on the band gap to stretch the transition. As a second topic, some materials act linearly and observe super position as a doubler hence SHG. I was talking about three different approaches. Sorry to confuse. If this involves anything more complex than a dpss green it is too complex. I'm looking for a cheap quick way to get into the far UVC range at significant power with significant conversion efficiency. Hence starting with cheap 445nm diodes seems a good way to pump in 5w and get out at least a few hundred mw. Now these new leds might make this a dead project. Plus the leds are probably safer to work with.
So yes optically pumped crystals that double 445nm without the requirement for feedback mirrors or heating/cooling.