The current IEEE Spectrum has a nice article on the quest for 100+ KW, solid state, missile-killing lasers. One of the systems described is the Airborne Laser (ABL). This 1-MW beast, which fills a 747, is a flowing gas laser. These are "powered by burning chemical fuels like those that drive rocket endings." Since the best high power lasers are only around 20% efficient, heat dissipation is a major problem. In rocket-engine lasers, the excess heat is carried away in the exhaust. The system will be tested later this year.
In another article, it's pointed out that the first operational death rays will kill mosquitoes, not missiles. Mosquito laser technology is now being funded by the Gates Foundation as a means to eradicate malaria.