Hi, Kalrag,
I'm not exactly sure what info you're looking for, but I'll try to answer your questions. A high-energy-density laser, fired through the atmosphere, will superheat the air at some critical point (~1 megajoule per cm3) and create a plasma (atoms of gas stripped of electrons) which essentially absorbs/scatters the beam and prevents it from reaching its target at full intensity. It isn't so much the absolute power output of the laser, (although it would have to be fairly high), but the energy concentration of the beam. Solutions include spreading out the energy density of the beam using a mirror, or--as is most often used--pulsing the beam on and off very quickly so that the heated air can dissipate between each pulse. As Wikipedia states, the effect is most pronounced when the air is not clear (fog/smog/etc.) as the particles absorb more energy and more quickly heat up the surrounding environment.
Does that help?