A saturable absorber is an absorbing medium that can only absorb so much light and becomes transparent at high intensities. The change in its absorption coefficient, Aa, depends on the irradiance, I(x,y), of an incident beam: Aa(x, y) = -1(x, y). Calculate I(x, y) for a laser beam with spot size, w, after it propagates a distance z through a saturable absorber. The electric field for the laser beam can be assumed to be gaussian: E(x, y,z,t) = Eoe-i(kz-wt) e-(x+y)/w