I looked more into the foam and it is neoprene foam. I originally thought it was foam rubber which should be ok to cut as long as you have good ventilation and don't breath the fumes. Neoprene on the other hand has to potential to generate chlorine gas when it decomposes and should not be cut.
We have two different focus lenses for the laser cutter at Hack Pittsburgh. I used the 55mm lens for cutting the wood and a 75mm lens for the foam. The laser very quickly cuts the foam leaving a a smooth edge. The edges are slightly melted. Unfortunately, I do not have the exact settings, but there were lower power with higher speeds.
Laser Cut Machinist ToolboxView Instructable »