It wasn't so much the laser power I was thinking of (that foam shouldn't take too much cutting), but the depth required under the laser head. I don't know much about lasers - I bought a new Blackcat laser 900x600x60watt a couple of years ago and have never
managed to get it set up!!! On that machine the focal length above the material is about 6mm (can't remember without checking) and probably only about another 20mm to the bed. If you do build the machine of your dreams I think that you will need to have a rise/fall table or use a packer system to cut thin material. When I have looked at cut-outs in that sort of material I have never had the impression that it was laser cut although the engraved logo on you link does look to be. G.