Laser diode to remove copper layer from PCB
An ordinary laser diode won't cut it (literally). You need something like a Q-switched laser, pulsed at 10's of kHz. The peak power has to be extremely high to ablate copper (>2500°C), and some nasty fumes come off the epoxy substrate, which have to be exhausted. 

Even a 40W \$CO_2\$ CW laser won't cut thin metal foil- it just bounces off. 

Here's a commercial unit (costs as much as a really nice automobile). 



If you really want to fool around with this sort of thing, you can find suitable lasers on the surplus market, but it's not going to be a matter of attaching a little diode to an engraver head. 

Class 4 lasers are not toys!