Andy,
it's not as simple as all that. There are two main problems in laser
cutting of copper. Firstly, it is very thermally conductive, so you need
to deposit a lot of power into a small volume in order to melt/ablate
the metal. And secondly, it is highly reflective in the mid-IR. (People
use polished copper for reflecting CO2 laser beams.)
So modifying the reflectivity is not a bad suggestion, although it still
isn't enough to make it work. The paint will ablate due to its excellent
optical absorption and poor thermal conductivity, and then expose the
shiny copper which will reflect the light and transport any heat away
from the laser spot.
The usual approach is to use short pulses of green or UV laser light,
where copper will absorb much more of the incident radiation and be
unable to transport the heat in such a short time-scale. (Typically
hundreds of ns or less.) These so-called "q-switched" lasers are much
more hazardous to work with, compared to the "continuous wave" laser
that we have.
Then there is "ultrafast" laser ablation, in which the electrons are
heated so quickly that they don't have time to transfer their energy to
the nuclei. (This is not the same as very quickly heating up the
material - in fact the temperature of the material is undefined while
this is happening.) This is done in a few ps (picoseconds) or less, and
it offers very clean cutting with virtually no heat damage to the
surrounding material. You can even use it to strip wax from a delicate
painting - without damaging the painting!
But back to what we have, which is basically a heater. It won't get PCB
copper hot enough to melt it :) You need a material which is blacker at
mid IR, and less thermally conductive. Wood and plastics are excellent
choices for this reason.
Have fun,
Darren