Wanting to make a small backlight sign, with solar powered LED’s providing the lighting. This would be indoor, and yes, the solar panel does provide enough power from the indoor lighting to fully illuminate the LED’s.
Plan is to laser cut the letters out of translucent white acrylic and fit those into laser cut black acrylic sheet. Anything much thicker than 1mm won’t allow enough light from the solar lights through to be really noticeable other than at night. Even 1/16" may not allow enough light through, but I can’t even find that to try out… at least not in translucent…
I thought about using a white light lens for a 2ft x 4ft fluorescent lighting fixture. Plaskolite Duralite which manufacturer says is premium acrylic and is about 1.3mm thick. I picked up one for about $3 because a corner of it was broken off, but it does not cut with the laser, even at 100% power (Atomstack X7 Pro 10W diode) 120mm/min it doesn’t even make a mark. If I paint it first, then it just melts the plastic 
Even tried to cut it from the back (rough) side, no-go there either.
I did order some acrylic from makerstock, but it’s “mostly opaque” 1/16" white, 1/8" clear frosted, and 1/8" white frosted. Would still like to find a translucent white 1mm to 1.5mm thick