AI file attached.
I used Illustrator to design a coaster with Leonard Nimoy's Spock from Star Trek: The Original Series. I cut this both in plywood and acrylic. This project is a little older, so unfortunately, I don't have a lot of photos.
Every laser cutter is a little different, which means you might need to adjust your settings, but I used an Epilog Zing and a Universal Laser to cut these coasters. To cut, set black to engrave at 100% power, 60% speed, cut at 100% power, 15% speed. You might need two passes. If you're using acrylic, I'd recommend trying to do it in one pass, because it can start to melt back together if you overdo it.
For the plywood ones, I also cut a cork backing (similar to this on Amazon, but I got it for much less from a local art supply store). When you're cutting cork, you need to be very careful because it can burn easily. It can catch on fire inside a laser cutter, which is bad! First, tape down the cork if it comes it a roll to keep it as flat as possible. When cutting, try to cut at low power and high speed, but do multiple passes if necessary. You can also rub down /spritz the surface of the cork with just a little bit of water before cutting. I glued the cork to the back of the coasters using contact cement. To cut the cork, you can use the same AI file as the coaster, just remove the engraving layer and only do the vector.
These cut pretty quickly, so you can easily make a lot as giveaways for a trek-themed event.
Step 1: Finishing Touches.
To help protect plywood, you can spray it with urethane coating. I used clear satin because I wanted it to be as matte as possible. Follow the directions on the can and leave to dry overnight before using. If you're doing acrylic instead, don't worry about coating.