Here is how to make a laser cut box with an engraving on 1/8" plywood using Rhinoceros 3d and an Epilogue Zing Laser cutter. Below is the complete file of the box pictured.
Step 1: Creating the Sides of the Boxes
1. Make a rectangular surface which will be one of the sides of the box.
2. Make a cutting tool, so you can cut in to the square surface 1/8" (0.11") by 1/2" or 1/4" rectangles so they can fit snugly into the other peace.
3. Repeat step three on all four sides of the base and three sides of the side walls.
4. Each opposite side on the box is symmetrical so you can make one and then copy it.
5. Make the lid by making it 0.11" bigger on each side of the size of the base.
6. Make sides to fit on the lid so it will fit over the sides of the base.
Step 2: The Engraving
1. Select Picture frame command to make a background photo.
2. Use Control Point Curve to trace the image outline.
3. Select the background photo and delete.
4. Select all curves and use the group command.
5. Select all curves and use command hatch.
6. Select all curves and delete to leave just the hatch.
7. Move the hatch on to one on the surfaces on the box