Laser engraving works on a variety of materials. One of the more interesting materials is granite. Granite is often used for counter tops, back splashes, flooring, and burial monuments.
Laser engravers work great for marking granite but they are typically not powerful enough to create much depth in harder materials like granite. With monuments, laser engravers are often used to engrave images and accurately cut the masking for sand blasting. Sand blasting is then used to add depth to the design.
There are many companies that utilize laser engravers to engrave images onto monuments. C & H Monuments have a nice post, Granite Etching Explained. They have images of the monument they created, the picture the customer provided, and a closeup of the final laser engraved image on the monument. They did a great job.