Stone does not turn gaseous very easily. As expected, this makes it generally a better candidate for other means of engraving, most notably sandblasting or cutting using diamonds and water.
But when a laser hits glass or stone, something else interesting happens: it fractures. Pores in the surface expose natural grains and crystalline "stubs" which, when heated very quickly, can separate a microscopic sized "chip" from the surface because the hot piece is expanding relative to its surroundings.
So lasers are indeed used to engrave on stone and excellent results can be achieved.
Click on the above links to see the different options available, from custom portaits to library images you can choose from.
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Fewell Monument Portrait Styles