For many reasons stone is a very difficult material to mark by laser. 10.6µm is the most commonly used wavelength but for some materials, such as black marble, granite or slate a 1µm can be used to achieve higher resolution results.
In all cases, for naturally occurring stones, no significant depth can be achieved by laser.
Some man-made stones, such as Alabaster or Corian for example, can be engraved by 10.6µ laser with significant depth.
It is not possible to cut naturally occurring stone by laser. Some rare exceptions apply such as soft and very thin marbles but in such case other forms of cutting technology deliver a far better result.