Engraving is more of a surface appearance finish than a guaranteed depth.
We calibrate our lasers to provide a crisp contrasting visual affect - on 3mm material it generally works out to be ~0.2mm.
Here's a sample of engraving on our amber bamboo. You can read more about the types of engraving here.
Not deep enough for your needs?
Some customers layer multiple cut parts to create deeper indentations EG