Generally, the thicker the material, the more crucial a high laser power level is in order to achieve a quality cut. As a rule of thumb when cutting acrylic, 10W per millimeter is required.
A comparison of 200W and 400W laser cutting times for acrylic sheets of varying thicknesses is shown in the graphic below.
Other plastics, such as polycarbonate or SAN, are also typically processed with lasers. A high power level (200W or 400W) is required to cut these materials cleanly, even if they are relatively thin (2mm or 3 mm).