A method of cutting a semiconductor wafer, comprising the steps of: a) providing a laser-cutting apparatus (10, 30) comprising: a laser source for emitting a laser beam, an optical guide system for receiving the laser beam and directing laser light to an irradiation region of the laser cutting apparatus (10, 30), a selectively actuatable optical polarizing component (19, 32) for switching a polarization state of the laser light directed to the irradiation region between a first polarization state and a second, different, polarization state, and a support for supporting a semiconductor wafer, and a drive for relatively moving the semiconductor wafer and the irradiation region such that the irradiation region follows a cut line of the semiconductor wafer; b) supporting the semiconductor wafer within the laser cutting apparatus (10, 30) such that the irradiation region is coincident with a point on a cut line of the semiconductor wafer, and c) irradiating the irradiation region of the semiconductor wafer with laser light having a first polarization state, and subsequently irradiating the irradiation region of the semiconductor wafer with laser light having a second polarization state, the second polarization state being different from the first polarization state, wherein the first and second polarization states each comprise one of the group consisting of: linear polarization perpendicular to the direction of relative movement along the cut line, linear polarization parallel to the direction of relative movement along the cut line, circular polarization, elliptical polarization and non-polarization; the method further comprising the step of: d) relatively moving the semiconductor wafer and the irradiation region in a direction parallel to the plane of the semiconductor wafer such that the irradiation region follows the cut line of the wafer, so that the semiconductor wafer is cut along the cut line. a) providing a laser-cutting apparatus (10, 30) comprising: a laser source for emitting a laser beam, an optical guide system for receiving the laser beam and directing laser light to an irradiation region of the laser cutting apparatus (10, 30), a selectively actuatable optical polarizing component (19, 32) for switching a polarization state of the laser light directed to the irradiation region between a first polarization state and a second, different, polarization state, and a support for supporting a semiconductor wafer, and a drive for relatively moving the semiconductor wafer and the irradiation region such that the irradiation region follows a cut line of the semiconductor wafer; b) supporting the semiconductor wafer within the laser cutting apparatus (10, 30) such that the irradiation region is coincident with a point on a cut line of the semiconductor wafer, and c) irradiating the irradiation region of the semiconductor wafer with laser light having a first polarization state, and subsequently irradiating the irradiation region of the semiconductor wafer with laser light having a second polarization state, the second polarization state being different from the first polarization state, wherein the first and second polarization states each comprise one of the group consisting of: linear polarization perpendicular to the direction of relative movement along the cut line, linear polarization parallel to the direction of relative movement along the cut line, circular polarization, elliptical polarization and non-polarization;