A laser processing machine comprising: a laser processing head for processing a workpiece by means of at least one laser beam (9, 9a-f), the laser processing head comprising: at least one birefringent beam splitter element (10, 10a-f) for splitting the at least one laser beam (9, 9a-f), which strikes a beam entrance surface (12, 12a, 12d) of the birefringent beam splitter element (10, 10a, 10d) in a randomly polarized or unpolarized state, into two partial beams (11a, 11b) with mutually perpendicular linear polarization, wherein the birefringent beam splitter element (10, 10a, 10d) has a beam exit surface (13, 13a, 13d) which is not aligned parallel to the beam entrance surface (12, 10a, 10d), for the exit of the two partial beams (11a, 11b), and a focusing optics for focusing the partial beams (11a, 11b) on at least two focal surfaces (F1, F2) in a focal plane which is located on an upper side of the workpiece or in the vicinity of the upper side of the workpiece, wherein both the beam entrance surface (12, 12a, 12d) and the beam exit surface (13, 13a, 13d) of the beam splitter element (10, 10a, 10d) are arranged at an angle not equal to 90° or 180° to an optical axis of the subsequent focusing optics, wherein the laser processing machine further comprises: a non-polarization-maintaining fiber optic light guide for supplying the laser beam to the laser processing head, characterized in that the laser processing head is designed to irradiate the laser beam perpendicular to the beam entrance surface (12, 12a, 12d) onto the birefringent beam splitter element (10, 10a, 10d). at least one birefringent beam splitter element (10, 10a-f) for splitting the at least one laser beam (9, 9a-f), which strikes a beam entrance surface (12, 12a, 12d) of the birefringent beam splitter element (10, 10a, 10d) in a randomly polarized or unpolarized state, into two partial beams (11a, 11b) with mutually perpendicular linear polarization, wherein the birefringent beam splitter element (10, 10a, 10d) has a beam exit surface (13, 13a, 13d) which is not aligned parallel to the beam entrance surface (12, 10a, 10d), for the exit of the two partial beams (11a, 11b), and a focusing optics for focusing the partial beams (11a, 11b) on at least two focal surfaces (F1, F2) in a focal plane which is located on an upper side of the workpiece or in the vicinity of the upper side of the workpiece, wherein both the beam entrance surface (12, 12a, 12d) and the beam exit surface (13, 13a, 13d) of the beam splitter element (10, 10a, 10d) are arranged at an angle not equal to 90° or 180° to an optical axis of the subsequent focusing optics, wherein the laser processing machine further comprises: a non-polarization-maintaining fiber optic light guide for supplying the laser beam to the laser processing head, characterized in that the laser processing head is designed to irradiate the laser beam perpendicular to the beam entrance surface (12, 12a, 12d) onto the birefringent beam splitter element (10, 10a, 10d). a non-polarization-maintaining fiber optic light guide for supplying the laser beam to the laser processing head, characterized in that the laser processing head is designed to irradiate the laser beam perpendicular to the beam entrance surface (12, 12a, 12d) onto the birefringent beam splitter element (10, 10a, 10d).