A treatment apparatus for producing a cut surface in a transparent material (7, 8), which apparatus comprises - a laser device which is adapted to generate a separation within the transparent material (7, 8) by means of optical radiation and which laser device comprises - optics which focus the optical radiation along an optical axis into a focus situated in the material and which have in the material (7, 8) an image field in which the focus lies and which have an image field size, and - a focus adjustment device for adjusting a position of the focus transverse to the optical axis and along the optical axis, - a control device which is connected to the laser device and controls the laser device such that the focus adjustment device moves the position of the focus of the optical radiation in the material (7, 8) along a path, wherein the control device controls the laser device such that the cut surface extends substantially parallel to the optical axis and, in projection along the optical axis, is a curve which has a maximum extent along the optical axis, wherein, during the movement along the curve, the control device defines the position of the focus by a multiple oscillating adjustment of the position of the focus along the optical axis between an upper axial focus position and a lower axial focus position, characterized in that - the focus adjustment device moves the position of the focus transverse to the optical axis by a shift of the image field transverse to the optical axis and - the control device controls the laser device such that the cut surface, transverse to the optical axis, has a maximum extent which is greater than the image field size and that the focus adjustment device defines a movement of the position of the focus transverse to the optical axis along the curve. - a laser device which is adapted to generate a separation within the transparent material (7, 8) by means of optical radiation and which laser device comprises - optics which focus the optical radiation along an optical axis into a focus situated in the material and which have in the material (7, 8) an image field in which the focus lies and which have an image field size, and - a focus adjustment device for adjusting a position of the focus transverse to the optical axis and along the optical axis, - optics which focus the optical radiation along an optical axis into a focus situated in the material and which have in the material (7, 8) an image field in which the focus lies and which have an image field size, and - a focus adjustment device for adjusting a position of the focus transverse to the optical axis and along the optical axis, - a control device which is connected to the laser device and controls the laser device such that the focus adjustment device moves the position of the focus of the optical radiation in the material (7, 8) along a path, wherein the control device controls the laser device such that the cut surface extends substantially parallel to the optical axis and, in projection along the optical axis, is a curve which has a maximum extent along the optical axis, wherein, during the movement along the curve, the control device defines the position of the focus by a multiple oscillating adjustment of the position of the focus along the optical axis between an upper axial focus position and a lower axial focus position, - the focus adjustment device moves the position of the focus transverse to the optical axis by a shift of the image field transverse to the optical axis and - the control device controls the laser device such that the cut surface, transverse to the optical axis, has a maximum extent which is greater than the image field size and that the focus adjustment device defines a movement of the position of the focus transverse to the optical axis along the curve.