The invention concerns an apparatus and its use for laser processing. The invention also concerns a method and an optical component. According to the invention, at a first laser device, providing a first optical feed fiber and a second laser device providing a second optical feed fiber is provided. A beam combining means connected to the first and second feed fibers and to a multi-core optical fiber is adapted to form a composite laser beam by having the first optical feed fiber aligned with a first core of the multi-core optical fiber and the second optical feed fiber aligned with at least one second core of the multi-core optical fiber. The first and second cores outputs a composite laser beam to a workpiece to be processed. A control unit controls power density of at least one of first and second laser beams of the composite laser beam in at least one of: in response to approaching a change point in direction of cutting progression and to cause change in relation between the power density of the first output laser beam and power density of the second output laser beam in accordance with thickness of the workpiece being cut.