Device and method for laser cutting a web of fibrous material

A device for cutting a web (3) of fibrous material comprises movement means (6) for moving a web (3) of fibrous material to be cut, defining a feed surface (B) for the web (3) and having at least one first cutting zone (Z1), at least one laser source (9a) configured to generate a laser beam (F) extending along its operating direction (C) towards the first cutting zone (Z1) to make, on the web (3), at least one incision (I) extending along a predetermined cutting line (D), where a portion (P) of the laser beam passes through the web (3) of fibrous material at the first cutting zone (Z1) The device also comprises recovery means (10) for recovering the portion (P) of the laser beam (F) and at least partly located along the operating direction (C), at the first cutting zone (Z1), in such a way as to intercept the portion (P) of the laser beam (F); and direct it towards a second cutting zone (Z2) to make a further incision or cut.