A medical or cosmetic hand-held laser device with an optical waveguide device is subdivided into a first section and a second section arranged at an angle thereto for emitting laser radiation onto a treatment area. To deflect the laser beam from the first section into the second section as effectively as possible and in particular to launch the laser beam with the lowest possible loss into a waveguide that conducts the laser beam further, the hand-held device is provided with a reflector that is arranged between the two sections and has an essentially elliptical reflective surface.