An illumination system (8) comprises an optical waveguide (18) which is made from optically transparent components and has four end faces (10, 10'). A light source (12) whose light is coupled into the optical waveguide (18) via one of the end faces (10), is situated opposite this end face (10). The optical waveguide (18) has a light guide (30). A number of fibers (34) are attached to a surface (32) of the light guide (30). The fibers (34) have birefringent properties. A preferred method of providing the birefringent properties is to stretch fibers (34) of a suitable polymer plastic material in their longitudinal direction. The light from the light source (12) will be polarized by the fibers (34) and polarized light will be outcoupled from the optical waveguide (18) via an exit surface (16). The illumination system (8) may be used for front or back lightning of LCD panels for e.g. mobile phones, PDA's, etc.