This invention consists in a nonimaging device for concentration or collimation of radiation on a receiver or from an emitter (14), depending on the case. The device is made up of the lens (50), which surrounds the receiver and consists of the aspheric surface (21), and the lens (15), whose upper refractive surface (16) may be aspheric, while the lower surface is aspheric (17) in its central portion (between points 18 and 19) and has a structure with discontinuous slope (20) in its external portion, in which the faces (22) fundamentally refract the rays while the faces (23) reflect them by total internal reflection. The design method provides that the device properties of concentration/collimation are noticeably superior to those of the existing inventions. Possible applications of this lens include: radiation sensors, illumination systems with LEDs, wireless optical communications and photovoltaic solar energy.