The present embodiments provide methods and apparatuses for providing prescribed illumination. Some embodiments provide lenses that include a two-dimensional beam-forming lens-profile where the profile acts to deflect light rays from a light source into a relatively narrow output beam. A zone of higher refractive index than that of the area outside the profile is enclosed where the higher refractive-index zone admits the light rays, a transverse axis of revolution is further included and extends transversely across and outside of the lens-profile so that the transverse axis extends generally laterally with respect to a luminous centroid-direction of the output beam. The lens further includes a surface of revolution formed by circularly sweeping the lens-profile about the axis of revolution forming a circumferential beam from the output beam emitted by said surface of revolution.