Fresnel waveguide lenses having a graded-index (GRIN) distribution for the segmented quadratic phase modulation are demonstrated. The GRIN Fresnel lenses exhibit excellent focusing characteristics and a very high efficiency, both limited only by diffraction. Graded-index Fresnel lenses (F/5, 1-mm aperture) were fabricated for the first time in amorphous As(2)S(3) film waveguides on a thermally oxidized silicon substrate by the electron-beam direct writing technique. The nearly diffraction-limited focusing characteristics and a high efficiency (48%) were experimentally obtained. The theoretical analysis and fabrication process are presented, and experimental results are discussed on the focusing characteristics of the fabricated GRIN Fresnel waveguide lens.