Abstract: Single crystal optical fibers are produced with a graded index structure. A modified approach of the Laser-Heated Pedestal Growth [LHPG] method is employed to produce optical fibers from a preform rod. Under laser irradiation, a thermal gradient is created with temperature peaking at the center of the molten zone on top of the preform. Dopant species are radially distributed, across a cross section of the single crystal fibers during their growth. A refractive index gradient, thus, occurs across the fiber's cross section. The gradient is controlled by choice of process parameters and by selection of dopant species which will yield higher dopant concentrations in the melt contacting the central part of the cross section of the growing single crystal fiber than dopant concentrations in the melt contacting the outer edge of the growing single crystal fiber.