Optical illuminators comprise optical fibers having a gradient index core and a cladding selected so that a refractive index difference at a core/cladding interface provides a numerical aperture less than, greater than, or equal to a numerical aperture of the gradient index core. In some examples, a maximum refractive index difference in the gradient index core is substantially the same as, less than, or greater than the refractive index difference at the core/cladding interface. Illuminators based on such fibers are configured to produce optical beams with a laser diode or diode array, and to provide stable, approximately Gaussian optical fluxes at a fiber output surface.