Optical fibers that provide stable output beam sizes have core refractive indices that decrease non-monotonically from a core center to a core/cladding interface. A maximum refractive index of the core is situated at a radius of between about ½ and ¾ of the core radius so that a core center has a depressed refractive index. Such fibers are included in diode pumped solid state lasers to deliver pump laser power to a laser medium.