A large mode area optical fiber includes a large diameter core (d1 up to 60 .mu.m), and a first cladding (diameter d2) wherein the difference between refractive index (n1) in the core and the first cladding (n2) is very small (.DELTA.n<0.002), thus providing a very low numerical aperture core (NA1 between 0.02 and 0.06). The preferred ratio of d2/d1<2. The fiber further has a second cladding, preferably a layer of air holes, having a very low refractive index n3 as compared to the core and first cladding such that the first cladding has a relatively high numerical aperture (NA2>0.4) (n3 is preferably less than 1.3). The small change in refractive index between the core and inner cladding combined with a large change in refractive index between the first cladding and second cladding provides a significantly improved single mode holding waveguide.