We report a strictly single-mode optical fiber with a record core diameter of 84 mu m and an effective mode area of similar to 3600 mu m(2) at 1 mu m. We also demonstrate fundamental mode operation in an optical fiber with a record core diameter of 252 mu m and a measured mode field diameter (MFD) of 149 mu m at 1.03 mu m, i.e. an effective mode area (A(eff)) of similar to 17,400 mu m(2) at 1.03 mu m, an A(eff) of 31,600 mu m(2) at 1.5 mu m. All these fibers have near parabolic index profiles with a peak refractive index difference Delta N approximate to similar to 6 x 10(-5), i.e. a record low numerical aperture (NA) of similar to 0.013 in an optical fiber. This low refractive index difference was achieved by frozen-in thermal stress as a result of two different types of glass in the fibers. When the fundamental mode was excited in the 252 mu m core fiber using a 1.03 mu m ASE source, the output beam was measured to have M-x(2) = 1.04 and M-y(2) = 1.18. (C) 2009 Optical Society of America