We report a strictly single-mode optical fiber with a record core diameter of 84 microm and an effective mode area of approximately 3600 microm(2) at 1 microm. We also demonstrate fundamental mode operation in an optical fiber with a record core diameter of 252 microm and a measured mode field diameter (MFD) of 149 microm at 1.03 microm, i.e. an effective mode area (Aeff) of approximately 17,400 microm(2) at 1.03 microm, an Aeff of 31,600 microm(2) at 1.5 microm. All these fibers have near parabolic index profiles with a peak refractive index difference DeltaN approximately approximately 6 x 10(-5), i.e. a record low numerical aperture (NA) of approximately 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 microm core fiber using a 1.03 microm ASE source, the output beam was measured to have M2x = 1.04 and M2y = 1.18.