The specification describes optical fiber designs that overcome the problem of self-induced damage to optical fibers due to excessive self-focusing. The refractive index of these fiber designs is grossly non-uniform in the center core of the optical fiber. In one embodiment, the optical fiber is designed with a deliberate and steep core trench. In addition, the nominal core region of these optical fibers has a very large area. The combination of these two properties restricts a large portion of the optical power envelope to a core ring, with reduced optical power inside the core ring. These designs substantially reduce self-focusing in the optical fiber. Photonic systems employing optical fibers having these modified core designs are expected to be especially effective for transmitting high power, e.g., greater than 1 MW, with short pulse duration.