A large-mode-area (LMA) optical fiber (10) that operates as a single-mode optical fiber. The optical fiber includes a core region (20) surrounded by an inner cladding (32), which in turn is surrounded by an outer cladding (40). The inner cladding includes at least one up-doped ring region (32R1). The ring region is configured to form a large attenuation differential between the higher-order modes and the fundamental mode so only that the fundamental mode remains traveling in the optical fiber. If necessary, the optical fiber can include a bend (10B) having a select “resonant” bend diameter (DB) that increases the relative attenuation of the fundamental and higher-order modes. The optical fiber supports an effective mode field diameter (MFD) of up to 40 μm to 50 μm. As a result, detrimental non-linear effects are suppressed, which allows the optical fiber to carry substantially more optical power than conventional LMA optical fibers. The LMA optical fiber is thus eminently suited for a number of optical-fiber-based applications calling for high optical power, such as fiber lasers and pump sources for wavelength conversion.