Light diffusing optical fibers and light emitting apparatuses including light diffusing optical fibers are disclosed. In one embodiment, a light emitting apparatus includes a base, a transparent or translucent enclosure affixed to the base, a light diffusing optical fiber including a coiled filament enclosed within the enclosure, and a light source optically coupled to the light diffusing optical fiber. The coiled filament includes a glass core, an outer surface, and a plurality of light scattering structures situated within the coiled filament for scattering light through the outer surface of the coiled filament. The coiled filament has a loss in a range of 0.5 dB/turn to 10.0 dB/turn at a turn radius of less than 50 mm.