An improved broadband light source for a Sagnac interferometer includes a waveguide, such as a fluorescent optical fiber, that is pumped by a pump source with a sufficient intensity to generate temporally incoherent light. The fluorescent optical fiber has first and second ends, one end being an input end of the fiber. The broadband light is provided at an output of the fluorescent optical fiber and is input to the interferometer. In order to prevent laser oscillations between the light source and the interferometer, one end of the fluorescent optical fiber is formed so as to prevent reflections. The light output from the fluorescent fiber to the interferometer comprises only that light that initially propagates toward the output of the optical fiber. In one embodiment of the light source, the pump light from the pump source is coupled into the fluorescent optical fiber in a direction so that it travels away from the output of the fluorescent optical fiber towards the first end. In an alternative embodiment, the fluorescent optical fiber is a doubly clad optical fiber having a first acceptance region and a second acceptance region at the first end. The pump light is introduced into an aperture window between the two acceptance regions so that the pump light can be introduced into the first end at an angle without requiring a reflective surface at the first end.