In this paper, we present a novel Fourier technique to calculate the emitter-to-fiber coupling efficiency between an incoherent source of arbitrary directivity and a multimode fiber. The technique expresses the 4-D integral that describes the coupling as a 2-D sum, and along with Fourier series expansion, the technique increases greatly the computational speed of emitter-to-fiber coupling calculations. We have simulation results of the emitter-to-fiber coupling analysis and coupling analysis for a single-fiber hi-directional link total using the Fourier technique. The results show that the large core plastic optical fiber gives rise to good emitter-to-fiber coupling alignment tolerance, but tends to overfill the detector and cause degradation in fiber-to-detector alignment tolerance. We find that a more directive resonant-cavity light emitting diode only improves emitter-to-fiber alignment tolerance slightly, though it can couple more light into the fiber.