A Loss Model for Parabolic-Profile Fiber Splices

Calculations for the loss in an optical fiber splice, as a function of offset, tilt, diameter, or numerical aperture mismatch, have been reported by several authors. 1 - 3 These calculations all assumed a uniform power distribution across the cone of radiation defined by the local numerical aperture (NA). This is consistent with assuming equal mode excitation, equal mode attenuation, and no mode coupling. 4 An assumption concerning the power distribution is necessary to characterize all combinations of both intrinsic and extrinsic splice imperfections. While these assumptions allow easy calculations, correspondence with measurement data has been unacceptable. 3 Gloge5 reported results based on a diffusion process from the uniform power distribution to the steady-state distribution calculated by Marcuse. 6 Correspondence with 3167 measurement data is much improved for the case of small offsets; however, approximations used in the theory make it difficult to characterize other splice imperfections or splice loss for large offsets. This paper presents a phenomenological model with an assumed power distribution selected solely due to resulting correspondence of calculated effects of splice imperfections with measurement data. The model is not intended for uses other than splice loss characterization, and since the model does not obey the laws of ray optics exactly, caution should be exercised in any other uses of it.