This paper proposes approximations of the angular transfer responses of fiber lightguides by mathematical functions associated with solutions of the diffusion equation. The parameters of the approximations are determined for various lightguides. The angular intensity distributions are investigated for the output radiation from the shortest possible lightguides. The possibility is demonstrated of calculating the directional patterns of lightguides based on the proposed approximations, including the case of lightguides with scattering end surfaces.
D. V. Kisevetter, "Approximating the angular transfer responses of fiber lightguides," J. Opt. Technol. 74, 592-599 (2007)