An expression for the transmitted fraction of the uniform and parallel radiation incident upon the coupler between two rectangular light pipes of different physical dimensions is derived. It is a function of the pipe dimension ratio and the angle of the incident radiation. It is shown that for radiation nearly parallel to the pipe axis, it is possible to design a coupler for any pipe dimension ratio so that all the radiation incident upon it is transmitted by it. Design curves for various incidence angles and the pipe dimensions are presented.
M. D. Wagh, "Coupling efficiency between light pipes of different dimensions," Appl. Opt. 15, 2840-2843 (1976)