Nowadays,the beam propagation method(BPM) is applied to analyze the optical elements.Though many kinds of BPMs have been advanced,one of the important parameters n eff still needs a precise method to solve.In this paper,we presented three methods to solve n eff and took a deep research to find their characteristics and application areas.Based on an important application,we analyzed a multi-mode rib waveguide,and solved its 9 modes′ n eff.We got some important results about these three methods th...