1. Introduction . With the emergence of new technologies, such as mobile internet, big data, and cloud computing, the transmission capacity of the traditional single-mode fiber is approaching its theoretical limit as was defined by Shannon [ 1 ]. Therefore, how to meet the increasing demand of data capacity has become a core problem of optical fiber communication research [ 2 , 3 ]. Currently, optical fiber can be multiplexed in several dimensions, including wavelength, polarization, ...