Terahertz metasurface for independent modulation of amplitude and phase in multi-channels

•A terahertz metasurface is proposed for simultaneously controlling the amplitude and phase of orthogonal linearly polarized lights in multi-channels.•For the x- and y- polarized lights incidence, the designed metasurface can simultaneously encode three pairs of complex amplitude information in co– and cross-polarized channels.•By combining a pair of anisotropic elliptic pillars and a pair of rectangular pillars rotating 45 degrees with high polarization conversion efficiency to realize the design of multifunctional metasurface.•In order to show the ability to modulate phase and amplitude simultaneously, a series of examples are designed to evaluate the performance of proposed metasurface in the terahertz band, and the simulation results are validated by the experiments.•Compared with traditional plasmonic structure, the proposed design based on single-layer structure has advantages of controllable focusing, compact structure, and simple fabrication.