Mode-division multiplexing (MDM) technology enables high-bandwidth data transmission using orthogonal waveguide modes to construct parallel data streams. However, few demonstrations have been realized for generating and supporting high-order modes, mainly due to the intrinsic large material group-velocity dispersion (GVD), which make it challenging to selectively couple different-order spatial modes. We show the feasibility of on-chip GVD engineering by introducing a gradient-index metamaterial structure, which enables a robust and fully scalable MDM process. We demonstrate a record-high-order MDM device that supports TE₀–TE₁₅ modes simultaneously. 40-GBaud 16-ary quadrature amplitude modulation signals encoded on 16 mode channels contribute to a 2.162 Tbit / s net data rate, which is the highest data rate ever reported for an on-chip single-wavelength transmission. Our method can effectively expand the number of channels provided by MDM technology and promote the emerging research fields with great demand for parallelism, such as high-capacity optical interconnects, high-dimensional quantum communications, and large-scale neural networks.