The disclosed embodiments relate to the design of a system that implements a reflectarray antenna. The system includes a time-modulated metasurface, which is configured to act as a planar reflector for an electromagnetic wave that is radiated by a feeder into free space at an operation frequency f0. The time-modulated metasurface includes time-modulated unit-cells that provide a nonlinear conversion between f0 and another desired frequency fd. The system also includes a phase-delay mechanism, which adjusts a phase delay by acting on a phase applied to a modulation frequency fm that modulates each unit-cell. The nonlinear conversion and the phase-delay mechanism operate collectively to facilitate angle-independent nonreciprocity by imposing different phase gradients during up-conversion and down-conversion processes, and by preventing generation of certain propagative harmonics due to total internal reflection.