Fig. 4.

Beam steering and shaping at the central frequency. a, b 3D space-time-coding matrix and corresponding 2D coding matrix for beam steering, respectively, in which the red, yellow, green, and blue dots represent “0”, “1”, “2”, and “3” digits, respectively. c, d Equivalent amplitude and phase distributions at different harmonic frequencies, respectively. This space-time-coding matrix results in equivalent 3-bit coding responses “0”, “1′”, “2′”, “3′”, “4′”, “5′”, “6′”, and “7′” at the central frequency. e Corresponding 2D scattering pattern at the central frequency for beam steering. f Corresponding 1D scattering pattern cuts (at φ = 90°) at different harmonic frequencies. g Comparison of scattering patterns pertaining to the original 2-bit coding and equivalent 3-bit coding for realizing the beam steering at the central frequency. h, i Equivalent amplitude and phase distributions for vortex-beam generation at the central frequency, which exhibit an equivalent 3-bit coding spiral phase profile (OAM mode l = 1). j, k Corresponding 2D and 3D scattering patterns at the central frequency for beam shaping, respectively