Passive-band-matched frequency–momentum routing in a time-modulated terahertz metasurface

Space–time metasurfaces translate frequency and momentum, but a passive resonance match is useful only if the modulation couples the participating modes and the illuminated angular spectrum is accepted. We numerically study a GaAs-like ridge-on-slab structure with a prescribed traveling permittivity perturbation. The full-field coupling retains its spatial phase explicitly. The two ridge subcells use the same modulation envelope, while the traveling phase varies continuously across the structure. A passive-band estimate selects a reference carrier of 318.29 GHz, modulation near 4.18 GHz, and momentum shift of 3.5 mm −1 . Five-harmonic Maxwell calculations give 6.75% transmitted upper-sideband conversion at normal incidence. For a Gaussian field waist of 4 mm on a 24.192 × 12.096 mm 2 aperture, the resolved angular-spectrum estimate is 2.84% of incident power. We quantify modulation work, numerical convergence, angular acceptance, amplitude and loss sensitivity, and defined surface-layer profiles. The results establish a frequency-shifting angular channel in an idealized numerical model.