How does beam steering with an RIS work—intuitively and mathematically?
Intuitively, we choose each element’s phase to align the reflected wavefront at the target, like turning many tiny mirrors. For a far‑field target, a common rule is to set element *n* to cancel the path‑length phase: ϕₙ ≈ −k·Δℓₙ (mod 2π), where k = 2π/λ and Δℓₙ is the extra distance via element *n*. Summing the coherent reflections yields a main lobe toward the desired angle and weaker sidelobes elsewhere.