This is the same Salisbury-screen transmission-line model as the 3D version, viewed through two 2D-native lenses instead of a rendered layered stack. A resistive sheet Rs sits a distance d above a metal ground plane, over a dielectric spacer εr:
X_stub = Z_d·tan(βd), β = (2πf/c)√ε_r, Z_d = Z_0/√ε_r
Z_in = [ 1/R_s + 1/(jX_stub) ]⁻¹, Γ = (Z_in−Z_0)/(Z_in+Z_0), A = 1−|Γ|²
Top panel — standing wave in front of the sheet. In free space outside the metasurface the incident wave (travelling toward the sheet) and the reflected wave (travelling away from it) superpose into a standing pattern whose complex envelope is V(s) = eiks + Γe−iks, s = distance from the sheet, k = 2πf/c. The bright curve is the instantaneous field, the dashed band is its envelope |V(s)|. At perfect match Γ→0 and the envelope flattens to a pure travelling wave — nothing bounces back to interfere.
Bottom-left — absorption spectrum. A(f) swept from 0.5–25 GHz, with a marker at the current frequency, showing how narrowband the match is.
Bottom-right — Γ-plane. The complex reflection coefficient plotted inside the unit circle (|Γ|=1, total reflection) as frequency sweeps the same range; perfect absorption pulls the trace through the origin at f₀.
- Rs slider — sheet's ohmic resistance.
- d slider — spacer thickness; sets quarter-wave resonance f₀ = c/(4d√ε_r).
- εr slider — spacer dielectric constant; higher εr shrinks d for the same f₀.
- f slider — incident frequency; sweeps off the narrowband resonance.
- Snap to Perfect Match — sets Rs=377 Ω and re-tunes d so f₀ equals the current frequency.
Real-world relevance: radar-absorbing coatings, anechoic-chamber tiles, thermal-emitter metasurfaces and narrowband sensor coatings all rely on this same standing-wave cancellation.