A perfect-absorber metasurface (Salisbury screen) is a thin resistive sheet with sheet resistance Rs, suspended a distance d above a metal (PEC) ground plane, separated by a lossless dielectric of relative permittivity εr. Looking into the stack from free space, the shorted dielectric spacer behaves as a transmission-line stub of reactance:
X_stub = Z_d · tan(β d), β = (2πf/c)·√ε_r, Z_d = Z_0/√ε_r
The resistive sheet sits in parallel with that stub, so the total input admittance is the sum of the two:
Z_in = [ 1/R_s + 1/(j·X_stub) ]⁻¹
Γ = (Z_in − Z_0) / (Z_in + Z_0), A = 1 − |Γ|² (opaque backing ⇒ no transmission)
Perfect absorption (A = 100%, Γ = 0) needs two conditions simultaneously: reactance cancellation — the spacer must be a quarter-wavelength thick, d = λ/(4√ε_r), which drives tan(βd) → ∞ so the stub reactance vanishes and Zin collapses to just Rs — and resistance matching — Rs must equal the free-space impedance Z0 ≈ 377 Ω. Miss either one and some of the incident wave reflects.
- Rs slider — the sheet's ohmic resistance (real metasurface designs realize this with sub-wavelength resistive patches or lossy metal patterning).
- d slider — spacer thickness; sets the quarter-wave resonance frequency f₀ = c/(4d√ε_r).
- εr slider — dielectric constant of the spacer; higher εr lets you shrink d for the same f₀ (why real absorbers use dense ceramics, not air).
- f slider — incident wave frequency; sweeps you off the narrowband resonance to show how absorption falls away.
- Snap to Perfect Match — sets Rs = 377 Ω and re-tunes d so the current frequency sits exactly at f₀.
Real-world relevance: this exact impedance-matching principle underlies radar-absorbing coatings, anechoic chamber tiles, thermal-emitter metasurfaces and narrowband photodetector/sensor coatings.