Wire Grid Polarizer Calculator
Model wire-grid polarizers as a grating of metal strips much finer than the wavelength: transmission for E across and along the strips, reflection, ohmic loss and extinction ratio.
shunt sheet across free space: t = 2Z/(2Z + Z₀), r = −Z₀/(2Z + Z₀), A = 1 − |t|² − |r|²
E ∥ strips: Z = iZ₀(p/λ) ln csc(πw/2p) + Zstrip p/w; E ⟂ strips: 1/Z = i(4/Z₀)(p/λ) ln csc(π(p − w)/2p)
valid for p ≪ λ; at p ≥ λ a diffraction order propagates
A free-standing grating of flat metal strips at normal incidence (no substrate). The strips' thickness enters only the ohmic loss, computed from the DC conductivity and the classical skin depth: indicative, best in the far infrared. Tall strips extinguish more than this thin-sheet model shows.
T (E ⟂ strips, passed)
99.71 %
reflects 0.29 %
T (E ∥ strips, blocked)
0.402 %
reflects 97.80 %, absorbs 1.79 %
Extinction ratio T⟂/T∥
23.9 dB
p/λ = 0.078
Grid impedances (per square)
Z∥ = 1.73 + 11.95i Ω
Z⟂ = -3470.6i Ω
Z₀ = 376.7 Ω; skin depth 15.4 nm
Against wavelength, from 1.1 p to 100 p (this grating)
Against the fill factor w/p (this wavelength)
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Quasi-static shunt sheet for p ≪ λ: Marcuvitz strip reactances (capacitive by Babinet), normal incidence, free-standing; loss from DC conductivity. Not modelled: strip height, substrate.
- Marcuvitz N. (1951; IET reprint 1986). Waveguide Handbook, ch. 5 Four-terminal structures, pp. 217–335: inductive and capacitive strip gratings. doi:10.1049/PBEW021E_ch5
- Ulrich R. (1967). Far-infrared properties of metallic mesh and its complementary structure. Infrared Phys. 7, 37–55. doi:10.1016/0020-0891(67)90028-0