Polymer (Sheet) Polarizer
Model iodine-PVA sheet polarizers (H-sheet type): principal transmittances k₁ and k₂, extinction ratio and efficiency from the film's absorption, dichroic ratio and thickness.
stretched PVA–iodine film: chains along the stretch absorb E ∥ stretch (α∥), pass E ⟂ (α⟂ = α∥/Rd)
k = (1 − R)² e−αd/(1 − R² e−2αd), k₁ = k(α⟂) pass, k₂ = k(α∥) block
extinction k₁/k₂, efficiency (k₁ − k₂)/(k₁ + k₂), one sheet (k₁ + k₂)/2, crossed pair k₁k₂
α is the natural-log (Napierian) absorption coefficient; a decadic absorbance A corresponds to αd = 2.303 A. One wavelength, normal incidence, uncoated faces in air. The defaults are illustrative, not a product's data.
k₁ (pass, E ⟂ stretch)
76.49 %
face reflectance 4.00 %
k₂ (block, E ∥ stretch)
5.10e-4
α∥d = 7.50
Extinction ratio k₁/k₂
31.8 dB
polarizing efficiency 99.8668 %
Unpolarized light
one sheet 38.3 %
parallel pair 29.3 %; crossed pair 3.90e-4
Principal transmittances against film thickness (log₁₀)
Extinction against pass transmittance as the film thickens
Model and references
Exact. The equations are exact within the stated assumptions, or are a standard's tabulated values. The results are as good as the inputs. About the tiers
Homogeneous film at one wavelength: Beer–Lambert absorption per axis (α∥ = R_d α⊥), face reflections, multiple reflections added in power. Not modelled: spectra, scattering, protective layers.
- Shurcliff W. A. (1962). Polarized Light: Production and Use, ch. 3 Polarizers: classes and performance parameters, pp. 32–42 (principal transmittances k₁, k₂). Harvard University Press. doi:10.4159/harvard.9780674424135.c4
- Shurcliff W. A. (1962). Polarized Light: Production and Use, ch. 4 Dichroic polarizers, pp. 43–64. Harvard University Press. doi:10.4159/harvard.9780674424135.c5
- Macleod H. A. (2010). Thin-Film Optical Filters, 4th ed., ch. 2 Basic Theory, pp. 13–71. CRC Press. doi:10.1201/9781420073034-c2