Dichroic Polarizer
Model absorbing dichroic polarizers from the complex index of each principal axis: principal transmittances, extinction ratio and crossed-pair leakage.
each principal axis: N = n − iκ, α = 4πκ/λ, R = ((n − 1)² + κ²)/((n + 1)² + κ²)
k = (1 − R)² e−αd/(1 − R² e−2αd) (normal incidence, incoherent reflections)
extinction k₁/k₂, efficiency (k₁ − k₂)/(k₁ + k₂), crossed pair H₉₀ = k₁k₂
κ is the imaginary part of the index (absorption index), not an absorption coefficient: κ = 3 × 10⁻³ at 550 nm is α = 68.5 mm⁻¹. A metal has κ of order 1 to 10 and blocks both axes. The defaults are illustrative, not a measured material.
k₁ (pass axis)
87.36 %
α = 0.2285 mm⁻¹, R = 5.60 % per face
k₂ (block axis)
9.34e-4
α = 68.54 mm⁻¹, R = 5.88 % per face
Extinction ratio k₁/k₂
29.7 dB
efficiency 99.7863 %; κ ratio 300
Unpolarized light
one sheet 43.73 %
two crossed: 8.16e-4; parallel: 38.16 %
Principal transmittances against thickness (log₁₀)
Extinction ratio and pass transmittance against thickness
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
Slab at normal incidence, N = n − iκ per principal axis, face reflectance including κ, multiple reflections added in power; ratios from logs. Not modelled: dispersion, scattering, oblique light.
- 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
- Born M., Wolf E. (1999). Principles of Optics, 7th ed., §1.5 Reflection and refraction of a plane wave (Fresnel formulae, total reflection). Cambridge University Press. doi:10.1017/CBO9781139644181.010