Single Layer AR Coating
Quarter-wave antireflection coating design with Snell’s law and explicit s/p polarization handling at oblique incidence.
Optimal n_film
1.233
Normal-incidence target
Quarter-wave thickness
99.6 nm
Uses θ₁ inside film
R @ design λ
1.26 %
Unpolarized average
Film angle θ₁
0.00°
Snell’s law
The external angle propagates through each interface with Snell’s law, and the coating reflectance is evaluated separately for s-polarized and p-polarized light before averaging.
The film is a quarter wave at the chosen angle (d = λ₀/(4n₁ cos θ₁)), so each angle shows a coating designed for that angle.
Reflectance vs wavelength
- Unpolarized
- s-pol
- p-pol
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
One lossless layer with constant indices, a quarter wave at the chosen angle; s and p by tilted admittances. Not modelled: dispersion, absorption, the substrate's back surface, thickness errors.
- Macleod H. A. (2010). Thin-Film Optical Filters, 4th ed., ch. 2 (tilted admittances) and ch. 4 (single-layer antireflection coatings). CRC Press. doi:10.1201/9781420073034
- Born M., Wolf E. (1999). Principles of Optics, 7th ed., §1.6. Cambridge University Press.