Two-Layer AR Coating
Transfer-matrix method for two-layer quarter-quarter (V-coat) AR designs. Both layers at quarter-wave optical thickness. Zero reflectance at λ₀ when n₂ = n₁·√(nsub/ninc), for example n₁ = (ninc³ · nsub)¼ and n₂ = (ninc · nsub³)¼.
d₁ = λ/(4n₁) = 99.6 nm
d₂ = λ/(4n₂) = 80.9 nm
n₂ for R = 0 at λ₀ (given n₁) = 1.701
R at λ₀ = 0.00006568%
Equal-step pair: n₁ = (n₀³ns)¼ = 1.110, n₂ = (n₀ns³)¼ = 1.369 (one of many R = 0 pairs)
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
Two lossless quarter-wave layers with constant indices at normal incidence on a semi-infinite substrate. R(λ₀) and the zero-reflection n₂ are closed forms. Not modelled: dispersion, absorption, the back surface.
- Macleod H. A. (2010). Thin-Film Optical Filters, 4th ed., ch. 2 and ch. 4 (quarter-quarter double-layer coatings). CRC Press. doi:10.1201/9781420073034