Wavelength Separation
Wavelength separation coatings combine multiple quarter-wave stacks at different design wavelengths to reflect specific bands while transmitting others. Two stacks centered at λ₁ and λ₂ demonstrate dichroic behavior; their stop bands stay apart only above a minimum ratio λ₂/λ₁. The combined stack shows how reflectance bands add when cascaded.
λ₁ = 550 nm, λ₂ = 770 nm
RA(λ₁) = 97.92%
TA(λ₂) = 1 − RA(λ₂) = 71.83% (stack A alone)
Smallest λ₂/λ₁ for separate stop bands = 1.359
Total layers (combined) = 20
Each stack: (HL)N. Combined: Stack₁ | Stack₂ on substrate.
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
Transfer matrix of two (HL)^N quarter-wave stacks at λ₁ and λ₂, alone and cascaded, normal incidence, constant lossless indices. No matching layers between the stacks; a demonstration, not a dichroic design.
- Macleod H. A. (2010). Thin-Film Optical Filters, 4th ed., ch. 2 and ch. 6 (high-reflectance zone width). CRC Press. doi:10.1201/9781420073034