Gradient Index Coating
Graded-index coating from the substrate index to a low surface index: broadband AR from a smooth profile (linear, cosine or exponential).
R at Design λ
0.18%
T at Design λ
99.82%
Formulas
linear: n_s + (n_t − n_s)f
cosine: n_s + (n_t − n_s)(1 − cos πf)/2
exponential: n_s(n_t/n_s)^f
f = height/thickness (n_s = n_substrate, n_t = n_surface)
Staircase of ≥ 50 sublayers (10 per λ_min/n_max, at most 4000), each at its mid-height index.
Index Profile
Reflectance / Transmittance
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
The profile is a staircase of at least 50 lossless sublayers (10 or more per λ/n), each by exact matrix. Constant indices, normal incidence, an abrupt step at the surface. Not modelled: dispersion, porosity, scatter.
- Southwell W. H. (1983). Gradient-index antireflection coatings. Opt. Lett. 8, 584–586. doi:10.1364/ol.8.000584
- Macleod H. A. (2010). Thin-Film Optical Filters, 4th ed., ch. 2 (characteristic matrix). CRC Press. doi:10.1201/9781420073034