Partial Reflector Design
Partial reflectors (output couplers, etalon mirrors) provide controlled reflectance between bare substrate and full HR. A single dielectric layer at QWL gives R determined by nfilm. Adjusting the thickness ratio tunes R via thin-film interference.
R for a quarter-wave film = 9.65%
R at λ₀ for this thickness = 9.65%
d = 80.9 nm
R = [r₁² + r₂² + 2r₁r₂cos(2δ)] / [1 + r₁²r₂² + 2r₁r₂cos(2δ)] where δ = 2πnfd/λ
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
Exact reflectance of one lossless film with constant indices at normal incidence (transfer matrix, equal to the two-surface Airy sum); back surface ignored. No multilayer or target-R design.
- Macleod H. A. (2010). Thin-Film Optical Filters, 4th ed., ch. 2 and ch. 5 (neutral mirrors and beam splitters). CRC Press. doi:10.1201/9781420073034
- Hecht E. (2016). Optics, 5th ed., §9.4.