Dielectric High Reflector
Quarter-wave dielectric stack HR mirror — stopband width, peak reflectance, and dispersion.
Reflectance at λ₀
99.9930 %
1 − R = 7.04e-5
Stop band (R ≥ 50 %)
372 nm
909.7 nm – 1281.4 nm
Group delay at λ₀
1.972 fs
Semi-infinite stack: 1.972 fs; GDD(λ₀) = 0
Zone of the infinite stack: 923.4 nm – 1255.0 nm (332 nm, Δg = 0.1522)
Layers: 21; dH = 113.2 nm, dL = 183.4 nm
R(λ₀) = ((n₀ − Y)/(n₀ + Y))², each quarter-wave layer mapping the admittance Y → n²/Y from Y = ns. The stop band is the actual stack's, from λ₀ out to the first 50 % points (side lobes excluded); the zone λ₀/(1 ± Δg), Δg = (2/π) asin((nH − nL)/(nH + nL)), is the limit of many pairs. Group delay τ = d(arg r)/dω and GDD = d²(arg r)/dω² on reflection, front face as reference. At λ₀ the semi-infinite stack gives τ = λ₀n₀/(2cΔn) with H outermost and λ₀nHnL/(2cn₀Δn) with L outermost.
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 (HL)^N H or (LH)^N quarter-wave stacks, normal incidence, constant lossless indices, back surface ignored. Group delay and GDD are central differences of arg r.
- Macleod H. A. (2010). Thin-Film Optical Filters, 4th ed., ch. 2 and ch. 6 (multilayer high-reflectance coatings). CRC Press. doi:10.1201/9781420073034
- Born M., Wolf E. (1999). Principles of Optics, 7th ed., §1.6.5 (periodically stratified media). Cambridge University Press.
- Babic D. I., Corzine S. W. (1992). Analytic expressions for the reflection delay, penetration depth, and absorptance of quarter-wave dielectric mirrors. IEEE J. Quantum Electron. 28, 514. doi:10.1109/3.123281