Enhanced Aluminum Mirror

Aluminium mirror with quarter-wave enhancing pairs: reflectance at the design wavelength and over 400–700 nm, against bare Al.

Model: Exact

Design wavelength λ₀ (nm)Enhancing pairs (L then H on the Al)n_L (next to the Al)n_H (outermost)Al thickness (nm)Cr adhesion layer under the Al (nm)n_substrate

R at λ₀ = 550 nm

96.58 %

Bare Al: 91.52 %; T = 1.4e-6

Mean R, 400–700 nm

95.17 %

Bare Al: 91.53 %; minimum 84.39 %

Opaque-Al limit at λ₀

96.58 %

|(1 − Y)/(1 + Y)|², Y = (n_H/n_L)^2N(n + iκ)

Quarter waves at λ₀: d_L = 94.2 nm, d_H = 58.5 nm

Each quarter-wave pair turns the metal's admittance Y = n + iκ into (n_H/n_L)² Y, which raises R near λ₀ and lowers it away from λ₀ (the enhanced band is narrower than the metal's). Al and Cr use the Rakić et al. (1998) Lorentz–Drude n, k, which includes aluminium's interband dip near 800 nm; the dielectrics have constant indices. Exact transfer matrix, normal incidence; evaporated films differ from the model by a few per cent, and the native oxide and the substrate's back face are ignored.

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 at normal incidence: quarter-wave (H L)ᴺ pairs on Al over an optional Cr layer. Al and Cr from the Rakić et al. 1998 Lorentz–Drude model; dielectrics lossless with constant n.

Macleod H. A. (2010). Thin-Film Optical Filters, 4th ed., ch. 5 (metal mirrors and reflection-enhancing layers). CRC Press. doi:10.1201/9781420073034
Rakić A. D., Djurišić A. B., Elazar J. M., Majewski M. L. (1998). Optical properties of metallic films for vertical-cavity optoelectronic devices. Appl. Opt. 37, 5271–5283. doi:10.1364/AO.37.005271

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