Heat Mirror Design
A heat mirror passes visible light and reflects thermal infrared. A silver film about 10–15 nm thick between two high-index layers (TiO₂/Ag/TiO₂) does both: it transmits most of the light and keeps the emittance low.
Light transmittance τv (D65)
91.9 %
ρv = 5.7 %; bare pane 91.8 %
Solar transmittance τe (AM1.5 G)
71.2 %
ρe = 25.7 %, absorbed 3.2 %
Normal emittance εn at 300 K
0.033
Uncoated glass (this model): 0.957
A heat mirror passes visible light and reflects thermal infrared: a silver film thin enough to see through (≈ 10–15 nm) reflects like a metal beyond about 2 µm, and the two high-index layers cancel its visible reflection (an induced-transmission filter). τv and ρv weight the pane's T and R with D65 × V(λ) (ISO 9050, EN 410), τewith the ASTM G173 AM1.5 global spectrum, 280–4000 nm; the glass's back face is included, its absorption isn't. εn is the Planck-weighted 1 − R of the coated face over 2.5–50 µm (Kirchhoff, glass opaque there), a band that holds 91–98 % of the blackbody emission for 200–600 K; glazing standards use the hemispherical value, which for a low-e surface is somewhat higher. Ag uses the n, k Yang et al. (2015) measured on template-stripped silver (0.27–24.9 µm, a matched Drude term beyond), the dielectric a constant index. Real Ag films this thin conduct worse than the model, which raises ε. The bare-glass ε here is too high: glass with a constant index lacks the strong reflection real glass has near 9 µm.
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
Transfer matrix at normal incidence; Ag from Yang et al. 2015, dielectric with constant n. Lossless glass, back face added incoherently. ε is the Planck-weighted normal 1 − R, not hemispherical.
- Fan J. C. C., Bachner F. J. (1976). Transparent heat mirrors for solar-energy applications. Appl. Opt. 15, 1012. doi:10.1364/AO.15.001012
- Yang H. U., D'Archangel J., Sundheimer M. L., Tucker E., Boreman G. D., Raschke M. B. (2015). Optical dielectric function of silver. Phys. Rev. B 91, 235137. doi:10.1103/PhysRevB.91.235137
- CIE (2019). CIE spectral luminous efficiency for photopic vision (dataset). doi:10.25039/CIE.DS.dktna2s3
- CIE (2022). CIE standard illuminant D65 (dataset). doi:10.25039/CIE.DS.hjfjmt59
- ASTM G173-03 (reapproved 2020). Standard Tables for Reference Solar Spectral Irradiances: Direct Normal and Hemispherical on 37° Tilted Surface. ASTM International. doi:10.1520/G0173-03R20
- Macleod H. A. (2010). Thin-Film Optical Filters, 4th ed., ch. 2 (absorbing layers, incoherent substrate). CRC Press. doi:10.1201/9781420073034