Cold Mirror Design

Cold mirrors reflect visible light and transmit the infrared, keeping heat out of projector and illumination optics. One quarter-wave stack reflects too narrow a band, so long-pass edge-filter stacks in series cover the visible.

Model: Exact

n_H (high index)n_L (low index)n_substraten_incidentReflected band (visible): from (nm)Reflected band (visible): to (nm)Transmitted band (IR): from (nm)Transmitted band (IR): to (nm)Periods per stack (N)

Mean R, 400–700 nm

99.49 %

Lowest R in the band: 86.8 %

Mean T, 800–1200 nm

95.2 %

Lowest T in the band: 90.3 %

50 % point (edge)

710.6 nm

Between the blocked and transmitted bands

Stacks: 2 × 10 periods, (H/2 L H/2)^N, quarter waves at λ₀ = 593.4, 460.9 nm (from the incident side)

Layers: 41

One stack reflects g = λ₀/λ in 1 ± Δg, Δg = (2/π) asin((n_H − n_L)/(n_H + n_L)) = 0.1522. K = ⌈ln(λ_to/λ_from) / ln((1 + Δg)/(1 − Δg))⌉ stacks with λ₀ from λ_from(1 + Δg) to λ_to(1 − Δg) cover the blocked band with overlapping zones. Each stack also reflects near λ₀/3.

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 long-pass edge-filter stacks in series covering the reflected band; lossless constant indices, normal incidence, semi-infinite substrate. A starting design: no matching layers or optimization.

Macleod H. A. (2010). Thin-Film Optical Filters, 4th ed., ch. 6 and ch. 7 (edge filters, extending the reflection zone). CRC Press. doi:10.1201/9781420073034
Epstein L. I. (1952). The design of optical filters. J. Opt. Soc. Am. 42, 806. doi:10.1364/JOSA.42.000806

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