Metal-Dielectric Coatings

Metal-dielectric coating design. Explore how a dielectric overcoat modifies the reflectance, transmittance, and absorptance of a thin metal layer.

Model: Exact

n (metal, real part)k (metal, extinction coeff)n (dielectric)Dielectric Thickness (nm)Metal Thickness (nm)n (substrate)

Absorptance @ 550 nm

17.2%

n²−k²

-8.75

Intensity penetration depth 1/α = λ/(4πk) @ 550 nm

14.6 nm

field (1/e amplitude) depth λ/(2πk) = 29.2 nm

Metal-Dielectric Theory

Complex index: ñ = n + ik

Single-pass attenuation in the metal: exp(−4πkd/λ)

Intensity penetration depth: 1/α = λ/(4πk); field (amplitude) depth: λ/(2πk)

R + T + A = 1 (energy conservation)

Dielectric overcoat tunes R via interference

n and k are held constant over the plotted range. Real metals are dispersive, so use the n, k for the wavelength of interest.

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 for the entered constant n, k of the metal and constant indices elsewhere, normal incidence, back surface ignored. Real metals are dispersive: the spectrum holds near the wavelength of the n, k.

Macleod H. A. (2010). Thin-Film Optical Filters, 4th ed., ch. 2 (absorbing layers). CRC Press. doi:10.1201/9781420073034

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