500 1000 1500
nAg ( 22 nm)
nAg ( 12 nm)
kAg ( 12 nm)
kAg ( 22 nm)
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1(a); green]. We consider Schott B270 crown glass as a sub-
strate and tantalum pentoxide (Ta2O5) and silicon dioxide
(SiO2) as layer materials. As a starting design, we specify a
combination of two quarter-wave stacks: the layers 1 through
26 have 1. 75 quarter-wave optical thicknesses (QWOT) and
the layers 27 through 46 have 1.0 QWOT (the reference wave-
length is 300 nm).
Transmittance of the starting design is plotted in Figure 1(a),
represented by a red curve. In the course of SDR, the thicknesses of only 11 layers were activated; 35 layers stayed frozen.
The final design can be seen in Figure 1(b); its transmittance
is shown in Figure 1(a) by a black curve. The design, obtained
by SDR, is shown to provide excellent spectral performance
and at the same time is nearly quarter-wave.
Metal-dielectric composite color coatings
Metal-dielectric composites are attracting interest in coating
design because they exhibit surface-plasmon resonance of
free electrons, which results in a strong absorption at specific wavelengths that depend on the particle size, shape, spatial
distribution, and dielectric environment. Incorporating metal
clusters in dielectric coatings can enable even more sophisticated spectral performance for multilayer systems than relying
on only traditional absorption or only interference properties.
Metal-dielectric coatings can be easily produced using stan-
dard thin-film equipment. Contrary to dielectrics with optical
constants n(λ) and k( λ), the effective optical constants of thin
metal layers are dependent on layer thickness d as well as on
their dielectric environment. Typically, the designers know optical constants n(λ, d) and k( λ, d) of certain combinations—for
example, a sandwich: dielectric layer/metal film/dielectric layer. Optical-coating engineers should be aware that when designing such coatings, conventional techniques allowing variations of film thicknesses are not suitable.
OptiLayer suggests specifying a starting design as a sandwich with fixed layer thicknesses and applying a gradual evolution technique with special settings, assuming insertion of
new layers either near the substrate or near the ambient medium only. In this case, the sandwich stays frozen. To improve
the design performance after this gradual evolution step, a
constrained optimization technique can be used.
For illustration, we designed coatings that have different colors for reflected light from their front and back sides and keep
transmittance at a level >50%. The first condition cannot be
fulfilled using dielectric layers only since different reflectance
from each side requires the use of absorbing layers. For example, if a coating is to have orange and violet colors reflect from
its front and back sides, then target color coordinates of reflectance (R) and backside reflectance (BR) in a CIE XYZ color
system are x = 0.5, y = 0.4 (orange) and x = 0.2, y = 0.1 (violet).
OptiLayer allows optimizing coatings with respect to spectral
target along with color targets, and we specify target integral
transmittance in the visible spectral range >50%. We consider a SiO2 ( 78 nm)/Ag ( 12 nm)/SiO2 ( 78 nm) combination as a
sandwich structure. The optical constants of this combination
are shown in Figure 2(a). Application of a gradual evolution
FIGURE 2. Refractive index and extinction coefficients of silver (Ag)
films (a), a CIE chromaticity diagram with the color coordinates for
the front- and back-reflection colors of the final design (b), the filter’s
final design (c), and experimental samples produced at IRB (d).