The authors are with Laboratoire d’Optique des Surfaces et des Couches Minces, Unité Propre de Recherche de l’Enseignement Supérieur Associé au Centre National de la Recherche Scientifique 6080, Ecole Nationale Supérieure de Physique de Marseille, Domaine Universitaire de Saint Jérôme, 13397 Marseille Cedex 20 France.
Metal–dielectric coatings can be used successfully to design
broadband absorbers. However, the understanding of the designs is
not easy. Here we present a new analytical method using achromatic
three-layer stacks. Such metal–dielectric basic structures permit
movement from a fixed admittance value to another one over a wide
spectral range. Efficient designs are calculated and explained with
this method.
Timothy D. Corrigan, Dong Hun Park, H. Dennis Drew, Shy-Hauh Guo, Paul W. Kolb, Warren N. Herman, and Raymond J. Phaneuf Appl. Opt. 51(8) 1109-1114 (2012)
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Physical Thicknesses for Two-, Four-, and Eight-Layer
Metal–Dielectric Absorbersa
Physical Thicknesses (µm)
Admittance Values
2 Layers
4 Layers
8 Layers
Y = 3.84 - 4.37
i
D = 0.118921
D = 0.031274
D = 0.012384
Y = 3.130 - 3.228
i
M = 0.009369
M = 0.007182
D = 0.024884
Y = 2.420 - 2.185
i
M = 0.006183
M = 0.002616
D = 0.107941
D = 0.049726
Y = 1.710 - 1.093
i
M = 0.003958
M = 0.001989
D = 0.092774
Y = 1
M = 0.001100
Calculated with a linear progression law
for intermediate admittance values, for a reference wavelength of
λo = 0.7 µm. The
intermediate admittance values reached after each pair of layers are
given in the last column. D and M correspond
to dielectric and metallic layer thicknesses, respectively.
Table 2
Physical Thicknesses for Two-, Four-, and Eight-Layer
Metal–Dielectric Absorbersa
Physical Thicknesses (µm)
Admittance Values
2 Layers
4 Layers
8 Layers
Y = 3.84 - 4.37
i
D = 0.118921
D = 0.075771
D = 0.035494
Y = 3.010 - 2.229
i
M = 0.010362
M = 0.006872
D = 0.067428
Y = 2.197 - 0.994
i
M = 0.006078
M = 0.002616
D = 0.105919
D = 0.087853
Y = 1.518 - 0.327
i
M = 0.002812
M = 0.001092
M = 0.000673
Y = 1
D = 0.097901
Calculated with a square-root progression
law for intermediate admittance values, for a reference wavelength of
λo = 0.7 µm. The
intermediate admittance values reached after each pair of layers are
given in the last column. D and M correspond
to dielectric and metallic layer thicknesses, respectively.
Table 3
Physical Thicknesses of Metal–Dielectric Absorbers
Designed with Three Three-Layer Achromatic
Structuresa
Design 1
Design 2
Design 3
—
Y = 3.84 - 4.37
i
—
—
D = 0.035399
—
—
M = 0.010633
—
—
D = 0.014441
—
—
Y = 1.718 - 2.047
i
—
—
D = 0.053809
—
—
M = 0.005803
—
—
D = 0.036589
—
—
Y = 1.112 - 0.839
i
—
D = 0.052724
D = 0.052724
D = 0.045423
M = 0.003031
D = 0.014980
M = 0.003192
D = 0.092792
M = 0.001036
D = 0.092792
Y = 1.076 - 0.001
i
Y = 1
Y = 1
Design 1 is the original
design. Designs 2 and 3 are modified designs that permit the final
admittance Y = 1 at the reference wavelength of
λo = 0.7 µm to be
reached. In design 2, layers eight and nine are modified. In
design 3, layers seven and eight are modified. The admittance
values Y are given after each three-layer
stack. D and M correspond to dielectric and
metallic layer thicknesses, respectively.
Tables (3)
Table 1
Physical Thicknesses for Two-, Four-, and Eight-Layer
Metal–Dielectric Absorbersa
Physical Thicknesses (µm)
Admittance Values
2 Layers
4 Layers
8 Layers
Y = 3.84 - 4.37
i
D = 0.118921
D = 0.031274
D = 0.012384
Y = 3.130 - 3.228
i
M = 0.009369
M = 0.007182
D = 0.024884
Y = 2.420 - 2.185
i
M = 0.006183
M = 0.002616
D = 0.107941
D = 0.049726
Y = 1.710 - 1.093
i
M = 0.003958
M = 0.001989
D = 0.092774
Y = 1
M = 0.001100
Calculated with a linear progression law
for intermediate admittance values, for a reference wavelength of
λo = 0.7 µm. The
intermediate admittance values reached after each pair of layers are
given in the last column. D and M correspond
to dielectric and metallic layer thicknesses, respectively.
Table 2
Physical Thicknesses for Two-, Four-, and Eight-Layer
Metal–Dielectric Absorbersa
Physical Thicknesses (µm)
Admittance Values
2 Layers
4 Layers
8 Layers
Y = 3.84 - 4.37
i
D = 0.118921
D = 0.075771
D = 0.035494
Y = 3.010 - 2.229
i
M = 0.010362
M = 0.006872
D = 0.067428
Y = 2.197 - 0.994
i
M = 0.006078
M = 0.002616
D = 0.105919
D = 0.087853
Y = 1.518 - 0.327
i
M = 0.002812
M = 0.001092
M = 0.000673
Y = 1
D = 0.097901
Calculated with a square-root progression
law for intermediate admittance values, for a reference wavelength of
λo = 0.7 µm. The
intermediate admittance values reached after each pair of layers are
given in the last column. D and M correspond
to dielectric and metallic layer thicknesses, respectively.
Table 3
Physical Thicknesses of Metal–Dielectric Absorbers
Designed with Three Three-Layer Achromatic
Structuresa
Design 1
Design 2
Design 3
—
Y = 3.84 - 4.37
i
—
—
D = 0.035399
—
—
M = 0.010633
—
—
D = 0.014441
—
—
Y = 1.718 - 2.047
i
—
—
D = 0.053809
—
—
M = 0.005803
—
—
D = 0.036589
—
—
Y = 1.112 - 0.839
i
—
D = 0.052724
D = 0.052724
D = 0.045423
M = 0.003031
D = 0.014980
M = 0.003192
D = 0.092792
M = 0.001036
D = 0.092792
Y = 1.076 - 0.001
i
Y = 1
Y = 1
Design 1 is the original
design. Designs 2 and 3 are modified designs that permit the final
admittance Y = 1 at the reference wavelength of
λo = 0.7 µm to be
reached. In design 2, layers eight and nine are modified. In
design 3, layers seven and eight are modified. The admittance
values Y are given after each three-layer
stack. D and M correspond to dielectric and
metallic layer thicknesses, respectively.