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80
60
Metallic
40
20
Semiconducting
(a)
0
Semiconducting
80
60
40
20
Metallic
(b)
0
1
Solar irradiance
1. 5
1
0.5
Relative luminous
efficiency of the eye
0.5
(c)
0
0
0
500
1000 1500
Wavelength (nm)
2000
2500
11.6
Spectral refl ectance (upper panel) and transmittance (middle
panel) for a 0.05-
μ
m-thick thermochromic VO
2
fi lm in semiconducting
c
) states. The lower panel illustrates typical
spectra for the luminous effi ciency of the human eye and for solar
irradiance. After Mlyuka
et al.
(2009a).
(
τ
<
τ
c
) and metallic (
τ
>
τ
()
=
∫
() (
)
∫
()
T
τ
d
λ
ϕ
λ
T
λ τ
,
d
λ
ϕ
λ
.
[11.1]
lum sol
,
lum sol
,
lum sol
,
This equation was used to compute data, shown in Fig. 11.7, on
T
lum
(
τ
,
t
)
and
T
sol
(
,
t
) where
t
is the thickness of the VO
2
fi lm (Li
et al.
, 2010). These
computations used standard formulas for thin-fi lm optics (Born and Wolf,
1999) together with optical constants
n
and
k
of VO
2
as evaluated before
(Mlyuka
et al.
, 2009b). The discussion below will also make use of the cor-
responding dielectric constant, denoted
τ
ε
=
ε
1
+
i
ε
2
, which is related to the
n
2
-
k
2
and
optical constants via
ε
1
=
ε
2
=
2
nk
.
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