13 Theoretical Generalization of the Optical Chirality to Arbitrary Optical Media
349
Fig. 13.2 Optical chirality
density for a silver, and b
silicon. Material parameters
describing ε are directly
taken from [72] and [73],
respectively (see Table 13.1).
For comparison, the curves
for lossy (green solid lines)
and lossless (red dashed
lines) dispersive media are
represented in terms of
C vacuum . The gray shaded
areas indicate the spectral
ranges showing anomalous
dispersion
Table 13.1 Material parameters characterizing the permittivity of silver [72] and silicon [73]
Ag [A. D. Raki´ c et al., Appl. Opt. 37, 5271 (1998)]
ε
(Ag)
D−L (ω) = 1 −
f0ω 2
p
ω 2 + iωγ0
−
f1ω 2
p
ω 2 − ω 2
1 + iωγ1
−
f2ω 2
p
ω 2 − ω 2
2 + iωγ2
−
f3ω 2
p
ω 2 − ω 2
3 + iωγ3
ωp
f0
γ0
f1
γ1
ω1
f2
γ2
ω2
f3
γ3
ω3
2178.61 0.845
11.61
0.065
939.63 197.31 0.124
109.29 1083.50 0.011
15.72
1979.12
Si [E. D. Palik (Academic Press, New York, 1985)]
ε
(Si)
D−L (ω) = 1 −
f0ω 2
0
ω 2 − ω 2
0 + iωγ0
−
f1ω 2
1
ω 2 − ω 2
1 + iωγ1
f0
γ0
ω0
f1
γ1
ω1
7.5
150
1000
3
50
830
χ
n
1 + ξ
n
− ξ
n
1 + χ
n
+ 2ωχ
n ξ
n
1
˜
γ n
−
1
γ n
= 0,
(13.73)
which is met when γ n = ˜
γ n = 0 for all n. At the same time, one can verify that this
solution is indeed the only one, just by substituting it into the real part of (13.72).